Correlation of Number Worlds to Common Core Standards for Mathematics including Building Blocks. Grade K

Transcription

1 including Counting and Cardinality Knowing numer names and the count sequence. Count to 00 y ones and tens. Count forward eginning from a given numer within the known sequence (instead of having to egin at ). Write numers from 0 to 0. Represent a numer of ojects with a written numeral 0-0 (with 0 representing a count of no ojects). K.CC Level B Weeks,, 5, 6 Weeks 4, 5, 7 Count and Race, Easy as Pie, School Supply Shop Level B Weeks,, 5, 6 Weeks 9,, 6, 4 Before and After Math, Bright Idea, Build Stairs, Sea to Shore Level B Weeks 0, 6 Weeks, 4, 5, 6 Dino Shop ; Memory Numer ; Numer Snapshots,, 5, 6, 8, 9; Party Time, Count to tell the numer of ojects. 4 Understand the relationship etween numers and quantities; connect counting to cardinality. a Grade K When counting ojects, say the numer names in the standard order, pairing each oject with one and only one numer name and each numer name with one and only one oject. Level B Week Weeks,, 6 Kitchen Counter; Pizza Pizzazz; Numeral Train; Party Time ; Pizza Pizzazz, (- 5), (-0); Road Race Counting Game, Sea to Shore; Space Race Understand that the last numer name said tells the numer of ojects counted. The numer of ojects is the same regardless of their arrangement or the order in which they were counted. Level B Weeks,, 5, 0 Weeks, Dino Shop ; Dino Shop ; Memory Numer ; Numer Snapshots 4, 7; Party Time, ; Pizza Pizzazz (-5), (-0) Page of 5

2 including Grade K c Understand that each successive numer name refers to a quantity that is one larger. Level B Week, 5, 7 Week, 6 Build Stairs, Build Stairs, Build Stairs 5 Compare numers. 6 7 Count to answer "how many?" questions aout as many as 0 things arranged in a line, a rectangular array, or a circle, or as many as 0 things in a scattered configuration; given a numer from -0, count out that many ojects. Identify whether the numer of ojects in one group is greater than, less than, or equal to the numer of ojects in another group, e.g., y using matching and counting strategies. Include groups with up to ten ojects. Compare two numers etween and 0 presented in written numerals. Level B Weeks, 5, 6 Weeks, Dino Shop ; Numer Snapshots,, 5, 6, 8, 9; Party Time, ; Pizza Pizzazz (- 5), (-0), (-5), (-0) Level B Weeks 5, 6, 8, 9 Weeks, Egg-stremely Equal; Numer Compare,, Level B Weeks 8, 0 Weeks 4, 5, 6 Rocket Blast, Space Race Page of 5

3 including Grade K Operations and Algeraic Thinking K.OA Understand addition as putting together and adding to, understand sutraction as taking apart and taking Level B Represent addition and sutraction with ojects, fingers, mental Weeks, 4,, 4 images, drawings, sounds (e.g., claps), acting out situations, veral explanations, expressions, or equations. Note that Weeks 9, 0, 6, 9 drawings need not show details, ut should show the mathematics in the prolem. Barkley's Bones -0 4 Solve addition and sutraction word prolems, and add and sutract within 0, e.g., y using ojects or drawings to represent the prolem. Note that drawings need not show details, ut should show the mathematics in the prolem. Decompose numers less than or equal to 0 into pairs in more than one way, e.g., y using ojects or drawings, and record each decomposition y a drawing or equation (e.g., 5 = + and 5 = 4 + ). Note that drawings need not show details, ut should show the mathematics in the prolem. For any numer from to 9, find the numer that makes 0 when added to the given numer, e.g., y using ojects or drawings, and record the answer with a drawing or equation. Note that drawings need not show details, ut should show the mathematics in the prolem. 5 Fluently add and sutract within 5. Numer and Operation in Base Ten Level B Weeks, 4,, 4 Weeks 6, 8, 9 Barkley's Bones -0; Dino Shop (-5), (-0), 4; Pizza Pizzazz 4, 5; Sea to Shore; Tidal Tally Level B Weeks 8 Weeks 6, 0 Dino Shop Free Explore Level B Week 8 Weeks 6, 0 Dino Shop 4, Tidal Tally Level B Weeks, 4,, 4 Week 6 Dino Shop (-5); Numer Snapshots 4, 5 K.NBT Work with numers -9 to gain foundations for place value. Compose and decompose numers from to 9 into tens and some further ones, e.g., y using ojects or drawings, and record each composition or decomposition y a drawing or equation Weeks 5, 7 (e.g., 8 = 0 + 8); understand that these numers are composed of ten ones and one, two, three, four, five, six, seven, Numer Snapshots 9 eight, or nine ones. Page of 5

4 including Grade K Measurement and Data Descrie and compare measurale attriutes. Descrie measurale attriutes of ojects, such as length or Week 8 weight. Descrie several measurale attriutes of a single oject. Comparisons Directly compare two ojects with a measurale attriute in common, to see which oject has "more of"/"less of" the attriute, Week 8 and descrie the difference. For example, directly compare the heights of two children and descrie one child as taller/shorter. Comparisons, Deep Sea Compare Classify ojects and count the numer of ojects in each category. Classify ojects into given categories; count the numers of ojects in each category and sort the categories y count. Limit category counts to e less than or equal to 0. Geometry Level B Week 8 K.G Identify and descrie shapes (squares, circles, triangles, rectangles, hexagons, cues, cones, cylinders, and Descrie ojects in the environment using names of shapes, and descrie the relative positions of these ojects using terms such as aove, elow, eside, in front of, ehind, and next to. Correctly name shapes regardless of their orientations or overall size. Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid"). Analyze, compare, create, and compose shapes. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to 4 descrie their similarities, differences, parts (e.g., numer of sides and vertices/"corners") and other attriutes (e.g., having sides of equal length). 5 6 Model shapes in the world y uilding shapes from components (e.g., sticks and clay alls) and drawing shapes. Compose simple shapes to form larger shapes. For example, "Can you join these two traingles with full sides touching to make a rectangle?" Week 0 Level B Week 8 Mystery Pictures, Mystery Pictures 4, Shape Shop K.MD Geometry Snapshots,,, 4, 5, 6; Memory Geometry,,, 4; Road Race: Shape Counting Shape Parts,,, 4 Create a Scene; Mystery Pictures Free Explore; Piece Puzzler,,, 4, 5; Piece Puzzler Free Explore;Super Shape,,, 4 Page 4 of 5

5 including 4 5 Grade Operations and Algeraic Thinking Represent and solve prolems involving addition and sutraction. Use addition and sutraction within 0 to solve word prolems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., y using ojects, drawings, and equations with a symol for the unknown numer to represent the prolem. Solve word prolems that call for addition of three whole numers whose sum is less than or equal to 0, e.g., y using ojects, drawings, and equations with a symol for the unknown numer to represent the prolem. Apply properties of operations as strategies to add and sutract. Students need not use formal terms for these properties.examples: If 8 + = is known, then + 8 = is also known. (Commutative property of addition.) To add , the second two numers can e added to make a ten, so = + 0 =. (Associative property of addition.) Understand sutraction as an unknown-addend prolem. For example, sutract 0 8 y finding the numer that makes 0 when added to 8. Relate counting to addition and sutraction (e.g., y counting on and add )..OA Weeks 6, 9 Unit Weeks -4 Unit 4 Weeks -4 Dino Shop (-5), (-0), 4; Pizza Pizzazz 4, 5; Tidal Tally; Word Prolems,, Weeks 6, 9 Unit Week Understand and apply properties of operations and the relationship etween addition and sutraction. Add and sutract within 0. Unit Week 4 Eggcellent, Lots O' Socks Week 0 Unit 4 Week 4 Barkley's Bones -0, Barkley's Bones - 0, Dino Shop 4, Tidal Tally Week 8 Unit Week Unit 4 Week Easy as Pie, Eggcellent, Lots O' Socks, Off the Tree, Sea to Shore Page 5 of 5

6 including 6 7 Grade Add and sutract within 0, demonstrating fluency for addition and sutraction within 0. Use strategies such as counting on; Weeks 8, 0, 6, 9 making ten (e.g., = = = 4); decomposing a numer leading to a ten (e.g., 4 = = 0 = 9); Unit Weeks -4 using the relationship etween addition and sutraction (e.g., Unit 4 Weeks -4 knowing that =, one knows 8 = 4); and creating equivalent ut easier or known sums (e.g., adding y Doule Compare -0; Doule Compare - creating the known equivalent = + = ). 0; Lots O' Socks; Numer Snapshots 8, 9 Work with addition and sutraction equations. Understand the meaning of the equal sign, and determine if equations involving addition and sutraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8, 5 + = + 5, 4 + = 5 +. Weeks, 7, 6, 9 Unit Week 4 Unit 4 Weeks, Unit 4 Week Page 6 of 5

7 including 8 Grade Determine the unknown whole numer in an addition or sutraction equation relating three whole numers. For example, determine the unknown numer that makes the equation true in each of the equations 8 +? =, 5 = _, = _. Numer and Operations in Base Ten Extend the counting sequence. Count to 0, starting at any numer less than 0. In this range, read and write numerals and represent a numer of ojects with a written numeral. Week 8, Unit Week 4 Function Machine Weeks 4, 5 Unit Week 4 Unit Week Book Stacks, Count and Race Understand place value. Understand that the two digits of a two-digit numer represents amounts of tens and ones. Understand the Unit Week 4 0 can e thought of as a undle of ten ones called a "ten." a Book Stacks, School Supply Shop c The numers from to 9 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. The numers 0, 0, 0, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). Compare two two-digit numers ased on meanings of the tens and ones digits, recording the results of comparison with the symols >, =, and <. Use place value understanding and properties of operations to add and sutract. Week 7 Unit Week 4 Numer Snapshots 9 Week 7 Unit Week 4 Book Stacks, Numer Snapshots 0, School Supply Shop Week 5 Unit Week Numer Compare 4, Rocket Blast.NBT Page 7 of 5

8 including Grade 4 5 Add within 00, including adding a two-digit numer and a onedigit numer, and adding a two-digit numer and a multiple of 0, using concrete models or drawings and strategies ased on place value, properties of operations, and/or the relationship etween addition and sutraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Given a two-digit numer, mentally find 0 more or 0 less than the numer, without having to count; explain the reasoning used. Week 7 Unit Week 4 Eggcellent, Lots O' Socks, Numer Snapshots 0 Week 7 Unit Week 4 Unit 4 Week 4 Math-O-Scope, School Supply Shop Page 8 of 5

9 including Grade Sutract multiples of 0 in the range 0-90 from multiples of 0 in the range 0-90 (positive or zero differences), using concrete models or drawings and strategies ased on place value, 6 properties of operations, and/or the relationship etween addition Unit 4 Week 4 and sutraction; relate the strategy to a written method and explain the reasoning used. Measurement and Data Measure lengths indirectly and y iterating length units. Order three ojects y length; compare the lengths of two ojects indirectly y using a third oject. Express the length of an oject as a whole numer of length units, y laying multiple copies of a shorter oject (the length unit) end to end; understand that the length measurement of an oject is the numer of same-size length units that span it with no gaps or overlaps. Limit to contexts where the oject eing measured is spanned y a whole numer of length units with no gaps or overlaps. Tell and write time. Tell and write time in hours and half-hours using analog and digital clocks. Represent and interpret data. Organize, represent, and interpret data with up to three categories; ask and answer questions aout the total numer of 4 data points, how many in each category, and how many more or less are in one category than in another. Geometry Reason with shapes and their attriutes. Distinguish etween defining attriutes (e.g., triangles are closed and three-sided) versus non-defining attriutes (e.g., color, orientation, overall size); uild and draw shapes to possess defining attriutes. Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or threedimensional shapes (cues, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. Students do not need to learn formal names such as right rectangular prism. Week 8 Unit 5 Week Deep Sea Compare Week 8 Unit 5 Week Workin' on the Railroad Unit 6 Weeks -4 Unit 5 Week Shape Shop,.MD.G Create a Scene, Mystery Pictures Free Explore; Piece Puzzler,,, 4, 5; Piece Puzzler Free Explore; Super Shape,,, 4 Page 9 of 5

10 including Grade Partition circles and rectangles into two and four equal shares, descrie the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Descrie the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. Page 0 of 5

11 including Grade Operations and Algeraic Thinking Represent and solve prolems involving addition and sutraction. Unit Weeks -4 Use addition and sutraction within 00 to solve one- and twostep word prolems involving situations of adding to, taking from, Level E Unit Weeks -4 putting together, taking apart, and comparing, with unknowns in all positions, e.g., y using drawings and equations with a symol for the unknown numer to represent the prolem. Add and sutract within 0. Fluently add and sutract within 0 using mental strategies. By end of Grade, know from memory all sums of two one-digit numers. Work with equal groups of ojects to gain foundations for multiplication. Determine whether a group of ojects (up to 0) has an odd or even numer of memers, e.g., y pairing ojects or counting them y s; write an equation to express an even numer as a sum of two equal addends. 4 Use addition to find the total numer of ojects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends..oa Unit 4 Weeks -4 Funtion Machine ; Word Prolems,,, 4 Unit Week 4 Unit 4 Weeks -4 Level E Unit Week Unit 4 Week Easy as Pie, Eggcellent, Numer Snapshots 9 Unit Week 4 Unit 4 Week 4 Unit Week Numer and Operations in Base Ten.NBT Understand place value. Understand that the three digits of a three-digit numer represent amounts of hundreds, tens,and ones; e.g., Level E 00 can e thought of as a undle of ten tens called a Unit Week a "hundred." School Supply Shop The numers 00, 00, 00, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). Count within 000; skip count y 5s, 0s, and 00s. Level E Unit Week Level E Unit Week Clean the Plates, Comic Book Shop, School Supply Shop, Tire Recycling Page of 5

12 including 4 Grade Read and write numers to 000 using ase-ten numerals, numer names, and expanded form. Compare two three-digit numers ased on meanings of the hundreds, tens, and ones digits, using >, =, and < symols to record the results of comparisons. Level E Unit Week, Rocket Blast Unit Week Level E Unit Week 4 Rocket Blast Page of 5

13 including Grade Use place value understanding and properties of operations to add and sutract Fluently add and sutract within 00 using strategies ased on place value, properties of operations, and/or the relationship etween addition and sutraction. Add up to four two-digit numers using strategies ased on place value and properties of operations. Add and sutract within 000, using concrete models or drawings and strategies ased on place value, properties of operations, and/or the relationship etween addition and sutraction; relate the strategy to a written method. Understand that in adding or sutracting threedigit numers, one adds or sutracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. Mentally add 0 or 00 to a given numer , and mentally sutract 0 or 00 from a given numer Explain why addition and sutraction strategies work, using place value and the properties of operations. Explanations may e supported y drawings or ojects. Measurement and Data Measure and estimate lengths in standard units. Measure the length of an oject y selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an oject twice, using length units of different lengths for the two measurements; descrie how the two measurements relate to the size of the unit chosen. Estimate lengths using units of inches, feet, centimeters, and meters. Measure to determine how much longer one oject is than 4 another, expressing the length difference in terms of a standard length unit. Relate addition and sutraction to length. Level E Unit Weeks, 4 Unit 4 Weeks, 4 Figure the Fact Level E Unit Weeks, 4 Word Prolems 7 Unit Weeks -4 Unit 4 Weeks -4 Level E Unit Weeks -4 Unit 4 Weeks -4 Word Prolems 4, 7, 8, 9 Unit Week Unit Week 4 Level E Unit Week Unit 4 Week Level E Unit Weeks, 4 Unit 4 Weeks, Unit 5 Week Reptile Ruler Unit 5 Week Unit 5 Week Unit 5 Week.MD Page of 5

14 including Grade 5 6 Use addition and sutraction within 00 to solve word prolems involving lengths that are given in the same units, e.g., y using drawings (such as drawings of rulers) and equations with a symol for the unknown numer to represent the prolem. Represent whole numers as lengths from 0 on a numer line diagram with equally spaced points corresponding to the numers 0,,,..., and represent whole-numer sums and differences within 00 on a numer line diagram. Unit 5 Week Unit 5 Week Eggcellent; Rocket Blast,, Page 4 of 5

15 including Grade Work with time and money. Tell and write time from analog and digital clocks to the nearest 7 five minutes, using a.m. and p.m. Solve word prolems involving dollar ills, quarters, dimes, nickels, and pennies, using $ and symols appropriately. 8 Example: If you have dimes and pennies, how many cents do you have? Represent and interpret data. Generate measurement data y measuring lengths of several ojects to the nearest whole unit, or y making repeated 9 measurements of the same oject. Show the measurements y making a line plot, where the horizontal scale is marked off in whole-numer units. Draw a picture graph and a ar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple puttogether, take-apart, and compare prolems using information 0 presented in a ar graph. Geometry Reason with shapes and their attriutes. Recognize and draw shapes having specified attriutes, such as a given numer of angles or a given numer of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cues. Sizes are compared directly or visually, not compared y measuring. Partition a rectangle into rows and columns of same-size squares and count to find the total numer of them. Partition circles and rectangles into two, three, or four equal shares, descrie the shares using the words halves, thirds, half of, a third of, etc., and descrie the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Level E Unit 5 Week 4 Unit Week 4 Level E Unit Week Unit 5 Week Unit 6 Weeks -4 Level E Unit 6 Weeks -4.G Unit 5 Week Level E Unit 5 Week Legend of the Lost Shape; Shape Parts 5, 6, 7; Shape Shop,, Arrays in Area Page 5 of 5

16 including Grade Operations and Algeraic Thinking Represent and solve prolems involving multiplication and division. Interpret products of whole numers, e.g., interpret 5 7 as the total numer of ojects in 5 groups of 7 ojects each. For example, descrie a context in which a total numer of ojects can e expressed as 5 7. Interpret whole-numer quotients of whole numers, e.g., interpret 56 8 as the numer of ojects in each share when 56 ojects are partitioned equally into 8 shares, or as a numer of shares when 56 ojects are partitioned into equal shares of 8 ojects each. For example, descrie a context in which a numer of shares or a numer of groups can e expressed as Use multiplication and division within 00 to solve word prolems in situations involving equal groups, arrays, and measurement quantities, e.g., y using drawings and equations with a symol for the unknown numer to represent the prolem. Determine the unknown whole numer in a multiplication or division equation relating three whole numers. For example, determine the unknown numer that makes the equation true in each of the equations 8? = 48, 5 = _, 6 6 =? Grade F Unit 4 Weeks, Unit 5 Week Comic Book Shop Apply properties of operations as strategies to multiply and divide. Examples: If 6 4 = 4 is known, then 4 6 = 4 is also known. (Commutative property of multiplication.) 5 can e found y 5 = 5, then 5 = 0, or y 5 = 0, then Unit 4 Weeks, 4 0 = 0. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 = 6, one can find 8 7 as 8 (5 + ) = (8 5) + (8 ) = = 56. (Distriutive property.) Understand division as an unknown-factor prolem. For example, find 8 y finding the numer that makes when multiplied y 8. Unit 4 Week, 4 Arrays in Area; Field Trip; Snack Time; Word Prolems 5, 6.OA Unit 4 Week 4 Function Machine, Function Machine Understand properties of multiplication and the relationship etween multiplication and division. Multiply and divide within 00. Unit 4 Week 4 Clean the Plates Fluently multiply and divide within 00, using strategies such as the relationship etween multiplication and division (e.g., knowing Unit 4 Week, 4 that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade, know from memory all Word Prolems 5, 6 products of two one-digit numers. Page 6 of 5

17 including Grade Solve prolems involving the four operations, and identify and explain patterns in arithmetic. Solve two-step word prolems using the four operations. Represent these prolems using equations with a letter standing 8 for the unknown quantity. Assess the reasonaleness of answers using mental computation and estimation strategies including rounding. 9 Identify arithmetic patterns (including patterns in the addition tale or multiplication tale), and explain them using properties of operations. For example, oserve that 4 times a numer is always even, and explain why 4 times a numer can e decomposed into two equal addends. Numer and Operations in Base Ten Level E Unit Week Unit 4 Week Unit Weeks, Unit 4 Weeks -4 Function Machine,, Use place value understanding and properties of operations to perform multi-digit arithmetic. Level E Use place value understanding to round whole numers to the Unit Week nearest 0 or 00. Unit Weeks, 4 Fluently add and sutract within 000 using strategies and algorithms ased on place value, properties of operations, and/or the relationship etween addition and sutraction. Multiply one-digit whole numers y multiples of 0 in the range 0 90 (e.g., 9 80, 5 60) using strategies ased on place value and properties of operations. Numer and Operations Fractions Develop understanding of fractions as numers. a Level E Unit Week 4 Unit 4 Week Unit Week Unit Weeks -4 Unit 4 Week 4 Understand a fraction / as the quantity formed y part when a whole is partitioned into equal parts; understand a fraction a/ Unit Week 4 as the quantity formed y a parts of size /. Understand a fraction as a numer on the numer line; represent fractions on a numer line diagram. Represent a fraction / on a numer line diagram y defining the interval from 0 to as the whole and partitioning it into equal parts. Recognize that each part has size / and that the endpoint of the part ased at 0 locates the numer / on the numer line. Represent a fraction a / on a numer line diagram y marking off a lengths / from 0. Recognize that the resulting interval has size a / and that its endpoint locates the numer a / on the numer line..nbt.nf Page 7 of 5

18 including Grade Explain equivalence of fractions in special cases, and compare fractions y reasoning aout their size. Understand two fractions as equivalent (equal) if they are the a same size, or the same point on a numer line. Recognize and generate simple equivalent fractions, e.g., / = /4, 4/6 = /). Explain why the fractions are equivalent, e.g., y Unit Week 4 using a visual fraction model. Express whole numers as fractions, and recognize fractions that are equivalent to whole numers. Examples: Express in the c form = /; recognize that 6/ = 6; locate 4/4 and at the same Unit Week 4 point of a numer line diagram. Compare two fractions with the same numerator or the same denominator y reasoning aout their size. Recognize that comparisons are valid only when the two fractions refer to the d same whole. Record the results of comparisons with the symols >, =, or <, and justify the conclusions, e.g., y using a visual fraction model. Measurement and Data.MD Solve prolems involving measurement and estimation of intervals of time, liquid volumes, and masses of ojec Tell and write time to the nearest minute and measure time intervals in minutes. Solve word prolems involving addition and sutraction of time intervals in minutes, e.g., y representing the prolem on a numer line diagram. Measure and estimate liquid volumes and masses of ojects using standard units of grams (g), kilograms (kg), and liters (l). Add, sutract, multiply, or divide to solve one-step word prolems involving masses or volumes that are given in the same units, e.g., y using drawings (such as a eaker with a measurement scale) to represent the prolem. Represent and interpret data. Draw a scaled picture graph and a scaled ar graph to represent a data set with several categories. Solve one- and two-step how many more and how many less prolems using information presented in scaled ar graphs. For example, draw a ar graph in which each square in the ar graph might represent 5 pets. Level E Unit 5 Week 4 Level E Unit 5 Week Unit 5 Week 4 Level E Unit 6 Weeks,4 Unit 6 Week 4 Generate measurement data y measuring lengths using rulers marked with halves and fourths of an inch. Show the data y making a line plot, where the horizontal scale is marked off in appropriate units whole numers, halves, or quarters. Page 8 of 5

19 including Grade Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 5 Recognize area as an attriute of plane figures and understand concepts of area measurement. A square with side length unit, called a unit square, is said to a have one square unit of area, and can e used to measure Unit 5 Week area. 6 7 a c d A plane figure which can e covered without gaps or overlaps y n unit squares is said to have an area of n square units. Measure areas y counting unit squares (square cm, square m, square in, square ft, and improvised units). Relate area to the operations of multiplication and addition. Find the area of a rectangle with whole-numer side lengths y tiling it, and show that the area is the same as would e found y multiplying the side lengths. Multiply side lengths to find areas of rectangles with wholenumer side lengths in the context of solving real world and mathematical prolems, and represent whole-numer products as rectangular areas in mathematical reasoning. Use tiling to show in a concrete case that the area of a rectangle with whole-numer side lengths a and + c is the sum of a and a c. Use area models to represent the distriutive property in mathematical reasoning. Recognize area as additive. Find areas of rectilinear figures y decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world prolems. Unit 5 Week Arrays in Area Unit 5 Week Arrays in Area Unit 5 Week Arrays in Area Unit 5 Week Unit 5 Week Unit 5 Week Geometric measurement: recognize perimeter as an attriute of plane figures and distinguish etween linear and Solve real world and mathematical prolems involving perimeters of polygons, including finding the perimeter given the side 8 lengths, finding an unknown side length, and exhiiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Page 9 of 5

20 including Geometry Reason with shapes and their attriutes. Grade Understand that shapes in different categories (e.g., rhomuses, rectangles, and others) may share attriutes (e.g., having four sides), and that the shared attriutes can define a larger category Unit 5 Week (e.g., quadrilaterals). Recognize rhomuses, rectangles, and squares as examples of quadrilaterals, and draw examples of Shape Shop,, quadrilaterals that do not elong to any of these sucategories..g 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, and descrie the area of each part as /4 of the area of the shape. Page 0 of 5

21 including Interpret a multiplication equation as a comparison, e.g., interpret 5 = 5 7 as a statement that 5 is 5 times as many as 7 and 7 times as many as 5. Represent veral statements of multiplicative comparisons as multiplication equations. Unit 4 Week Level G Unit Week Unit 4 Week Multiply or divide to solve word prolems involving multiplicative Level G comparison, e.g., y using drawings and equations with a symol Unit Week for the unknown numer to represent the prolem, distinguishing Unit Weeks, multiplicative comparison from additive comparison. Unit 4 Weeks - Solve multistep word prolems posed with whole numers and having whole-numer answers using the four operations, including prolems in which remainders must e interpreted. Represent these prolems using equations with a letter standing for the unknown quantity. Assess the reasonaleness of answers using mental computation and estimation strategies including rounding. Gain familiarity with factors and multiples. Find all factor pairs for a whole numer in the range 00. Recognize that a whole numer is a multiple of each of its factors. Determine whether a given whole numer in the range 4 00 is a multiple of a given one-digit numer. Determine whether a given whole numer in the range 00 is prime or composite. Generate and analyze patterns. 5 Grade 4 Operations and Algeraic Thinking Use the four operations with whole numers to solve prolems. Generate a numer 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 and the starting numer, generate terms in the resulting sequence and oserve that the terms appear to alternate etween odd and even numers. Explain informally why the numers will continue to alternate in this way. Word Prolems 0, Unit 4 Week 4 Level G Unit Week Unit Weeks, Unit 4 Week 4 Word Prolems 7, 8, 9, Unit 4 Week Level G Unit Week 4 Unit Weeks - Level G Unit Week, 4 Function Machine,,, 4, 5 4.OA Page of 5

22 including Grade 4 Numer & Operations in Base Ten¹ Generalize place value understanding for multi-digit whole numers. Recognize that in a multi-digit whole numer, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 0 y applying concepts of place value and division. Read and write multi-digit whole numers using ase-ten numerals, numer names, and expanded form. Compare two multi-digit numers ased on meanings of the digits in each place, using >, =, and < symols to record the results of comparisons. Use place value understanding to round multi-digit whole numers to any place. Unit 4 Week 4 Unit Weeks,,4 Rocket Blast Unit Week Level G Unit Week Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and sutract multi-digit whole numers using the Unit Weeks, 4 standard algorithm. Word Prolems 7, 8, Multiply a whole numer of up to four digits y a one-digit whole numer, and multiply two two-digit numers, using strategies ased on place value and the properties of operations. Illustrate and explain the calculation y using equations, rectangular arrays, and/or area models. Find whole-numer quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies ased on place value, the properties of operations, and/or the relationship etween multiplication and division. Illustrate and explain the calculation y using equations, rectangular arrays, and/or area models. Numer & Operations-Fractions¹ Extend understanding of fraction equivalence and ordering. Explain why a fraction a / is equivalent to a fraction (n a )/(n ) y using visual fraction models, with attention to how the numer and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. Unit 4 Weeks, 4 Level G Unit Weeks -4 Field Trip Unit 4 Week 4 Level G Unit 4 Weeks -4 Level G Unit Week 4.NBT 4.NF Page of 5

23 including Grade 4 Compare two fractions with different numerators and different denominators, e.g., y creating common denominators or numerators, or y comparing to a enchmark fraction such as /. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symols >, =, or <, and justify the conclusions, e.g., y using a visual fraction model. Level G Unit Week Page of 5

24 including Grade 4 Build fractions from unit fractions y applying and extending previous understandings of operations on whole n Understand a fraction a / with a > as a sum of fractions /. Unit Week 4 Level G Unit Week a Understand addition and sutraction of fractions as joining and separating parts referring to the same whole. Unit Week 4 c d 4 a c Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition y an equation. Justify decompositions, e.g., y using a visual fraction model. Examples: /8 = /8 + /8 + /8 ; /8 = /8 + /8 ; /8 = + + /8 = 8/8 + 8/8 + /8 Add and sutract mixed numers with like denominators, e.g., y replacing each mixed numer with an equivalent fraction, and/or y using properties of operations and the relationship etween addition and sutraction. Solve word prolems involving addition and sutraction of fractions referring to the same whole and having like denominators, e.g., y using visual fraction models and equations to represent the prolem. Apply and extend previous understandings of multiplication to multiply a fraction y a whole numer. Understand a fraction a / as a multiple of /. For example, use a visual fraction model to represent 5/4 as the product 5 (/4), recording the conclusion y the equation 5/4 = 5 (/4) Understand a multiple of a/ as a multiple of /, and use this understanding to multiply a fraction y a whole numer. For example, use a visual fraction model to express (/5) as 6 (/5), recognizing this product as 6/5. (In general, n (a/) = (n a)/.) Solve word prolems involving multiplication of a fraction y a whole numer, e.g., y using visual fraction models and equations to represent the prolem. For example, if each person at a party will eat /8 of a pound of roast eef, and there will e 5 people at the party, how many pounds of roast eef will e needed? Between what two whole numers does your answer lie? Level G Unit Week Unit Week 4 Page 4 of 5

25 including Grade 4 Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 0 as an equivalent fraction with denominator 00, and use this technique to add two 5 fractions with respective denominators 0 and 00. For example, express /0 as 0/00, and add /0 + 4/00 = 4/00. Use decimal notation for fractions with denominators 0 or Level G For example, rewrite 0.6 as 6/00; descrie a length as Unit Week meters; locate 0.6 on a numer line diagram. Compare two decimals to hundredths y reasoning aout their size. Recognize that comparisons are valid only when the two Level G 7 decimals refer to the same whole. Record the results of Unit Week 4 comparisons with the symols >, =, or <, and justify the conclusions, e.g., y using a visual model. Measurement and Data 4.MD Solve prolems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; l, 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 two-column tale. For example, know that ft is times as long as in. Express the length of a 4 ft snake as 48 in. Generate a conversion tale for feet and inches listing the numer pairs (, ), (, 4), (, 6),... Use the four operations to solve word prolems involving distances, intervals of time, liquid volumes, masses of ojects, and money, including prolems involving simple fractions or decimals, and prolems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as numer line diagrams that feature a measurement scale. Apply the area and perimeter formulas for rectangles in real world and mathematical prolems.for example, find the width of a rectangular room given the area of the flooring and the length, y viewing the area formula as a multiplication equation with an unknown factor. Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (/, /4, /8). Solve prolems involving addition and sutraction of fractions y using information 4 presented in line plots.for example, from a line plot find and interpret the difference in length etween the longest and shortest specimens in an insect collection. Unit 5 Week Level G Unit Week Page 5 of 5

26 including Grade 4 Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever 5 two rays share a common endpoint, and understand concepts of Unit 5 Week angle measurement: a 6 7 An angle is measured with reference to a circle with its center at the common endpoint of the rays, y considering the fraction of the circular arc etween the points where the two rays intersect the circle. An angle that turns through /60 of a circle is called a one-degree angle, and can e used to measure angles. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Measure angles in whole-numer degrees using a protractor. Sketch angles of specified measure. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and sutraction prolems to find unknown angles on a diagram in real world and mathematical prolems, e.g., y using an equation with a symol for the unknown angle measure. Geometry Draw and identify lines and angles, and classify shapes y properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, otuse), and perpendicular and parallel lines. Identify these in Field Trip two-dimensional figures. Classify two-dimensional figures ased on the presence or asence of parallel or perpendicular lines, or the presence or asence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can e folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. 4.G Unit 5 Week Legends of the Lost Shape; Shape Shop Page 6 of 5

27 including Operations and Algeraic Thinking Write and interpret numerical expressions. Use parentheses, rackets, or races in numerical expressions, and evaluate expressions with these symols. Write simple expressions that record calculations with numers, and interpret numerical expressions without evaluating them. For example, express the calculation add 8 and 7, then multiply y as (8 + 7). Recognize that (89 + 9) is three times as large as , without having to calculate the indicated sum or product. Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships etween corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule Add and the starting numer 0, and given the rule Add 6 and the starting numer 0, generate terms in the resulting sequences, and oserve that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Numer and Operations in Base Ten Understand the place value system. a Grade 5 Recognize that in a multi-digit numer, a digit in one place represents 0 times as much as it represents in the place to its right and /0 of what it represents in the place to its left. Explain patterns in the numer of zeros of the product when multiplying a numer y powers of 0, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided y a power of 0. Use whole-numer exponents to denote powers of 0. Read, write, and compare decimals to thousandths. Read and write decimals to thousandths using ase-ten numerals, numer names, and expanded form, e.g., 47.9 = (/0) + 9 (/00) + (/000). Compare two decimals to thousandths ased on meanings of the digits in each place, using >, =, and < symols to record the results of comparisons. 4 Use place value understanding to round decimals to any place. Unit Week Level G Unit Week 4 Unit Week 4 4.OA 5.NBT Page 7 of 5

28 including 5 Grade 5 Perform operations with multi-digit whole numers and with decimals to hundredths. Fluently multiply multi-digit whole numers using the standard algorithm. Find whole-numer quotients of whole numers with up to fourdigit dividends and two-digit divisors, using strategies ased on place value, the properties of operations, and/or the relationship 6 etween multiplication and division. Illustrate and explain the calculation y using equations, rectangular arrays, and/or area models. Add, sutract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies ased on place 7 value, properties of operations, and/or the relationship etween addition and sutraction; relate the strategy to a written method and explain the reasoning used. Numer and Operations-Fractions Use quivalent fractions as a strategy to add and sutract fractions. Add and sutract fractions with unlike denominators (including mixed numers) y 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, / + 5/4 = 8/ + 5/ = /. (In general, a/ + c/d = (ad + c)/d.) Level G Unit Weeks, Unit 4 Weeks, 4 Level G Unit 4 Weeks - Unit 4 Weeks, 4 Level G Unit 4 Week 4 Unit Weeks, 4 Unit Week 5.NF Solve word prolems involving addition and sutraction of fractions referring to the same whole, including cases of unlike denominators, e.g., y using visual fraction models or equations to represent the prolem. Use enchmark fractions and numer sense of fractions to estimate mentally and assess the reasonaleness of answers. For example, recognize an incorrect result /5 + / = /7, y oserving that /7 < /. Unit Week Page 8 of 5

29 including 4 a Grade 5 Apply and extend previous understanding of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator y the denominator (a / = a ). Solve word prolems involving division of whole numers leading to answers in the form of fractions or mixed numers, e.g., y using visual fraction models or equations to represent the prolem. For example, interpret /4 as the result of dividing y 4, noting that /4 multiplied y 4 Unit Week equals, and that when wholes are shared equally among 4 people each person has a share of size /4. If 9 people want to share a 50-pound sack of rice equally y weight, how many pounds of rice should each person get? Between what two whole numers does your answer lie? Apply and extend previous understandings of multiplication to multiply a fraction or whole numer y a Interpret the product (a / ) q as a parts of a partition of q into equal parts; equivalently, as the result of a sequence of operations a q. For example, use a visual fraction model to show (/) 4 = 8/, and create a story context for this equation. Do the same with (/) (4/5) = 8/5. (In general, (a/) (c/d) = ac/d.) Unit Week 5 a 6 Find the area of a rectangle with fractional side lengths y tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would e found y multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Interpret multiplication as scaling (resizing), y: Comparing the size of a product to the size of one factor on the asis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given numer y a fraction greater than results in a product greater than the given numer (recognizing multiplication y whole numers greater than as a familiar case); explaining why multiplying a given numer y a fraction less than results in a product smaller than the given numer; and relating the principle of fraction equivalence a / = (n a )/(n ) to the effect of multiplying a / y. Solve real world prolems involving multiplication of fractions and mixed numers, e.g., y using visual fraction models or equations to represent the prolem. Unit 4 Week Unit Week Page 9 of 5

30 including 7 a Grade 5 Apply and extend previous understandings of division to divide unit fractions y whole numers and whole Interpret division of a unit fraction y a non-zero whole numer, and compute such quotients.for example, create a story context for (/) 4, and use a visual fraction model to show the quotient. Use the relationship etween multiplication and division to explain that (/) 4 = / ecause (/) 4 = /. Interpret division of a whole numer y a unit fraction, and compute such quotients. For example, create a story context for 4 (/5), and use a visual fraction model to show the quotient. Use the relationship etween multiplication and division to explain that 4 (/5) = 0 ecause 0 (/5) = 4. Unit Week c Solve real world prolems involving division of unit fractions y non-zero whole numers and division of whole numers y unit fractions, e.g., y using visual fraction models and equations to represent the prolem. For example, how much chocolate will each person get if people share / l of chocolate equally? How many /-cup servings are in cups of raisins? Measurement and Data Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world prolems. Represent and interpret data. Unit Week Make a line plot to display a data set of measurements in fractions of a unit (/, /4, /8). Use operations on fractions for this grade to solve prolems involving information presented in line plots.for example, given different measurements of liquid in identical eakers, find the amount of liquid each eaker would contain if the total amount in all the eakers were redistriuted equally. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attriute of solid figures and understand concepts of volume measurement. a A cue with side length unit, called a unit cue, is said to have one cuic unit of volume, and can e used to measure volume. A solid figure which can e packed without gaps or overlaps using n unit cues is said to have a volume of n cuic units. Level G Unit 5 Week 4 Unit 5 Week 4 Unit 5 Week 4 5.MD Page 0 of 5

31 including 4 Grade 5 Measure volumes y counting unit cues, using cuic cm, cuic in, cuic ft, and improvised units. Level G Unit 5 Week 4 Unit 5 Week 4 Page of 5

32 including 5 a Grade 5 Find the volume of a right rectangular prism with whole-numer side lengths y packing it with unit cues, and show that the volume is the same as would e found y multiplying the edge lengths, equivalently y multiplying the height y the area of the ase. Represent threefold whole-numer products as volumes, e.g., to represent the associative property of multiplication. Apply the formulas V = l w h and V = h for rectangular prisms to find volumes of right rectangular prisms with wholenumer edge lengths in the context of solving real world and mathematical prolems. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms y c adding the volumes of the non-overlapping parts, applying this technique to solve real world prolems. Geometry Relate volume to the operations of multiplication and addition and solve real world and mathematical Use a pair of perpendicular numer 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 and a given point in the plane located y using an ordered pair of numers, called its coordinates. Understand that the first numer indicates how far to travel from the origin in the direction of one axis, and the second numer indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x -axis and x -coordinate, y - axis and y -coordinate). Represent real world and mathematical prolems y graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. Level G Unit 5 Week 4 Unit 5 Week 4 Level G Unit 5 Week 4 Unit 5 Week 4 Graph points on the coordinate place to solve real-world and mathematical prolems. Level G Unit Weeks, Unit 6 Week Unit Weeks, 5.G Page of 5

33 including Grade 5 Classify two-dimensional figures into categories ased on their properties. 4 Understand that attriutes elonging to a category of twodimensional figures also elong to all sucategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles. Classify two-dimensional figures in a hierarchy ased on properties. Unit 5 Week Page of 5

34 including Ratios and Proportional Relationships Understand ratio concepts and use ratio reasoning to solve prolems. Understand the concept of a ratio and use ratio language to descrie a ratio relationship etween two quantities. For example, The ratio of wings to eaks in the ird house at the zoo was :, ecause for every wings there was eak. For every vote candidate A received, candidate C received nearly three votes. Understand the concept of a unit rate a / associated with a ratio a: with 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of cups of flour to 4 cups of sugar, so there is /4 cup of flour for each cup of sugar. We paid $75 for 5 hamurgers, which is a rate of $5 per hamurger. a c d Grade 6 Unit Weeks, Unit Weeks, 4 Unit Weeks, Unit Weeks, 4 Use ratio and rate reasoning to solve real-world and mathematical prolems, e.g., y reasoning aout tales Make tales of equivalent ratios relating quantities with whole numer measurements, find missing values in the tales, and plot the pairs of values on the coordinate plane. Use tales to Unit Weeks, compare ratios. Solve unit rate prolems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could e mowed in 5 hours? At what rate werfind a percent of a quantity as a rate per 00 (e.g., 0% of a quantity means 0/00 times the quantity); solve prolems involving finding the whole, given a part and the percent.e lawns eing mowed? Find a percent of a quantity as a rate per 00 (e.g., 0% of a quantity means 0/00 times the quantity); solve prolems involving finding the whole, given a part and the percent. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Unit Week 4 Unit Week Unit Week Unit Week The Numer System Apply and extend previous understandings of multiplication and division to divide fractions y fractions. 6.RP 6.NS Page 4 of 5

35 including Grade 6 Interpret and compute quotients of fractions, and solve word prolems involving division of fractions y fractions, e.g., y using visual fraction models and equations to represent the prolem. For example, create a story context for (/) (/4) and use a visual fraction model to show the quotient; use the relationship Unit Week etween multiplication and division to explain that (/) (/4) = 8/9 ecause /4 of 8/9 is /. (In general, (a/) (c/d) = ad/c.) Unit Week How much chocolate will each person get if people share / l of chocolate equally? How many /4-cup servings are in / of a cup of yogurt? How wide is a rectangular strip of land with length /4 mi and area / square mi? Page 5 of 5

36 including Grade 6 Compute fluently with multi-digit numers and find common factors and multiples. Fluently divide multi-digit numers using the standard algorithm. Unit 4 Week 4 Fluently add, sutract, multiply, and divide multi-digit decimals Unit Weeks,4 using the standard algorithm for each operation. Unit Week 4 4 Find the greatest common factor of two whole numers less than or equal to 00 and the least common multiple of two whole numers less than or equal to. Use the distriutive property to express a sum of two whole numers 00 with a common factor as a multiple of a sum of two whole numers with no common factor. For example, express as 4 (9 + ). Unit Week Apply and extend previous understandings of numers to the system of rational numers. Understand that positive and negative numers are used together to descrie quantities having opposite directions or values (e.g., temperature aove/elow zero, elevation Unit Week 5 aove/elow sea level, credits/deits, positive/negative electric charge); use positive and negative numers to represent Unit Week 4 quantities in real-world contexts, explaining the meaning of 0 in each situation. 6 Understand a rational numer as a point on the numer line. Extend numer line diagrams and coordinate a c Recognize opposite signs of numers as indicating locations on opposite sides of 0 on the numer line; recognize that the opposite of the opposite of a numer is the numer itself, e.g., ( ) =, and that 0 is its own opposite. Understand signs of numers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only y signs, the locations of the points are related y reflections across one or oth axes. Find and position integers and other rational numers on a horizontal or vertical numer line diagram; find and position pairs of integers and other rational numers on a coordinate plane. Unit Week Unit Week 4 Unit 4 Week Unit Week Unit Week 4 Page 6 of 5

37 including 7 a c d 8 Grade 6 Understand ordering and asolute value of rational numers. Interpret statements of inequality as statements aout the relative position of two numers on a numer line diagram. For example, interpret > 7 as a statement that is located to the right of 7 on a numer line oriented from left to right. Write, interpret, and explain statements of order for rational numers in real-world contexts. For example, write o C > 7 o C to express the fact that o C is warmer than 7 o C. Understand ordering and asolute value of rational numers. Understand the asolute value of a rational numer as its distance from 0 on the numer line; interpret asolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account alance of 0 dollars, write 0 = 0 to descrie the size of the det in dollars. Distinguish comparisons of asolute value from statements aout order. For example, recognize that an account alance less than 0 dollars represents a det greater than 0 dollars. Solve real-world and mathematical prolems y graphing points in all four quadrants of the coordinate plane. Include use of coordinates and asolute value to find distances etween points with the same first coordinate or the same second coordinate. Unit Week Unit Week 4 Expressions and Equations Apply and extend previous understandings of arithmetic to algeraic expressions. Write and evaluate numerical expressions involving wholenumer exponents. Unit Week Write, read, and evaluate expressions in which letters stand for numers. Write expressions that record operations with numers and with a letters standing for numers. For example, express the Unit 4 Week 4 calculation Sutract y from 5 as 5 y. Write, read, and evaluate expressions in which letters stand for numers. 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, descrie the expression (8 + 7) as a product of two factors; view (8 + 7) as otha single entity and a sum of two terms. 6.EE Page 7 of 5

38 including c 4 Grade 6 Write, read, and evaluate expressions in which letters stand for numers. Evaluate expressions at specific values of their variales. Include expressions that arise from formulas used in real-world prolems. Perform arithmetic operations, including those involving whole-numer exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s and A = 6 s to find the volume and surface area of a cue with sides of length s = /. Apply the properties of operations to generate equivalent expressions. For example, apply the distriutive property to the expression ( + x) to produce the equivalent expression 6 + x; apply the distriutive property to the expression 4x + 8y to produce the equivalent expression 6 (4x + y); apply properties of operations to y + y + y to produce the equivalent expression y. Identify when two expressions are equivalent (i.e., when the two expressions name the same numer regardless of which value is sustituted into them). For example, the expressions y + y + y and y are equivalent ecause they name the same numer regardless of which numer y stands for. Reason aout and solve one-variale equations and inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, 5 make the equation or inequality true? Use sustitution to determine whether a given numer in a specified set makes an equation or inequality true. 6 7 Use variales to represent numers and write expressions when solving a real-world or mathematical prolem; understand that a variale can represent an unknown numer, or, depending on the purpose at hand, any numer in a specified set. Solve real-world and mathematical prolems y writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numers. Unit Week Unit 5 Week 4 Unit 5 Weeks -4 Unit Week Unit Week Unit Week Unit 4 Weeks, 4 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical prolem. 8 Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on numer line diagrams. Represent and analyze quantitative relationships etween dependent and independent variales. Page 8 of 5

39 including Grade 6 9 Use variales to represent two quantities in a real-world prolem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variale, in terms of the other quantity, thought of as the independent variale. Analyze the relationship etween the dependent and independent variales using graphs and tales, and relate these Unit Week to the equation. For example, in a prolem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship etween distance and time. Page 9 of 5

40 including Grade 6 Geometry Solve real-world and mathematical prolems involving area, surface area, and volume. Find the area of right triangles, other triangles, special quadrilaterals, and polygons y composing into rectangles or Unit 5 Week decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical Unit 5 Week prolems. 4 Find the volume of a right rectangular prism with fractional edge lengths y packing it with unit cues of the appropriate unit fraction edge lengths, and show that the volume is the same as would e found y multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical prolems. 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 and mathematical prolems. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical prolems. Statistics and Proaility Develop understanding of statistical variaility. Recognize a statistical question as one that anticipates variaility in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, ut How old are the students in my school? is a statistical question ecause one anticipates variaility in students ages. Understand that a set of data collected to answer a statistical question has a distriution which can e descried y its center, spread, and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single numer, while a measure of variation descries how its values vary with a single numer. Summarize and descrie distriutions. 4 Display numerical data in plots on a numer line, including dot plots, histograms, and ox plots. Unit 4 Week Unit 5 Week 4 Unit 5 Week Unit 6 Week Unit 6 Week Unit 6 Week 6.G 6.SP Page 40 of 5

41 including 5 a c d Grade 6 Summarize numerical data sets in relation to their context, such as y: Reporting the numer of oservations. Unit 6 Week Descriing the nature of the attriute under investigation, including how it was measured and its units of measurement. Giving quantitative measures of center (median and/or mean) and variaility (interquartile range and/or mean asolute deviation), as well as descriing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Relating the choice of measures of center and variaility to the shape of the data distriution and the context in which the data were gathered. Unit 6 Week Page 4 of 5

42 a c d Grade 7 Ratios and Proportional Relationships Analyze proportional relationships and use them to solve real-world and mathematical prolems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks / mile in each /4 hour, compute the unit rate as the complex fraction ///4 miles per hour, equivalently miles per hour. Recognize and represent proportional relationships etween quantities. Decide whether two quantities are in a proportional relationship, e.g., y testing for equivalent ratios in a tale or graphing on a coordinate plane and oserving whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tales, graphs, equations, diagrams, and veral descriptions of proportional relationships. Represent proportional relationships y equations. For example, if total cost t is proportional to the numer n of items purchased at a constant price p, the relationship etween the total cost and the numer of items can e expressed as t = pn. 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) and (, r) where r is the unit rate. Use proportional relationships to solve multistep ratio and percent prolems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Unit Weeks,4 Unit Weeks, 4 Unit 5 Week Unit Week Unit Weeks Unit 4 Weeks, Unit Week 4 Unit Week 4 Unit 4 Week Unit 4 Week Unit Week Unit 4 Week Unit Weeks,4 7.RP Page 4 of 5

43 Grade 7 The Numer System 7.NS Apply and extend previous understandings of operations with fractions to add, sutract, multiply, and divide Apply and extend previous understandings of addition and sutraction to add and sutract rational Descrie situations in which opposite quantities comine to make 0. For Unit Week a example, a hydrogen atom has 0 charge ecause its two constituents are oppositely charged. Unit Week c d a Understand p + q as the numer located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a numer and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numers y descriing realworld contexts. Understand sutraction of rational numers as adding the additive inverse, p q = p + ( q ). Show that the distance etween two rational numers on the numer line is the asolute value of their difference, and apply this principle in real-world contexts. Apply properties of operations as strategies to add and sutract rational numers. Understand that multiplication is extended from fractions to rational numers y requiring that operations continue to satisfy the properties of operations, particularly the distriutive property, leading to products such as ( )( ) = and the rules for multiplying signed numers. Interpret products of rational numers y descriing real-world contexts. Unit Weeks, Unit Week Unit Week Unit Weeks, Unit Week Apply and extend previous understandings of multiplication and division and of fractions to multiply and Unit Week Unit Week c d Understand that integers can e divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational numer. If p and q are integers, then (p /q ) = ( p )/q = p /( q ). Interpret quotients of rational numers y descriing real world contexts. Apply properties of operations as strategies to multiply and divide rational numers. Convert a rational numer to a decimal using long division; know that the decimal form of a rational numer terminates in 0s or eventually repeats. Unit Week Unit Week Unit Week Unit Week Page 4 of 5

44 Grade 7 Solve real-world and mathematical prolems involving the four operations with rational numers. Expressions and Equations Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, sutract, factor, and expand linear expressions with rational coefficients. Understand that rewriting an expression in different forms in a prolem context can shed light on the prolem and how the quantities in it are related. For example, a a =.05a means that increase y 5% is the same as multiply y a Solve multi-step real-life and mathematical prolems posed with positive and negative rational numers in any form (whole numers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numers in any form; convert etween forms as appropriate; and assess the reasonaleness of answers using mental computation and estimation strategies. For example: If a woman making $5 an hour gets a 0% raise, she will make an additional /0 of her salary an hour, or $.50, for a new salary of $7.50. If you want to place a towel ar 9 /4 inches long in the center of a door that is 7 / inches wide, you will need to place the ar aout 9 inches from each edge; this estimate can e used as a check on the exact computation. Unit Weeks,, 4 Unit Weeks, Unit Week Unit Week Solve real-life and mathematical prolems using numerical and algeraic expressions and equations. Unit Weeks -4 Unit 4 Weeks,4 Unit Week 4 Unit Week 4 Use variales to represent quantities in a real-world or mathematical prolem, and construct simple Solve equations of these forms fluently. Compare an algeraic solution to an arithmetic solution, identifying the sequence of the operations used in Unit 4 Weeks, 4 each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Unit Week Graph the solution set of the inequality and interpret it in the context of the prolem. For example: As a salesperson, you are paid $50 per week plus $ per sale. This week you want your pay to e at least $00. Write an Unit Week 4 inequality for the numer of sales you need to make, and descrie the solutions. 7.EE Page 44 of 5

45 Grade 7 Geometry Draw, construct, and descrie geometrical figures and descrie the relationships etween them. Solve prolems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing Unit 6 Week a scale drawing at a different scale. Draw (freehand, with ruler and protractor, and 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. Unit 5 Week Unit 6 Week 7.G Descrie the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical prolems involving angle measure, area, surface area, and volume. Know the formulas for the area and circumference of a circle and use them 4 to solve prolems; give an informal derivation of the relationship etween Unit 5 Week 4 the circumference and area of a circle. Use facts aout supplementary, complementary, vertical, and adjacent 5 angles in a multi-step prolem to write and solve simple equations for an Unit 5 Week unknown angle in a figure. 6 Solve real-world and mathematical prolems involving area, volume and surface area of two- and three-dimensional ojects composed of triangles, quadrilaterals, polygons, cues, and right prisms. Statistics and Proaility Use random sampling to draw inferences aout a population. Understand that statistics can e used to gain information aout a population y examining a sample of the population; generalizations aout a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences aout 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 ook y randomly sampling words from the ook; predict the winner of a school election ased on randomly sampled survey data. Gauge how far off the estimate or prediction might e. Draw informal comparative inferences aout two populations. Unit 5 Weeks, Unit 5 Week Unit 6 Week Unit 6 Week Unit 6 Week 7.SP Page 45 of 5

46 4 5 6 Grade 7 Informally assess the degree of visual overlap of two numerical data distriutions with similar variailities, measuring the difference etween the centers y expressing it as a multiple of a measure of variaility. For example, the mean height of players on the asketall team is 0 cm greater than the mean height of players on the soccer team, aout twice the variaility (mean asolute deviation)on either team; on a dot plot, the separation etween the two distriutions of heights is noticeale. Use measures of center and measures of variaility for numerical data from random samples to draw informal comparative inferences aout two populations. For example, decide whether the words in a chapter of a seventh-grade science ook are generally longer than the words in a chapter of a fourth-grade science ook. Investigate chance processes and develop, use, and evaluate proaility models. 7 a Understand that the proaility of a chance event is a numer etween 0 and that expresses the likelihood of the event occurring. Larger numers indicate greater likelihood. A proaility near 0 indicates an unlikely event, a proaility around / indicates an event that is neither unlikely nor likely, and a proaility near indicates a likely event. Approximate the proaility of a chance event y collecting data on the chance process that produces it and oserving its long-run relative frequency, and predict the approximate relative frequency given the proaility. For example, when rolling a numer cue 600 times, predict that a or 6 would e rolled roughly 00 times, ut proaly not exactly 00 times. Unit 6 Week Unit 6 Week Unit 6 Week, Unit 6 Week 4 Unit 6Week Unit 6 Week 4 Unit 6 Week Develop a proaility model and use it to find proailities of events. Compare proailities from a model to Develop a uniform proaility model y assigning equal proaility to all outcomes, and use the model to determine proailities of events. For Unit 6 Week 4 example, if a student is selected at random from a class, find the proaility that Jane will e selected and the proaility that a girl will e Unit 6 Week selected. Develop a proaility model (which may not e uniform) y oserving frequencies in data generated from a chance process. For example, find the approximate proaility that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to e equally likely ased on the oserved frequencies? Unit 6 Week 4 Unit 6 Week Page 46 of 5

47 8 a c Grade 7 Find proailities of compound events using organized lists, tales, tree diagrams, and simulation. Understand that, just as with simple events, the proaility of a compound Unit 6 Week 4 event is the fraction of outcomes in the sample space for which the compound event occurs. Unit 6 Week 4 Represent sample spaces for compound events using methods such as organized lists, tales and tree diagrams. For an event descried in Unit 6 Week 4 everyday language (e.g., rolling doule sixes ), identify the outcomes in the sample space which compose the event. Unit 6 Week 4 Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A lood, what is the proaility that it will take at least 4 donors to find one with type A lood? Unit 6 Week 4 Page 47 of 5

48 Grade 8 THE NUMBER SYSTEM Know that there are numers that are not rational, and approximate them y rational numers. Know that numers that are not rational are called irrational. Understand informally that every numer has a decimal expansion; for rational numers show that the decimal expansion repeats eventually, and convert a decimal Unit Week expansion which repeats eventually into a rational numer. 8.NS Use rational approximations of irrational numers to compare the size of irrational numers, locate them approximately on a numer line diagram, and estimate the value of expressions (e.g., π ). For example, y truncating the decimal expansion of, show that is etween and, then etween.4 and.5, and explain how to continue on to get etter approximations. EXPRESSIONS AND EQUATIONS Work with radicals and integer exponents. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 5 = = / = /7. Unit Week 4 8.EE 4 Use square root and cue root symols to represent solutions to equations of the form x = p and x = p, where p is a positive rational numer. Evaluate square roots of small perfect squares and cue roots of small perfect cues. Know that is irrational. Use numers expressed in the form of a single digit times an integer power of 0 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 0 8 and the population of the world as 7 0 9, and determine that the world population is more than 0 times larger. Perform operations with numers expressed in scientific notation, including prolems where oth decimal and scientific notation are used. Use scientific notation and 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 een generated y technology. Unit Week 4 Understand the connections etween proportional relationships, lines, and linear equations. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in 5 different ways. For example, compare a distance-time graph to a distancetime equation to determine which of two moving ojects has greater speed. 6 Use similar triangles to explain why the slope m is the same etween any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + for a line intercepting the vertical axis at. Unit Week 4 Unit Week Unit 4 Weeks, Unit 4 Week Page 48 of 5

49 Grade 8 Analyze and solve linear equations and pairs of simultaneous linear equations. 7 Solve linear equations in one variale. Give examples of linear equations in one variale with one solution, infinitely many solutions, or no solutions. Show which of these possiilities a is the case y successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = results (where a and are different numers). Solve linear equations with rational numer coefficients, including equations whose solutions require expanding expressions using the distriutive property and collecting like terms. 8 Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two a variales correspond to points of intersection of their graphs, ecause points of intersection satisfy oth equations simultaneously. Solve systems of two linear equations in two variales algeraically, and estimate solutions y graphing the equations. Solve simple cases y inspection. For example, x + y = 5 and x + y = 6 have no solution ecause x + y cannot simultaneously e 5 and 6. Solve real-world and mathematical prolems leading to two linear equations in two variales. For example, given coordinates for two pairs of c points, determine whether the line through the first pair of points intersects the line through the second pair. Functions Define, evaluate, and compare functions. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of orderef pairs consisting of an input and the corresponding output. Compare properties of two functions each represented in a different way (algeraically, graphically, numerically in tales, or y veral descriptions). For example, given a linear function represented y a tale of values and a linear function represented y an algeraic expression, determine which function has the greater rate of change. Interpret the equation y = mx + as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s giving the area of a square as a function of its side length is not linear ecause its graph contains the points (,), (,4) and (,9), which are not on a straight line. Unit 4 Week Unit Week Unit 4 Weeks, Unit 4 Week Unit 4 Week Unit 4 Week 4 8.F Page 49 of 5

50 Grade 8 Use functions to model relationships etween quantities. Construct a function to model a linear relationship etween two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y ) values, including reading 4 these from a tale or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a tale of values. Descrie qualitatively the functional relationship etween two quantities y analyzing a graph (e.g., where the function is increasing or decreasing, 5 linear or nonlinear). Sketch a graph that exhiits the qualitative features of a function that has een descried verally. GEOMETRY Understand congruence and similarity using physical models, transparencies, or geometry software. 8 Verify experimentally the properties of rotations, reflections, and translations. Lines are taken to lines, and line segments to line segments of the same a length. Angles are taken to angles of the same measure. c Parallel lines are taken to parallel lines. Understand that a two-dimensional figure is congruent to another if the second can e otained from the first y a sequence of rotations, reflections, and translations; given two congruent figures, descrie a sequence that exhiits the congruence etween them. Descrie the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Understand that a two-dimensional figure is similar to another if the second can e otained from the first y a sequence of rotations, reflections, 4 translations, and dilations; given two similar two-dimensional figures, descrie a sequence that exhiits the similarity etween them. 8.G Use informal arguments to estalish facts aout the angle sum and exterior angle of triangles, aout the angles created when parallel lines are cut y a transversal, and the angle-angle criterion for similarity of triangles. For 5 example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. Understand and apply the Pythagorean Theorem. 6 Explain a proof of the Pythagorean Theorem and its converse. Apply the Pythagorean Theorem to determine unknown side lengths in right 7 triangles in real-world and mathematical prolems in two and three dimensions. 8 Apply the Pythagorean Theorem to find the distance etween two points in a coordinate system. Unit 5 Week 4 Page 50 of 5

51 Grade 8 Solve real-world and mathematical prolems involving volume of cylinders, cones, and spheres. Know the formulas for the volumes of cones, cylinders, and spheres and 9 use them to solve real-world and mathematical prolems. Unit 5 Week 4 STATISTICS AND PROBABILITY Investigate patterns of association in ivariate data. Construct and interpret scatter plots for ivariate measurement data to investigate patterns of association etween two quantities. Descrie Unit 6 Week patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Unit 6 Week Know that straight lines are widely used to model relationships etween two quantitative variales. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit y judging the closeness of the data points to the line. Use the equation of a linear model to solve prolems in the context of ivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a iology experiment, interpret a slope of.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional.5 cm in mature plant height. Understand that patterns of association can also e seen in ivariate categorical data y displaying frequencies and relative frequencies in a twoway tale. Construct and interpret a two-way tale summarizing data on two categorical variales collected from the same sujects. Use relative frequencies calculated for rows or columns to descrie possile 4 association etween the two variales. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? 8.SP Page 5 of 5