Mathletics Common Core State Standards Alignment

Transcription

1 Mathletics Common Core State Stards Alignment Grades K High School Supported by independent evidence-based research practice CCSS ready Powerful reporting Student centered

2 V

3 CCSS Stards Content CCSS Kindergarten CCSS Grade 1 CCSS Grade 2 CCSS Grade 3 CCSS Grade 4 CCSS Grade 5 CCSS Grade 6 CCSS Grade 7 CCSS Grade 8 CCSS Algebra I CCSS Geometry CCSS Algebra II Integrated Math I Integrated Math II Integrated Math III

4 CCSS Stards Mathletics the CCSS Stards The team at Mathletics is committed to providing a resource that is powerful, targeted,, most importantly, relevant to all students. Mathletics includes well over 1,200 individual adaptive practice activities ebooks available for grades K 8. Our team of educational publishers has created a course that specifically follows the Common Core State Stards. You can be assured that students have access to relevant targeted content. Courses consist of topics based on domains, clusters, stards. Activities within each topic provide adaptive practice each topic has a pre post assessment. What s more, Mathletics contains an extensive library of ebook for use on screen or as a printable resource that are also mapped to the requirements of the Common Core. This document outlines this mapping acts as a useful guide when using Mathletics in your school. Peter Walters, CEO, 3P Learning USA Engage Target Diagnose Assess Report Fluency Mobile 1 3P Learning

5 CCSS Stards CCSS Kindergarten Domain Cluster Stard Description Activities ebooks Counting & Cardinality Counting & Cardinality Counting & Cardinality Counting & Cardinality Counting & Cardinality Counting & Cardinality Counting & Cardinality 1: Know number names the count sequence. 1: Know number names the count sequence. 1: Know number names the count sequence. 2: Count to tell the number of objects. 2: Count to tell the number of objects. 3: Compare numbers. 3: Compare numbers. K.CC.1 K.CC.2 K.CC.3 K.CC.4 K.CC.2.5 K.CC.6 K.CC.7 Count to 100 by ones tens. Count forward beginning from a given number within the known sequence (instead of having to begin at 1). Write numbers from Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Underst the relationship between numbers quantities; connect counting to cardinality. Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching counting strategies. Compare two numbers between 1 10 presented as written numerals. Count to 5 Order Numbers to 10 Order Numbers to 20 Count by Tens Reading Numbers to 30 1 to 30 Before, After Between to 20 Counting Up to 20 Making Numbers Count Ordinal Numbers Counting Forwards Going Up Concept of zero Matching Numbers to 10 Matching Numbers to 20 How Many? How many dots? How Many? How many dots? More or Less? Who has the Goods? Arranging Numbers More, less or the same to 10 More, less or the same to 20 Kindergarten Numbers Patterns Kindergarten Numbers Patterns Kindergarten Numbers Patterns Kindergarten Numbers Patterns Kindergarten Numbers Patterns Kindergarten Numbers Patterns Kindergarten Numbers Patterns 3P Learning 2

6 CCSS Stards CCSS Kindergarten Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Number & Operations in Base Ten 1: Underst addition, underst subtraction. 1: Underst addition, underst subtraction. 1: Underst addition, underst subtraction. 1: Underst addition, underst subtraction. 1: Underst addition, underst subtraction. 1: Work with numbers to gain foundations for place value. K.OA.1 K.OA.2 K.OA.3 K.OA.4 K.OA.5 (fluency stard) K.NBT.1 Represent addition subtraction with objects, fingers, mental images drawings, sounds (claps),acting out situations, verbal explanations, expressions, or equations. Solve addition subtraction word problems, add subtract within 10, e.g., by using objects or drawings to represent the problem. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, record each decomposition by a drawing or equation (e.g., 5 = = 4 + 1). For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, record the answer with a drawing or equation. Fluently add subtract within 5. Compose decompose numbers from 11 to 19 into ten ones some further ones, e.g., by using objects or drawings, record each composition or decomposition by a drawing or equation; underst that these numbers are composed of ten ones one, two, three, four, five, six, seven, eight or nine ones. Model Addition Model Subtraction Adding to 5 Subtracting from 5 Adding to Ten All about Ten Subtracting from Ten Simple Subtraction Adding to make 5 10 Doubles Halves to 10 Balance Numbers to 10 Adding to 5 Subtracting from 5 Adding to Make 5 10 Adding to Ten Subtracting from Ten Adding to 5 Subtracting from 5 Making Teen Numbers Share the Treasure Related Facts 1 Subtraction Facts to 18 Addition Facts Kindergarten Operations with Numbers Kindergarten Operations with Numbers Kindergarten Operations with Numbers Kindergarten Operations with Numbers Kindergarten Operations with Numbers 3 3P Learning

7 CCSS Stards CCSS Kindergarten Domain Cluster Stard Description Activities ebooks Measurement & Data 1: Describe compare measurable attributes. K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Everyday Length Everyday Mass Balancing Act How Full? Kindergarten Measurement Measurement & Data Measurement & Data Geometry Geometry Geometry 1: Describe compare measurable attributes. 2: Classify objects count the number of objects in each category. 1: Identify describe shapes. 1: Identify describe shapes. 1: Identify describe shapes. K.MD.2 K.MD.3 K.G.1 K.G.2 K.G.3 Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, describe the difference. Classify objects into given categories; count the numbers of objects in each category sort the categories by count. Describe objects in the environment using names of shapes, describe the relative positions of these objects using terms such as above, below, inside, in front of, behind next to. Correctly name shapes regardless of their orientations or overall size. Identify shapes such as two-dimensional (lying in a plane, "flat") or threedimensional ("solid"). Compare Length Which Holds More? Sort It Same Different Where is it? Left or Right? Collect the Shapes Collect the Shapes 1 Collect the Shapes 2 Collect Simple Shapes Collect the Objects 1 Match the Solid 1 Match the Object Collect the Shapes Collect the Shapes 1 Collect the Shapes 2 Collect Simple Shapes Collect the Objects 1 Match the Solid 1 Match the Object Kindergarten Measurement Kindergarten Measurement Kindergarten Space, Shape Position Kindergarten Space Shape Kindergarten Space Shape 3P Learning 4

8 CCSS Stards CCSS Kindergarten Domain Cluster Stard Description Activities ebooks Geometry Geometry Geometry 2: Analyze, compare, create, compose shapes. 2: Analyze, compare, create, compose shapes. 2: Analyze, compare, create, compose shapes. K.G.4 K.G.5 K.G.6 Analyze compare two three-dimensional shapes, in different sizes orientations, using informal language to describe their Count Sides Corners similarities, differences, parts How many Edges? (e.g., number of sides vertices/corners) other attributes (e.g., having sides of equal length). Model shapes in the world by building shapes from components (e.g., sticks clay balls) drawing shapes. Compose simple shapes to form larger shapes. Kindergarten Space Shape Kindergarten Space Shape Kindergarten Space Shape 5 3P Learning

9 CCSS Stards CCSS Grade 1 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking 1: Represent solve problems involving addition subtraction. 1: Represent solve problems involving addition subtraction. 2: Underst apply properties of operations the relationship between addition subtraction. 2: Underst apply properties of operations the relationship between addition subtraction. 3: Add subtract within OA.1 1.OA.2 1.OA.3 1.OA.4 1.OA.5 Use addition subtraction within 20 to solve word problems involving situations of adding to, taking from, putting Add Subtract Using together, taking apart, Graphs comparing with unknowns Add Subtract Problems in all positions, e.g., by Adding to 10 Word Problems using objects, drawings, equations with a symbol for the unknown number to represent the problem. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to Add Three 1-Digit Numbers 20, e.g., by using objects, Add 3 numbers using bonds drawings, equations with to 10 a symbol for the unknown number to represent the problem. Apply properties of operations as strategies to add subtract. Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) Underst subtraction as an unknown-addend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. Relate counting to addition subtraction (e.g., by counting on 2 to add 2). Commutative Property of Addition Adding in Any Order Related Facts 1 Grade 1 Operations with Numbers Grade 1 Operations with Numbers Grade 1 Operations with Numbers Grade 1 Operations with Numbers Grade 1 Operations with Numbers 3P Learning 6

10 CCSS Stards CCSS Grade 1 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Number & Operations in Base Ten 3: Add subtract within 20. 4: Work with addition subtraction equations. 4: Work with addition subtraction equations. 1: Extend the counting sequence. 1.OA.6 fluency stard 1.OA.7 1.OA.8 1.NBT.1 Add subtract within 20, demonstrating fluency for addition subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 4 = = 10 1 = 9); using the relationship between addition subtraction (e.g., knowing that = 12, one knows 12 8 = 4); creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). Underst the meaning of the equal sign, determine if equations involving addition subtraction are true or false. For example, which of the following equations are true which are false? 6 = 6, 7 = 8 1, = 2 + 5, = Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 = [] 3, = []. Count to 120, starting at any number less than 120. In this range, read write numerals represent a number of objects with a written numeral. Fact Families: Add Subtract Adding to Ten Subtracting from Ten Composing Additions to 20 Addition Properties Balance Numbers to 20 Related Facts 1 Missing Numbers Missing Numbers: Variables Counting on a 100 grid Make Big Numbers Count Make Numbers Count Before, After & Between to 100 Count by 2s, 5s 10s Grade 1 Operations with Numbers Grade 1 Operations with Numbers Grade 1 Operations with Numbers Grade 1 Numbers 7 3P Learning

11 CCSS Stards CCSS Grade 1 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten 2: Underst place value. 2: Underst place value. 3: Use place value understing properties of operations to add subtract. 3: Use place value understing properties of operations to add subtract. 1.NBT.2 1.NBT.3 1.NBT.4 1.NBT.5 Underst that the two digits of a two-digit number represent amounts of tens ones. a. 10 can be thought of as a bundle of ten ones called Place Value 1 a ten. Making Teen Numbers b. The numbers from 11 to 19 Complements to 10, 20, 50 are composed of a ten Compliments to one, two, three, four, five, six, Doubles Near Doubles seven, eight, or nine ones. Doubles Halves to 20 c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens ( 0 ones). Compare two two-digit numbers based on meanings of the tens ones digits, recording the results of comparisons with the symbols >, =, <. Add within 100, including adding a two-digit number a one-digit number, adding a two-digit number a multiple of 10, using concrete models or drawings strategies based on place value, properties of operations, /or the relationship between addition subtraction; relate the strategy to a written method explain the reasoning used. Underst that in adding two-digit numbers, one adds tens tens, ones ones; sometimes it is necessary to compose a ten. Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. Greater or Less to 100 Compare Numbers to 20 Compare Numbers to 100 Complements to Columns that Add Addictive Addition Column Addition 1 Mental Addition 10 more, 10 less 1 more, 10 less Groups of Ten Grade 1 Numbers Grade 1 Numbers Grade 1 Operations with Numbers Grade 1 Operations with Numbers 3P Learning 8

12 CCSS Stards CCSS Grade 1 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten 3: Use place value understing properties of operations to add subtract. 1.NBT.6 Subtract multiples of 10 in the range from multiples of 10 in the range (positive or zero differences), using concrete models or drawings strategies based on place value, properties of operations, /or the relationship between addition subtraction; relate the strategy to a written method explain the reasoning used Complements to 10, 20, 50 Grade 1 Operations with Numbers Measurement & Data 1: Measure lengths indirectly by iterating length units. 1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. Compare Length Compare Length 1 Comparing Length Everyday Length Grade 1 Measurement Measurement & Data 1: Measure lengths indirectly by iterating length units. 1.MD.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; underst that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole of length units with no gaps or overlaps. How Long Is That (Customary)? Measuring length with blocks Grade 1 Measurement Measurement & Data Measurement & Data 2: Tell write time. 3: Represent interpret data. 1.MD.3 1.MD.4 Tell write time in hours half-hours using analog digital clocks. Organize, represent, interpret data with up to three categories; ask answer questions about the total number of data points, how many in each category, how many more or less are in one category than in another. Hour Times Half Hour Times Tell Time to the Half Hour Who has the Goods? Pictographs Sorting Data 1 Grade 1 Time Money Grade 1 Chance Data 9 3P Learning

13 CCSS Stards CCSS Grade 1 Domain Cluster Stard Description Activities ebooks Geometry Geometry Geometry 1: Reason with shapes their attributes. 1: Reason with shapes their attributes. 1: Reason with shapes their attributes. 1.G.1 1.G.2 1.G.3 Distinguish between defining attributes (e.g., triangles are closed three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build draw shapes to possess defining attributes. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, right circular cylinders) to create a composite shape, compose new shapes from the composite shape. Partition circles rectangles into two four equal shares, describe the shares using the words halves, fourths, quarters, use the phrases half of, fourth of, quarter of. Describe the whole as two of, or four of the shares. Underst for these examples that decomposing into more equal shares creates smaller shares. Same Different Sort It Collect the Shapes 2 Collect Simple Shapes Collect the Objects 2 Match the Solid 2 Halves Halves Quarters Shape Fractions Grade 1 Space Shape Grade 1 Space Shape Grade 1 Space Shape 3P Learning 10

14 CCSS Stards CCSS Grade 2 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Number & Operations in Base Ten 1: Represent solve problems involving addition subtraction. 2: Add subtract within 20. 3: Work with equal groups of objects to gain foundations for multiplication. 3: Work with equal groups of objects to gain foundations for multiplication. 1: Underst place value. 2.OA.1 2.OA.2 fluency stard 2.OA.3 2.OA.4 2.NBT.1 Use addition subtraction within 100 to solve one- two-step word problems involving situations of adding to, taking from, putting together, taking apart, comparing, with unknowns in all positions, e.g., by using drawings equations with a symbol for the unknown number to represent the problem. Fluently add subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows up to 5 columns; write an equation to express the total as a sum of equal addends. Underst that the three digits of a three-digit number represent amounts of hundreds, tens, ones; e.g., 706 equals 7 hundreds, 0 tens, 6 ones. Underst the following as special cases: a. 100 can be thought of as a bundle of ten tens called a hundred. b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds ( 0 tens 0 ones). Word Problems with Letters Problems: Add Subtract Bar model problems 1 Model Addition Model Subtraction Simple Subtraction Add to 18 Addition Facts to 18 Fact Families: Add Subtract Odd Even Numbers 1 Odd or Even Groups of Two Groups of Three Groups of Four Groups of Five Groups Place Value Partitioning Model Numbers Understing Place Value 1 Place Value 1 Place Value 2 Repartition Two-digit Numbers Grade 2 Operations with Numbers Grade 2 Operations with Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Numbers 11 3P Learning

15 CCSS Stards CCSS Grade 2 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten 1: Underst place value. 1: Underst place value. 1: Underst place value. 2: Use place value understing properties of operations to add subtract. 2: Use place value understing properties of operations to add subtract. 2: Use place value understing properties of operations to add subtract. 2.NBT.2 2.NBT.3 2.NBT.4 2.NBT.5 fluency stard 2.NBT.6 2.NBT.7 Count within 1000; skipcount by 5s, 10s, 100s. Read write numbers to 1000 using base-ten numerals, number names, exped form. Compare two three-digit numbers based on meanings of the hundreds, tens, ones digits, using >, =, < symbols to record the results of comparisons. Fluently add subtract within 100 using strategies based on place value, properties of operations, / or the relationship between addition subtraction. Add up to four two-digit numbers using strategies based on place value properties of operations. Add subtract within 1000, using concrete models or drawings strategies based on place value, properties of operations, / or the relationship between addition subtraction; relate the strategy to a written method. Underst that in adding or subtracting three digit numbers, one adds or subtracts hundreds hundreds, tens tens, ones ones; sometimes it is necessary to compose or decompose tens or hundreds. Skip Counting with Coins Counting by Fives Counting by Tens Counting by 2s, 5s 10s Model Numbers Repartition Two-digit Numbers Place value 1 Place value 2 Understing Place Value 1 Which is Bigger? Which is Smaller? Complements to 10, 20, 50 Adding to 2-digit numbers Subtract Tens Complements to Strategies for Column Addition Decompose Numbers to Subtract Add Subtract Using Graphs Add 3 Numbers: Bonds to 100 Add 3 Numbers: Bonds to Multiples of 10 Columns that Add Columns that Subtract Add Two-2-Digit Numbers Add Two 2-Digit Numbers: Regroup Add Three 2-Digit Numbers Add Three 2-Digit Numbers: Regroup Add 3-Digit Numbers Add 3-Digit Numbers: Regroup 2-Digit Differences 2-Digit Differences: Regroup 3-Digit Differences 3-Digit Differences: 1 Regrouping 3-Digit Differences: 2 Regroupings 3-Digit Differences with Zeros Grade 2 Numbers Grade 2 Numbers Grade 2 Numbers Grade 2 Operations with Numbers Grade 2 Operations with Numbers Grade 2 Operations with Numbers 3P Learning 12

16 CCSS Stards CCSS Grade 2 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations in Base Ten Measurement & Data Measurement & Data Measurement & Data Measurement & Data Measurement & Data 2: Use place value understing properties of operations to add subtract. 2: Use place value understing properties of operations to add subtract. 1: Measure estimate lengths in stard units. 1: Measure estimate lengths in stard units. 1: Measure estimate lengths in stard units. 1: Measure estimate lengths in stard units. 2: Relate addition subtraction to length. 2.NBT.8 2.NBT.9 2.MD.1 2.MD.2 2.MD.3 2.MD.4 2.MD.5 Mentally add 10 or 100 to a given number , mentally subtract 10 or 100 from a given number Explain why addition subtraction strategies work, using place value the properties of operations. Measure the length of an object by selecting using appropriate tools such as rulers, yardsticks, meter sticks, measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Estimate lengths using units of inches, feet, yards, centimeters, meters. Measure to determine how much longer one object is than another, expressing the length difference in terms of a stard length unit. Use addition subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) equations with a symbol for the unknown number to represent the problem. Magic Mental Addition Magic Mental Subtraction Measuring Length Comparing Length How Long is That (Customary)? Inches, Feet, Yards Comparing Length Grade 2 Operations with Numbers Grade 2 Operations with Numbers Grade 2 Measurement Grade 2 Measurement Grade 2 Measurement Grade 2 Measurement Grade 2 Operations with Numbers 13 3P Learning

17 CCSS Stards CCSS Grade 2 Domain Cluster Stard Description Activities ebooks Measurement & Data 2: Relate addition subtraction to length. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,..., represent whole-number sums differences within 100 on a number line diagram. Number Lines Grade 2 Numbers Measurement & Data 3: Work with time money. 2.MD.7 Tell write time from analog digital clocks to the nearest five minutes using a.m. p.m. Five Minute Times What is the Time? Quarter to Quarter Past Grade 2 Time Money Measurement & Data Measurement & Data Measurement & Data Geometry 3: Work with time money. 4: Represent interpret data. 4: Represent interpret data. 1: Reason with shapes their attributes. 2.MD.8 2.MD.9 2.MD.10 2.G.1 Solve one- two-step word problems involving dollar bills, quarters, dimes, nickels, pennies, using the $ symbols appropriately. Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units. Draw a picture graph a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, compare problems using information presented in a bar graph. Recognize draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, cubes. Using Fewest Coins to Make an Amount Count Money Pennies, Nickels, Dimes Count More Money Make Graphs Making Graphs Pictographs Sorting Data Collect the Polygons How many Faces? How many Edges? How many Corners? Count Sides Corners? Grade 2 Time Money Grade 2 Chance Data Grade 2 Chance Data Grade 2 Space Shape 3P Learning 14

18 CCSS Stards CCSS Grade 2 Domain Cluster Stard Description Activities ebooks Geometry 1: Reason with shapes their attributes. 2.G.2 Partition a rectangle into rows columns of same-size squares count to find the total number of them. Grade 2 Space Shape Geometry 1: Reason with shapes their attributes. 2.G.3 Partition circles rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Fractions Halves Quarters Thirds Sixths Grade 2 Space Shape 15 3P Learning

19 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking 1: Represent solve problems involving multiplication division. 1: Represent solve problems involving multiplication division. 1: Represent solve problems involving multiplication division. 1: Represent solve problems involving multiplication division. 3.OA.1 3.OA.2 3.OA.3 3.OA.4 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7. Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as Use multiplication division within 100 to solve word problems in situations involving equal groups, arrays, measurement quantities, e.g., by using drawings equations with a symbol for the unknown number to represent the problem. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = [] 3, 6 6 =?. Times Tables Multiplication Arrays Frog Jump Multiplication Groups of Two Groups of Three Groups of Four Groups of Five Groups of Six Groups of Seven Groups of Eight Groups of Nine Groups of Ten Make Fair Shares Divide Into Equal Groups Dividing Threes Dividing Fours Dividing Fives Dividing Sixes Dividing Sevens Dividing Eights Dividing Nines Dividing Tens Division Facts Divide: 1-Digit Divisor Problems: Multiply Divide Word Problems with Letters I am Thinking of a Number! Related Facts 2 Grade 3 Multiplication Division Grade 3 Multiplication Division Grade 3 Multiplication Division Grade 3 Multiplication Division 3P Learning 16

20 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking 2: Underst properties of multiplication the relationship between multiplication division. 2: Underst properties of multiplication the relationship between multiplication division. 3: Multiply divide within : Solve problems involving the four operations, identify explain patterns in arithmetic. 3.OA.5 3.OA.6 3.OA.7 fluency stard 3.OA.8 Apply properties of operations as strategies to multiply divide. Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = = (Distributive property). Underst division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Fluently multiply divide within 100, using strategies such as the relationship between multiplication division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve two-step word problems using the four operations. Represent these problems using equations with a letter sting for the unknown quantity. Assess the reasonableness of answers using mental computation estimation strategies including rounding. Arithmetic Laws Related Facts 2 Division Facts Multiplication Facts Related Facts 2 Fact Families: Multiply Divide Times Tables Problems: Add Subtract Problems: Multiply Divide Word Problems with Letters I am Thinking of a Number! Grade 3 Multiplication Division Grade 3 Multiplication Division Grade 3 Multiplication Division Grade 3 Multiplication Division Grade 3 Reading Understing Whole Numbers 17 3P Learning

21 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Number & Operations in Base Ten Number & Operations in Base Ten 4: Solve problems involving the four operations, identify explain patterns in arithmetic. 1: Use place value understing properties of operations to perform multi-digit arithmetic. 1: Use place value understing properties of operations to perform multi-digit arithmetic. 3.OA.9 3.NBT.1 3.NBT.2 fluency stard Identify arithmetic patterns (including patterns in the addition table or multiplication table), explain them using properties of operations. For example, observe that 4 times a number is always even, explain why 4 times a number can be decomposed into two equal addends. Use place value understing to round whole numbers to the nearest 10 or 100. Fluently add subtract within 1000 using strategies algorithms based on place value, properties of operations, / or the relationship between addition subtraction. Increasing Patterns Decreasing Patterns Nearest Ten? Nearest Hundred? Place Value 3 Understing Place Value 1 Missing Numbers 1 Estimate Sums Estimate Differences Strategies for Column Addition Add 3-Digit Numbers Add Three 3-Digit Numbers: Regroup Adding Colossal Columns Subtracting Colossal Columns Add Multi-Digit Numbers 1 Add Multi-Digit Numbers 2 Add Three 1-Digit Numbers Add Three 2-Digit Numbers Model Addition Model Subtraction Simple Subtraction Fact Families: Add Subtract Commutative Property of Addition Addition Properties Bar Model Problems 2 Grade 3 Patterns Algebra Grade 3 Readig Understing Whole Numbers Grade 3 Addition Subtractions 3P Learning 18

22 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations- Fractions Number & Operations- Fractions 1: Use place value understing properties of operations to perform multi-digit arithmetic. 1: Develop understing of fractions as numbers. 1: Develop understing of fractions as numbers. 3.NBT.3 3.NF.1 3.NF.2 Multiply one-digit whole numbers by multiples of 10 in the range (e.g., 9 80, 5 60) using strategies based on place value properties of operations. Underst a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; underst a fraction a/b as the quantity formed by a parts of size 1/b. Underst a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole partitioning it into b equal parts. Recognize that each part has size 1/b that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b that its endpoint locates the number a/b on the number line. Missing Numbers: x facts Multiplication Turn-Abouts Arrays 2 Equivalent Facts: Multiply Double Halve to Multiply Multiplication Problems 1 Arrays 1 Model Multiplication to 5 5 Multiplication Grids Multiply Multiples of 10 Multiply More Multiples of 10 Multiply: 1-Digit Number Mental Methods Multiplication Multiplication Facts Multiplication Properties Multiply: 1-Digit Number, Regroup Short Multiplication Multiply: 2-Digit by 1-Digit Uneven partitioned shapes 1 Uneven partitioned shapes 2 Model Fractions Fractions What Fraction Is Shaded? Part-whole rods 1 Part-whole rods 2 Fraction Fruit Sets 1 Fractions of a Collection Halves Quarters Thirds Sixths Counting with Fractions on a Number Line Identifying fractions beyond 1 Grade 3 Multiplication Division Grade 3 Fractions Grade 3 Fractions 19 3P Learning

23 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions Measurement & Data 1: Develop understing of fractions as numbers. 1: Solve problems involving measurement estimation. 3.NF.3 3.MD.1 Explain equivalence of fractions in special cases, compare fractions by reasoning about their size. a. Underst two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, justify the conclusions, e.g., by using a visual fraction model. Tell write time to the nearest minute measure time intervals in minutes. Solve word problems involving addition subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Shading Equivalent Fractions Equivalent Fractions on a Number Line 1 Equivalent Fraction Wall 1 Comparing Fractions 1 Fraction Wall Labeling 1 What is the Time? Time Mentals Half Hour Times Elapsed Times Grade 3 Fractions Grade 3 Time 3P Learning 20

24 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Measurement & Data Measurement & Data Measurement & Data Measurement & Data 21 3P Learning 1: Solve problems involving measurement estimation of intervals of time, liquid volumes, masses of objects. 2: Represent interpret data. 2: Represent interpret data. 3: Geometric measurement: underst concepts of area relate area to multiplication to addition. 3.MD.2 3.MD.3 3.MD.4 3.MD.5 Measure estimate liquid volumes masses of objects using stard units of grams (g), kilograms (kg), liters (l). Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units. Draw a scaled picture graph a scaled bar graph to represent a data set with several categories. Solve one- two-step how many more how many less problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. Generate measurement data by measuring lengths using rulers marked with halves fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units whole numbers, halves, or quarters. Recognize area as an attribute of plane figures underst concepts of area measurement. a. A square with side length 1 unit, called a unit square, is said to have one square unit of area, can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. Mass Word Problems How Full? Comparing Volume Cups, Pints, Quarts, Gallons Grams Milligrams Milliliters Liters Grams Kilograms Pictographs Picture Graphs Bar Graphs 1 Bar Graphs 2 Making Graphs Add Subtract Using Graphs Read Graphs Measuring Length Measuring to the Nearest Half Inch How Long is That (Customary)? Equal Areas Area of Shapes Grade 3 Measurement Grade 3 Chance Data Grade 3 Measurement Grade 3 Measurement

25 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Measurement & Data Measurement & Data 3: Geometric measurement: underst concepts of area relate area to multiplication to addition. 3: Geometric measurement: underst concepts of area relate area to multiplication to addition. 3.MD.6 3.MD.7 Measure areas by counting unit squares (square cm, square m, square in, square ft, improvised units). Relate area to the operations of multiplication addition. a. Find the area of a rectangle with whole-number side lengths by tiling it, show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangles with wholenumber side lengths in the context of solving real world mathematical problems, represent whole-number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a b + c is the sum of a b a c. Use area models to represent the distributive property in mathematical reasoning. d. Recognize area as additive. Find areas of rectilinear figures by decomposing them into nonoverlapping rectangles adding the areas of the nonoverlapping parts, applying this technique to solve real world problems. Biggest Shape Equal Areas Area of Shapes Area: Squares Rectangles Area of Shapes (inches, feet, yards) Grade 3 Measurement Grade 3 Measurement 3P Learning 22

26 CCSS Stards CCSS Grade 3 Domain Cluster Stard Description Activities ebooks Measurement & Data Geometry Geometry 4: Geometric measurement: recognize perimeter as an attribute of plane figures distinguish between linear area measures. 1: Reason with shapes their attributes. 1: Reason with shapes their attributes. 3.MD.8 3.G.1 3.G.2 Solve real world mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, exhibiting rectangles with the same perimeter different areas or with the same area different perimeters. Underst that shapes in different categories (e.g., rhombuses, rectangles, others) may share attributes (e.g., having four sides), that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, squares as examples of quadrilaterals, draw examples of quadrilaterals that do not belong to any of these subcategories. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, describe the area of each part as 1/4 of the area of the shape. Perimeter Detectives 1 Perimeter Perimeter of Shapes Perimeter: Squares Rectangles Collect the Shapes Collect the Shapes 1 Collect the Shapes 2 Collect More Shapes Collect the Polygons How many Corners? How many Edges? How many Faces? Shapes Properties of Quadrilaterals Shape Fractions Area of Shapes Grade 3 Measurement Grade 3 Space, Shape Position Grade 3 Space, Shape Position 23 3P Learning

27 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking Operations & Algebraic Thinking 1: Use the four operations with whole numbers to solve problems. 1: Use the four operations with whole numbers to solve problems. 1: Use the four operations with whole numbers to solve problems. 2: Gain familiarity with factors multiples. 4.OA.1 4.OA.2 4.OA.3 4.OA.4 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Solve multistep word problems posed with whole numbers having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter sting for the unknown quantity. Assess the reasonableness of answers using mental computation estimation strategies including rounding. Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. Multiplication Properties Related Facts 2 Find the Missing Number 1 Find the Missing Number 2 Problems: Multiply Divide Write an : Word Problems Solve : Add, Subtract 1 Solve : Multiply, Divide 1 Pyramid Puzzles 1 Word problems with letters Magic Symbols 1 Prime or Composite? Factors Multiples Prime Factorization Find the Factor Grade 4 Multiplication Division Grade 4 Multiplication Division Grade 4 Multiplication Division Grade 4 Addition Subtraction Grade 4 Multiplication Division 3P Learning 24

28 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Operations & Algebraic Thinking Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten 3: Generate analyze patterns. 1: Generalize place value understing for multidigit whole numbers. 1: Generalize place value understing for multidigit whole numbers. 1: Generalize place value understing for multidigit whole numbers. 4.OA.5 4.NBT.1 4.NBT.2 4.NBT.3 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add Increasing Patterns 3 the starting number 1, Decreasing Patterns generate terms in the resulting sequence observe that Pattern Rules Tables the terms appear to alternate between odd even numbers. Explain informally why the numbers will continue to alternate in this way. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value division. Read write multi-digit whole numbers using base-ten numerals, number names, exped form. Compare two multi- digit numbers based on meanings of the digits in each place, using >, =, < symbols to record the results of comparisons. Use place value understing to round multi-digit whole numbers to any place. Place Value to Millions Understing Place Value 3 Place Value 3 Place Value 1 (x 10 10) Exped Notation Exping Numbers Greater Than or Less Than? Comparing Numbers Numbers from Words to Digits 1 Numbers from Words to Digits 2 Nearest Whole Number Nearest 10? Nearest 100? Nearest 1000? Rounding Numbers Grade 4 Patterns Algebra Grade 4 Reading Understing Whole Numbers Grade 4 Reading Understing Whole Numbers Grade 4 Reading Understing Whole Numbers 25 3P Learning

29 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten 2: Use place value understing properties of operations to perform multi-digit arithmetic. 2: Use place value understing properties of operations to perform multi-digit arithmetic. 2: Use place value understing properties of operations to perform multi-digit arithmetic. 4.NBT.4. fluency stard 4.NBT.5 4.NBT.6 Fluently add subtract multidigit whole numbers using the stard algorithm. Multiply a whole number of up to four digits by a one-digit whole number, multiply two two-digit numbers, using strategies based on place value the properties of operations. Illustrate explain the calculation by using equations, rectangular arrays, /or area models. Find whole-number quotients remainders with up to four-digit dividends onedigit divisors, using strategies based on place value, the properties of operations, / or the relationship between multiplication division. Illustrate explain the calculation by using equations, rectangular arrays, /or area models. Add Multi-Digit Numbers 2 Adding Colossal Columns Add Multi-Digit Numbers 1 Subtracting Colossal Columns 2-Digit Differences 2-Digit Differences: Regroup 3-Digit Differences 3-Digit Differences with Zeros 3-Digit Differences: 1 Regrouping 3-Digit Differences: 2 Regroupings Add 3-Digit Numbers Add Three 3-Digit Numbers: Regroup Problems: Add Subtract Double Halve to Multiply Bar Model X Multiply: 1-Digit Number Multiply: 1-Digit Number, Regroup Contracted Multiplication Multiply: 2-Digit Number, Regroup Multiply Multiples of 10 Multiply 2 Digits Area Model Multiply Divide Problems 1 Frog Jump Division Divide: 1-Digit Divisor 1 Divide: 1-Digit Divisor 2 Grade 4 Addition Subtraction Grade 4 Multiplication Division Grade 4 Multiplication Division 3P Learning 26

30 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions 1: Extend understing of fraction equivalence ordering. 4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n a)/(n b) by using visual fraction models, with attention to how the number size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize generate equivalent fractions. Fraction Wall Labelling 2 Equivalent Fractions Shading Equivalent Fractions Equivalent Fraction Wall 1 Equivalent Fraction Wall 2 Simplifying Fractions Grade 4 Fractions Number & Operations- Fractions 1: Extend understing of fraction equivalence ordering. 4.NF.2 Compare two fractions with different numerators different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, justify the conclusions, e.g., by using a visual fraction model. Compare Fractions 1a Compare Fractions 1b Grade 4 Fractions 27 3P Learning

31 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions 2: Build fractions from unit fractions. 4.NF.3 Underst a fraction a/b with a > 1 as a sum of fractions 1/b. a. Underst addition subtraction of fractions as joining separating parts referring to the same whole. b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = /8 = 8/8 + 8/8 + 1/8. c. Add subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, /or by using properties of operations the relationship between addition subtraction. d. Solve word problems involving addition subtraction of fractions referring to the same whole having like denominators, e.g., by using visual fraction models equations to represent the problem. Add Like Fractions Subtract Like Fractions Add Like Mixed Numbers Subtract Like Mixed Numbers Add subtract fractions 1 Fraction Fruit Sets 2 Identifying fractions beyond 1 Mixed Improper Numbers on a Number Line Grade 4 Fractions 3P Learning 28

32 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions Number & Operations- Fractions 2: Build fractions from unit fractions. 3: Underst decimal notation for fractions, compare decimal fractions. 4.NF.4 4.NF.5 Apply extend previous understings of multiplication to multiply a fraction by a whole number. a. Underst a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (1/4). b. Underst a multiple of a/b as a multiple of 1/b, use this understing to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n a)/b.) c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? Express a fraction with denominator 10 as an equivalent fraction with denominator 100, use this technique to add two fractions with respective denominators For example, express 3/10 as 30/100, add 3/10 + 4/100 = 34/100. Fraction by Whole Number Multiply: Whole Number Fraction Under Review Grade 4 Fractions Under Review 29 3P Learning

33 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions Number & Operations- Fractions Measurement & Data 3: Underst decimal notation for fractions, compare decimal fractions. 3: Underst decimal notation for fractions, compare decimal fractions. 1: Solve problems involving measurement conversion of measurements. 4.NF.6 4.NF.7 4.MD.1 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, justify the conclusions, e.g., by using a visual model. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a twocolumn table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet inches listing the number pairs (1, 12), (2, 24), (3, 36),... Fractions to Decimals Decimals to Fractions 1 Decimals to Fractions 2 Comparing Decimals Decimal Order 1 Decimal Place Value Decimals on the Number Line Decimals from Words to Digits 1 Inches, Feet, Yards Ounces Pounds Cups, Pints, Quarts, Gallons Meters Kilometers Customary Units of Length Converting cm mm Customary Units of Capacity Milliters Liters Centimeters Millimeters Operations with Length Converting Units of Length Kilogram Conversions Grams Kilograms Customary Units of Weight 1 Customary Units of Weight 2 Converting Units of Mass Fraction Length Models 2 Grade 4 Fractions Grade 4 Fractions Grade 4 Length, Area Perimeter Grade 4 Time 3P Learning 30

34 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Measurement & Data Measurement & Data Measurement & Data Measurement & Data 31 3P Learning 1: Solve problems involving measurement conversion of measurements. 1: Solve problems involving measurement conversion of measurements. 2: Represent interpret data. 3: Geometric measurement: underst concepts of angle measure angles. 4.MD.2 4.MD. 3 4.MD.4 4.MD.5 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, money, including Fraction Length problems involving simple fractions Models 1 or decimals, problems that What Time Will it Be? require expressing measurements Elapsed Time given in a larger unit in terms of a Making Change (USD) smaller unit. Represent measurement Mass Word Problems quantities using diagrams such as number line diagrams that feature a measurement scale. Apply the area perimeter formulas for rectangles in real Perimeter: Squares world mathematical problems. Rectangles For example, find the width of a Perimeter Detectives 1 rectangular room given the area of Area: Squares the flooring the length, by viewing Rectangles the area formula as a multiplication Area of Shapes equation with an unknown factor. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4,1/8). Solve problems involving addition subtraction of fractions by using information presented in line plots. For example, from a line plot find interpret the difference in length between the longest shortest specimens in an insect collection. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, underst concepts of angle measurement: a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a onedegree angle, can be used to measure angles. b. An angle that turns through n onedegree angles is said to have an angle measure of n degrees. Fraction Length Models 2 Angles in a Revolution Comparing Angles Equal Angles Estimating Angles Under Review Grade 4 Length, Area Perimeter Grade 4 Length, Area Perimeter Grade 4 Space, Shape Position

35 CCSS Stards CCSS Grade 4 Domain Cluster Stard Description Activities ebooks Measurement & Data Measurement & Data Geometry Geometry Geometry 3: Geometric measurement: underst concepts of angle measure angles. 3: Geometric measurement: underst concepts of angle measure angles. 1: Draw identify lines angles, classify shapes by properties of their lines angles. 1: Draw identify lines angles, classify shapes by properties of their lines angles. 1: Draw identify lines angles, classify shapes by properties of their lines angles. 4.MD.6 4.MD.7 4.G.1 4.G.2 4.G.3 Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition subtraction problems to find unknown angles on a diagram in real world mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. Draw points, lines, line segments, rays, angles (right, acute, obtuse), perpendicular parallel lines. Identify these in twodimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, identify right triangles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify linesymmetric figures draw lines of symmetry. Measuring Angles Angles of Revolution: Unknown Values Angles of Revolution: Value of x Angle Measures in a Triangle Labelling Angles What Line Am I? Sides, Angles Diagonals Triangles: Acute, Right, Obtuse Collect the Shapes 2 Shapes Symmetry or Not? Grade 4 Space, Shape Position Grade 4 Space, Shape Position Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry Grade 5 Geometry 3P Learning 32

36 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Operations Algebraic Thinking Operations Algebraic Thinking Operations Algebraic Thinking Number & Operations in Base Ten 33 3P Learning 1: Write interpret numerical expressions. 1: Write interpret numerical expressions. 2: Analyze patterns relationships. 1: Underst the place value system. 5.OA.1 5.OA.2 5.OA.3 5.NBT.1 Use parentheses, brackets, or braces in numerical expressions, evaluate expressions with these symbols. Write simple expressions that record calculations with numbers, interpret numerical expressions without evaluating them. For example, express the calculation add 8 7, then multiply by 2 as 2 (8 + 7). Recognize that 3 ( ) is three times as large as , without having to calculate the indicated sum or product. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, graph the ordered pairs on a coordinate plane. For example, given the rule Add 3 the starting number 0, given the rule Add 6 the starting number 0, generate terms in the resulting sequences, observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right 1/10 of what it represents in the place to its left. Order of Operations 1 Magic Symbols 1 Magic Symbols 2 Problems: Multiply Divide Problems: Multiply Divide 1 I am Thinking of a Number! Write an Equation: Word Problems Writing Algebraic Missing Values Pyramid Puzzles 2 Related Facts 2 Find the Missing Number 1 Table of Values Ordered Pairs Pick the Next Number Describing Patterns Decreasing Patterns Increasing Patterns Find the Pattern Rule Multiplying by 10, 100, 1000 Dividing by 10, 100, 1000 Place Value to Millions Place Value to Billions Place Value 2 (x 10 10) Grade 6 Patterns Algebra Grade 6 Patterns Algebra Grade 6 Patterns Algebra Grade 5 Reading Understing Whole Numbers

37 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations in Base Ten 1: Underst the place value system. 1: Underst the place value system. 1: Underst the place value system. 2: Perform operations with multidigit whole numbers with decimals to hundredths. 5.NBT.2 5.NBT.3 5.NBT.4 5.NBT.5 fluency stard Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use wholenumber exponents to denote powers of 10. Read, write, compare decimals to thousths. a. Read write decimals to thousths using base-ten numerals, number names, exped form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). b. Compare two decimals to thousths based on meanings of the digits in each place, using >, =, < symbols to record the results of comparisons. Use place value understing to round decimals to any place. Fluently multiply multi-digit whole numbers using the stard algorithm. Multiply Decimals Powers of 10 Divide by Powers of 10 Comparing Decimals 2 Decimal Order Decimal Order 1 Decimal Order 2 Decimals from Words to Digits 1 Decimals from Words to Digits 2 Rounding Decimals Rounding Decimals 1 Rounding Decimals 2 Long Multiplication Multiply 2 Digits Area Model Multiply: 2-Digit Number, Regroup Double Halve to Multiply Grade 5 Fractions, Decimals Percentages Grade 6 Fractions, Decimals Percentages Grade 5 Fractions, Decimals Percentages Grade 6 Fractions, Decimals Percentages Grade 5 Fractions, Decimals Percentages Grade 6 Fractions, Decimals Percentages Grade 5 Addition Subtraction 3P Learning 34

38 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Number & Operations in Base Ten Number & Operations in Base Ten Number & Operations- Fractions 35 3P Learning 2: Perform operations with multi-digit whole numbers with decimals to hundredths. 2: Perform operations with multi-digit whole numbers with decimals to hundredths. 1: Use equivalent fractions as a strategy to add subtract fractions. 5.NBT.6 5.NBT.7 5.NF.1 Find whole-number quotients of whole numbers with up to four-digit dividends twodigit divisors, using strategies based on place value, the properties of operations, /or the relationship between multiplication division. Illustrate explain the calculation by using equations, rectangular arrays, /or area models. Add, subtract, multiply, divide decimals to hundredths, using concrete models or drawings strategies based on place value, properties of operations, /or the relationship between addition subtraction; relate the strategy to a written method explain the reasoning used. Add subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/ /12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Divide: 1-Digit Divisor 1 Divide: 1-Digit Divisor 2 Divide: 1-Digit Divisor, Remainder Divide: 2-Digit Divisor, Remainder Add Decimals 1 Add Decimals 2 Subtract Decimals 1 Subtract Decimals 2 Decimal by Whole Number Money Problems: Four Operations Decimal by Decimal Divide Decimal by Decimal Divide Decimal by Whole Number Multiply decimals Subtract Unlike Mixed Numbers Shading Equivalent Fractions 1 Add Unlike Fractions Subtract Unlike Fractions One Take Fraction Add: No Common Denominator Add Unlike Mixed Numbers Simplifying Fractions Equivalent Fractions on a Number Line 1 Equivalent Fractions on a Number Line 2 Shading Equivalent Fractions Equivalent Fraction Wall 2 Equivalent Fractions Equivalent Fractions 1 Comparing Fractions 1 Comparing Fractions 2 Scaling Fractions Fraction Wall Labelling 2 Compare Fractions 2 Grade 5 Multiplication Division Grade 6 Fractions, Decimals Percentages Grade 7 Decimals Grade 7 Fractions

39 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions Number & Operations- Fractions 1: Use equivalent fractions as a strategy to add subtract fractions. 2: Apply extend previous understings of multiplication division. 5.NF.2 5.NF.3 Solve word problems involving addition subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions number sense of fractions to estimate mentally assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie? Fraction Word Problems Divide Fractions Visual Model Unit Fractions Grade 7 Fractions Grade 7 Fractions 3P Learning 36

40 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions Number & Operations- Fractions 2: Apply extend previous understings of multiplication division. 2: Apply extend previous understings of multiplication division. 5.NF.4 5.NF.5 Apply extend previous understings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. For example, use a visual fraction model to show (2/3) 4 = 8/3, create a story context for this equation. Do the same with (2/3) (4/5) = 8/15. (In general, (a/b) (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, represent fraction products as rectangular areas. Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. Fraction by Whole Number Multiply: Whole Number Fraction Model fractions to multiply Multiply Two Fractions 1 Grade 7 Fractions Grade 7 Fractions 37 3P Learning

41 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Number & Operations- Fractions Number & Operations- Fractions 2: Apply extend previous understings of multiplication division. 2: Apply extend previous understings of multiplication division to multiply divide fractions. 5.NF.6 5.NF.7 Solve real world problems involving multiplication of fractions mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Apply extend previous understings of division to divide unit fractions by whole numbers whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, compute such quotients. For example, create a story context for (1/3) 4, use a visual fraction model to show the quotient. b. Interpret division of a whole number by a unit fraction, compute such quotients. For example, create a story context for 4 (1/5), use a visual fraction model to show the quotient. c. Solve real world problems involving division of unit fractions by non-zero whole numbers division of whole numbers by unit fractions, e.g., by using visual fraction models equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? Estimate Products with Fractions Improper to Mixed Mixed to Improper Divide Fractions Visual Model Unit Fractions Grade 7 Fractions Grade 7 Fractions 3P Learning 38

42 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Measurement & Data Measurement & Data Measurement & Data 1: Convert like measurement units within a given measurement system. 2: Represent interpret data. 3: Geometric measurement: underst concepts of volume. 5.MD.1 5.MD.2 5.MD.3 Convert among different-sized stard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), use these conversions in solving multistep, real world problems. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. Recognize volume as an attribute of solid figures underst concepts of volume measurement. a. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Converting Units of Length Customary Units of Length Operations with Length Customary Units of Weight 1 Customary Units of Weight 2 Meters Kilometers Milliliters Liters Customary Units of Capacity Converting Units of Mass Mass Word Problems Capacity Addition Mass Addition Fraction Length Models 2 Grade 3 Measurement Grade 5 Length, Area Perimeter Grade 5 Volume, Capacity Mass 39 3P Learning

43 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Measurement & Data Measurement & Data 3: Geometric measurement: underst concepts of volume. 3: Geometric measurement: underst concepts of volume. 5.MD.4 5.MD.5 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, improvised units. Relate volume to the operations of multiplication addition solve real world mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l w h V = B h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Grade 5 Volume, Capacity Mass Grade 5 Volume, Capacity Mass 3P Learning 40

44 CCSS Stards CCSS Grade 5 Domain Cluster Stard Description Activities ebooks Geometry Geometry Geometry Geometry 1: Graph points on the coordinate plane to solve real-world mathematical problems. 1: Graph points on the coordinate plane to solve real-world mathematical problems. 2: Classify twodimensional figures into categories based on their properties. 2: Classify twodimensional figures into categories based on their properties. 5.G.1 5.G.2 5.G.3 5.G.4 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line a given point in the plane located by using an ordered pair of numbers, called its coordinates. Underst that the first number indicates how far to travel from the origin in the direction of one axis, the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes the coordinates correspond (e.g., x-axis x-coordinate, y-axis y-coordinate). Represent real world mathematical problems by graphing points in the first quadrant of the coordinate plane, interpret coordinate values of points in the context of the situation. Underst that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles squares are rectangles, so all squares have four right angles. Classify organize twodimensional figures in a hierarchy based on properties. Ordered Pairs Map Coordinates Coordinate Meeting Place Coordinate Graphs Coordinate Graphs: 1st Quadrant Number Plane Coordinate Graphs: 1st Quadrant Sides, Angles Diagonals Collect More Shapes Collect the Shapes 2 Collect the Polygons What Line Am I? Shapes Properties of Quadrilaterals Grade 7 The Number Plane Grade 6 Position Grade 5 Position Grade 5 Position Grade 6 Position Grade 5 Geometry 41 3P Learning

45 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks Ratios & Proportional Relationships Ratios & Proportional Relationships Ratios & Proportional Relationships 1: Underst ratio concepts use ratio reasoning to solve problems. 1: Underst ratio concepts use ratio reasoning to solve problems. 1: Underst ratio concepts use ratio reasoning to solve problems. 6.RP.1 6.RP.2 6.RP.3 Underst the concept of a ratio use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote cidate A received, cidate C received nearly three votes. Underst the concept of a unit rate a/b associated with a ratio a:b with b 0, use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. Use ratio rate reasoning to solve real-world mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part the percent. d. Use ratio reasoning to convert measurement units; manipulate transform units appropriately when multiplying or dividing quantities. e. Underst the concept of Pi as the ratio of the circumference of a circle to its diameter. Simplify Ratios Ratios Rates Using Similar Triangles Solve Proportions Dividing a Quantity in a Ratio Unitary Method Mixed decimal, percentage fraction conversions Common Fractions as Percentages Percentage to Fraction Decimals to Percentages Mixed Numerals to Percentages greater than 100% Percentages greater than 100% to Mixed Numerals Rate Word Problems Ratio Word Problems Equivalent Ratios Table of Values Average Speed Best Buy Pick the Next Number Percentage of a Quantity Percentage Increase Decrease Solve Percent Percentage Word Problems Centimeters Millimeters Converting cm mm Converting Units of Area Customary Units of Length Customary Units of Capacity Customary Units of Weight 1 Customary Units of Weight 2 3P Learning 42

46 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks The Number System The Number System The Number System 1: Apply extend previous understings of multiplication division to divide fractions by fractions. 2: Compute fluently with multi-digit numbers find common factors multiples. 2: Compute fluently with multi-digit numbers find common factors multiples. 6.NS.1 6.NS.2 fluency stard 6.NS.3 fluency stard Interpret compute quotients of fractions, solve word problems involving division of fractions by fractions, e.g., by using visual fraction models equations to represent the problem. For example, create a story context for (2/3) (3/4) use a visual fraction model to show the quotient; use the relationship between multiplication division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of l with length 3/4 mi area 1/2 square mi? Fluently divide multi-digit numbers using the stard algorithm. Fluently add, subtract, multiply, divide multi-digit decimals using the stard algorithm for each operation. Divide fractions visual model Divide Whole Number by Fraction Divide Fractions by Fractions 1 Divide by a unit fraction Dividing Fractions Divide by Powers of 10 Divide: 1-Digit Divisor 2 Divide: 2-Digit Divisor, Remainder Divisibility Tests Adding Decimals Subtracting Decimals Decimal by Decimal Divide Decimal by Decimal Divide Decimal by Whole Number Greatest Common Factor Multiply Decimals: Area Model Multiply Decimals 1 Divide Decimals Grade 7 Fractions Grade 6 Addition Subtraction Grade 7 Whole Numbers Grade 6 Multiplication Division Grade 7 Whole Numbers 43 3P Learning

47 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks The Number System The Number System The Number System 2: Compute fluently with multi-digit numbers find common factors multiples. 3: Apply extend previous understings of numbers to the system of rational numbers. 3: Apply extend previous understings of numbers to the system of rational numbers. 6.NS.4 6.NS.5 6.NS.6 Find the greatest common factor of two whole numbers less than or equal to 100 the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). Underst that positive negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive negative numbers to represent quantities in realworld contexts, explaining the meaning of 0 in each situation. Underst a rational number as a point on the number line. Extend number line diagrams coordinate axes familiar from previous grades to represent points on the line in the plane with negative number coordinates. a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, that 0 is its own opposite. b. Underst signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. c. Find position integers other rational numbers on a horizontal or vertical number line diagram; find position pairs of integers other rational numbers on a coordinate plane. Greatest Common Factor More with Integers Add Integers Subtract Integers Integers: Subtraction Integers: Add Subtract Integers on a Number Line Ordering Integers Comparing Integers Grade 7 Whole Numbers Grade 7 Directed Numbers Grade 7 Directed Numbers 3P Learning 44

48 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks The Number System The Number System 45 3P Learning 3: Apply extend previous understings of numbers to the system of rational numbers. 3: Apply extend previous understings of numbers to the system of rational numbers. 6.NS.7 6.NS.8 Underst ordering absolute value of rational numbers. a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. b. Write, interpret, explain statements of order for rational numbers in real-world contexts. For example, write 3 ºC > 7 ºC to express the fact that 3 ºC is warmer than 7 ºC. c. Underst the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Solve real-world mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates absolute value to find distances between points with the same first coordinate or the same second coordinate. Absolute Value Vertical horizontal shift Ordered Pairs Horizontal Vertical Change Table of Values Find the Pattern Rule Graphing from a Table of Values Graphing from a Table of Values 2 Absolute Value Graphs Coordinate Graphs Number Plane Grade 7 Directed Numbers Grade 7 The Number Plane

49 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks & & & 1: Apply extend previous understings of arithmetic to algebraic expressions. 1: Apply extend previous understings of arithmetic to algebraic expressions. 1: Apply extend previous understings of arithmetic to algebraic expressions. 6.EE.1 6.EE.2 6.EE.3 Write evaluate numerical expressions involving whole-number exponents. Write, read, evaluate expressions in which letters st for numbers. a. Write expressions that record operations with numbers with letters sting for numbers. For example, express the calculation Subtract y from 5 as 5 y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ A = 6 s² to find the volume surface area of a cube with sides of length s = 1/2. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Exponents Exponent Laws Algebra Exponent Notation Properties of Exponents Multiplication with Exponents Integers: Order of Operations Grouping in Pairs Integers: Order of Operations Grouping in Pairs Exp then Simplify Grade 7 Whole Numbers Grade 6 Patterns Algebra Grade 7 Algebra Basics Grade 7 Algebra Basics 3P Learning 46

50 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks & & & & 1: Apply extend previous understings of arithmetic to algebraic expressions. 2: Reason about solve one-variable equations inequalities. 2: Reason about solve one-variable equations inequalities. 2: Reason about solve one-variable equations inequalities. 6.EE.4 6.EE.5 6.EE.6 6.EE.7 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y 3y are equivalent because they name the same number regardless of which number y sts for. Underst solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. Use variables to represent numbers write expressions when solving a real-world or mathematical problem; underst that a variable can represent an unknown number, or, depending on the purpose at h, any number in a specified set. Solve real-world mathematical problems by writing solving equations of the form x + p = q px = q for cases in which p, q x are all non-negative rational numbers. Simplifying Simple Substitution 1 Simple Substitution 2 : Variables, Both Sides Write an Equation: Word Problems Dividing I am Thinking of a Number! Writing Find the Missing Number 1 Solve : Add, Subtract 1 Solve : Add, Subtract 2 Solve : Multiply, Divide 1 Solve : Multiply, Divide 2 Solve Multi-Step Solve Two-Step Solving More Magic Symbols 1 Magic Symbols 2 Grade 7 Algebra Basics Grade 7 Algebra Basics Grade 6 Patterns Algebra Grade 7 Algebra Basics Grade 6 Patterns Algebra Grade 7 Algebra Basics 47 3P Learning

51 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks & & Geometry Geometry 2: Reason about solve onevariable equations inequalities. 3: Represent analyze quantitative relationships between dependent independent variables. 1: Solve realworld mathematical problems involving area, surface area, volume. 1: Solve realworld mathematical problems involving area, surface area, volume. 6.EE.8 6.EE.9 6.G.1 6.G.2 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent independent variables using graphs tables, relate these to the equation. For example, in a problem involving motion at constant speed, list graph ordered pairs of distances times, write the equation d = 65t to represent the relationship between distance time. Find the area of right triangles, other triangles, special quadrilaterals, polygons by composing into rectangles or decomposing into triangles other shapes; apply these techniques in the context of solving real-world mathematical problems. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world mathematical problems. Graphing Inequalities 1 Solving Inequalities 1 Solving One-Step Inequalities 1 Solving One-Step Inequalities 2 Solve Two-Step Inequalities Find the Function Rule Function Rules Tables Area: Squares Rectangles Area: Parallelograms Area: Quadrilaterals Area: Triangles Area: Compound Figures Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Grade 6 Patterns Algebra Grade 7 Algebra Basics Grade 6 Patterns Algebra Grade 7 Algebra Basics Grade 6 Length, Perimeter Area Grade 7 Area Perimeter Grade 6 Volume, Capacity Mass Grade 7 Solids 3P Learning 48

52 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks Geometry Geometry Statistics & Statistics & Statistics & 1: Solve realworld mathematical problems involving area, surface area, volume. 1: Solve realworld mathematical problems involving area, surface area, volume. 1: Develop understing of statistical variability. 1: Develop understing of statistical variability. 1: Develop understing of statistical variability. 6.G.3 6.G.4 6.SP.1 6.SP.2 6.SP.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world mathematical problems. Represent three-dimensional figures using nets made up of rectangles triangles, use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world mathematical problems. Recognize a statistical question as one that anticipates variability in the data related to the question accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages. Underst that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Coordinate Graphs Rotations: Coordinate Plane Transformations: Coordinate Plane Nets Surface Area: Rectangular Prisms Surface Area: Triangular Prisms Mean Median Mode Mode Mode from Frequency Table Median Median from Frequency Table Median Cumulative Frequency Mean Mean from Frequency Table Grade 6 Geometry Grade 6 Position Grade 6 Data Representation Grade 6 Data Representation Grade 6 Data Representation 49 3P Learning

53 CCSS Stards CCSS Grade 6 Domain Cluster Stard Description Activities ebooks Statistics & Statistics & 2: Summarize describe distributions. 2: Summarize describe distributions. 6.SP.4 6.SP.5 Display numerical data in plots on a number line, including dot plots, histograms, box plots. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured its units of measurement. c. Giving quantitative measures of center (median /or mean) variability (interquartile range / or mean absolute deviation), as well as describing any overall pattern any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center variability to the shape of the data distribution the context in which the data were gathered. Box- Whisker Plots 1 Histograms Dot Plots Calculating Interquartile Range Mode Mode from Frequency Table Median Median from Frequency Table Median Cumulative Frequency Mean Mean from Frequency Table Grade 6 Data Representation Grade 6 Data Representation 3P Learning 50

54 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Ratios & Proportional Relationships Ratios & Proportional Relationships 1: Analyze proportional relationships use them to solve realworld mathematical problems. 1: Analyze proportional relationships use them to solve realworld mathematical problems. 7.RP.1 7.RP.2 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Recognize represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) (1, r) where r is the unit rate. Simplify Ratios: 2 Whole Numbers Simplify Ratios: 3 Whole Numbers Simplifying Ratios with Decimals Simplifying Ratios: Mixed Numbers Simplify Ratios: Fractions Equivalent Ratios Unitary Method Solve Proportions Converting Rates Dividing a Quantity in a Ratio Direct Variation Determining a Rule for a Line Pattern Rules Tables Graphing from a Table of Values 2 Find the Pattern Rule Reading Values from a Line Function Rules Tables y=ax 51 3P Learning

55 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Ratios & Proportional Relationships 1: Analyze proportional relationships use them to solve realworld mathematical problems. 7.RP.3 Use proportional relationships to solve multistep ratio percent problems. Examples: simple interest, tax, markups markdowns, gratuities commissions, fees, percent increase decrease, percent error. Percentages greater than a whole Percentage of an amount using decimals Percentages to Fractions (with without simplification) Percentage of an amount using fractions (<100%) Percentages greater than 100% to Mixed Numbers Mixed Numerals to Percentages greater than 100% Fractions to Percentages (Calculator) Fractions to Percentages (Non-Calculator) Quantities to Percentages (no units) Quantities to Percentages (with units) Ratio Word Problems Rate Word Problems Percentage of a Quantity Percent Increase Decrease Calculating Percentages Percentage Error Percentage Word Problems Solve Percent Piecework Royalties Commission Percent of a Number Percentage Composition Simple Interest Compound Interest Best Buy Purchase Options Wages Salaries Grade 8 Percentage Calculation 3P Learning 52

56 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks The Number System 1: Apply extend previous understings of operations with fractions to add, subtract, multiply, divide rational numbers. 7.NS.1 Apply extend previous understings of addition subtraction to add subtract rational numbers; represent addition subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged. b. Underst p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. Underst subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, apply this principle in realworld contexts. d. Apply properties of operations as strategies to add subtract rational numbers. Mixed Inequalities on a Number Line Basic Inequalities on a Number Line Adding Integers: Positive, Negative or Zero Identifying errors in applying the order of operations Ordered Pairs Subtract Negative Mixed Numbers Integers: Add Subtract Integers on a Number Line Integers: Order of Operations (PEDMAS) Subtract Mixed Numbers: Signs Differ Subtract Integers Add Decimals: Different Signs Add Mixed Numbers: Signs Differ Divide Mixed Numbers with Signs Grade 7 Whole Numbers 53 3P Learning

57 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks The Number System The Number System & 1: Apply extend previous understings of operations with fractions to add, subtract, multiply, divide rational numbers. 1: Apply extend previous understings of operations with fractions to add, subtract, multiply, divide rational numbers. 1: Use properties of operations to generate equivalent expressions. 7.NS.2 7.NS.3 7.EE.1 Apply extend previous understings of multiplication division of fractions to multiply divide rational numbers. a. Underst that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as ( 1)( 1) = 1 the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Underst that integers can be divided, provided that the divisor is not zero, every quotient of integers (with non-zero divisor) is a rational number. If p q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply properties of operations as strategies to multiply divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Solve real-world mathematical problems involving the four operations with rational numbers. Apply properties of operations as strategies to add, subtract, factor, exp linear expressions with rational coefficients. Divide Mixed Numbers with Signs Integers: Multiply Divide Comparing Fractions with Signs Multiply Two Fractions 2 Divide Fractions by Fractions 2 Fraction to Terminating Decimal Multiplying Dividing Integers Integers: Multiplication Division Identifying errors in applying the order of operations Problems: Add Subtract Problems: Multiply Divide Order of Operations 1 Exping with Negatives Exp then Simplify Exping Brackets with Grouping Symbols Grade 7 Directed Numbers Grade 7 Whole Numbers Grade 7 Whole Numbers Grade 7 Algebra Basics 3P Learning 54

58 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks & & & 1: Use properties of operations to generate equivalent expressions. 2: Solve real-life mathematical problems using numerical algebraic expressions equations. 2: Solve real-life mathematical problems using numerical algebraic expressions equations. 7.EE.2 7.EE.3 7.EE.4 Underst that rewriting an expression in different forms in a problem context can shed light on the problem how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by Solve multi-step real-life mathematical problems posed with positive negative rational numbers in any form (whole numbers, fractions, decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; assess the reasonableness of answers using mental computation estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $ If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. Use variables to represent quantities in a realworld or mathematical problem, construct simple equations inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r p(x + q) = r, where p, q, r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, r are specific rational numbers. Graph the solution set of the inequality interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, describe the solutions. Like Terms: Add Subtract Complex Substitution Solve Multi-Step Using the Distributive Property Find the Mistake Checking Solutions Solve One-Step Inequalities 1 Solve One-Step Inequalities 2 Solve Two-Step Inequalities Graphing Inequalities 2 Solve : Add, Subtract 2 Solving Simple Solving More : Variables, Both Sides Solve : Multiply, Divide 2 to Solve Problems Grade 7 Algebra Basics Grade 7 Algebra Basics Grade 8 Grade 8 Simplifying Algebra 55 3P Learning

59 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Geometry Geometry Geometry Geometry 1: Draw, construct, describe geometrical figures describe the relationships between them. 1: Draw, construct, describe geometrical figures describe the relationships between them. 1: Draw, construct, describe geometrical figures describe the relationships between them. 2: Solve real-life mathematical problems involving angle measure, area, surface area, volume. 7.G.1 7.G.2 7.G.3 7.G.4 Solve problems involving scale drawings of geometric figures, including computing actual lengths areas from a scale drawing reproducing a scale drawing at a different scale. Draw (freeh, with ruler protractor, with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms right rectangular pyramids. Know the formulas for the area circumference of a circle use them to solve problems; give an informal derivation of the relationship between the circumference area of a circle. Scale Scale Factor Floor Plans Properties of Solids Naming 3D Solids Area: Circles Circumference: Circles Grade 6 Length, Area Perimeter Grade 7 Solids Grade 7 Area Perimeter 3P Learning 56

60 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Geometry 2: Solve real-life mathematical problems involving angle measure, area, surface area, volume. 7.G.5 Use facts about supplementary, complementary, vertical, adjacent angles in a multi-step problem to write solve simple equations for an unknown angle in a figure. Complementary, Supplementary or Neither Equal, Complement or Supplement? Plane Figure Theorems Plane Figure Terms Grade 7 Angles Geometry Statistics & 2: Solve real-life mathematical problems involving angle measure, area, surface area, volume. 1: Use rom sampling to draw inferences about a population. 7.G.6 7.SP.1 Solve real-world mathematical problems involving area, volume surface area of two- three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, right prisms. Underst that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Underst that rom sampling tends to produce representative samples support valid inferences. Area of Shapes Area: Triangles Area: Right Angled Triangles Area: Quadrilaterals Area: Squares Rectangles Surface Area: Rectangular Prisms Surface Area: Square Pyramids Surface Area: Cylinders Surface Area: Spheres Volume: Prisms Volume: Rectangular Prisms 1 Volume: Rectangular Prisms 2 Volume: Triangular Prisms Volume: Composite Figures Volume: Cones Volume of Solids Prisms - 1cm 3 blocks Data Analysis: Scatter Plots Data Terms Data sampling Data Types Data Extremes Range Grade 7 Solids Grade 6 Volume, Capacity Mass" Grade 6 Data Representation Grade 9 Data 57 3P Learning

61 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Statistics & Statistics & Statistics & 1: Use rom sampling to draw inferences about a population. 2: Draw informal comparative inferences about two populations. 2: Draw informal comparative inferences about two populations. 7.SP.2 7.SP.3 7.SP.4 Use data from a rom sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by romly sampling words from the book; predict the winner of a school election based on romly sampled survey data. Gauge how far off the estimate or prediction might be. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. Use measures of center measures of variability for numerical data from rom samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. Mean difference deviation Which Measure of Central Tendency? Mean Mean from Frequency Table Median Median Cumulative Frequency Mode Mode from Frequency Table Mode from Stem Leaf Plot Cumulative Frequency Table Grouped Frequency Grade 9 Data Grade 9 Data Grade 9 Data 3P Learning 58

62 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Statistics & Statistics & Statistics & 3: Investigate chance processes develop, use, evaluate probability models. 3: Investigate chance processes develop, use, evaluate probability models. 3: Investigate chance processes develop, use, evaluate probability models. 7.SP.5 7.SP.6 7.SP.7 Underst that the probability of a chance event is a number between 0 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, a probability near 1 indicates a likely event. Approximate the probability of a chance event by collecting data on the chance process that produces it observing its long-run relative frequency, predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Develop a probability model use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, use the model to determine probabilities of events. For example, if a student is selected at rom from a class, find the probability that Jane will be selected the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will l heads up or that a tossed paper cup will l open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Relative Frequency Tree Diagrams Relative Frequency Tree Diagrams Scale Simple Find the Dice Coins Grade 8 Grade 8 Grade P Learning

63 CCSS Stards CCSS Grade 7 Domain Cluster Stard Description Activities ebooks Statistics & 3: Investigate chance processes develop, use, evaluate probability models. 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, simulation. a. Underst that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. c. Design use a simulation to generate frequencies for compound events. For example, use rom digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?" Tree Diagrams Tables Two-Way Table Complementary Events with Replacement without Replacement Grade 8 3P Learning 60

64 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks The Number System The Number System & 1: Know that there are numbers that are not rational, approximate them by rational numbers. 1: Know that there are numbers that are not rational, approximate them by rational numbers. 1: Work with radicals integer exponents. 8.NS.1 8.NS.2 8.EE.1 Know that numbers that are not rational are called irrational. Underst informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, convert a decimal expansion which repeats eventually into a rational number. Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, estimate the value of expressions (e.g., π²). For example, by truncating the decimal expansion of 2, show that 2 is between 1 2, then between , explain how to continue on to get better approximations. Know apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² 3-5 = 33 = 1/3³=1/27. Recurring Decimals Fraction to Terminating Decimal Estimate Square Roots Simplifying Irrational Numbers Adding Subtracting Irrational Numbers Multiplying Irrational Numbers Dividing Irrational Numbers Exponents Properties of Exponents Exponent Notation Algebra The Zero Exponent Zero Exponent Algebra Integer Exponents Simplifying with Exponent Laws 1 Simplifying with Exponent Laws 2 Irrational Number to Exponent Form Multiplication with Exponents Multiplication Division with Exponents Fractional Exponents Negative Exponents Powers of Integers Powers Patterns Grade 9 Decimals Grade 9 Simplifying Algebra Grade 8 Linear Relationships Grade 8 Simplifying Algebra 61 3P Learning

65 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks & & & 1: Work with radicals integer exponents. 1: Work with radicals integer exponents. 1: Work with radicals integer exponents. 8.EE.2 8.EE.3 8.EE.4 Use square root cube root symbols to represent solutions to equations of the form x² = p x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares cube roots of small perfect cubes. Know that 2 is irrational. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, to express how many times as much one is than the other. For example, estimate the population of the United States as 3 10 ^8 the population of the world as 7 10^9, determine that the world population is more than 20 times larger. Perform operations with numbers expressed in scientific notation, including problems where both decimal scientific notation are used. Use scientific notation choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Square Roots with Square Roots Estimating Square Roots Estimate Square Roots Estimating Cube Roots Square Cube Roots Irrational Numbers Adding Subtracting Irrational Numbers Multiplying Irrational Numbers Dividing Irrational Numbers Exping Binomial Irrational Numbers Simplifying Irrational Numbers Exping Irrational Number Scientific Notation 1 Scientific Notation 2 Factoring with Exponents Prime Factoring: Exponents Ordering Scientific Notation Scientific notation to decimal Scientific Notation 1 Scientific Notation 2 Grade 8 Simplifying Algebra Grade 9 Exponents Grade 9 Exponents 3P Learning 62

66 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks & & & 2: Underst the connections between proportional relationships, lines, linear equations. 2: Underst the connections between proportional relationships, lines, linear equations. 3: Analyze solve linear equations pairs of simultaneous linear equations. 8.EE.5 8.EE.6 8.EE.7 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance- time equation to determine which of two moving objects has greater speed. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin the equation y = mx + b for a line intercepting the vertical axis at b. Solve linear equations in one variable. a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a b are different numbers). b. Solve linear equations with rational number coefficients, including equations whose solutions require exping expressions using the distributive property collecting like terms. Slope of a Line Equation of Line 1 Equation of a Line 2 Intercepts Conversion Graphs Breakeven Point Equation of a Line 1 Equation of a Line 2 Using Similar Triangles Using Similar Triangles 1 Modelling Linear Relationships Rationalising Binomials Direct Variation Indirect Variation Grade 8 Linear Relationships Grade 8 Linear Relationships Grade 8 Linear Relationships 63 3P Learning

67 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks & 3: Analyze solve linear equations pairs of simultaneous linear equations. 1: Define, evaluate, compare functions. 1: Define, evaluate, compare functions. 8.EE.8 8.F.1 8.F.2 Analyze solve pairs of simultaneous linear equations. a. Underst that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 6. c. Solve real-world mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Underst that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input the corresponding output. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values a linear function represented by an algebraic expression, determine which function has the greater rate of change. Simultaneous Linear Simultaneous 1 Simultaneous 2 with Grouping Symbols with Fractions with Fractions 2 to Solve Problems : Simple Quadratics Special Binomial Products Solve Systems by Graphing Algebraic Multiplication Exp then Simplify Simplifying Simplifying Binomial Using the Distributive Property Find the Function Rule Function Rules Tables y = ax Function Notation 1 Function Notation 2 Equation of a Line 1 Equation of a Line 2 Equation of a Line 3 Equation from Point Gradient Equation from Two Points Grade 8 Grade 8 Exping Factorizing Grade 10 Grade 8 Linear Relationships 3P Learning 64

68 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks Geometry 1: Define, evaluate, compare functions. 2: Use functions to model relationships between quantities. 2: Use functions to model relationships between quantities. 1: Underst congruence similarity using physical models, transparencies, or geometry software. 8.F.3 8.F.4 8.F.5 8.G.1 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1, 1), (2, 4) (3, 9), which are not on a straight line. Slope of a Line Reading Values from a Line Construct a function to model a linear relationship between two quantities. Determine Modelling Linear the rate of change initial Relationships value of the function from a Direct Variation description of a relationship or Indirect Variation from two (x, y) values, including Graphing from a Table of reading these from a table or Values from a graph. Interpret the Graphing from a Table of rate of change initial value Values 2 of a linear function in terms of Determining a Rule for a the situation it models, in Line terms of its graph or a table of values. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Verify experimentally the properties of rotations, reflections, translations: a. Lines are taken to lines, line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. Which Straight Line? Conversion Graphs Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Grade 8 Linear Relationships Grade 8 Straight Lines Grade 8 Linear Relationships Grade 8 Straight Lines Grade 8 Linear Relationships Grade 8 Straight Lines Grade 6 Geometry 65 3P Learning

69 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks Geometry Geometry Geometry Geometry 1: Underst congruence similarity using physical models, transparencies, or geometry software. 1: Underst congruence similarity using physical models, transparencies, or geometry software. 1: Underst congruence similarity using physical models, transparencies, or geometry software. 1: Underst congruence similarity using physical models, transparencies, or geometry software. 8.G.2 8.G.3 8.G.4 8.G.5 Underst that a twodimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Describe the effect of dilations, translations, rotations, reflections on two-dimensional figures using coordinates. Underst that a twodimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, dilations; given two similar twodimensional figures, describe a sequence that exhibits the similarity between them. Use informal arguments to establish facts about the angle sum exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, give an argument in terms of transversals why this is so. Congruent Triangles Congruent Figures Congruent Figures: Find Values Tranformations: Coordinate Plane Rotations: Coordinate Plane Similar Figures Similar Figures 1 Similarity Proofs Using Similar Triangles Vertically Opposite Angles: Unknown Values Vertically Opposite Angles: Value of x Are the Lines Parallel? Introduction to Angles on Parallel Lines 1 Introduction to Angles on Parallel Lines 3 Angle Measures in a Triangle Angles Parallel Lines Exterior Angles of a Triangle Grade 9 Similarity Congurence Grade 6 Geometry Grade 9 Similarity Congurence Grade 7 Angles 3P Learning 66

70 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks Geometry 2: Underst apply the Pythagorean Theorem. 8.G.6 Explain a proof of the Pythagorean Theorem its converse. Pythagorean Theorem Grade 8 Pythagoras' Theorm Geometry Geometry Geometry Statistics & 2: Underst apply the Pythagorean Theorem. 2: Underst apply the Pythagorean Theorem. 3: Solve realworld mathematical problems involving volume of cylinders, cones, spheres. 1: Investigate patterns of association in bivariate data. 8.G.7 8.G.8 8.G.9 8.SP.1 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world mathematical problems in two three dimensions. Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Know the formulas for the volumes of cones, cylinders, spheres use them to solve real-world mathematical problems. Construct interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, nonlinear association. Pythagoras: Find a Short Side (decimal values) Pythagoras: Find a Short Side (integers) Pythagoras: Find a Short Side (rounding needed) Pythagoras Perimeter Pythagorean Triads Hypotenuse of a Right Triangle Find Slant Height Distance Between Two Points Volume: Cylinders Volume: Cones Volume: Spheres Volume: Composite Figures Scatter Plots Correlation Data Analysis: Scatter Plots Grade 8 Pythagoras' Theorm Grade 8 Pythagoras' Theorm Grade 7 Solids Grade 9 Data 67 3P Learning

71 CCSS Stards CCSS Grade 8 Domain Cluster Stard Description Activities ebooks Statistics & Statistics & Statistics & 1: Investigate patterns of association in bivariate data. 1: Investigate patterns of association in bivariate data. 1: Investigate patterns of association in bivariate data. 8.SP.2 8.SP.3 8.SP.4 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, informally assess the model fit by judging the closeness of the data points to the line. Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Underst that patterns of association can also be seen in bivariate categorical data by displaying frequencies relative frequencies in a two-way table. Construct interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Relative Frequency Direct Variation Indirect Variation Tables Two-Way Table Grade 8 Straight Lines Grade 8 Straight Lines Grade 8 3P Learning 68

72 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity The Real Number System The Real Number System The Real Number System Quantities Extend the properties of exponents to rational exponents. Extend the properties of exponents to rational exponents. Use properties of rational irrational numbers. Reason quantitatively use units to solve problems. N.RN.1 N.RN.2 N.RN.3 N.Q.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 = 5 (1/3)3 to hold, so (5 1/3 ) 3 must equal 5. Rewrite expressions involving radicals rational exponents using the properties of exponents. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number an irrational number is irrational; that the product of a nonzero rational number an irrational number is irrational. Use units as a way to underst problems to guide the solution of multistep problems; choose interpret units consistently in formulas; choose interpret the scale the origin in graphs data displays. Exponents Exponents Irrational Numbers Under review Exponent Laws Algebra Exponent Notation Algebra Simplifying with Exponent Laws 2 Fractional Exponents Irrational Number to Exponent Form Zero Exponent Algebra Fractional Exponents Irrational Number to Exponent Form Zero Exponents Algebra Simplifying with Exponent Laws 1 Multiplication with Exponents Exponent Laws Algebra Exponent Laws with Brackets Adding Subtracting Irrational Numbers Multiplying Irrational Numbers Exping Binomial Irrational Numbers Under Consideration Radicals Exponents Exponents Grade 8 Pythagoras' Theorem 69 3P Learning

73 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity Quantities Quantities Reason quantitatively use units to solve problems. Reason quantitatively use units to solve problems. Conceptual Category: Algebra Seeing Structure in Seeing Structure in Seeing Structure in Interpret the structure of expressions. Interpret the structure of expressions. Interpret the structure of expressions. N.Q.2 N.Q.3 A.SSE.1.a A.SSE.1.b A.SSE.2 Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, coefficients. Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P a factor not depending on P. Under Consideration Quantities Solving Linear Linear Quadratic Inequalities Exponents Quadratic Inequalities Use the structure of an expression to identify ways Quadratic to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of Inequalities squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). Error in Measurement Percentage Error Gradients for Real Write an Equation: Word Problems Vertex of a Parabola Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation The Discriminant Constructing Formulae Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Decimals Depreciation Interest Exping Factorizing 3P Learning 70

74 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Seeing Structure in Seeing Structure in Seeing Structure in Arithmetic with Polynomials Rational Write expressions in equivalent forms to solve problems. Write expressions in equivalent forms to solve problems. Write expressions in equivalent forms to solve problems. Perform arithmetic operations on polynomials. A.SSE.3.a A.SSE.3.b A.SSE.3.c A.APR.1 Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Quadratic Inequalities Choose produce an equivalent form of an expression to reveal explain properties of the Quadratic quantity represented by the expression.complete the square in a quadratic Inequalities expression to reveal the maximum or minimum value of the function it defines. Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression.use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.15 1/12 ) 12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Underst that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication; add, subtract, multiply polynomials. Under review Add, Subtract, Multiply Polynomials Highest Common Algebraic Factor Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Completing the Square Completing the Square 2 Vertex of a Parabola Under Consideration Like Terms: Add Subtract Simplifying Algebraic Fractions 1 Algebraic Fractions 2 Algebraic Multiplication Exp then Simplify Exping Binomial Products Special Binomial Products Exping Factorizing 71 3P Learning

75 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Creating Creating Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. A.CED.1 A.CED.2 A.CED.3 Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Represent constraints by equations or inequalities, by systems of equations /or inequalities, interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional cost constraints on combinations of different foods. Linear Quadratic Inequalities Linear Exponents Quadratic Inequalities Writing Algebraic to Solve Problems Writing Write an Equation: Word Problems Constructing Formulae Equation from Point Gradient Equation from Two Points Graphing from a Table of Values Graphing from a Table of Values 2 Which Straight Line? y=ax Determining a Rule for a Line Equation of a Line 1 Modeling Linear Relationships Graphing Exponentials Vertex of a Parabola Graphing Parabolas Quadratic Depreciation Interest Linear Relationships Exponential Power Graphs Under Consideration 3P Learning 72

76 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Reasoning with Inequalities Create equations that describe numbers or relationships. Underst solving equations as a process of reasoning explain the reasoning. A.CED.4 A.REI.1 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Quantities Solving Linear Quantities Solving Linear Changing the Subject Find the Mistake Addition Properties Multiplication Properties Using the Distributive Property Linear Relationships Depreciation Quadratic 73 3P Learning

77 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Reasoning with Inequalities Reasoning with Inequalities Solve equations inequalities in one variable. Solve equations inequalities in one variable. A.REI.3 A.REI.4.a. Solve linear equations inequalities in one variable, including equations with coefficients represented by letters. Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 = q that has the same solutions. Derive the quadratic formula from this form. Quantities Solving Linear Linear Linear Inequalities Quadratic Inequalities Recognising Like Terms Checking Solutions Solving Simple Solving More Solve Two-Step with Grouping Symbols Solve Multi-Step : Variables, Both Sides with Decimals with Fractions Simple Substitution Simple Substitution 3 Real Formulae to Solve Problems Writing Write an Equation: Word Problems Solve One-Step Inequalities 1 Solve One-Step Inequalities 2 Solve Two-Step Inequalities Solving Inequalities 1 Solving Inequalities 2 Solving Inequalities 3 Graphing Inequalities 1 Graphing Inequalities 2 Graphing Inequalities 3 Quadratic 1 Quadratic 2 Roots of the Quadratic Inequalities Inequalities Inequalities Inequalities Quadratic 3P Learning 74

78 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities 75 3P Learning Solve equations inequalities in one variable. Solve systems of equations. Solve systems of equations. Solve systems of equations. Represent solve equations inequalities graphically. A.REI.4.b A.REI.5 A.REI.6 A.REI.7 A.REI.10 Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions write them as a ± bi for real numbers a b. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Solve a simple system consisting of a linear equation a quadratic equation in two variables algebraically graphically. For example, find the points of intersection between the line = 3x the circle x 2 + y 2 = 3. Underst that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Quadratic Inequalities Systems of Linear Linear Quadratic Systems Linear Quadratic 1 Quadratic 2 Quadratic Formula The Discriminant Grouping in Pairs Quadratic Inequalities Under Consideration Solve Systems by Graphing Are they Parallel? Simultaneous Linear Breakeven Point Simultaneous 1 Simultaneous 2 Intersection: Line & Parabola Simultaneous 3 Intersection: Line & Circle Reading Values from a Line Inequalities Factorizing Quadratic Inequalities Inequalities Quadratic

79 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Reasoning with Inequalities Reasoning with Inequalities Represent solve equations inequalities graphically. Represent solve equations inequalities graphically. Conceptual Category: Underst the concept of a function use function notation. Underst the concept of a function use function notation. A.REI.11 A.REI.12 F.IF.1 F.IF.2 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) /or g(x) are linear, polynomial, rational, absolute value, exponential, logarithmic functions. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Underst that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Use function notation, evaluate functions for inputs in their domains, interpret statements that use function notation in terms of a context. Under Consideration Linear Inequalities Linear Regions Intersecting Linear Regions Function Rules Tables Horizontal Vertical Lines Function Notation 1 Function Notation 2 Function Notation 3 3P Learning 76

80 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Underst the concept of a function use function notation. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of the context. F.IF.3 F.IF.4 F.IF.5 F.IF.6 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1. For a function that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Relate the domain of a function to its graph, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Arithmetic Geometric Sequences Linear Quadratic Inequalities Linear Table of Values Terms: Arithmetic Progressions Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Intercepts Slope of a Line y=ax Gradients for Real Vertex of a Parabola Graphing Parabolas Parabolas Rectangles Parabolas Marbles Sequences & Series: Arithmetic Sequences & Series: Geometric Linear Relationships Parabolas Under Consideration Equation from Two Points 77 3P Learning

81 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. F.IF.7.a F.IF.7.b F.IF.7.e F.IF.8.a Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph linear quadratic functions show intercepts, maxima, minima. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph square root, cube root, piecewise-defined functions, including step functions absolute value functions. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph exponential logarithmic functions, showing intercepts end behavior, trigonometric functions, showing period, midline, amplitude. Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the process of factoring completing the square in a quadratic function to show zeros, extreme values, symmetry of the graph, interpret these in terms of a context. Linear Quadratic Inequalities Absolute Value, Step, Piecewise Exponents Quadratic Inequalities Graphing from a Table of Values Graphing from a Table of Values 2 Which Straight Line? Graphing Parabolas Absolute Value Absolute Value Absolute Value Graphs Step Graphs Piecemeal Graphing Exponentials Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Completing the Square Completing the Square 2 Vertex of a Parabola Linear Relationships Parabolas Exponential Power Graphs Factorizing Parabolas Quadratic 3P Learning 78

82 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Analyze functions using different representations. Analyze functions using different representations. Build a function that models a relationship between two quantities. F.IF.8.b F.IF.9 F.BF.1.a Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the properties of exponents to interpret expressions for exponential Exponents functions. For example, identify percent rate of change in functions such as = (1.02) t, y = (0.97) t, y = (1.01) 12t, y = (1.2) t/10, classify them as representing exponential growth or decay. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function algebraic expression for another, say which has the larger maximum. Linear Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Exponents Quadratic Inequalities Multiplication with Exponents Under Consideration Modeling Linear Relationships Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation Constructing Formulae Linear Relationships Exponential Power Graphs Depreciation Interest Parabolas 79 3P Learning

83 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building Building Building Build a function that models a relationship between two quantities. Build a function that models a relationship between two quantities. Build new functions from existing functions. Build new functions from existing functions. F.BF.1.b F.BF.2 F.BF.3 F.BF.4.a Write a function that describes a relationship between two quantities. Combine stard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, relate these functions to the model. Write arithmetic geometric sequences both recursively with an explicit formula, use them to model situations, translate between the two forms. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), f(x + k) for specific values of k (both positive negative); find the value of k given the graphs. Experiment with cases illustrate an explanation of the effects on the graph using technology. Include recognizing even odd functions from their graphs algebraic expressions for them. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse write an expression for the inverse. For example, f(x) =2x 3 or f(x) = (x + 1)/(x 1) for x 1. Arithmetic Geometric Sequences Under Consideration Table of Values Terms: Arithmetic Progressions Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Under Consideration Sequences & Series: Arithmetic Sequences & Series: Geometric Exponential Power Graphs Parabolas Inverse 3P Learning 80

84 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models 81 3P Learning Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. F.LE.1.a F.LE.1.b F.LE.1.c F.LE.2 Distinguish between situations that can be modeled with linear functions with exponential functions. Prove that linear functions grow by equal differences over equal intervals, that exponential functions grow by equal factors over equal intervals. Distinguish between situations that can be modeled with linear functions with exponential functions. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Distinguish between situations that can be modeled with linear functions with exponential functions. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Construct linear exponential functions, including arithmetic geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Linear Arithmetic Geometric Sequences Under Consideration What Type of Function? What Type of Function? Find the Function Rule to Solve Problems Writing Write an Equation: Word Problems Equation from Two Points Equation of a Line 1 Modeling Linear Relationships Terms: Geometric Progressions 2 Sequences & Series: Arithmetic Sequences & Series: Geometric Straight Lines Sequences & Series: Arithmetic Depreciation Interest Sequences & Series: Geometric Sequences & Series: Arithmetic Depreciation Interest Sequences & Series: Geometric

85 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Construct compare linear, quadratic, exponential models solve problems. Interpret expressions for functions in terms of the situation they model. F.LE.3 F.LE.5 Conceptual Category: Statistics Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Summarize, represent, interpret data on a single count or measurement variable. Summarize, represent, interpret data on a single count or measurement variable. Summarize, represent, interpret data on a single count or measurement variable. S.ID.1 S.ID.2 S.ID.3 Observe using graphs tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Interpret the parameters in a linear or exponential function in terms of a context. Represent data with plots on the real number line (dot plots, histograms, box plots). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) spread (interquartile range, stard deviation) of two or more different data sets. Interpret differences in shape, center, spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Linear Descriptive Statistics Descriptive Statistics Descriptive Statistics Under Consideration Gradients for Real Dot Plots Histograms Box--Whisker Plots 1 Box--Whisker Plots 2 Data Terms Mean Mean 1 Median Median 1 Mode Calculating Interquartile Range Calculating Stard Deviation Stard Deviation Skewness of Data Data Data Data Data Data 3P Learning 82

86 CCSS Stards CCSS Algebra I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Summarize, represent, interpret data on two categorical quantitative variables. Summarize, represent, interpret data on two categorical quantitative variables. Summarize, represent, interpret data on two categorical quantitative variables. Summarize, represent, interpret data on two categorical quantitative variables. Interpret linear models. Interpret linear models. Interpret linear models. S.ID.5 S.ID.6.a S.ID.6.b S.ID.6.c S.ID.7 S.ID.8 S.ID.9 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, conditional relative frequencies). Recognize possible associations trends in the data. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, exponential models. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. Informally assess the fit of a function by plotting analyzing residuals. Fit a linear function for a scatter plot that suggests a linear association. Interpret the slope (rate of change) the intercept (constant term) of a linear model in the context of the data. Compute (using technology) interpret the correlation coefficient of a linear fit. Distinguish between correlation causation Under review Under review Under review Descriptive Statistics Under review Descriptive Statistics Under review Under Consideration Under Consideration Under Consideration Data Analysis: Scatter Plots Scatter Plots Under Consideration Correlation Under Consideration 83 3P Learning

87 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Congruence Congruence Congruence Congruence Congruence Experiment with transformations in the plane. Experiment with transformations in the plane. Experiment with transformations in the plane. Experiment with transformations in the plane. Experiment with transformations in the plane. G.CO.1 G.CO.2 G.CO.3 G.CO.4 G.CO.5 Know precise definitions of angle, circle, perpendicular line, parallel line, line segment, based on the undefined notions of point, line, distance along a line, distance around a circular arc. Represent transformations in the plane using, e.g., transparencies geometry software; describe transformations as functions that take points in the plane as inputs give other points as outputs. Compare transformations that preserve distance angle to those that do not (e.g., translation versus horizontal stretch). Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations reflections that carry it onto itself. Develop definitions of rotations, reflections, translations in terms of angles, circles, perpendicular lines, parallel lines, line segments. Given a geometric figure a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Line Angle Basics Rigid Transformations Rigid Transformations What Line Am I? Classifying Angles Labelling Angles Angles in a Revolution Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Symmetry or Not 1 Symmetry or Not? Rotational Symmetry Under Consideration Under Consideration 3P Learning 84

88 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Congruence Congruence Congruence Congruence Congruence Underst congruence in terms of rigid motions. Underst congruence in terms of rigid motions. Underst congruence in terms of rigid motions. Prove Geometric Theorems. Prove Geometric Theorems. G.CO.6 G.CO.7 G.CO.8 G.CO.9 G.CO.10 Use geometric descriptions of rigid motions to transform figures to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if only if corresponding pairs of sides corresponding pairs of angles are congruent. Explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions. Prove theorems about lines angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side half the length; the medians of a triangle meet at a point. Rigid Transformations Rigid Transformations Geometric Theorems Geometric Theorems Congruent Figures (Grid) Congruent Figures (Dots) Congruent Triangles Under Consideration Parallel Lines Angles Parallel Lines Angle Measures in a Triangle Plane Figure Theorems Ratio of Intercepts Similarity Congruence Similarity Congruence Polygons Angles 85 3P Learning

89 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Congruence Congruence Congruence Similarity, Right Triangles, Trigonometry Prove geometric theorems. Make geometric constructions. Make geometric constructions. Underst similarity in terms of similarity transformations. G.CO.11 G.CO.12 G.CO.13 G.SRT.1.a Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, conversely, rectangles are parallelograms with congruent diagonals. Make formal geometric constructions with a variety of tools methods (compass straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; constructing a line parallel to a given line through a point not on the line. Construct an equilateral triangle, a square, a regular hexagon inscribed in a circle. Verify experimentally the properties of dilations given by a center a scale factor: A dilation takes a line not passing through the center of the dilation to a parallel line, leaves a line passing through the center unchanged. Geometric Theorems Plane Figure Theorems Under Consideration Under Consideration Under Consideration Constructions Constructions 3P Learning 86

90 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Underst similarity in terms of similarity transformations. Underst similarity in terms of similarity transformations. Underst similarity in terms of similarity transformations. Prove theorems involving similarity. Prove theorems involving similarity. G.SRT.1.b G.SRT.2 G.SRT.3 G.SRT.4 G.SRT.5 Verify experimentally the properties of dilations given by a center a scale factor: The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles the proportionality of all corresponding pairs of sides. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, conversely; the Pythagorean Theorem proved using triangle similarity. Use congruence similarity criteria for triangles to solve problems to prove relationships in geometric figures. Similarity Similarity Similarity Geometric Theorems Congruence Similarity Scale Measurement Scale Factor Similar Figures Similar Figures 1 Similarity Proofs Ratio of Intercepts Congruent Figures: Find Values Using Similar Triangles Using Similar Triangles 1 Similarity Congruence Similarity Congruence Similarity Congruence Similarity Congruence 87 3P Learning

91 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Circles Define trigonometric ratios solve problems involving right triangles. Define trigonometric ratios solve problems involving right triangles. Define trigonometric ratios solve problems involving right triangles. Apply trigonometry to general triangles. Apply trigonometry to general triangles. Apply trigonometry to general triangles. Underst apply theorems about circles. G.SRT.6 G.SRT.7 G.SRT.8 G.SRT.9 G.SRT.10 G.SRT.11 G.C.1 Underst that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Explain use the relationship between the sine cosine of complementary angles. Use trigonometric ratios the Pythagorean Theorem to solve right triangles in applied problems. Derive the formula A = 1/2 ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Prove the Laws of Sines Cosines use them to solve problems. Underst apply the Law of Sines the Law of Cosines to find unknown measurements in right non-right triangles (e.g., surveying problems, resultant forces). Prove that all circles are similar. Trigonometry Trigonometry Trigonometry Trigonometry Trigonometry Exact Trigonometric Ratios Sin A Cos A Tan A Under Consideration Pythagorean Theorem Find Unknown Sides Find Unknown Angles Elevation Depression Trigonometry Problems 2 Area Rule 1 Area Rule 2 Area Problems Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Under Consideration Trigonometry Trigonometric Relationships Pythagorean Theorem Trigonometry Non Right Angled Triangles Non Right Angled Triangles Non Right Angled Triangles 3P Learning 88

92 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Circles Circles Circles Circles Expressing Geometric Properties with Expressing Geometric Properties with 89 3P Learning Underst apply theorems about circles. Underst apply theorems about circles. Underst apply theorems about circles. Find arc lengths areas of sectors of circles. Translate between the geometric description the equation for a conic section. Translate between the geometric description the equation for a conic section. G.C.2 G.C.3 G.C.4 G.C.5 G.GPE.1 G.GPE.2 Identify describe relationships among inscribed angles, radii, chords. Include the relationship between central, inscribed, circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radiusintersects the circle. Construct the inscribed circumscribed circles of a triangle, prove properties of angles for a quadrilateral inscribed in a circle. Construct a tangent line from a point outside a given circle to the circle. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Derive the equation of a circle of given center radius using the Pythagorean Theorem; complete the square to find the center radius of a circle given by an equation. Derive the equation of a parabola given a focus directrix. Circles Under review Circles Circles Circles of Parabolas Circle Terms Circle Theorem Tangents Secants Under Consideration Intersection: Line & Circle Converting Radians Degrees Perimeter Circles Arc Length Length of an Arc Area of a Sector (degrees radians) Centre Radius 1 Centre Radius 2 Graphing Circles Vertex of a Parabola Graphing Parabolas Focus Directrix 1 Focus Directrix 2 Focus Directrix 3 Focus Directrix 4 Tangents Secants Chords Angles Constructions Perimeter Area Circle Graphs

93 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Expressing Geometric Properties with Expressing Geometric Properties with Expressing Geometric Properties with Expressing Geometric Properties with Geometric Measurement Dimension Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. Explain volume formulas use them to solve problems. G.GPE.4 G.GPE.5 G.GPE.6 G.GPE.7 G.GMD.1 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin containing the point (0, 2). Prove the slope criteria for parallel perpendicular lines use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Use coordinates to compute perimeters of polygons areas of triangles rectangles, e.g., using the distance formula. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, cone. Use dissection arguments, Cavalieri s principle, informal limit arguments. Connecting Geometry Algebra Circles Connecting Geometry Algebra Connecting Geometry Algebra Connecting Geometry Algebra Coordinate Methods in Geometry Perpendicular Distance 1 Perpendicular Distance 2 Intersection: Line & Circle Are they Parallel? Are they Perpendicular? Equation of a Line 3 Equation from Point Gradient Midpoint by Formula Distance Between Two Points Under Consideration Coordinate Geometry Circle Graphs Circle Graphs Linear Relationships Straight Lines Coordinate Geometry Coordinate Geometry 3P Learning 90

94 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Geometric Measurement Dimension Geometric Measurement Dimension Modeling with Geometry Modeling with Geometry Modeling with Geometry 91 3P Learning Explain volume formulas use them to solve problems. Visualize relationships between twodimensional three-dimensional objects. Apply geometric concepts in modeling situations. Apply geometric concepts in modeling situations. Apply geometric concepts in modeling situations. G.GMD.3 G.GMD.4 G.MG.1 G.MG.2 G.MG.3 Use volume formulas for cylinders, pyramids, cones, spheres to solve problems. Identify the shapes of two-dimensional cross-sections of three -dimensional objects, identify threedimensional objects generated by rotations of two-dimensional objects. Three- Dimensional Figures Three- Dimensional Figures Use geometric shapes, their measures, their Threeproperties to describe Dimensional objects (e.g., modeling Figures a tree trunk or a human torso as a cylinder). Apply concepts of density based on area volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy Trigonometry physical constraints or minimize cost; working with typographic grid systems based on ratios). Volume: Triangular Prisms Volume: Prisms Volume: Cylinders Volume Pyramids What Pyramid am I? Volume: Cones Volume: Spheres Volume Composite Figures Volume: Rearrange Formula Relate Shapes Solids Nets Right Oblique Objects Match the Solid 2 Under Consideration Trigonometry Problems 2 Measuring Solids Measuring Solids

95 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Conditional the Rules of Conditional the Rules of Conditional the Rules of Conditional the Rules of Underst independence conditional probability use them to interpret data. Underst independence conditional probability use them to interpret data. Underst independence conditional probability use them to interpret data. Underst independence conditional probability use them to interpret data. S.CP.1 S.CP.2 S.CP.3 S.CP.4 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or,, not ). Underst that two events A B are independent if the probability of A B occurring together is the product of their probabilities, use this characterization to determine if they are independent. Underst the conditional probability of A given B as P(A B)/P(B), interpret independence of A B as saying that the conditional probability of A given B is the same as the probability of A, the conditional probability of B given A is the same as the probability of B. Construct interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent to approximate conditional probabilities. For example, collect data from a rom sample of students in your school on their favorite subject among math, science, English. Estimate the probability that a romly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects compare the results. Complementary Events Venn Diagrams - 'And' 'Or' Under Consideration Under Consideration Two-way Table Tables 3P Learning 92

96 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Conditional the Rules of Conditional the Rules of Conditional the Rules of Conditional the Rules of Conditional the Rules of Using to Make Decisions Underst independence conditional probability use them to interpret data. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use probability to evaluate outcomes of decisions. S.CP.5 S.CP.6 S.CP.7 S.CP.8 S.CP.9 S.MD.6 Recognize explain the concepts of conditional probability independence in everyday language everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, interpret the answer in terms of the model. Apply the Addition Rule, P(A or B) = P(A) + P(B) P(A B), interpret the answer in terms of the model. Apply the general Multiplication Rule in a uniform probability model, P(A B) = P(A) P(B A) = P(B)P(A B), interpret the answer in terms of the model. Use permutations combinations to compute probabilities of compound events solve problems. Use probabilities to make fair decisions (e.g., drawing by lots, using a rom number generator). Under Consideration Under Consideration Find the With Replacement Without Replacement Counting Techniques 1 Counting Techniques 2 Tree Diagrams Fair Games 93 3P Learning

97 CCSS Stards CCSS Geometry Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Using to Make Decisions Use probability to evaluate outcomes of decisions. S.MD.7 Analyze decisions strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Under Consideration 3P Learning 94

98 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity The Complex Number System The Complex Number System The Complex Number System The Complex Number System The Complex Number System 95 3P Learning Perform arithmetic operations with complex numbers. Perform arithmetic operations with complex numbers. Use complex numbers in polynomial identities equations. Use complex numbers in polynomial identities equations. Use complex numbers in polynomial identities equations. Conceptual Category: Algebra Seeing Structure in Seeing Structure in Interpret the structure of expressions. Interpret the structure of expressions. N.CN.1 N.CN.2 N.CN.7 N.CN.8 N.CN.9 A.SSE.1.a A.SSE.1.b Know there is a complex number i such that i 2 = 1, every complex number has the form a + bi with a b real. Use the relation i 2 = 1 the commutative, associative, distributive properties to add, subtract, multiply complex numbers. Solve quadratic equations with real coefficients that have complex solutions. Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x 2i). Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, coefficients. Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P a factor not depending on P. Complex Numbers Complex Numbers Modeling with Solving Higher Order Introduction to Complex Numbers Powers of i Adding Complex Numbers Subtracting Complex Numbers Complex Multiplication Under Consideration Under Consideration Under Consideration Gradients for Real Exponential Growth Decay Factoring Reducible to Quadratics Sketching Polynomials Geometric Series in Finance

99 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Seeing Structure in Seeing Structure in Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. Perform arithmetic operations on polynomials. Underst the relationship between zeros factors of polynomials. Underst the relationship between zeros factors of polynomials. A.SSE.2 A.SSE.4 A.APR.1 A.APR.2 A.APR.3 Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). Solving Higher Order Polynomial Arithmetic Derive the formula for the sum of a finite geometric series (when the common ratio is Sequences not 1), use the formula to Series solve problems. For example, calculate mortgage payments. Underst that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication; add, subtract, multiply polynomials. Know apply the Remainder Theorem: For a polynomial p(x) a number a, the remainder on division by x a is p(a), so p(a) = 0 if only if (x a) is a factor of p(x). Identify zeros of polynomials when suitable factorizations are available, use the zeros to construct a rough graph of the function defined by the polynomial. Polynomial Arithmetic Solving Higher Order Solving Higher Order Reducible to Quadratics Polynomial Long Division Simplifying Binomial Limiting Sum Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Sum: Geometric Progressions Like Terms: Add, Subtract Algebraic Multiplication Multiplication with Exponents Dividing Algebraic Fractions 1 Indirect Variation Special Binomial Products Exping Brackets Exp then Simplify Exping Binomial Products Polynomial Factor Theorem More Substitution in Formulae Rationalising the Denominator Rationalising Binomials Factoring Reducible to Quadratics Polynomial Factor Theorem Graphing Cubics Factorizing Factorizing Sequences & Series: Geometric Geometric Series Loan Repayments Geometric Series in Finance Polynomials Exping Factorizing Simplifying Algebra Binomials Pascal's Triangle Polynomials Factorizing Polynomials Sketching Polynomials 3P Learning 96

100 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Creating Creating 97 3P Learning Use polynomial identities to solve problems. Use polynomial identities to solve problems. Rewrite rational expressions. Rewrite rational expressions. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. A.APR.4 A.APR.5 A.APR.6 A.APR.7 A.CED.1 A.CED.2 Prove polynomial identities use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 - y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. Know apply the Binomial Theorem for the expansion of (x + y) n in powers of x y for a positive integer n, where x y are any numbers, with coefficients determined for example by Pascal s Triangle. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Underst that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, division by a nonzero rational expression; add, subtract, multiply, divide rational expressions. Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Solving Higher Order Under review Polynomial Arithmetic Rational Modeling with Modeling with Reducible to Quadratics Under Consideration Polynomial Long Division Simplifying Binomial Algebraic Fractions 2 Algebraic Fractions 3 Factoring Fractions 1 Factoring Fractions 2 Write an Equation: Word Problems y=ax Find the Function Rule Modeling Linear Relationships Linear Modelling Parabolas Marbles Parabolas Rectangles Factorizing The Binomial Theorem Binomials Pascal's Triangle Polynomials Factorizing

101 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Create equations that describe numbers or relationships. A.CED.3 Represent constraints by equations or inequalities, by systems of equations /or inequalities, interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional cost constraints on combinations of different foods. Under review Under Consideration Inverse Inverse Creating Reasoning with Inequalities Reasoning with Inequalities Create equations that describe numbers or relationships. Underst solving equations as a process of reasoning explain the reasoning. Represent solve equations inequalities graphically. A.CED.4 A.REI.2 A.REI.11 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V = IR to highlight resistance R. Solve simple rational radical equations in one variable, give examples showing how extraneous solutions may arise. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) /or g(x) are linear, polynomial, rational, absolute value, exponential, logarithmic functions. Exponents Logarithms Radical Radical Solving Higher Order Rational Change of Base Surface Area: Rearrange Formula Volume: Rearrange Formula Rearranging the Equation with Square Roots with Cube Roots More Substitution in Formulae Rationalising the Denominator Rationalising Binomials Solve Systems by Graphing Graphing Hyperbolas Logarithms 3P Learning 98

102 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of the context. Analyze functions using different representations. F.IF.4 F.IF.5 F.IF.6 F.IF.7.b For a function that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Relate the domain of a function to its graph, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph square root, cube root, piecewise-defined functions, including step functions absolute value functions. Modeling with Modeling with Inverse Gradients for Real Parabolas Marbles Parabolas Rectangles Perpendicular Distance 1 Absolute Value Graphs Conversion Graphs What Type of Function? Domain Domain Range Under Consideration Graphing Inverse Piecemeal Sketching Polynomials 99 3P Learning

103 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. F.IF.7.c F.IF.7.e F.IF.8.a F.IF.9 Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, showing end behavior. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph exponential logarithmic functions, showing intercepts end behavior, trigonometric functions, showing period, midline, amplitude. Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the process of factoring completing the square in a quadratic function to show zeros, extreme values, symmetry of the graph, interpret these in terms of a context. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function an algebraic expression for another, say which has the larger maximum. Solving Higher Order Trigonometric Exponents Logarithms Polynomial Arithmetic Graphing Cubics Sine Cosine Curves Trig Graphs in Radians Graph Inverse Trig Graphing Exponentials Exponential or Log Graph? Polynomial Long Division Simplifying Binomial Under Consideration Exponential Power Graphs Sketching Polynomials Trigonometric Relationships Logarithms Simple Nonlinear Graphs Factorizing Polynomials Sketching Polynomials 3P Learning 100

104 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building Building Building Linear, Quadratic, Exponential Models Build a function that models a relationship between two quantities. Build a function that models a relationship between two quantities. Build new functions from existing functions. Build new functions from existing functions. Construct compare linear, quadratic, exponential models solve problems. F.BF.1.a F.BF.1.b F.BF.3 F.BF.4.a F.LE.4 Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Write a function that describes a relationship between two quantities. Combine stard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, relate these functions to the model. Modeling with Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), f(x + k) for specific values of k (both positive negative); find the value of k given the graphs. Modeling with Experiment with cases illustrate an explanation of the effects on the graph using technology. Include recognizing even odd functions from their graphs algebraic expressions for them. Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse write an expression for the inverse. For example, f(x) =2x 3 or f(x) = (x + 1)/(x 1) for x 1. For exponential models, express as a logarithm the solution to ab ct = d where a, c, d are numbers the base b is 2, 10, or e; evaluate the logarithm using technology. Inverse Exponents Logarithms Gradients for Real Write an Equation: Word Problems Under Consideration Odd Even Inverse Log Laws with Logs Log Base 'e' Exponential Power Graphs Sketching Polynomials Logarithms 101 3P Learning

105 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Trigonometric Trigonometric Trigonometric Trigonometric Extend the domain of trigonometric functions using the unit circle. Extend the domain of trigonometric functions using the unit circle. Model periodic phenomena with trigonometric functions. Prove apply trigonometric identities. F.TF.1 F.TF.2 F.TF.5 F.FT.8 Underst radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, midline. Prove the Pythagorean identity sin 2 (θ) + cos 2 (θ) = 1 use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) the quadrant of the angle. Trigonometric Trigonometric Trigonometric Trigonometric Converting Radians Degrees Unit Circle Reductions Sign of the Angle Unit Circle Reductions Trigonometric Relationships Trigonometric Intercepts Inverse Trigonometric Period Amplitude Rationalising the Denominator Trig 1 Trig 2 Trig 3 Trig 4 Trigonometric Relationships Conceptual Category: Statistics Categorical Quantitative Data Summarize, represent, interpret data on a single count or measurement variable. S.ID.4 Use the mean stard deviation of a data set to fit it to a normal distribution to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, tables to estimate areas under the normal curve. Collecting Analyzing Data Normal Distribution Calculating z-scores Comparing z-scores Equivalent z-scores 3P Learning 102

106 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions 103 3P Learning Underst evaluate rom processes underlying statistical experiments. Underst evaluate rom processes underlying statistical experiments. Make inferences justify conclusions from sample surveys, experiments, observational studies. Make inferences justify conclusions from sample surveys, experiments, observational studies. Make inferences justify conclusions from sample surveys, experiments, observational studies. Make inferences justify conclusions from sample surveys, experiments, observational studies. S.IC.1 S.IC.2 S.IC.3 S.IC.4 S.IC.5 S.IC.6 Underst statistics as a process for making inferences about population parameters based on a rom sample from that population. Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Recognize the purposes of differences among sample surveys, experiments, observational studies; explain how romization relates to each. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for rom sampling. Use data from a romized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Evaluate reports based on data. Collecting Analyzing Data Capture Recapture Technique Tables Two-way Table Under Consideration Under Consideration Under Consideration Under Consideration Under Consideration

107 CCSS Stards CCSS Algebra II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Using to Make Decisions Using to Make Decisions Use probability to evaluate outcomes of decisions. Use probability to evaluate outcomes of decisions. S.MD.6 S.MD.7 Use probabilities to make fair decisions (e.g., drawing by lots, using a rom number generator). Analyze decisions strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Collecting Analyzing Data Fair Games Under Consideration 3P Learning 104

108 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity Quantities Quantities Quantities Reason quantitatively use units to solve problems. Reason quantitatively use units to solve problems. Reason quantitatively use units to solve problems. Conceptual Category: Algebra Seeing Structure in Seeing Structure in Seeing Structure in Interpret the structure of expressions. Interpret the structure of expressions. Interpret the structure of expressions. N.Q.1 N.Q.2 N.Q.3 A.SSE.1.a A.SSE.1.a A.SSE.1.b Use units as a way to underst problems to guide the solution of multistep problems; choose interpret units consistently in formulas; choose interpret the scale the origin in graphs data displays. Define appropriate quantities for the purpose of descriptive modeling. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, coefficients. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, coefficients. Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P a factor not depending on P. Number Quantity Writing Graphing Linear Exponential Exponential Error in Measurement Percentage Error Gradients for Real Write an Equation: Word Problems Compound Interest by Formula Depreciation Declining Balance Depreciation Compound Interest by Formula Depreciation Declining Balance Depreciation Decimals Depreciation Interest Depreciation Interest 105 3P Learning

109 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Creating Creating Creating Creating Creating Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. A.CED.1 A.CED.1 A.CED.2 A.CED.2 A.CED.2 A.CED.3 Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Represent constraints by equations or inequalities, by systems of equations /or inequalities, interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional cost constraints on combinations of different foods. Writing Graphing Linear Exponential Writing Graphing Linear Writing Graphing Linear Exponential Under review Writing Algebraic to Solve Problems Writing Write an Equation: Word Problems Compound Interest by Formula Depreciation Declining Balance Depreciation Equation from Point Gradient Equation from Two Points y=ax Determining a Rule for a Line Modeling Linear Relationships Which Straight Line? Equation of a Line 1 Graphing Exponentials Depreciation Interest Linear Relationships Exponential Power Graphs Straight Lines 3P Learning 106

110 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Create equations that describe numbers or relationships. Underst solving equations as a process of reasoning explain the reasoning. Underst solving equations as a process of reasoning explain the reasoning. Underst solving equations as a process of reasoning explain the reasoning. A.CED.4 A.REI.1 A.REI.1 A.REI.3 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V=IR to highlight resistance R. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve linear equations inequalities in one variable, including equations with coefficients represented by letters. Number Quantity Solving Linear Systems Exponential Solving Linear Systems Changing the Subject Find the Mistake Addition Properties Multiplication Properties Using the Distributive Property Exponent Laws Algebra Exponent Laws with Brackets Solving Simple Solving More Solve Two-Step with Grouping Symbols Solve Multi-Step : Variables, Both Sides with Decimals with Fractions Linear Relationships Depreciation Exponents Inequalities 107 3P Learning

111 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Underst solving equations as a process of reasoning explain the reasoning. Solve equations inequalities in one variable. Solve systems of equations. Solve systems of equations. Represent solve equations inequalities graphically. A.REI.3 A.REI.3 A.REI.5 A.REI.6 A.REI.10 Solve linear equations inequalities in one variable, including equations with coefficients represented by letters. Solve linear equations inequalities in one variable, including equations with coefficients represented by letters. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation a multiple of the other produces a system with the same solutions. Solve systems of linear equations exactly approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Underst that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Solving Linear Systems Linear Inequalities to Solve Problems Writing Write an Equation: Word Problems Solve One-Step Inequalities 1 Solve One-Step Inequalities 2 Solve Two-Step Inequalities Solving Inequalities 1 Solving Inequalities 2 Solving Inequalities 3 Graphing Inequalities 1 Graphing Inequalities 2 Graphing Inequalities 3 Solving Linear Systems Writing Graphing Linear Solve Systems by Graphing Simultaneous Linear Breakeven Point Simultaneous 1 Simultaneous 2 Reading Values from a Line Inequalities Inequalities Inequalities Inequalities Inequalities 3P Learning 108

112 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Reasoning with Inequalities Reasoning with Inequalities Represent solve equations inequalities graphically. Represent solve equations inequalities graphically. Conceptual Category: Underst the concept of a function use function notation. Underst the concept of a function use function notation. A.REI.11 A.REI.12 F.IF.1 F.IF.2 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) /or g(x) are linear, polynomial, rational, absolute value, exponential, logarithmic functions. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Underst that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Use function notation, evaluate functions for inputs in their domains, interpret statements that use function notation in terms of a context. Linear Inequalities Sequences Sequences Linear Regions Intersecting Linear Regions Function Rules Tables Function Notation 1 Function Notation 2 Function Notation P Learning

113 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Underst the concept of a function use function notation. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of the context. F.IF.3 F.IF.4 F.IF.5 F.IF.6 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence Sequences is defined recursively by f(0)=f(1)=1, f(n + 1)=f(n) + f(n - 1) for n 1. For a function that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Relate the domain of a function to its graph, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Writing Graphing Linear Under review Writing Graphing Linear Terms: Arithmetic Progressions Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Intercepts Slope of a Line y=ax Gradients for Real Equation from Two Points Sequences & Series: Arithmetic Sequences & Series: Geometric Linear Relationships 3P Learning 110

114 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. Build a function that models a relationship between two quantities. Build a function that models a relationship between two quantities. F.IF.7.a F.IF.7.e F.IF.9 F.BF.1.a F.BF.1.a Graph functions expressed symbolically show key features of the graph, by h Writing in simple cases using Graphing technology for more complicated Linear cases. Graph linear quadratic functions show intercepts, maxima, minima. Graph functions expressed symbolically show key features of the graph, by h in simple cases using Exponential technology for more complicated cases. Graph exponential logarithmic functions, showing intercepts end behavior, trigonometric functions, showing period, midline, amplitude. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function an algebraic expression for another, say which has the larger maximum. Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Which Straight Line? Graphing Exponentials Writing Graphing Linear Exponential Modeling Linear Relationships Compound Interest Compound Interest by Formula Depreciation Declining Balance Depreciation Linear Relationships Exponential Power Graphs Linear Relationships Exponential Power Graphs Depreciation Interest 111 3P Learning

115 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building Building Linear, Quadratic, Exponential Models Build a function that models a relationship between two quantities. Build a function that models a relationship between two quantities. Build new functions from existing functions. Construct compare linear, quadratic, exponential models solve problems. F.BF.1.b F.BF.2 F.BF.3 F.LE.1.a Write a function that describes a relationship between two quantities. Combine stard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, relate these functions to the model. Write arithmetic geometric sequences both recursively with an explicit formula, use them to model situations, translate between the two forms. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), f(x + k) for specific values of k (both positive negative); find the value of k given the graphs. Experiment with cases illustrate an explanation of the effects on the graph using technology. Include recognizing even odd functions from their graphs algebraic expressions for them. Distinguish between situations that can be modeled with linear functions with exponential functions. Prove that linear functions grow by equal differences over equal intervals, that exponential functions grow by equal factors over equal intervals. Sequences Writing Graphing Linear Table of Values Terms: Arithmetic Progressions Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Linear Expression for the Nth Term Vertical horizontal shift Sequences & Series: Arithmetic Sequences & Series: Geometric Exponential Power Graphs Sequences & Series: Arithmetic Sequences & Series: Geometric 3P Learning 112

116 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. Construct compare linear, quadratic, exponential models solve problems. F.LE.1.b F.LE.1.c F.LE.2 F.LE.2 F.LE.2 Distinguish between situations that can be modeled with linear functions with exponential functions. Recognize situations in which one quantity changes at Sequences a constant rate per unit interval relative to another. Distinguish between situations that can be modeled with linear functions with exponential functions. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. Construct linear exponential functions, including arithmetic geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Construct linear exponential functions, including arithmetic geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Construct linear exponential functions, including arithmetic geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Sequences Sequences Writing Graphing Linear Sequences Terms: Arithmetic Progressions Terms: Geometric Progressions 1 Terms: Geometric Progressions 2 Find the Function Rule to Solve Problems Writing Write an Equation: Word Problems Equation from Two Points Equation of a Line 1 Modeling Linear Relationships Terms: Geometric Progressions 2 Straight Lines Sequences & Series: Arithmetic Depreciation Interest Sequences & Series: Geometric Sequences & Series: Arithmetic Depreciation Interest Sequences & Series: Geometric 113 3P Learning

117 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Linear, Quadratic, Exponential Models Linear, Quadratic, Exponential Models Construct compare linear, quadratic, exponential models solve problems. Interpret expressions for functions in terms of the situation they model. Conceptual Category: Geometry Congruence Congruence Congruence Experiment with transformations in the plane. Experiment with transformations in the plane. Experiment with transformations in the plane. F.LE.3 F.LE.5 G.CO.1 G.CO.2 G.CO.3 Observe using graphs tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Interpret the parameters in a linear or exponential function in terms of a context. Know precise definitions of angle, circle, perpendicular line, parallel line, line segment, based on the undefined notions of point, line, distance along a line, distance around a circular arc. Represent transformations in the plane using, e.g., transparencies geometry software; describe transformations as functions that take points in the plane as inputs give other points as outputs. Compare transformations that preserve distance angle to those that do not (e.g., translation versus horizontal stretch). Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations reflections that carry it onto itself. Writing Graphing Linear Line Angle Basics Rigid Transformations Rigid Transformations Gradients for Real What Line Am I? Classifying Angles Labelling Angles Angles in a Revolution Transformations Transformations: Coordinate Plane Rotations: Coordinate Plane Symmetry or Not? Rotational Symmetry 3P Learning 114

118 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Congruence Congruence Congruence Congruence Congruence Experiment with transformations in the plane. Experiment with transformations in the plane. Underst congruence in terms of rigid motions. Underst congruence in terms of rigid motions. Underst congruence in terms of rigid motions. G.CO.4 G.CO.5 G.CO.6 G.CO.7 G.CO.8 Develop definitions of rotations, reflections, translations in terms of angles, circles, perpendicular lines, parallel lines, line segments. Given a geometric figure a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Use geometric descriptions of rigid motions to transform figures to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if only if corresponding pairs of sides corresponding pairs of angles are congruent. Explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions. Rigid Transformations Rigid Transformations Congruent Figures (Grid) Congruent Figures (Dots) Congruent Triangles Similarity Congruence Similarity Congruence 115 3P Learning

119 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Congruence Congruence Expressing Geometric Properties with Expressing Geometric Properties with Expressing Geometric Properties with Make geometric constructions. Make geometric constructions. Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. G.CO.12 G.CO.13 G.GPE.4 G.GPE.5 G.GPE.7 Make formal geometric constructions with a variety of tools methods (compass straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; constructing a line parallel to a given line through a point not on the line. Construct an equilateral triangle, a square, a regular hexagon inscribed in a circle. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin containing the point (0, 2). Prove the slope criteria for parallel perpendicular lines use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Use coordinates to compute perimeters of polygons areas of triangles rectangles, e.g., using the distance formula. Constructions Constructions Connecting Geometry Algebra Connecting Geometry Algebra Connecting Geometry Algebra Coordinate Methods in Geometry Perpendicular Distance 1 Perpendicular Distance 2 Are they Parallel? Are they Perpendicular? Perpendicular Parallel Lines Equation of a Line 3 Distance Between Two Points Coordinate Geometry Linear Relationships Straight Lines Coordinate Geometry 3P Learning 116

120 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Summarize, represent, interpret data on a single count or measurement variable Summarize, represent, interpret data on a single count or measurement variable Summarize, represent, interpret data on a single count or measurement variable Summarize, represent, interpret data on two categorical quantitative variables S.ID.1 S.ID.2 S.ID.3 S.ID.5 Represent data with plots on the real number line (dot plots, histograms, box plots). Use statistics appropriate to the shape of the data distribution to compare center (median, mean) spread (interquartile range, stard deviation) of two or more different data sets. Interpret differences in shape, center, spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, conditional relative frequencies). Recognize possible associations trends in the data. Descriptive Statistics Descriptive Statistics Descriptive Statistics Dot Plots Histograms Box-- Whisker Plots 1 Box-- Whisker Plots 2 Mean Mean 1 Median Median 1 Mode Calculating Interquartile Range Calculating Stard Deviation Stard Deviation Skewness of Data Data Data Data Data Data 117 3P Learning

121 CCSS Stards Integrated Math I Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Categorical Quantitative Data Summarize, represent, interpret data on two categorical quantitative variables Summarize, represent, interpret data on two categorical quantitative variables Summarize, represent, interpret data on two categorical quantitative variables Interpret linear models. Interpret linear models. Interpret linear models. S.ID.6.a S.ID.6.b S.ID.6.c S.ID.7 S.ID.8 S.ID.9 Represent data on two quantitative variables on a scatter plot, describe how the variables are related. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, exponential models. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. Informally assess the fit of a function by plotting analyzing residuals. Represent data on two quantitative variables on a scatter plot, describe how the variables Descriptive Scatter Plots are related. Fit a linear Statistics function for a scatter plot that suggests a linear association. Interpret the slope (rate of change) the intercept (constant term) of a linear model in the context of the data. Compute (using technology) interpret the correlation coefficient of a linear fit. Distinguish between correlation causation. Descriptive Statistics Correlation 3P Learning 118

122 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity The Real Number System The Real Number System The Real Number System The Complex Number System Extend the properties of exponents to rational exponents. Extend the properties of exponents to rational exponents. Use properties of rational irrational numbers. Perform arithmetic operations with complex numbers. N.RN.1 N.RN.2 N.RN.3 N.CN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5 1/3 to be the cube root of 5 because we want (5 1/3 ) 3 =5 (1/3)3 to hold, so (5 1/3 ) 3 must equal 5. Rewrite expressions involving radicals rational exponents using the properties of exponents. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number an irrational number is irrational; that the product of a nonzero rational number an irrational number is irrational. Know there is a complex number i such that i 2 = 1, every complex number has the form a + b i with a b real. Exponents Exponents Irrational Numbers Complex Numbers Fractional Exponents Irrational Number to Exponent Form Zero Exponents Algebra Radicals Exponents Exponents Fractional Exponents Irrational Number to Exponent Form Zero Exponents Algebra Simplifying with Exponent Laws 1 Radicals Exponents Simplifying with Exponents Exponent Laws 2 Multiplication with Exponents Exponent Laws Algebra Exponent Laws with Brackets Adding Subtracting Irrational Numbers Multiplying Irrational Numbers Exping Binomial Irrational Numbers Introduction to Complex Numbers 119 3P Learning

123 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity The Complex Number System The Complex Number System The Complex Number System The Complex Number System Perform arithmetic operations with complex numbers. Use complex numbers in polynomial identities equations. Use complex numbers in polynomial identities equations. Use complex numbers in polynomial identities equations. Conceptual Category: Algebra Seeing Structure in Seeing Structure in Interpret the structure of expressions. Interpret the structure of expressions. N.CN.2 N.CN.7 N.CN.8 N.CN.9 A.SSE.1.a A.SSE.1.b Use the relation i 2 = 1 the commutative, associative, distributive properties to add, subtract, multiply complex numbers. Solve quadratic equations with real coefficients that have complex solutions. Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x 2i). Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, coefficients. Complex Numbers Powers of i Adding Complex Numbers Subtracting Complex Numbers Complex Multiplication Quadratic Interpret expressions that represent a quantity in terms of its context. Interpret Quadratic complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P a factor not depending on P. Vertex of a Parabola The Discriminant Constructing Formulae Reducible to Quadratics Parabolas 3P Learning 120

124 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Seeing Structure in Seeing Structure in Seeing Structure in Seeing Structure in Seeing Structure in 121 3P Learning Interpret the structure of expressions. Interpret the structure of expressions. Write expressions in equivalent forms to solve problems. Write expressions in equivalent forms to solve problems. Write expressions in equivalent forms to solve problems. A.SSE.1.b A.SSE.2 A.SSE.3.a A.SSE.3.b A.SSE.3.c Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P a factor not depending on P. Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression. Factor a quadratic expression to reveal the zeros of the function it defines. Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Exponents Quadratic Solving Quadratic Quadratic Choose produce an equivalent form of an expression to reveal explain properties of the quantity represented by the expression. Use the properties of exponents to Under transform expressions for exponential review functions. For example the expression 1.15t can be rewritten as (1.15 1/12 ) 12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Fractional Exponents Compound Interest by Formula Depreciation Declining Balance Depreciation Factoring Quadratics 1 Factoring Quadratics 2 Reducible to Quadratics Highest Common Algebraic Factor Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Completing the Square Completing the Square 2 Vertex of a Parabola Geometric Series in Finance Exping Factorizing Quadratic Quadratic

125 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Arithmetic with Polynomials Rational Creating Creating Creating Creating Perform arithmetic operations on polynomials. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. A.APR.1 A.CED.1 A.CED.1 A.CED.2 A.CED.2 Underst that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication; add, subtract, multiply polynomials. Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Polynomial Arithmetic Quadratic Exponents Exponents Quadratic Like Terms: Add Subtract Simplifying Algebraic Fractions 1 Algebraic Fractions 2 Algebraic Multiplication Exp then Simplify Exping Brackets Exping Binomial Products Special Binomial Products Multiplication with Exponents Constructing Formulae Compound Interest by Formula Depreciation Declining Balance Depreciation Graphing Exponentials Vertex of a Parabola Graphing Parabolas Constructing Formulae Polynomials Exping Factorizing Simplifying Algebra Binomials Pascal's Triangle Quadratic "Depreciation Interest" Exponential Power Graphs Parabolas 3P Learning 122

126 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Create equations that describe numbers or relationships. A.CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm s law V=IR to highlight resistance R. Changing the Subject Linear Relationships Depreciation Reasoning with Inequalities Reasoning with Inequalities Reasoning with Inequalities Solve equations inequalities in one variable. Solve equations inequalities in one variable. Solve systems of equations. A.REI.4.a. A.REI.4.b A.REI.7 Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x p) 2 =q that has the same solutions. Derive the quadratic formula from this form. Solve quadratic equations in one variable. Solve quadratic equations by inspection (e.g., for x 2 =49), taking square roots, completing the square, the quadratic formula factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions write them as a ± bi for real numbers a b. Solve a simple system consisting of a linear equation a quadratic equation in two variables algebraically graphically. For example, find the points of intersection between the line y= 3x the circle x 2 + y 2 =3. Solving Quadratic Solving Quadratic Linear Quadratic Systems Quadratic 1 Quadratic 2 Quadratic 1 Quadratic 2 Quadratic Formula The Discriminant Factoring Quadratics 1 Factoring Quadratics 2 Checking Quadratic Intersection: Line & Parabola Simultaneous 3 Intersection: Line & Circle Quadratic Inequalities Factorizing Quadratic Quadratic 123 3P Learning

127 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of the context. Analyze functions using different representations. Analyze functions using different representations. F.IF.4 F.IF.5 F.IF.6 F.IF.7.a F.IF.7.b For a function that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features Quadratic given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Relate the domain of a function to its graph, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph linear quadratic functions show intercepts, maxima, minima. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph square root, cube root, piecewise-defined functions, including step functions absolute value functions. Quadratic Absolute Value, Step, Piecewise Vertex of a Parabola Graphing Parabolas Parabolas Rectangles Parabolas Marbles Domain Domain Range Equation from Two Points Graphing Parabolas Absolute Value Graphs Step Graphs Piecemeal Parabolas Parabolas 3P Learning 124

128 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building 125 3P Learning Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. Build a function that models a relationship between two quantities. Build a function that models a relationship between two quantities. F.IF.8.a F.IF.8.b F.IF.9 F.BF.1.a F.BF.1.a Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the process of factoring completing the square in a quadratic function to show zeros, extreme values, symmetry of the graph, interpret these in terms of a context. Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y=(1.02) t, y=(0.97) t, y=(1.01) 12t, y=(1.2) t/10, classify them as representing exponential growth or decay. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function an algebraic expression for another, say which has the larger maximum. Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Write a function that describes a relationship between two quantities. Determine an explicit expression, a recursive process, or steps for calculation from a context. Quadratic Exponents Under review Exponents Quadratic Factoring Quadratics 1 Factoring Quadratics 2 Grouping in Pairs Completing the Square Completing the Square 2 Vertex of a Parabola Multiplication with Exponents Fractional Exponents Compound Interest by Formula Depreciation Declining Balance Depreciation Constructing Formulae Factorizing Parabolas Quadratic Linear Relationships Exponential Power Graphs Depreciation Interest Parabolas

129 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building Building Linear, Quadratic, Exponential Models Trigonometric Build a function that models a relationship between two quantities. Build new functions from existing functions. Build new functions from existing functions. Construct compare linear, quadratic, exponential models solve problems. Prove apply trigonometric identities. F.BF.1.b F.BF.3 F.BF.4.a F.LE.3 F.FT.8 Write a function that describes a relationship between two quantities. Combine stard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, relate these functions to the model. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), f(x + k) for specific values of k (both positive negative); find the value of k given the graphs. Experiment with cases illustrate an explanation of the effects on the graph using technology. Include recognizing even odd functions from their graphs algebraic expressions for them. Find inverse functions. Solve an equation of the form f(x)=c for a simple function f that has an inverse write an expression for the inverse. For example, f(x)=2x 3 or f(x)=(x + 1)/(x 1) for x 1. Observe using graphs tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Prove the Pythagorean identity sin 2 (θ) + cos 2 (θ)=1 use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) the quadrant of the angle. Under review Under review Under review Vertical horizontal shift Symmetries of Graphs 1 Odd Even Inverse Parabolas Sketching Polynomials 3P Learning 126

130 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Congruence Congruence Congruence Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Prove Geometric Theorems Prove Geometric Theorems Prove geometric theorems. Underst similarity in terms of similarity transformations. Underst similarity in terms of similarity transformations. G.CO.9 G.CO.10 G.CO.11 G.SRT.1.a G.SRT.1.b Prove theorems about lines angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. Similarity, Congruence, Theorems Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles Similarity, triangles are congruent; the Congruence, segment joining midpoints of two sides of a triangle is parallel to Theorems the third side half the length; the medians of a triangle meet at a point. Prove theorems about parallelograms. Theorems include: opposite sides are Similarity, congruent, opposite angles are Congruence, congruent, the diagonals of a parallelogram bisect each other, Theorems conversely, rectangles are parallelograms with congruent diagonals. Verify experimentally the properties of dilations given by a center a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, leaves a line passing through the center unchanged. Verify experimentally the properties of dilations given by a center a scale factor: b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. Angles Parallel Lines Parallel Lines Angle Measures in a Triangle Plane Figure Theorems Ratio of Intercepts Plane Figure Theorems Similarity, Congruence, Theorems Scale Measurement Scale Factor Polygons Angles 127 3P Learning

131 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Underst similarity in terms of similarity transformations. Underst similarity in terms of similarity transformations. Prove theorems involving similarity. Prove theorems involving similarity. Define trigonometric ratios solve problems involving right triangles. Define trigonometric ratios solve problems involving right triangles. Define trigonometric ratios solve problems involving right triangles. G.SRT.2 G.SRT.3 G.SRT.4 G.SRT.5 G.SRT.6 G.SRT.7 G.SRT.8 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles the proportionality of all corresponding pairs of sides. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, conversely; the Pythagorean Theorem proved using triangle similarity. Use congruence similarity criteria for triangles to solve problems to prove relationships in geometric figures. Underst that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. Explain use the relationship between the sine cosine of complementary angles. Use trigonometric ratios the Pythagorean Theorem to solve right triangles in applied problems. Similarity, Congruence, Theorems Similarity, Congruence, Theorems Similarity, Congruence, Theorems Similarity, Congruence, Theorems Trigonometry Trigonometry Similar Figures 1 Similarity Proofs Ratio of Intercepts Similar Figures Using Similar Triangles Using Similar Triangles 1 Exact Trigonometric Ratios Sin A Cos A Tan A Similarity Congruence Similarity Congruence Similarity Congruence Trigonometry Trigonometric Relationships Find Unknown Sides Find Unknown Pythagorean Angles Theorem Elevation Trigonometry Depression Trigonometry Problems 2 3P Learning 128

132 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Circles Circles Circles Circles Circles Expressing Geometric Properties with Expressing Geometric Properties with 129 3P Learning Underst apply theorems about circles. Underst apply theorems about circles. Underst apply theorems about circles. Underst apply theorems about circles. Find arc lengths areas of sectors of circles. Translate between the geometric description the equation for a conic section. Translate between the geometric description the equation for a conic section. G.C.1 G.C.2 G.C.3 G.C.4 G.C.5 G.GPE.1 G.GPE.2 Prove that all circles are similar. Identify describe relationships among inscribed angles, radii, chords. Include the relationship between central, inscribed, circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Construct the inscribed circumscribed circles of a triangle, prove properties of angles for a quadrilateral inscribed in a circle. Construct a tangent line from a point outside a given circle to the circle. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Derive the equation of a circle of given center radius using the Pythagorean Theorem; complete the square to find the center radius of a circle given by an equation. Derive the equation of a parabola given a focus directrix. Under review Circles Parabolas Under review Under review Circles Parabolas Circles Parabolas Circles Parabolas Circle Theorem Tangents Secants Converting Radians Degrees Perimeter Circles Arc Length Length of an Arc Area of a Sector (degrees radians) Centre Radius 1 Centre Radius 2 Focus Directrix 1 Focus Directrix 2 Focus Directrix 3 Focus Directrix 4 Tangents Secants Chords Angles Constructions Constructions Perimeter Area Circle Graphs

133 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Expressing Geometric Properties with Expressing Geometric Properties with Geometric Measurement Dimension Geometric Measurement Dimension Use coordinates to prove simple geometric theorems algebraically. Use coordinates to prove simple geometric theorems algebraically. Explain volume formulas use them to solve problems. Explain volume formulas use them to solve problems. G.GPE.4 G.GPE.6 G.GMD.1 G.GMD.3 Conceptual Category: Statistics Conditional the Rules of Underst independence conditional probability use them to interpret data. S.CP.1 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin containing the point (0, 2). Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, cone. Use dissection arguments, Cavalieri s principle, informal limit arguments. Use volume formulas for cylinders, pyramids, cones, spheres to solve problems. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or,, not ). Circles Parabolas Similarity, Congruence, Theorems Centre Radius 1 Centre Radius 2 Focus Directrix 1 Focus Directrix 2 Focus Directrix 3 Focus Directrix 4 Midpoint by Formula Coordinate Geometry Circle Graphs Coordinate Geometry Three- Dimensional Figures Volume: Cylinders Volume: Pyramids Volume: Cones Volume: Spheres Volume Composite Figures Volume: Rearrange Formula Venn Diagrams - 'And' 'Or' Measuring Solids 3P Learning 130

134 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Conditional the Rules of Conditional the Rules of Conditional the Rules of Conditional the Rules of Underst independence conditional probability use them to interpret data. Underst independence conditional probability use them to interpret data. Underst independence conditional probability use them to interpret data. Underst independence conditional probability use them to interpret data. S.CP.2 S.CP.3 S.CP.4 S.CP.5 Underst that two events A B are independent if the probability of A B occurring together is the product of their probabilities, use this characterization to determine if they are independent. Underst the conditional probability of A given B as P(A B)/P(B), interpret independence of A B as saying that the conditional probability of A given B is the same as the probability of A, the conditional probability of B given A is the same as the probability of B. Construct interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent to approximate conditional probabilities. For example, collect data from a rom sample of students in your school on their favorite subject among math, science, English. Estimate the probability that a romly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects compare the results. Conditional Two-way Table Tables Recognize explain the concepts of conditional probability independence in everyday language everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer P Learning

135 CCSS Stards Integrated Math II Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Conditional the Rules of Conditional the Rules of Conditional the Rules of Conditional the Rules of Using to Make Decisions Using to Make Decisions Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use the rules of probability to compute probabilities of compound events in a uniform probability model. Use probability to evaluate outcomes of decisions. Use probability to evaluate outcomes of decisions. S.CP.6 S.CP.7 S.CP.8 S.CP.9 S.MD.6 S.MD.7 Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, interpret the answer in terms of the model. Apply the Addition Rule, P(A or B)=P(A) + P(B) P(A B), interpret the answer in terms of the model. Apply the general Multiplication Rule in a uniform probability model, P(A B)=P(A)P(B A) =P(B)P(A B), interpret the answer in terms of the model. Use permutations combinations to compute probabilities of compound events solve problems. Use probabilities to make fair decisions (e.g., drawing by lots, using a rom number generator). Analyze decisions strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Conditional probability - 'And' 'Or' Without Replacement Counting Techniques 1 Counting Techniques 2 Introduction to Permutations Combinations Permutations Combinations Fair Games Under review 3P Learning 132

136 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Number Quantity The Complex Number System The Complex Number System Use complex numbers in polynomial identities equations. Use complex numbers in polynomial identities equations. Conceptual Category: Algebra Seeing Structure in Seeing Structure in Seeing Structure in Interpret the structure of expressions. Interpret the structure of expressions. Interpret the structure of expressions. N.CN.8 N.CN.9 A.SSE.1.a A.SSE.1.b A.SSE.2 Extend polynomial identities to the complex numbers. For example, rewrite x as (x + 2i)(x 2i). Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Interpret expressions that represent a quantity in terms of its context. Interpret parts of an expression, such as terms, factors, coefficients. Interpret expressions that represent a quantity in terms of its context. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1 + r) n as the product of P a factor not depending on P. Use the structure of an expression to identify ways to rewrite it. For example, see x 4 y 4 as (x 2 ) 2 (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 y 2 )(x 2 + y 2 ). Solving Higher Order Complex Conjugate Modeling with Rational Solving Higher Order Solving Higher Order Polynomial Arithmetic Gradients for Real Exponential Growth Decay Vertical Horizontal Asymptotes Factoring Reducible to Quadratics Reducible to Quadratics Polynomial Long Division Simplifying Binomial Sketching Polynomials Geometric Series in Finance Factorizing Factorizing 133 3P Learning

137 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Seeing Structure in Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Write expressions in equivalent forms to solve problems. Perform arithmetic operations on polynomials. "Underst the relationship between zeros factors of polynomials." "Underst the relationship between zeros factors of polynomials." Use polynomial identities to solve problems. A.SSE.4 A.APR.1 A.APR.2 A.APR.3 A.APR.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), use the formula to solve problems. For example, calculate mortgage payments. Underst that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, multiplication; add, subtract, multiply polynomials. Know apply the Remainder Theorem: For a polynomial p(x) a number a, the remainder on division by x a is p(a), so p(a)=0 if only if (x a) is a factor of p(x). Identify zeros of polynomials when suitable factorizations are available, use the zeros to construct a rough graph of the function defined by the polynomial. Prove polynomial identities use them to describe numerical relationships. E20 Sequences Series Polynomial Arithmetic Solving Higher Order Solving Higher Order Solving Higher Order Sum: Geometric Progressions Sigma Notation 1 Sigma Notation 2 Like Terms: Add, Subtract Algebraic Multiplication Multiplication with Exponents Special Binomial Products Exping Brackets Exp then Simplify Exping Binomial Products Polynomial Factor Theorem Factoring Reducible to Quadratics Polynomial Factor Theorem Graphing Cubics Reducible to Quadratics Sequences & Series: Geometric Geometric Series Loan Repayments Geometric Series in Finance Polynomials Exping Factorizing Simplifying Algebra Binomials Pascal's Triangle Polynomials Factorizing Polynomials Sketching Polynomials Factorizing 3P Learning 134

138 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Arithmetic with Polynomials Rational Creating Creating 135 3P Learning Use polynomial identities to solve problems. Rewrite rational expressions. Rewrite rational expressions. Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. A.APR.5 A.APR.6 A.APR.7 A.CED.1 A.CED.2 Know apply the Binomial Theorem for the expansion of (x + y) n in powers of x y for a positive integer n, where x y are any numbers, with coefficients determined for example by Pascal s Triangle. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. Underst that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, division by a nonzero rational expression; add, subtract, multiply, divide rational expressions. Create equations inequalities in one variable use them to solve problems. Include equations arising from linear quadratic functions, simple rational exponential functions. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels scales. Polynomial Arithmetic Polynomial Arithmetic Rational Modeling with Modeling with Pascal's Triangle, Expansion Polynomial Long Division Simplifying Binomial Algebraic Fractions 2 Algebraic Fractions 3 Factoring Fractions 1 Factoring Fractions 2 Write an Equation: Word Problems y=ax Find the Function Rule Modeling Linear Relationships Linear Modeling Parabolas Marbles Parabolas Rectangles Constructing Formulae The Binomial Theorem Binomials Pascal's Triangle Polynomials Factorizing

139 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Algebra Creating Creating Reasoning with Inequalities Reasoning with Inequalities Create equations that describe numbers or relationships. Create equations that describe numbers or relationships. Underst solving equations as a process of reasoning explain the reasoning. Represent solve equations inequalities graphically. A.CED.3 A.CED.4 A.REI.2 A.REI.11 Represent constraints by equations or inequalities, by systems of equations /or inequalities, interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional cost constraints on combinations of different foods. Rearrange formulas to highlight a quantity of interest, using the same Inverse reasoning as in solving equations. For example, rearrange Ohm s law V=IR to highlight resistance R. Solve simple rational radical equations in one variable, give examples showing how extraneous solutions may arise. Explain why the x-coordinates of the points where the graphs of the equations y=f(x) y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) /or g(x) are linear, polynomial, rational, absolute value, exponential, logarithmic functions. Radical Solving Higher Order Inverse Graphing Inverse with Square Roots with Cube Roots Solve Systems by Graphing 3P Learning 136

140 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of a context. Interpret functions that arise in applications in terms of the context. Analyze functions using different representations. F.IF.4 F.IF.5 F.IF.6 F.IF.7.b For a function that models a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums minimums; symmetries; end behavior; periodicity. Modeling with Relate the domain of a function to its graph, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the Modeling with number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Calculate interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph square root, cube root, piecewise-defined functions, including step functions absolute value functions. Modeling with Inverse Modeling with Gradients for Real Parabolas Marbles Parabolas Rectangles Domain Domain Range Equation from Two Points Graph Inverse Absolute Value Graphs Piecemeal Step Graphs Sketching Polynomials 137 3P Learning

141 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. Analyze functions using different representations. F.IF.7.c F.IF.7.e F.IF.8.a F.IF.8.b Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available, showing end behavior. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. Graph exponential logarithmic functions, showing intercepts end behavior, trigonometric functions, showing period, midline, amplitude. Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the process of factoring completing the square in a quadratic function to show zeros, extreme values, symmetry of the graph, interpret these in terms of a context. Write a function defined by an expression in different but equivalent forms to reveal explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y=(1.02) t, y=(0.97) t, y=(1.01) 12t, y=(1.2) t/10, classify them as representing exponential growth or decay. Solving Higher Order Trigonometry Exponents Logarithms Polynomial Arithmetic Exponents Logarithms Graphing Cubics Sine Cosine Curves Trig Graphs in Radians Graph Inverse Trig Graphing Exponentials Exponential or Log Graph? Polynomial Long Division Simplifying Binomial Change of Base Sketching Polynomials Trigonometric Relationships Exponential Power Graphs Logarithms Simple Nonlinear Graphs Factorizing Polynomials Sketching Polynomials 3P Learning 138

142 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Building Building Building Analyze functions using different representations. Build a function that models a relationship between two quantities. Build new functions from existing functions. Build new functions from existing functions. F.IF.9 F.BF.1.b F.BF.3 F.BF.4.a Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function an algebraic expression for another, say which has the larger maximum. Write a function that describes a relationship between two quantities. Combine stard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, relate these functions to the model. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), f(x + k) for specific values of k (both positive negative); find the value of k given the graphs. Experiment with Modeling with cases illustrate an explanation of the effects on the graph using technology. Include recognizing even odd functions from their graphs algebraic expressions for them. Find inverse functions. Solve an equation of the form f(x)=c for a simple function f that has an inverse write an expression for the inverse. For example, f(x)=2x 3 or f(x)=(x + 1)/(x 1) for x 1. Inverse Odd Even Symmetries of Graphs 1 Vertical horizontal shift Inverse Exponential Power Graphs Sketching Polynomials 139 3P Learning

143 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Linear, Quadratic, Exponential Models Trigonometric Trigonometric Trigonometric Construct compare linear, quadratic, exponential models solve problems. Extend the domain of trigonometric functions using the unit circle. Extend the domain of trigonometric functions using the unit circle. Model periodic phenomena with trigonometric functions. Conceptual Category: Geometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Similarity, Right Triangles, Trigonometry Apply trigonometry to general triangles. Apply trigonometry to general triangles. Apply trigonometry to general triangles. F.LE.4 F.TF.1 F.TF.2 F.TF.5 G.SRT.9 G.SRT.10 G.SRT.11 For exponential models, express as a logarithm the solution to ab ct =d where a, c, d are numbers the base b is 2, 10, or e; evaluate the logarithm using technology. Underst radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, midline. Derive the formula A=1/2 ab sin(c) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. Prove the Laws of Sines Cosines use them to solve problems. Underst apply the Law of Sines the Law of Cosines to find unknown measurements in right non-right triangles (e.g., surveying problems, resultant forces). Exponents Logarithms Trigonometry Trigonometry Trigonometry Trigonometry Trigonometry Trigonometry Log Laws with Logs Log Base 'e' Converting Radians Degrees Unit Circle Reductions Sign of the Angle Unit Circle Reductions Trigonometric Relationships Period Amplitude Area Rule 1 Area Rule 2 Area Problems Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Sine Rule 1 Cosine Rule 1 Cosine Rule 2 Logarithms Trigonometric Relationships Non Right Angled Triangles Non Right Angled Triangles Non Right Angled Triangles 3P Learning 140

144 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Geometry Geometric Measurement Dimension Modeling with Geometry Modeling with Geometry Modeling with Geometry 141 Visualize relationships between twodimensional threedimensional objects. Apply geometric concepts in modeling situations. Apply geometric concepts in modeling situations. Apply geometric concepts in modeling situations. experiments. 3P Learning G.GMD.4 G.MG.1 G.MG.2 G.MG.3 Conceptual Category: Statistics Categorical Quantitative Data Making Inferences Justifying Conclusions Summarize, represent, interpret data on a single count or measurement variable Underst evaluate rom processes underlying statistical S.ID.4 S.IC.1 Identify the shapes of twodimensional cross-sections of three-dimensional objects, identify three-dimensional objects generated by rotations of two-dimensional objects. Use geometric shapes, their measures, their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Apply concepts of density based on area volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Use the mean stard deviation of a data set to fit it to a normal distribution to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, tables to estimate areas under the normal curve. Underst statistics as a process for making inferences about population parameters based on a rom sample from that population. Three- Dimensional Figures Three- Dimensional Figures Relate Shapes Solids Nets Match the Solid 2 Measuring Solids Trigonometry Collecting Analyzing Data Collecting Analyzing Data Trigonometry Problems 2 Normal Distribution Normal Distribution Calculating Stard Deviation Calculating z-scores Comparing z-scores Equivalent z-scores Capture Recapture Technique Data

145 CCSS Stards Integrated Math III Domain Cluster Stard Description Topic Activities ebooks Conceptual Category: Statistics Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Making Inferences Justifying Conclusions Using to Make Decisions Using to Make Decisions Underst evaluate rom processes underlying statistical experiments. Make inferences justify conclusions from sample surveys, experiments, observational studies. Make inferences justify conclusions from sample surveys, experiments, observational studies. Make inferences justify conclusions from sample surveys, experiments, observational studies. Make inferences justify conclusions from sample surveys, experiments, observational studies. Use probability to evaluate outcomes of decisions. Use probability to evaluate outcomes of decisions. S.IC.2 S.IC.3 S.IC.4 S.IC.5 S.IC.6 S.MD.6 S.MD.7 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? Recognize the purposes of differences among sample surveys, experiments, observational studies; explain how romization relates to each. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for rom sampling. Use data from a romized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. Evaluate reports based on data. Use probabilities to make fair decisions (e.g., drawing by lots, using a rom number generator). Analyze decisions strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). Under review Under review Under review Under review Under review Collecting Analyzing Data Under review Fair Games 3P Learning 142

146 Notes

147

148 3P Learning 37 West 26th Street Suite 201 New York, NY USA Tel: powered by