Curriculum Planning Manual Mathematics

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1 Curriculum Planning Manual Mathematics 3LIT Windmill Parkway #142 Henderson, NV, Toll Free:

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3 Table of Contents Mathematics Curriculum Planning Manual Teachers Guides and Scope and Sequences Please note: Courses are listed in grade level sequence. Mathematics I VIII... 5 Mathematics I...10 Mathematics II...14 Mathematics III...18 Mathematics IV...23 Mathematics V...27 Mathematics VI...31 Mathematics VII...34 Mathematics VIII...37 Pre-Algebra...44 Algebra I: Part 1 and Algebra I: Part Algebra I: Part Algebra I: A Function Approach Part Algebra I: A Function Approach Part Algebra II: Part 1 and Algebra II: Part Algebra II: Part Geometry...80 Trigonometry...84 Calculus I and II...87 Calculus I...88 Calculus II...90 i

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5 Mathematics Grade Levels 1 12 GlobalCourseware Mathematics are comprehensive, completely integrated courses for grades The Mathematics courses develop strategies to solve real-world problems and are designed to move the student beyond the level of basic knowledge into critical thinking and learning activities. Mathematics is a collection of one- and two- semester long courses. All lessons in the eighteen titles contain a study guide, a practice test, and a mastery test. Many lessons have an essay or other constructed response. Some Mathematics lessons are certified by MetaMetrics with Lexile scores. Some courses are enriched by National Library of Virtual Manipulatives (NLVM) applets or Encyclopædia Britannica Online School Edition (EB) workspaces that contain learning materials. Learning materials may contain articles, games, images, maps, and/or videos. 1

6 Mathematics Grade Levels 1 12 The content in these titles is designed to meet and exceed the requirements of the National Council of Teachers in Mathematics. The standards for school mathematics describe a comprehensive set of goals for mathematics instruction. Students will understand meanings of operations and how they relate to one another. Students will understand numbers, ways of representing numbers, relationships among numbers, and number systems. Students will compute fluently and make reasonable estimates. In addition, students will build new mathematical knowledge through problem solving. Third-Party Content in GlobalCoursewear Lessons The National Library of Virtual Manipulatives is a library of uniquely interactive, web-based virtual manipulatives or concept tutorials for mathematics instruction supported by the National Science Foundation. Each applet provides interactive math lessons and activities. The launch icon for NLVM objects is located on the study guide pages of the GC lesson. 2

7 Mathematics Grade Levels 1 12 The Encyclopædia Britannica Online School Edition has teacher resources and student learning materials. The materials include a wide range of interactive lessons, research projects, animations, and worksheets that support many GlobalCourseware lessons. Each workspace may contain an article, diagram, study guide, video, or interactive media. The launch icon for EB objects is located at the top of the GC screen in the study guide section. Software Web Browser Plug-ins Media Player Third Party Content NLVM, EB NLVM, EB, PDFs EB Recommendation Software Requirements Microsoft Internet Explorer 6.0 or higher or Safari 2.0 or higher Adobe Flash Player Adobe Shockwave Player Adobe Reader Java 1.41 or higher Quicktime or Link for Download (select Get ADOBE FLASH PLAYER) (select Get SHOCKWAVE PLAYER) (select Get ADOBE READER) normally installed with your GlobalCourseware client Windows Media Player For further exploration, resource links to the Internet may be provided in some lessons. An Internet connection is required to utilize the EB components of the GlobalCourseware. 3

8 Mathematics Grade Levels 1 12 The Mathematics courses each contain a variety of lessons and differ in length, grade level, and available features. Listed below are the courses found within the entire curriculum planning manual. Course Name Number of Lessons Length of Course in Semesters Grade Levels Lexile Measure Mathematics I L Yes Mathematics II L Yes Mathematics III L Yes Mathematics IV L Yes Mathematics V L Yes Mathematics VI L Yes Mathematics VII L Yes Mathematics VIII L Yes Pre-Algebra Algebra I: Part Yes Algebra I: Part Yes Algebra I: A Function Approach Part Yes Algebra II: Part Yes Algebra II: Part Yes Geometry Trigonometry Calculus I Calculus II NLVM 4

9 Mathematics I VIII Grade Levels 1 8 GlobalCourseware Mathematics I VIII introduces students to the following concepts, skills, and more: numbers and counting addition and subtraction story problems multiplication writing decimals to the tenths and hundredths positions writing, adding and subtracting decimals uses of line and circle graphs circles, perimeter, circumference, pyramids, and probability capacity and weight units, temperature, lines and rays positive and negative integers calculating perimeter, area, volume, using a number line graphing ordered pairs on a coordinate axis positive and negative rational numbers translating word phrases into algebraic expressions with integers, slope, binomials, determinants, and Cramer s rule 5

10 Mathematics Grade Levels 1 8 GlobalCourseware Mathematics are comprehensive, completely integrated courses for grades 1 8. The Mathematics courses develop strategies to solve real-world problems and are designed to move the student beyond the level of basic knowledge into critical thinking and learning activities. Mathematics I-VIII is presented as a collection of year-long courses. All lessons in the eight titles contain a study guide, a practice test, and mastery test. Many lessons have an essay or other constructed response. These Mathematics lessons are certified by MetaMetrics with Lexile scores. Some courses are enriched by National Library of Virtual Manipulatives (NLVM) applets or Encyclopædia Britannica Online School Edition (EB) workspaces that contain learning materials. Learning materials may include articles, games, images, maps, and/or videos. 6

11 Mathematics Grade Levels 1 8 The content in these titles is designed to meet and exceed the requirements of the National Council of Teachers in Mathematics. The standards for school mathematics describe a comprehensive set of goals for mathematics instruction. Students will understand meanings of operations and how they relate to one another. Students will understand numbers, ways of representing numbers, relationships among numbers, and number systems. Students will compute fluently and make reasonable estimates. In addition, students will build new mathematical knowledge through problem solving. Third-Party Content in GlobalCourseware Lessons The National Library of Virtual Manipulatives is a library of uniquely interactive, web-based virtual manipulatives or concept tutorials for mathematics instruction supported by the National Science Foundation. Each applet provides interactive math lessons and activities. The launch icon for NLVM objects is located on the study guide pages of the GC lesson. 7

12 Mathematics Grade Levels 1 8 The Encyclopædia Britannica Online School Edition has teacher resources and student learning materials. The materials include a wide range of interactive lessons, research projects, animations, and worksheets that support many GlobalCourseware lessons. Each workspace may contain an article, diagram, study guide, video, or interactive media. The launch icon for EB objects is located at the top of the GC screen in the study guide section. Software Web Browser Plug-ins Media Player Third Party Content NLVM, EB NLVM, EB, PDFs EB Recommendation Software Requirements Microsoft Internet Explorer 6.0 or higher or Safari 2.0 or higher Adobe Flash Player Adobe Shockwave Player Adobe Reader Java 1.41 or higher Quicktime or Windows Media Player Link for Download (select Get ADOBE FLASH PLAYER) (select Get SHOCKWAVE PLAYER) (select Get ADOBE READER) normally installed with your GlobalCourseware client For further exploration, resource links to the Internet may be provided in some lessons. An Internet connection is required to utilize the EB components of the GlobalCourseware. 8

13 Mathematics Grade Levels 1 8 The Mathematics courses I VIII each contain a variety of lessons and differ in length, grade level, and available features. Additional features for these courses are found in the table below. Course Name Number of Lessons Length of Course in Semesters Grade Levels Lexile Measure NLVM Mathematics I Yes Yes Mathematics II Yes Yes Mathematics III Yes Yes Mathematics IV Yes Yes Mathematics V Yes Yes Mathematics VI Yes Yes Mathematics VII Yes Yes Mathematics VIII Yes Yes For information on Pre-Algebra and Algebra mid-level courses see the curriculum-planning manual for Mathematics Grade Levels

14 Mathematics I Grade Level 1 Mathematics I is an introduction to mathematical concepts. The lessons cover numbers and counting; ordering numbers; ordinal numbers; addition readiness; vertical addition; subtraction readiness; number sense; vertical subtraction; fact families; word problems; addition sentences; subtraction sentences; identifying the operation needed to solve a problem; reading and creating graphs; identifying and counting coins; measuring length, weight, and temperature; telling time; three-dimensional figures; symmetry; and fractions. The Mathematics I course includes other topics such as: adding with number lines mathematical patterns counting by tens number sets 10

15 Mathematics I Grade Level 1 Identify the numbers 1 through 5. Match numbers with the amounts they stand 1 Using Numbers to 5 for. Using Numbers to Identify the numbers 6 through 10. Match numbers with the amounts they 2 Essay: Counting 10 stand for. Learn to compare numbers and amounts by using the symbols for greater 3 Number Sets than, less than, and equals. Numbers and Use the 100's chart and counting patterns to count to 100. Find missing 4 Counting Patterns to numbers. 100 Essay: Counting Learn the concepts of greater than and less than. Practice putting numbers in 5 Ordering Numbers correct counting order. Essay: Counting 6 Ordinal Numbers to Fifth Learn about the ordinal numbers that match the numbers 1 through 5. Study: Drag and Drop Activity Essay: Logic 7 Ordinal Numbers to Review the ordinal numbers that match the numbers 1 through 5. Learn about Tenth the ordinal numbers that match the numbers 6 through More or Less Compare two sets of objects by counting and using more or less. Study: 9 Addition Readiness Learn how to add by putting numbers together to make a new, larger number. Essay: Writing Equations 10 Adding With Number Study: Learn how to use number lines to add. Lines Essay: Writing Equations 11 Vertical Addition Learn how to add numbers vertically. Essay: Writing Equations 12 Subtraction Learn how to subtract by taking a part away from a whole to create an new, Readiness smaller number. 13 Number Sense Sort, group, and count objects. Learn to compare and order numbers. Essay: Writing Equations 14 Subtracting With Study: Learn how to use number lines to subtract. Number Lines Essay: Writing Equations 15 Vertical Subtraction Learn how to subtract numbers vertically. Essay: Writing Equations 16 Fact Families Recognize fact families and find missing numbers in addition and subtraction problems. Essay: Writing Equations 17 Counting On Use the counting on strategy to add. 18 Addition and Subtraction Patterns Find out how to use patterns to add and subtract. 11

16 Mathematics I Grade Level 1 19 Addition Sentences Write addition sentences using given information and answer questions about how many. Study: Study: Drag and Drop 20 Adding Three Activity Learn how to work addition problems using three numbers. Numbers EB Learning Material NLVM Activities (2) 21 Continuing Patterns Discover how to continue a pattern by figuring out what comes next. Study: 22 Subtraction Study: Create subtraction sentences from existing data. Sentences 23 Missing Numbers Learn how to find missing numbers in addition and subtraction problems. Essay: Writing Equations 24 Word Problems Learn the steps needed to solve word problems. Study: 25 Counting By Tens Learn how to count in groups of tens. Essay: Counting Meaning of Addition and Subtraction Understanding Numbers Before, After, and Between Numbers Recognize clue words for addition and subtraction word problems. Identify the operation needed to solve problems. Learn how to identify the value of each digit in a number. Recognize and write numbers up to 99 in standard and expanded form. Identify and write numbers that come before, after, or in between given numbers. 29 Skip Counting Learn how to skip count by twos, fives, and tens. 30 Reading Graphs Use graphs to represent data and solve problems. 31 Creating Graphs Learn how to represent data by completing graphs. Essay: Writing Equations Essay: Writing Equations Essay: Counting Essay: Counting Study: Essay: Writing Equations Study: Essay: Written Essay 32 Introduction to Money Identify and count pennies and nickels. Study: Drag and Drop 33 Counting Coins Count various groups of coins. Practice spending money by deciding if there is Activity enough money to but certain items. 34 Extra Information Identify unneeded information in word problems. 12

17 Mathematics I Grade Level 1 35 Spending Money Students see objects with price tags and groups of coins. Students decide if Study: Drag and Drop they have enough money to purchase the items. Activity 36 Is There Enough? Learn how to spend money by counting coins to see if there is enough money to buy some things. Essay: Estimating 37 Estimating and Measure the length of objects using a ruler. Estimate length using nonstandard Measuring Length measuring tools. 38 Learn about different types of measurement and measurement tools. Practice Study: Drag and Drop Types of estimating and comparing the length and weight of different objects. Learn Activity Measurements about quantitative change. Essay: Listing Estimating and Measuring Temperature Properties of Operations Sums and Differences Estimate and measure temperature. Recognize different types of thermometers. Identify the Commutative and Identity properties of addition and subtraction. Review clue words for addition and subtraction word problems. Write addition and subtraction sentences from groups of objects. Observe how the number sentences you write create a fact family. 42 Telling Time Learn how to tell time to the hour and half hour on different types of clocks. Study: Drag and Drop Activity Essay: Estimation Essay: Writing Equations Study: Drag and Drop Activity Essay: Listing 43 Telling Time Review Review telling time by the hour and half hour. 44 Combinations Make combinations of objects, numbers, and letters. Essay: Logic 45 Calendars Study the parts of a calendar and learn how to read it. 46 Shapes 47 Symmetry 48 Fractions Recognize and name two- and three-dimensional shapes. Identify the shapes of different objects. Identify objects that have two parts that match. Predict and investigate what happens when you take apart and put together different shapes. Understand the concept of dividing objects into equal parts called fractions. Recognize the fractions 1/2, 1/3, and 1/4. Study: Drag and Drop Activities (2) Essay: Listing 49 Symbols Recognize symbols and solve code problems using numbers and letters. Essay: Logic Study: Drag and Drop Activity EB Learning Material 13

18 Mathematics II Grade Level 2 Mathematics II strengthens mathematical skills in the following areas: numbers and counting, odds and evens, money and money strategy, graphing, addition and subtraction, using a calculator, measurement, telling time, solving story problems, fractions, and estimating. It also introduces students to measuring perimeter, congruent and symmetrical objects, probability, problem-solving strategies, logic, ordered pairs, multiplication, and division. The lessons also review reading time on digital or analog clocks. The Mathematics II course includes other topics such as: advanced graphing ordinal numbers calculator usage measuring weight measuring temperature introduction to multiplication introduction to division coin values 14

19 Mathematics II Grade Level 2 Understanding Learn about the many different ways in which numbers are used. Identify place 1 Numbers value in the tens place and ones place. Identify place value to the hundreds place using base ten blocks and write 2 Place Value whole numbers in expanded and standard form. Essay: Counting 3 Numbers and Counting Use number lines to skip count by twos, fives, and tens. Identify even and odd numbers. 4 Odds and Evens Identify even and odd numbers. Complete even and odd number patterns. 5 Money Value 6 Counting Money 7 Introduction to Word Problems 8 Number Sense 9 Money Strategy 10 Beginning Word Problems 11 Ordinal Numbers 12 Beginning Graphing 13 Advanced Graphing 14 Addition and Subtraction Sentences Learn the value of pennies, nickels, dimes, quarters, and half dollars. Use different combinations of coins to make equal values. Learn how to make change by counting up. Compare values of items to determine which costs more and which costs less. Learn the 4 important steps to use when solving a word problem. Put numbers in correct counting order. Determine which number comes before, between, or after certain numbers. Use the symbols >, <, and = to compare numbers. Count money to determine if there is enough to purchase certain items. Decide which items to buy given a certain amount to spend. Read word problems carefully to find needed information. Practice solving word problems. Learn about the ordinal numbers first through tenth. Use ordinal numbers to identify the position or order of objects. Answer questions about graphs, complete graphs with information, and use objects and graphs to represent addition and subtraction. Define and give examples of bar graphs, tables, lists, and pictures. Answer questions, solve problems, and understand symbolic notions. Learn the parts of addition and subtraction sentences. Write addition and subtraction number sentences. Essay: Counting Study: Drag and Drop Activity Study: Study: Drag and Drop Activity EB Learning Material Essay: Counting Study: Essay: Written Essay Essay: Writing Equations Study: Essay: Listing 15

20 15 Mathematics II Grade Level 2 Adding and Add and subtract numbers with two digits. Learn how to line up place values Subtracting With when writing problems and find out how to solve addition problems with Essay: Writing Equations Two Digits regrouping. 16 Fact Families Learn how to identify fact families. Discover how to use related addition and subtraction facts to solve problems that have missing terms. 17 Intermediate Word Problems Determine the questions in word problems, and solve the problems. 18 Addition and Look for clue words in math problems and choose the correct operation needed Subtraction Clues to solve problems. 19 Using a Calculator Use a calculator to skip count, build numbers, and solve problems. 20 Adding Three Numbers Solve vertical and horizontal addition problems using three addends. 21 Extra Information Identify unneeded information in word problems. Solve word problems that contain extra information. 22 Choosing Operations Learn how to solve word problems by first reading the information and then determining which operation to use. 23 Introduction to Measurement 24 Measuring Length 25 Measuring Weight and Temperature 26 Measuring Capacity 27 Estimating 28 Telling Time Learn about types of measurement, tools used for measurement, and units of measurement. Identify quantitative change over time. Estimate and measure length using standard and nonstandard measuring instruments. Measure objects in centimeters and inches and choose appropriate units of measurement for different objects. Interpret and apply direction and distance in navigating space. Learn about the measurements of weight and temperature. Compare the weight of different objects and identify the units of measure used for weight. Learn how to measure temperature by reading a thermometer. Estimate and measure capacity. Compare the capacity of different containers and discover how the size of the objects in a container can affect the container s capacity. Learn how to estimate sums and differences and then check the answers for reasonableness. Learn how to tell time on a digital and analog clocks. Find out how to add and subtract time. Essay: Writing Equations Essay: Writing Equations Study: Drag and Drop Activity EB Learning Material Essay: Listing Study: Drag and Drop Activities (2) Study: Drag and Drop Activity Study: NLVM Activities (2) 16

21 Mathematics II Grade Level 2 Understand the terms half past, a quarter to, noon, and midnight. Learn how Expressing and 29 the write time in words. Estimate the length of time needed for certain Study: Estimating Time activities. Review the order of the days of the week and the months of the year. Learn 30 Time Sequence how to use timelines and calendars to obtain information. 31 Shapes and Perimeter Identify, describe, and compare two- and three-dimensional figures. Learn how to measure the perimeter of a 2-dimensional shape. Study: Drag and Drop Activities (2) Essay: Listing 32 Congruent and Understand the difference between congruent and similar figures. Identify Symmetrical Objects symmetrical figures and lines of symmetry. Study: NLVM Activities (2) 33 Beginning Find out what the term probability means. Learn how to gather data and write Study: Probability probability statements. Essay: Graphing 34 Using Probability to Use graphs to gather data and solve problems. Write probability statements Predict and predict outcomes. 35 Missing Patterns Learn how to look for patterns in addition and subtraction problems and find missing numbers to complete patterns. 36 Patterns and Extend patterns and find what comes next. Learn how to locate a particular Study: Ordered Pairs point using ordered pairs. Essay: Logic 37 Sorting Sort and group objects according to similarities and differences. Study: Essay: Logic 38 Strategy Learn how to use different strategies to solve the same problem. 39 Logic Use logical reasoning to solve problems. Essay: Written Essay 40 Identifying Fractions Learn what a fraction is. Identify fractions of various sizes. Study: Drag and Drop Activity EB Learning Material NLVM Activities (2) 41 Writing Fractions Identify and write fractional parts of a whole. Study: Drag and Drop Activity Introduction to Use multiplication and division to share and group equally. 42 Multiplication and Division 17

22 Mathematics III Grade Level 3 Mathematics III covers the following topics: addition and subtraction with regrouping; counting bills and coins; using a number line; using mental math; measuring length with standard and nonstandard measurements; using bar graphs; using a calculator; finding mean, median, mode, and range; estimating and measuring capacity, time, and weight; reading temperatures in Celsius and Fahrenheit; multiplying three numbers; measuring area; dividing by tens and hundreds; adding and subtracting fractions; solving problems using pictographs; decimals; probability; plane figures; ordered pairs; identifying faces, edges, and corners; and using logical reasoning. The Mathematics III course includes other topics such as: nonstandard measurement patterns and calculations conclusions and predictions multi-step word problems lines, rays, and segments 18

23 1 2 Mathematics III Grade Level 3 Addition and Learn about the concept of regrouping. Find out when regrouping must occur Subtraction with and how to add and subtract with regrouping. Regrouping Understanding Numbers 3 Counting Money 4 Adding and Subtracting Money 5 Ordering Numbers Identify place value as well as odd and even numbers. Skip count by 2, 3, 4, 5, and 10. Use ordinal numbers to show order. Identify and count money. Learn how to round money to the nearest dollar, ten dollars, and one hundred dollars. Learn how to add and subtract money amounts. Discover how place value is used when comparing, ordering, and rounding numbers. Use place value when writing Roman numerals. NLVM Activities (2) Study: Study: Drag and Drop Activity Study: Drag and Drop Activity EB Learning Material Essay: Writing Equations 6 Fact Families Identify fact families and determine missing numbers. 7 Using Mental Math Use mental math to add and subtract whole numbers and to regroup. 8 Choosing the Learn how to determine if you should use the operation of addition or Operation subtraction in a word problem. 9 Adding Numbers Discover how to solve horizontal addition problems by grouping numbers with Horizontally parentheses. 10 Extra Information Identify unneeded information in word problems. Essay: Logic 11 Standard and Measure length using nonstandard and standard measurements. Estimate Nonstandard length and apply appropriate units of length to measurement. Essay: Logic Measurements 12 Using Graphs and Gather information and apply the information to bar graphs. Solve problems Study: Charts using bar graphs, compare ways to organize and display data. Essay: Graphing 13 Addition With Review how to regroup numbers when adding. Practice adding 2 and 3 digit Study: Regrouping numbers with regrouping. Essay: Writing Equations 14 Understanding Word Learn the five steps needed to solve problems which involve mathematical Problems operations. 15 Perimeter Measure the perimeter of given shapes and estimate the perimeter of irregular Study: shapes. Learn how perimeter is affected when shapes change. Essay: Logic 16 Subtraction With Regrouping Review how to regroup numbers when subtracting. Practice subtracting two and three digit numbers with regrouping. Study: Essay: Writing Equations 19

24 Mathematics III Grade Level 3 17 Using a Calculator Use calculators to repeat and extend patterns. Follow multiple steps of instructions on the calculator. 18 Solving Word Problems Review the five steps to solving word problems. 19 Deciding When to Solve subtraction word problems that require regrouping. Find out how to Regroup regroup twice in the same problem and solve problems with zeros. Study: NLVM Activities (2) 20 Mean, Median, Discover how to find the mean, median, mode, and range in a group of Mode, and Range numbers Capacity, Time, and Weight Measuring Temperature Finding Needed Facts Introduction to Multiplication Multiplying by 2, 3, 4, and 5 Multiplying by 6, 7, 8, 9, 10, and 100 Multiplying Three Numbers 28 Area Introduction to Division Division: The Opposite of Multiplication Dividing by 2, 3, 4, and 5 Understand how to estimate and measure capacity, time, and weight. Learn about the Fahrenheit and Celsius temperature scales. Estimate temperatures. Identify missing information in word problems. Convert addition sentences to multiplication sentences, and learn how to create models of multiplication. Understand the commutative property of multiplication. Use skip counting and number lines to multiply by 2, 3, 4, and 5. Study multiplication tables for 2, 3, 4, and 5. Identify patterns in multiplication tables. Study multiplication tables for 6, 7, 8, and 9. Learn how to multiply by tens and hundreds. Find out how multiplication is like addition. Discover the associative and distributive properties of multiplication. Learn how to multiply three factors, and practice solving problems that have missing factors. Learn the concept of area and discover how to calculate the area of rectangles and squares. Estimate the area of irregular shapes and find out how area is affected when a shape changes. Learn about the concept of division. Find out how to divide numbers and how to write division sentences. Discover how multiplication and division are related. Learn how to divide by tens and hundreds. Divide using 2, 3, 4, and 5. Check division by multiplying, and identify fact families. Study: Drag and Drop Activities (2) NLVM Activities (2) Study: Study: Essay: Writing Equations 20

25 Mathematics III Grade Level 3 32 Multi-step Word Learn clue words for solving words. Practice solving word problems that have Problems multiple steps. 33 Dividing by 6, 7, 8, Divide using 6, 7, 8, and 9. Make comparisons and identify patterns. Complete and 9 division problems with remainders. 34 Long Division Learn how to divide three and four digit numbers by a one digit number. 35 Learn about taking surveys, comparing sets of data, drawing conclusions, and Conclusions and making predictions. Find out how to display the information obtained from a Predictions survey in a pictograph. 36 Expressing Numbers 37 Data Collection 38 Introduction to Fractions Determine whether addition, subtraction, and multiplication problems will result in even or odd numbers. Compare numbers in expanded and standard forms. Learn how to create and gather information from charts, maps, and graphs. Determine how data collection affects problem solving. Learn how to divide shapes into equal parts to form fractions. Identify various fractions made from whole objects. Study: Essay: Writing Equations Study: Drag and Drop Activity EB Learning Material NLVM Activities (2) 39 Parts of a Set Learn how to write different types of fractions made by dividing whole sets into separate equal parts. Identify the numerator and denominator in fractions. Study: NLVM Activities (2) 40 Equivalent Fractions Find out how to compare fractions by creating common denominators. Recognize equivalent fractions. 41 Adding and Subtracting Add and subtract fractions with like denominators. Fractions 42 Mixed Numbers Learn how to identify, create, and compare mixed numbers. 43 Decimals Learn how to write decimals and how to relate fractions to decimals. 44 Adding and Subtracting Decimals 45 Probability 46 Lines, Rays, and Segments Discover the skills necessary to add and subtract decimals. Learn how to gather data and write probability statements. Make predictions based on probability. Identify lines, rays, segments, and angles, and learn how they relate to each other. Study: Essay: Logic Study: Drag and Drop Activity 21

26 Mathematics III Grade Level 3 47 Plane Figures Study: Drag and Drop Identify different types of plane figures. Learn about congruent shapes and Activity lines of symmetry. Make interesting designs using shapes. 48 Solids Recognize three-dimensional shapes. Identify faces, edges, and corners on solid figures. Learn how to find volume. Study: 49 Ordered Pairs Learn how to use ordered pairs to find a location on a map. Study: 50 Logical Reasoning Use logic to solve problems and check for reasonability of answers. 22

27 Mathematics IV Grade Level 4 Mathematics IV contains lessons covering these concepts: the five-step process for problem solving; grouping addends; addition and subtraction; odd and even numbers; multiplication and division problems using money; using a calendar; temperature; writing decimals to the tenths and hundredths positions; line segments and angles; comparing maps and grids; comparing graph types; and formulating information into a story problem. The Mathematics IV course includes other topics such as: Using logic to solve problems Identifying missing information using pictographs mental math computations 23

28 Mathematics IV Grade Level 4 1 Story Problems 1 The five-step process for problem solving. Essay: Writing Word Problems 2 Number Sense 1 Order of addends in relation to the sum. Adding zero. Students rewrite addition facts in inverse order. Grouping addends. 3 Number Sense 2 Rounding numbers and money amounts to nearest 10, 100, and Addition & Given an addition fact, students write a related subtraction fact. Given a Subtraction 1 subtraction fact, students write a related addition fact. Essay: Writing Word Problems 5 Addition & Subtraction 2 6 Patterns Addition and subtraction fact families. Students complete fact families using missing elements. Students read story problems and choose the correct operation to solve the problem. Odd and even numbers. Students recognize the relationships between numbers to determine patterns. Essay: EB Learning Material Written Response 7 Ordinal Numbers Cardinal and ordinal numbers. Review counting bills and coins. Addition and subtraction problems using 8 Money 1 could purchase. money. Students make change for dollar amounts up to $20 and coin change. Students are given a dollar amount to spend and choose which items they 9 Money 2 Multiplication and division problems using money. Locating the dollar sign and decimal points when multiplying and dividing money. 10 Measurement 1 Estimating, determining, and measuring time to the nearest minute. Finding elapsed time. Using the appropriate time units to measure time. Writing time using AM or PM. Adding and subtracting time. 11 Measurement 2 Using a calendar. Looking for patterns on a calendar. Learning the number of days in each month. 12 Measurement 3 Estimating and measuring capacity, mass, temperature, and distance. Using customary units of measurement. Standard and Metric measurements. Essay: Listing 13 Multiplication 1 Multiplication by two and three digit numbers. Multiplication problems with missing factors. 14 Multiplication 2 Commutative, associative, zero, one, and distributive multiplication properties. Mental math techniques. Estimating. 15 Multiplication 3 Estimation and mental math. Decimal multiplication. Zero in decimals. 16 Division 1 Dividing whole numbers by one and two digit numbers. Estimating quotients. 24

29 Mathematics IV Grade Level 4 17 Division 2 Dividing decimals. Estimation and mental math. 18 Fractions 1 Review of fractions. Reading, writing, and renaming mixed numbers. Comparing and ordering fractions and mixed numbers. NLVM Activities (2) 19 Fractions 2 Addition and subtraction of fractions and mixed numbers. Equivalent fractions. Students read story problems, choose strategies, and solve problems. NLVM Activities (2) 20 Decimals 1 Students read and write decimals to tenths and hundredths positions. Relating decimals and fractions. Relating decimals and money. Writing mixed numbers as decimals. 21 Decimals 2 Adding and subtracting decimals of the same place value. The use of zero in decimals. Writing decimals as fractions. 22 Geometry 1 Identifying faces, edges, and corners of solid and plane figures. Comparing solid figures. Comparing plane figures. Differences in solid and plane figures. Essay: Listing 23 Geometry 2 Line segments and angles. Identifying right angles. Using greater than and less than with right angles. Definition and examples of intersecting lines, parallel lines, and perpendicular lines. Definition and examples of congruence and symmetry. Open and closed 24 Geometry 3 figures. Identifying parts of angles. Identifying and continuing patterns using Study: geometrical shapes. 25 Geometry 4 Measuring perimeter and area of polygons. Finding the volume of solid figures. Difference in area and volume. 26 Graphs 1 Students locate and name ordered pairs on a coordinate grid. Comparing maps and grids. Students locate points by writing ordered pairs. 27 Graphs 2 Students gather data from visual aid and complete bar graph. Students make predictions from bar graph information. Students complete line graph. Essay: Graphing 28 Graphs 3 Using tables and pictographs. Gathering information with a pictograph. Using pictograph information to create line and bar graphs. Comparing graph types. Students decide what type graph to use. 29 Probability Definition and examples of probability. Identifying possible outcomes. The probability equation. Students predict if outcome of given situation is probable, certain, or impossible. Using graphs to chart probability and predict outcomes. 30 Using Mental Math Examples of different methods of computation using mental math. 31 Choosing the Operation Students decide which operation to use and solve problems. 32 Extra Information Students read problems, identify unneeded information, and solve problems. 25

30 Mathematics IV Grade Level 4 33 Story Problems 2 Students are given information to formulate into problems. Students check for reasonableness of answers. 34 Finding Needed Facts Students read information and identify missing information. 35 Story Problems 3 Students read information, form a plan, choose the correct operation, and solve problems having more than two steps. 36 Logical Reasoning Students use logic to solve problems. Students check for reasonability of answers. Essay: Written Essay 26

31 Mathematics V Grade Level 5 Mathematics V covers these concepts: exponents; standard, expanded, and word forms of numbers; writing decimals; adding and subtracting decimals; the properties of addition; the five-step thinking plan; multiplying twoand three-digit numbers; surveys; uses of line and circle graphs; Venn diagrams; least common multiples; units of length; elapsed time; lines and angles; circles; perimeter; circumference; pyramids; and probability. The Mathematics V course includes other topics such as: organizing data rounding whole numbers polygons vertices, edges, and prisms 27

32 Mathematics V Grade Level 5 1 Whole Numbers 1 Place value through millions. Exponents. Standard, expanded, and word forms of numbers. 2 Whole Numbers 2 Comparing and ordering whole numbers. Rounding through millions. 3 Decimals 1 Place value through thousandths. Zero in decimals. Writing decimals. Essay: Listing 4 Decimals 2 Comparing and ordering decimals. Patterns in decimals. Rounding decimals. 5 Properties of Addition Commutative, associative, and zero properties of addition. 6 Addition & Inverse operations. Estimating sums. Subtraction 1 7 Addition & Addition and subtraction across zeros. Regrouping with zeros. Subtraction 2 NLVM Activities (2) 8 Addition & Subtraction 3 Addition and subtraction of decimals. Clustering. Study: 9 Problem Solving 1 The five step thinking plan. Using inverse operations. 10 Organizing Data 1 Using tables to organize, analyze, and solve problems. 11 Problem Solving 2 Multi-step problems. Using the five step thinking plan. 12 Multiplication 1 Commutative, associative, zero, one, and distributive multiplication properties. Mental math techniques. Estimating. 13 Multiplication 2 Multiplication by two and three digit numbers. Multiplication problems with missing factors. 14 Multiplication 3 Estimation. Mental math. Decimal multiplication. Zero in decimals. 15 Division 1 Dividing whole numbers by one and two digit numbers. Estimating quotients. NLVM Activities (2) 16 Division 2 Short division. Dividing larger numbers. Using zeros in division. Identifying patterns. Checking division. 17 Division 3 Dividing decimals. Estimation and mental math. 18 Organizing Data 2 Surveys. Sample groups. Range, mode, mean, median. 28

33 19 Mathematics V Grade Level 5 Parts of a bar graph. Selecting a scale. Displaying data on bar graph. Bar Graphs & Displaying data on pictograph. Reading data. Analyzing data. Making Study: Pictographs inferences. 20 Line Graphs Uses of line graphs. Parts of line graphs. Displaying data. 21 Circle Graphs Circle graphs. Venn diagrams. Analyzing data. 22 Ordered Pairs Ordered pairs. Graphing on a grid. 23 Fractions 1 Fraction parts. Equivalent fractions. Prime numbers. Composite numbers. Greatest common factors. Simplest form. Least common multiples. NLVM Activities (4) 24 Fractions 2 Comparing fractions. Reducing fractions. Improper fractions. Mixed numbers. 25 Fractions 3 Estimation. Adding and subtracting like fractions. Adding and subtracting unlike fractions. Adding and subtracting mixed numbers. 26 Fractions 4 Multiplying fractions and mixed numbers. 27 Metric Measurement Units of length. Units of capacity. Units of mass. Changing metric units. Essay: Listing 28 Customary Measurement Units of length. Units of capacity. Units of weight. 29 Time Measurement Time. Elapsed time. Schedules. 30 Lines & Angles Point, line, line segment, ray, angle, plane. Intersecting lines. Parallel lines. Perpendicular lines. Acute, obtuse, and right angles. Angle measurement. Plane figures. Triangles. Classifying by sides. Classifying by angles. 31 Polygons Quadrilaterals. Classifying quadrilaterals. Symmetry. Congruent figures. Similar figures. Study: 32 Circles Circles. Circle parts. Circumference, diameter, radius, chord. Compass. Relationships of parts. Pi. 33 Space Figures Faces, vertices, edges. Prisms. Pyramids. Cones. Cylinders. Spheres. 34 Geometric Perimeter. Circumference. Area of rectangles, triangles, parallelograms, circles. Measurement Area of irregular shapes. Volume of space figures. 35 Ratios Meaning of ratio. Equivalent ratios. Use of ratio in scale drawings. 29

34 Mathematics V Grade Level 5 36 Percent Ratio. Percent of decimals. Finding percent of a numbers. 37 Probability Definition and examples of probability. Prediction of outcomes. Fractions and probability. 30

35 Mathematics VI Grade Level 6 Mathematics VI strengthens mathematical knowledge and ability in the following areas: rounding numbers, estimation, place value; properties of numbers, multiplying decimals, dividing by one- or two-digit numbers, prime numbers; equivalent fractions, tallies, identifying variables, solving equations; length, capacity and weight units; temperature; lines and rays; parts of a circle; perimeter; positive and negative integers; and ordered pairs. The Mathematics VI course includes other topics such as: geometric measurements using scales coordinate planes formulas and pi 31

36 Mathematics VI Grade Level 6 1 Number Values Place value through billions. Decimal place value through thousandths. Word form. Standard form. Expanded form. 2 Number Sense 1 Rounding numbers. Number Ranges. Estimation. 3 Number Operations Order of operations. Exponents and powers of numbers. 4 Number Sense 2 Square numbers and square roots. 5 Problem Solving 1 Five step thinking plan. Strategies solving problems. Essay: Writing Word Problems 6 Problem Solving 2 Review of 5 step plan. Selecting relevant information. Working with misleading or unnecessary data. Finding strategy in patterns. Choosing strategy to solve problems. 7 Multiplication 1 Estimating products. Commutative, zero, associative, and one properties. 8 Multiplication 2 Multiplying decimals. Zeros in multiplication. 9 Division Estimating quotients. Multiplying and dividing by powers of ten. Dividing by one-digit numbers. Dividing by two-digit numbers. Dividing decimals. 10 Number Sense 3 Factors. Divisibility. Prime numbers. Composite numbers. Factor trees. Prime factorization. Greatest common factors. Multiples. Least common multiples. NLVM Activities (2) 11 Fractions 1 Equivalent fractions. Comparing fractions. Simplest form. Relating fractions to decimals. 12 Fractions 2 Estimating sums and differences. Adding and subtracting like fractions. Adding and subtracting unlike fractions. Adding and subtracting mixed numbers. 13 Fractions 3 Estimating products. Multiplying fractions and mixed numbers. Simplifying. Dividing fractions and mixed numbers. 14 Organizing Data Collecting data. Tallies, frequency tables. Mean, median, mode, and range. 15 Graphing Data Variables & Equations Equations & Inequalities 18 Metric Measures Bar graphs. Pictographs, histograms, circle graphs, and stem and leaf plots. Analyzing graphed information. Identifying variables. Numerical expressions. Algebraic expressions. Addition and subtraction equations. Multiplication and division equations. Rational numbers in equations. Solving equations. Solving Inequalities. Metric place value. Comparing metric units. Length units. Capacity units. Mass units. Essay: Writing Equations NLVM Activities (2) Essay: Written Essay 32

37 Mathematics VI Grade Level 6 19 Customary Measures Length units. Capacity units, weight units. 20 Other Measures Time and temperature. Essay: Logic 21 Plane Geometry Points, lines, rays. Angles. Parallel, intersecting, perpendicular, and skew lines. Bisecting lines. 22 Polygons Triangle classifications. Quadrilateral classifications. Other polygons. Congruence. Similar figures. Symmetry. Motion geometry. NLVM Activities (3) 23 Circles Parts of a circle. Pi. Formulas. 24 Space Figures Prisms. Pyramids. Faces, edges, and vertices. Bases. 25 Geometric Perimeter. Circumference. Area. Surface Area. Volume. NLVM Activities (2) Measurements 26 Ratio & Proportion Ratio. Proportion. Solving proportions. Rates. Using scales. 27 Percent Percents and decimals. Percents and fractions. Estimation. Finding percents of whole numbers. 28 Probability Outcomes. Predicting outcomes. Identifying independent events. 29 Integers Positive integers. Negative integers. Zero. Comparing integers. Adding and subtracting integers. NLVM Activities (2) 30 Coordinate Graphing Ordered pairs. Coordinate planes. X-axis. Y-axis. 33

38 Mathematics VII Grade Level 7 Mathematics VII covers these concepts: place value; commutative, associative, zero, one, and distributive properties; inverse operations; factors; number theory; mixed numbers; ratios; percent concepts; markups; commissions; steps to solving equations; measurement of length; mass/weight; metric units; points; angles; calculating perimeter; area; volume; using a number line; and graphing ordered pairs on a coordinate axis. The Mathematics VII course includes other topics such as: inverse operations steps to solving equations statistics and data collection adding and subtracting integers 34

39 Mathematics VII Grade Level 7 1 Decimal Number Concepts Place value, exponents, powers of ten, expanded notation, scientific notation. 2 Number Operations Commutative, associative, zero, one, and distributive properties. Inverse operations, order of operations. 3 Decimal Number Expanding skills in addition, subtraction, multiplication, and division. Operations NLVM Activities (2) 4 Problem Solving 1 Solving practical problems that deal with decimal numbers. 5 Number Theory Inverse operations. Prime and composite numbers. Divisibility rules, factors, greatest common factor. Multiples, least common multiple. Square numbers, square roots. 6 Problem Solving 2 Practical application of number theory in problem solving. 7 Fraction Concepts Simplest form, equivalent fractions. Comparing and ordering fractions. Improper fractions. Mixed numbers, relating fractions to decimals. 8 Fraction Operations Expanding skills in addition, subtraction, multiplication, and division with fractions and mixed numbers. NLVM Activities (2) 9 Problem Solving 3 Practical situations dealing with fractions in problem solving. 10 Ratio & Proportion Ratios, equivalent ratios, cross products, rates, proportions, and solving proportions. 11 Problem Solving 4 Problem solving with ratios, rates, proportions, scale drawings. 12 Probability Properties of probability. Making predictions. Outcomes and permutations. 13 Percent Concepts 14 Problem Solving 5 15 Algebra Concepts 16 Expressions & Equations Percent, decimals, fractions, finding percents of a whole. Finding parts of a whole, finding the whole. Problem solving with percents. Percent of increase or decrease. Discounts, markups, commissions, interest, and sales tax. Numerical expressions, variables, equations, algebraic expressions, inequalities, inverse operations. Replacing variables to evaluate expressions. Steps to solving equations. Essay: Writing Word Problems 35

40 Mathematics VII Grade Level 7 17 Problem Solving 6 Writing equations to solve word problems. Solving multi-step equations. Essay: Writing Word Problems 18 Measurement Measurement of length, capacity, mass/weight, and time dealing with both metric and customary units. 19 Problem Solving 7 Problem solving applications of measurement. 20 Geometric Concepts Definitions and examples of points, lines, planes, and angles. Bisecting lines and angles. Relationships of lines. Relationships of angles. 21 Plane Figures Polygons: triangles, quadrilaterals, pentagon, octagon, decagon; diagonal; circles: parts of a circle, calculate circumference and area 22 Motion Geometry Similar and congruent figures. Rotation, translation, and reflection. NLVM Activities (2) Essay: Listing 23 Space Figures Review and expansion of ideas about prisms, pyramids, cones, and cylinders. 24 Geometric Length, area, volume, surface area of geometric figures. NLVM Activities (2) Measurement 25 Statistics Data collection. Mean, median, mode, and range. 26 Graphs and Plots 27 Integers Adding & Subtracting Integers Multiplying & Dividing Integers Bar, circle, and line graphs; stem and leaf plots; box and whisker plots; frequency plots Negative and positive numbers, comparing and ordering integers. Using a number line. Absolute value. Finding sums and differences with integers; additional properties of integers Finding products and quotients with integers; using multiplication properties with integers 30 Coordinate Graphing Graphing ordered pairs on a coordinate axis. Essay: Graphing Essay: Writing Word Problems 36

41 Mathematics VIII Grade Level 8 Mathematics VIII strengthens mathematical knowledge and ability in the following areas: rounding numbers, positive and negative rational numbers, order of operations, proportion, scales, randomly occurring events, counting principle factorials, introduction to algebra, points, rays, quadrilaterals, polyhedrons, cones, formulas for the area of plane figures, the Pythagorean Theorem, statistics, translating word phrases into algebraic expressions with integers, slope, binomials, determinants, and Cramer's rule. The Mathematics VIII course includes other topics such as: coefficients and constants slope formulas method tree diagrams random and compound events 37

42 1 Mathematics VIII Grade Level 8 Number Concepts Place value. Rounding. Estimation, Compatible numbers. Essay: Estimating/Problem Review Solving 2 Properties Commutative property of addition; associative property of addition; commutative property of multiplication; associative property of multiplication; identity properties; distributive property 3 Problem Solving 1 Five step thinking plan. Problem solving strategies. 4 Basic Operations 1 Positive and negative rational numbers; equivalent fractions; cross products; absolute value; order of operations; fractions to decimals; comparing and ordering. NLVM Activities (2) 5 Basic Operations 2 Addition, subtraction, multiplication, division. 6 Ratio & Proportion Ratio, rates. Equivalent ratios. Proportion. 7 Problem Solving 2 Practical problems dealing with ratio, proportion, unit rates, rates, and scale. 8 Percent 1 Percent to decimals; percent to fractions; finding percents 9 Percent 2 Percent of increase or decrease; sales tax and discounts 10 Probability Probability. Finding samples. Randomly occurring events. Compound events. Independent events. Dependent events. Making predictions. Capture and recapture. Method tree diagrams. Counting principle factorials. Venn diagrams. NLVM Activities Essay: Writing Equations 11 Algebra 1 Numerical expressions; variables; variable expressions; order of operations; equations; solutions 12 Algebra 2 Simplifying numerical and variable expressions; coefficients; constants; evaluating algebraic expressions 13 Algebra 3 Properties of equality; inverse operations; inequality; solving inequalities 14 Algebra 4 Guides for practice in solving multi-step equations and inequalities 15 Algebra 5 Translating data into equations and inequalities; using equations and inequalities to solve practical problems Essay: Writing Word Problems Essay: Writing Equations Essay: Writing Equations 38

43 Mathematics VIII Grade Level 8 16 Geometric Concepts Point, line, ray; line relationships; angles; angle relationships; angle measurement and classifications; bisecting line segments and angles 17 Plane Figures Regular polygons. Triangles. Quadrilaterals. Congruent figures. Circles. NLVM Activities (2) 18 Space Figures Polyhedrons. Prisms. Pyramids. Cylinders, cones, and spheres. 19 Geometric Perimeter and circumference; formulas for area of plane figures; surface area Measurement of polyhedrons; volume of space figures NLVM Activities (2) 20 Square roots. Principal square roots. Perfect squares. Irrational numbers and Square Roots & real numbers. Pythagorean Theorem. Similar triangles. Special right triangles. Triangles Trigonometry. 21 Statistics 1 Samples. Mean, median, mode, and range. Binomial data. Line plots. Bar graphs. Line graphs. Double bar and double line graphs. Circle graphs. Frequency distribution. NLVM Activities (3) 22 Statistics 2 Stem and leaf plots. Box and whiskers plots. Histograms. Line plots. 23 Integer Concepts Positive and negative numbers. Zero. Opposites. Absolute value. 24 Integer Operations Addition, subtraction, multiplication, and division of integers. Essay: Writing Equations 25 Problem Solving 3 Translating word phrases into algebraic expressions with integers. Problem solving strategies. 26 Coordinate Graphing Coordinate planes. Ordered pairs. Solutions. Graphing equations. Linear 1 equations. Slope. Slope formula. 27 Coordinate Graphing Using coordinate graphing to solve problems. Solving and graphing equations 2 and inequalities. Quadrants. 28 Polynomials 1 Monomials. Binomials. Trinomials. Operations with polynomials. 29 Polynomials 2 Using the distributive property. FOIL method of multiplying binomials. Squaring binomials. 30 Solving Equation Systems Matrices. Determinants. Cramer's rule. 39

44 Mathematics Grade Levels 9 12 GlobalCourseware Mathematics are comprehensive, completely integrated courses for grades The Mathematics courses develop strategies to solve real-world problems and are designed to move the student beyond the level of basic knowledge into critical thinking and learning activities. Mathematics is a collection of one- and twosemester long courses. All lessons in the nine titles contain a study guide, a practice test, and mastery test. Some courses are enriched by National Library of Virtual Manipulatives (NLVM) applets or Encyclopædia Britannica Online School Edition (EB) workspaces that contain learning materials. Learning materials may contain articles, games, images, maps, and/or videos. 40

45 Mathematics Grade Levels 9 12 The content in these titles is designed to meet and exceed the requirements of the National Council of Teachers in Mathematics. The standards for school mathematics describe a comprehensive set of goals for mathematics instruction. Students will understand meanings of operations and how they relate to one another. Students will understand numbers, ways of representing numbers, relationships among numbers, and number systems. Students will compute fluently and make reasonable estimates. In addition, students will build new mathematical knowledge through problem solving. Third-Party Content in GlobalCourseware Lessons The National Library of Virtual Manipulatives is a library of uniquely interactive, web-based virtual manipulatives or concept tutorials for mathematics instruction supported by the National Science Foundation. Each applet provides interactive math lessons and activities. The launch icon for NLVM objects is located on the study guide pages of the GC lesson. 41

46 Mathematics Grade Levels 9 12 The Encyclopædia Britannica Online School Edition has teacher resources and student learning materials. The materials include a wide range of interactive lessons, research projects, animations, and worksheets that support many GlobalCourseware lessons. Each workspace may contain an article, diagram, study guide, video, or interactive media. The launch icon for EB objects is located at the top of the GC screen in the study guide section. Software Web Browser Plug-ins Media Player Third Party Content NLVM, EB NLVM, EB, PDFs EB Recommendation Software Requirements Microsoft Internet Explorer 6.0 or higher or Safari 2.0 or higher Adobe Flash Player Adobe Shockwave Player Adobe Reader Java 1.41 or higher Quicktime or Windows Media Player Link for Download (select Get ADOBE FLASH PLAYER) (select Get SHOCKWAVE PLAYER) (select Get ADOBE READER) normally installed with your GlobalCourseware client For further exploration, resource links to the Internet may be provided in some lessons. An Internet connection is required to utilize the EB components of the GlobalCourseware. 42

47 Mathematics Grade Levels 9 12 Course Name Number of Lessons Length of Course in Semesters Grade Levels Pre-Algebra NLVM Algebra I: Part Yes Algebra I: Part Yes Algebra I: A Function Approach Part Yes Algebra II: Part Yes Algebra II: Part Yes Geometry Trigonometry Calculus I Calculus II

48 Pre-Algebra Grade Levels 8 10 GlobalCourseware Pre-Algebra introduces students to the following concepts, skills, and more: number notation the multiplicative property of zero operational symbols inverse operations of multiplication and division rules for solving equations by adding and subtracting integers factors and exponents fractions graphing on the coordinate plane slope and intercept statistics scatter plots definitions of basic geometric terms circles, area, volume, sine and cosine ratios Pythagorean Theorem 44

49 Pre-Algebra Grade Levels Number Notation Writing numbers in standard, written, expanded, and factor form, and scientific notation. 2 Expressions and Writing numeric expressions, introduction to variables, writing algebraic Equations expressions, evaluating algebraic expressions. 3 Properties Review of commutative, associative, distributive, zero, and identity properties and examples of steps in solving problems using each one, multiplicative property of zero. 4 Simplifying Terms, operational symbols, numerical coefficients, identifying like terms and Expressions constants, using various properties to simplify expressions. 5 Solving Equations 1 6 Solving Equations 2 7 Integers Properties of equality, using inverse operations, using equivalent equations and inverse operations to solve problems. Inverse operations of multiplication and division, the multiplication and division properties of equality. Integers and their opposites, using number lines to identify, locate, and compare integers, absolute value of integers, using integers in real life situations. Rules for solving equations by adding and subtracting integers with the same sign or different signs, examples of strategies to solve equations. Rules for solving equations by multiplying and dividing integers with the same or different signs, examples of strategies to solve equations. NLVM Activities (5) 8 Equations with Integers 1 Study: NLVM Activities (3) 9 Equations with Integers 2 10 Inequalities Definition and examples of inequalities, signs that indicate inequality. 11 Solving Inequalities 1 Solving inequalities by reversing signs. Study: NLVM Activities (2) 12 Solving Inequalities Study: Other strategies for solving inequalities; checking for reasonability Factors and Exponents 14 Rational Numbers 15 Equations/ Inequalities 1 Identifying laws of exponents, writing numbers in exponential form, writing exponents and variables, rules for determining exponents when adding, subtracting, multiplying, and dividing. Identifying parts of fractions, relating fractions to rational numbers, locating rational numbers on the number line, comparing rational numbers, writing rational numbers in decimal form, algebraic fractions. Solving equations and inequalities with addition and subtractions, two-step equations, and equations with variables on both sides. NLVM Activities (2) Study: 45

50 Pre-Algebra Grade Levels 8 10 Solving equations and inequalities with multiplication and division, two-step Equations/ 16 equations and solving equations with variables on both sides with combined Inequalities 2 operations. Graphing on the coordinate plane, graphing linear equations, slope and 17 Graphing Study: NLVM Activities (2) intercept, graphing linear equalities. 18 Ratio & Proportion 19 Percent 20 Problem Solving 21 Statistics & Graphing 22 Probability 23 Algebra with Geometry 24 Polygons and Circles 25 Area and Volume Definition and examples of ratios, writing ratios in lowest terms, rates, unit rates, equivalent ratios, cross products, definition of proportions, solving proportions. Decimals and percents, figuring percents, place value in percent problems, relating percent to wholes. Examples of solving percent problems in everyday life, discounts, commission, checking answers for reasonableness, numbers larger than one hundred percent. Frequency tables; range, mean, mode, and median; bar, line, and circle graphs; scatter plots; stem and leaf plots. The counting principle, permutations, combinations, independent events, dependent events. Definitions of basic geometric terms, length, perimeter, circumference, angles, and angle measures, parallel and perpendicular lines. Triangles, quadrilaterals, other polygons, congruent figures, similar triangles, circles. Finding area of polygons, finding volume and surface area of pyramids, prisms, and cones. Essay: Compare & Contrast Study: 26 Special Triangles Square roots, Pythagorean theorem, tangents, sine and cosine ratios. 46

51 Algebra I: Part 1 and 2 Grade Levels 8 10 GlobalCourseware Algebra I: Part 1 and 2 introduces students to the following concepts and functions and more: Algebra I: Part 1 identify variables and algebraic expressions perform operations with standard and scientific calculators identify absolute value apply algebra to real world problems absolute values identification of the x and y axes binomials and trinomials factoring out monomials, trinomial squares, and quadratic equations Algebra I: Part 2 finding solutions of linear systems of equations by graphing eliminating variables using negative one as a factor ratio and proportion using inequalities to solve problems equations with absolute values irrational numbers problem solving involving joint and combined variation identifying and evaluating the discriminant of a quadratic equation. 47

52 1 Algebra I: Part 1 Grade Levels 8 10 Students identify variables, numerical expressions, algebraic expressions and Expressions & equations, coefficients and constants. Students evaluate algebraic expressions, Equations calculate numerical expressions, and identify open equations. 2 Exponents & Factors 3 Properties 4 Order of Operations 5 Numbers & Sets 6 Absolute Values 7 Problem Solving Adding Real Numbers Subtracting Real Numbers 10 Distributive Property Students evaluate expressions with exponents and expressions with repeated factors in exponential form. Students identify base, exponent, and use zero as exponent. Students write numbers in exponential form. Identification and examples of commutative properties of addition and multiplication, identity properties of addition and multiplication, associative properties of addition and multiplication, and distributive property of multiplication over addition. Students use standard and scientific calculators to perform operations and compare answers. Students identify order of operations and practice simplifying expressions using order of operations. Identification and examples of whole numbers, integers, rational numbers, real numbers, odd and even numbers, and the number line. Students use set notation and Venn diagrams to answer questions and solve problems. Students identify intersection and union of sets, empty sets, subsets, natural numbers, and positive and negative numbers. Students identify absolute value and use number lines to find opposites. Students simplify and evaluate expressions with absolute values and solve for variables. Apply algebra to real world problems. Introduction of steps to solve word problems, students write let statements and use labeled diagrams as let statements. Students identify known information to solve problem. Students use the number line to add real numbers (positive and negative). Review of additive identity and opposites. Students use additive inverse, the addition property of zero, addition property of opposites, and opposite of opposite s properties to solve problems. Students subtract real numbers and simplify expressions that include both sums and differences. Introduction of algebraic definition of subtraction. Students rewrite and simplify problems and evaluate expressions with given values. Students use distributive property to simplify expressions. Comparison of solving problems by using the distributive property and by using order of operations. Essay: Writing Equations NLVM Activities (3) 48

53 Algebra I: Part 1 Grade Levels Like Terms Identification and examples of like terms and solving expressions by collecting like terms. Students identify single numbers, numbers containing products of variables, and similar terms. Students multiply positive and negative numbers, negative and negative 12 Multiplying Real numbers, multiply by zero, and use reciprocals to solve problems. Students Numbers discover products of problems containing both odd and even numbers of Essay: Writing Equations negatives Dividing Real Numbers Evaluating Expressions From Words to Equations Properties of Equality 1 17 Solving Equations 1 18 Properties of Equality 2 19 Solving Equations 2 20 Properties of Equality 3 21 Eliminating Fractions 22 Solving Word Problems Division of real numbers by using multiplication of reciprocals. Introduction of rules for dividing positive and negative numbers. Using zero in division. Students evaluate expressions using order of operations, distributive property, addition, subtraction, multiplication, and division of real numbers and solving for unknowns. Students use words to write equations. Students identify terms used in equations and use alternative methods to solve problems. Students solve problems using addition property of equality, equivalent equations, and isolating variables by using additive inverses. Students choose operations to solve for variables. Students use addition property of equality and inverse operations to solve problems and compare results. Students check work by substituting values for variables. Students solve equations using multiplicative property of equality to isolate both positive and negative variables. Students solve problems using inverse operations and choose the operation to isolate variables and solve problems. Students solve equations using multiplication and division of constants and check solutions by collecting like terms. Students solve equations involving multiple operations. Review of steps for solving equations. Importance of balance in equations. Introduction to new concept of eliminating fractions from equations to simplify problems. Students examine both traditional and fraction elimination methods to solve equations and compare results. Students determine lowest common denominators and write equivalent equations. Students solve equations using addition, subtraction, multiplication, and division, parentheses, and fractions. Students find correct information needed to solve problems. Importance of relative value in solving problems. 49

54 Algebra I: Part 1 Grade Levels 8 10 The Coordinate Identification and examples of x and y axes, quadrants, origin, ordered pairs, x 23 NLVM Activities (2) Plane and y coordinates, abscissa and ordinates. Students locate points on a plane. Definition and examples of linear equations. Students determine if an ordered 24 Linear Equations pair is a solution to an equation. Determining if an equation is linear. Graphing with the T- Given linear equations, students determine multiple solutions and graph 25 Study: table equations. T-tables. Introduction of steps for determining solutions. 26 The x and y Intercepts 27 Slope of a Line Slope-Intercept Equations Fitting Equations to Data 30 Rules of Exponents 31 Polynomial Types Polynomial Operations 1 Polynomial Operations 2 Students locate x and y intercepts for linear equations from graphs and from equations. Students graph by determining x and y intercepts. Graphing with constants. Definition and examples of positive, negative, and zero slope. Given 2 points in a line, students find slope. Students find slope of line when line is graphed on a coordinate plane. Definition and examples of positive and negative rise and run, importance of order in graphing points. Slope-intercept form of linear equations. Students rewrite linear equations in slope-intercept form and use slope-intercept equations to solve problems. Given 2 points on a line, students find equation. Students study and identify mathematical relationships between 2 variables as used in real world situations. Students find equations of a line which models given data. Identification and examples of dependent and independent events. Use linear equations to make predictions. Multiplication and division in exponential form. Students determine powers of products and quotients. Multiplying and dividing powers with like bases. Students identify patterns in exponents and express numbers in exponential form. Rules for raising a power to a power, a product to a power, and a quotient to a power. Identification and examples of polynomials, binomials, and trinomials. Students determine degree of terms and degree of polynomials and write polynomials in descending order. Finding opposites of polynomials. Students add and subtract polynomials by collecting like terms and by inverse operations. Multiplying and dividing monomials by using properties of rational numbers and properties of exponents. Study: Study: NLVM Activities (2) 50

55 Algebra I: Part 1 Grade Levels Scientific Notation Students convert numbers in scientific form to standard form and vice versa. Students use scientific notation in multiplication and division. Relating decimals to scientific notation in positive and negative numbers. 35 Polynomial Students use the distributive property to multiply polynomials by using rules of Operations 3 multiplying variables with exponents. 36 Using the FOIL method for multiplying a binomial by a binomial. Relating the Polynomial distributive property to polynomial multiplication. Students multiply binomials Operations 4 by trinomials and arrange polynomials in descending order. 37 Equations & Students use polynomials to solve word equations. Review of guidelines for Polynomials solving word problems Factoring Out Monomials Difference of Squares 40 Trinomial Squares 41 Factoring Trinomials 42 Factoring by Grouping 43 Methods of Factoring 44 Solving by Factoring 45 Factoring Word Problems Guidelines for factoring polynomials by determining greatest common factors. Factoring monomials from polynomials. Review of guidelines for factoring polynomials. Importance of number of terms in factors. Determining square terms. Factoring binomials. Determining difference of squares. Students choose terms that are difference of squares. Students factor trinomials by factoring out monomials. Identification and traits of trinomial squares. Patterns in trinomial factoring. Students write trinomials in factored form. Factoring trinomials that are not square. Quadratic trinomials with positive or negative constants. Factoring quadratic trinomials with coefficient integers other than one. Rules for factoring polynomials with more than three terms by grouping. Students use distributive property to factor polynomials and check work. Students determine steps to take in factoring and solve problems by factoring polynomials in descending order. Identification and examples of quadratic equations. Solving quadratic equations by factoring. Zero product rule in factoring. Students solve word problems by writing and factoring quadratic equations. Students identify viable solutions in polynomial equations. Study: Essay: Logic Study: 51

56 Algebra I: Part 2 Grade Levels Solving by Graphing Determining if an ordered pair is a solution of a system of linear equations; finding solutions of linear systems of equations by graphing 2 Solving by Substitution Solving systems of equations by substituting for a variable 3 Addition & Solving systems of linear equations by using addition and subtraction; Subtraction eliminating variables by adding and subtracting 4 Multiplication & Solving linear systems of equations by first multiplying one or both equations Addition by a constant and then using the addition method 5 Using Two Variables Solving word problems related to real life situations using a variety of methods, writing let statements 6 Motion Problems Solving problems involving uniform motion; formula for motion 7 Coin & Digit Problems Solving linear systems of equations involving digits and coins 8 Rational Expressions 1 Review of definition for rational expressions; simplifying rational expressions 9 Using -1 as a Factor Factoring negative one from a polynomial in order to simplify rational expressions 10 Rational Expressions 2 Multiplying rational expressions to simplify products 11 Rational Expressions 3 Dividing two rational expressions and simplifying the answer 12 Rational Expressions 4 Addition and Subtraction of rational expressions with like denominators 13 Rational Expressions 5 14 Dividing Polynomials Identifying the least common multiple of expressions; adding and subtracting rational expressions with unlike denominators by converting rational expressions to equivalent rational expressions with common denominators Dividing one polynomial by another using long division; introduction to synthetic division 15 Complex Rationals Identifying complex rational expressions and simplifying them 16 Rational Equations 1 Identify and solve rational equations; skills necessary for solving rational equations Essay: Writing Equations 17 Rational Equations 2 Solving word problems by using rational equations 18 Mixture Problems Solving word problems with rational equations which relate to mixtures 19 Work Problems Solving word problems relating to work being done by two or more individuals working separately and together; using rational equations Essay: Writing Equations 52

57 Algebra I: Part 2 Grade Levels Ratio & Proportion Solving problems that require the use of ratios and proportions Investment Solving problems dealing with investments; solving for future worth of present 21 Problems amounts Graphing 22 Graphing inequalities on a number line Inequalities Solving inequalities using the addition method; solving inequalities by adding 23 Solving Inequalities and subtracting from both sides of the inequality Solving inequalities by using the multiplication method; multiplying and/or 24 Using Inequalities dividing both sides of the inequality by a constant 25 Problem Solving Using inequalities in word problems to solve problems Intersections & Review of terminology of sets, unions, and intersections, identifying sets 26 Unions finding union and intersection of sets Compound 27 Reading, writing, and solving compound inequalities Inequalities Equations/Absolute 28 Solving equations that contain absolute values Value 29 Linear Inequalities 1 Inequalities and the coordinate plane and solving for absolute value 30 Linear Inequalities 2 Graphing inequalities that contain two variables on the coordinate plane Graphing systems of linear inequalities on the coordinate plane; using shading 31 Linear Inequalities 3 Essay: Writing Equations to identify requirements of both inequalities Square Root & Finding square roots of perfect squares; determining if numbers are rational or 32 Irrationals irrational; using calculators to give approximations for irrational numbers Radical Expressions 33 Simplifying radical expressions. 1 Radical Expressions 34 Multiplying two or more radical expressions 2 Radical Expressions Dividing radical expressions by another radical expression; rationalizing the 35 3 denominator Radical Expressions 36 Adding and subtracting radical expressions The Distance 38 Finding the distance between any two points on the coordinate plane Formula The Pythagorean Introduction to the Pythagorean Theorem; solving triangles using the Theorem 1 Pythagorean Theorem 53

58 Algebra I: Part 2 Grade Levels The Pythagorean Using the Pythagorean Theorem to solve problems. Theorem 2 Essay: Logic 40 Radical Equations Solving equations that contain a radical term 41 Relations & Definition of relation; determining domain and range of relations; definition of Functions function; determining if a relation is a function; finding the value of functions NLVM Activities (2) 42 Function Graphs Graphing functions; recognizing the graph of function; learning to use function notation Study: 43 Quadratic Functions Graphing quadratic functions; using vertex and axis of symmetry or the T-table Study: 44 Direct Variation Giving equations of direct variation and solving problems involving direct variation 45 Inverse Variation Finding equations of inverse variation; solving problems involving inverse variations 46 Variations Problem solving involving joint and combined variation 47 Quadratic Equations Solving quadratic equations in three different forms involving exponents 48 Completing the Square Solving quadratic equations by completing the square 49 The Quadratic Defining the quadratic formula; using the quadratic formula to solve quadratic Formula 1 equations 50 The Discriminant Identifying and evaluating the discriminant of a quadratic equation; using the discriminant to determine the number of solutions to an equation 51 The Quadratic Formula 2 Solving word problems by utilizing the quadratic formula 54

59 Algebra I: A Function Approach Part 1 Grade Levels 9 10 GlobalCourseware Algebra I: A Function Approach Part 1 introduces students to: independent and dependent variables verbal and algebraic models to write algebraic expressions patterns as algebraic expressions the relationship between variables in a situation domain and range for an application problem positive and negative correlations in a real-world context graphs to represent a described situation functions from tables, graphs, descriptions, and mappings conversion between fractions, decimals, and percents direct variation relationship between diameter and circumference proportional reasoning to create tables, graphs, and equations to make predictions from data interpretation of constant of variation in real-world context proportions as linear functions slope as a rate of change from a graphical and physical point of view lines with no slope, zero slope, positive slope, and negative slope graphing an equation from slope-intercept form drawing graphs of lines in y = mx + b form writing the equation of a line 55

60 Algebra I: A Function Approach Part 1 Grade Levels 9 10 Algebra I: A Function Approach Part 1 is designed to provide students with varied approaches to solving real-world application problems. This course focuses on identifying functional relationships including determining dependence, identifying and analyzing rate of change, making predictions from data, and using data to generalize and develop equations to predict trends. The primary focus is on developing linear functions and solving linear equations, linear inequalities, and linear systems. Developing quadratic functions and solving quadratic equations are covered to a lesser extent and exponential functions are introduced. Algebra I: A Function Approach Part 1 is presented as a semester-long high school course. All lessons contain a study guide, a practice test, and a mastery test. Many lessons include graphing calculator activities designed to expand the student's understanding of functional relationships and data representation. A virtual, fully functional graphing calculator designed specifically for this course is included. A graphing calculator tutorial is also included. Enriched interactive features include animations, off-line investigations, drag and drop, layered sequence activities, and other processes that allow the student to respond to the material in a variety of ways. Each feature is designed to fully engage the student with the course content and provide the student varied methods to master the skills presented. 56

61 Algebra I: A Function Approach Part 1 Grade Levels 9 10 Study guides contain practice problems with immediate feedback and additional explanation of algebraic applications, allowing students to self-correct as they progress through the course. This course is enriched by National Library of Virtual Manipulatives (NLVM) applets. The content in this course addresses many objectives of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics. The Algebra I: A Function Approach Part 1 course is designed to help the student understand that functions represent a relationship of dependence, which can be represented in a variety of ways including tabular, graphical, and symbolic. The student will integrate the mechanics of algebra with real-life applications and gain an appreciation of the many ways algebra is used in everyday situations. The student will gain an understanding of how algebra can be used to express generalizations, learn to recognize and use the power of symbols to represent situations, and understand different algebraic methods used to solve problems. The student will learn to identify and solve proportional or non-proportional linear relationships in application situations. They will obtain an understanding for the meaning of the slope, intercepts, and zeros of the graphs of linear functions. They will learn to interpret and describe the effects of parameter changes for linear functions in real world and mathematical situations. The student will formulate systems of linear equations and inequalities from problem situations, use a variety of methods to solve the system, and analyze the system's solution in terms of the situation. The student will understand that graphs of quadratic functions are affected by the parameters of the function and interpret and describe the effects of changes to these parameters. They will learn different methods to solve quadratic equations and determine which method is appropriate for a given situation. The student will understand there are situations modeled by functions that are neither linear nor quadratic and model those situations. 57

62 Algebra I: A Function Approach Part 1 Grade Levels 9 10 The National Library of Virtual Manipulatives is a library of uniquely interactive, web-based virtual manipulatives or concept tutorials for mathematics instruction supported by the National Science Foundation. Each applet provides interactive math lessons and activities. The launch icon for NLVM objects is located on the study guide pages of the GC lesson. Software Web Browser Plug-ins Third Party Content NLVM NLVM, PDFs Recommendation Software Requirements Microsoft Internet Explorer 6.0 or higher or Safari 2.0 or higher Adobe Flash Player Adobe Shockwave Player Adobe Reader Java 1.41 or higher Link for Download (select Get ADOBE FLASH PLAYER) (select Get SHOCKWAVE PLAYER) (select Get ADOBE READER) normally installed with your GlobalCourseware client For further exploration, resource links to the Internet may be provided in some lessons. An Internet connection is required to utilize the EB components of the GlobalCourseware. 58

63 Algebra I: A Function Approach Part 1 Grade Levels 9 10 The lessons in Algebra I: A Function Approach Part 1 are divided into three units of study. These units are designed to guide the student through mastery of algebra concepts. Each lesson contains a primary skill and utilizes multiple skills from the group skill set. Units Algebra I: A Function Approach Part 1 Lessons Unit 1: Foundations for Functions Lessons: 1 15 Unit 2: Introduction to Linear Functions Lessons: Unit 3: Linear Functions Lessons: The following lessons contain Reflect and Apply worksheets: Independent and Dependent Variables, Domain and Range, Interpreting Graphs, Slope and Rate of Change, The Slope-Intercept Equation, and Linear Functions and Parameter Changes. These worksheets provide additional problems that can be completed independently or presented for whole-class instruction. A Solutions Manual for instructor use is provided as a separate document in.pdf form. This manual contains the questions and answers for all Reflect and Apply worksheet problems. 59

64 1 Algebra I: A Function Approach Part 1 Grade Levels 9 10 Unit 1: Foundations for Functions Study: Drag and Drop Making a Model with Identify independent and dependent variables; organize and represent Activities (2), Mathematics independent and dependent values in a graph or tabular model Layered Sequence 2 Mathematical Models 2 3 Identifying Patterns 1 4 Identifying Patterns 2 5 Independent and Dependent Variables 6 Domain and Range 7 Graphing a Story 8 Domain and Range from Equations 9 Correlations 1 10 Correlations 2 11 Correlations 3 Convert between verbal and algebraic models to write algebraic expressions; use the model to make predictions; find specific function values Express a pattern as an algebraic expression, use the algebraic expression to make predictions about the pattern Find a rate of change; find an algebraic rule for a pattern, determine the constant value in a pattern, use the rule to make predictions about the pattern Determine the relationship between variables in a situation; determine independent and dependent quantities on a graph, table, situation, or equation Identify a reasonable domain and range for an application problem; determine domain and range from graph or table; express domain and range in set-builder notation; identify discrete and continuous graphs Identify independent/dependent quantities for a situation; determine reasonable domain and range for a situation; develop a graph for a functional relationship Calculate a range for a given domain; calculate a domain for a given range Recognize positive correlations in a real-world context; develop a scatter plot; determine domain and range for a scatter plot Recognize negative correlations in a real-world context; recognize negative correlations from a graph; develop a scatter plot Recognize no correlation, positive correlation, and negative correlation in varied real-world contexts Study: Graphing Calculator, Drag and Drop Activity Study: Fill in Charts (2) Study: Drag and Drop Activity, Fill in Charts (2), Layered Sequence Study: Fill in Chart, Reflect and Apply Worksheet Study: Drag and Drop Activity, Layered Sequence, Reflect and Apply Worksheet Study: Drag and Drop Activity, Reflect and Apply Worksheet Study: Graphing Calculator Drag and Drop Activity, Fill in Chart Study: Graphing Calculator Study: Graphing Calculator Drag and Drop Activities (2) 60

65 Algebra I: A Function Approach Part 1 Grade Levels 9 10 Graphs of Real-World Create graphs to represent a described situation; read a graph 12 Situations representing a relationship between two variables, e.g., height vs. time Match or create real-world descriptions of graphs; determine reasonable Study: Layered Sequences 13 Interpreting Graphs domain and range for a situation; distinguish between continuous and (3) discrete graphs; identify graphs with a constant rate of change Develop the definition of function; identify a relation; identify a mapping Study: Animations (2), 14 Functions 1 Drag and Drop 15 Functions Proportions as Functions 1 Proportions as Functions 2 Proportions as Functions 3 Investigations with the Constant of Variation 20 Predictions from Data 21 Direct Variation 22 Summary of Direct Variation Functions Identify functions from tables, graphs, descriptions, and mappings; vertical line test Unit 2: Introduction to Linear Functions Convert between fractions, decimals, and percents; identify ways to express a ratio; collect and organize data to use in proportions; use data to determine functional relationships; solve problems using percents and proportions Function concepts in proportions; relate direct variation to constant of variation; solve problems involving proportional change Use simple proportions to solve one-step equations; determine constant of variation; convert proportions to direct variation functions Learn direct variation relationship between diameter and circumference; introduce slope as a constant of variation; determine the constant of variation for linear data; use proportional change to solve problems Use proportional reasoning to create tables, graphs, and equations to make predictions from data; create a scatter plot; identify a line of best fit Interpret constant of variation in real-world context; identify direct variation relationship from a table or graph; interpret meaning of axes intercepts in real-world contexts Summary of proportions as linear functions; represent data in graphs, tables, and scatter plots; calculate the constant of variation; generate a direct variation equation to solve a problem or make a prediction about data Activity Study: Animations (3), Layered Sequence Study: Fill in Charts (5) Study: Drag and Drop Activity, Fill in Chart Study: Drag and Drop Activity Study: Graphing Calculator Fill in Charts (4), Off-Line Investigation Study: Graphing Calculator Fill in Charts (3), Off-Line Investigation Study: Graphing Calculator Fill in Chart Study: Fill in Charts (4) 61

66 Algebra I: A Function Approach Part 1 Grade Levels 9 10 Unit 3: Linear Functions Introduction to Rate of Change Slope and Rate of Change Rate of Change Given 2 Points Rate of Change and Slope Summary 27 Graphing with Slope 1 28 Graphing with Slope 2 29 Constant of Variation 30 The Slope-Intercept Equation Introduce slope as a rate of change from a graphical and physical point of view; introduce formal definition of slope; determine slope of a line from graphs and tables Slope in additional real-world situations; slope as a rate of change between two quantities; interpret how changes in the rate affect changes in a graph Slope formula Slope in additional real-world situations; slope as rise/run; find slope from graph of a line; relate slope formula to graph Identify lines with no slope, zero slope, positive slope, and negative slope; use slope formula to calculate no slope, zero slope, positive and negative slope Slope as a parameter change of the equation y = mx; identify how the value of the slope affects the steepness of a line Real-world situations for y = mx; identify how changes in rate of change affect the possible outcome for a situation Introduce meaning of y-intercept in real-world contexts Study: Animation, Fill in Charts (3), Layered Sequences (4), NLVM Activities (2), Plot the Line Study: Drag and Drop Activity, Fill in Charts (2), Layered Sequences (2), Plot the Point, Reflect and Apply Worksheet Study: Graphing Calculator Study: Drag and Drop Activity, Layered Sequence Study: Graphing Calculator Drag and Drop Activities (3), Layered Sequences (2) Study: Graphing Calculator Fill in Charts (3) Study: Graphing Calculator Plot the Line, Reflect and Apply Worksheet 62

67 Algebra I: A Function Approach Part 1 Grade Levels 9 10 Linear Functions and Parameter Changes Applications of y = mx + b Parameter Changes in y = mx + b Linear Equations from Two Points The Point-Slope Equation 36 Graphs of y = mx + b 37 Summary of Linear Equations Slope and y-intercept as parameter changes; graph an equation from slope-intercept form; evaluate a function using function notation Advanced real-world contexts for linear functions; identify slope and y- intercept to develop a linear function for the real-world context; identify the domain and range for the real-world context Identify numerical and graphical parameter changes for slope and y- intercept; write an equation of a line in slope-intercept form from a graph Write an equation of a line in slope-intercept form when given two points on the line, a graph of the line, or data in an application problem Write the point-slope equation for a line given the slope and point on a line; use the equation to answer questions about the function Draw graphs of lines in y = mx + b form; name slope-intercept equation from a graph; change an equation from point-slope to slope-intercept form Review of concepts in lessons Study: Graphing Calculator Animations (4), Fill in Charts (2), Layered Sequences (3), Plot the Line, Reflect and Apply Worksheet Study: Animation, Drag and Drop Activities (2) Study: Graphing Calculator Animation, Drag and Drop Activities (2), Layered Sequences (3) Study: Graphing Calculator Study: Drag and Drop Activity Study: Layered Sequences (3),, Plot the Line Study: Fill in Charts (3), Layered Sequence 63

68 Algebra I: A Function Approach Part 2 Grade Levels 9 10 GlobalCourseware Algebra I: A Function Approach Part 2 introduces students to: the slope and y-intercept for linear functions in the context of real-life applications solving compound inequalities and graphing compound inequalities algebraically determining the number of solutions to a system determining the solution region for an inequality in standard form identifying the parameters of a quadratic function using the power rule of exponents to simplify exponential expression identifying the graph and the equation of an inverse variation function writing linear equations using two points. determining which linear equation form is most appropriate for a given situation writing and graphing compound inequalities using matrices to represent real-world data factoring polynomials by the greatest common factor and difference of squares solving equations using the quadratic formula simplifying expressions using negative exponents identifying exponential growth and decay analyzing data involving inverse variation 64

69 Algebra I: A Function Approach Part 2 Grade Levels 9 10 Algebra I: A Function Approach Part 2 is a continuation of Algebra I: A Function Approach Part 1. Part 2 provides students with more approaches to the real-world application of algebra. The continued focus of this course is on functional relationships and the various uses of a rate of change. This course moves on to writing and solving equations, linear models in two variables, linear inequalities, and systems of equations and inequalities. Polynomials, their applications, and the factoring of polynomials are examined. Quadratics, their roots, factors, zeros, and solutions are introduced, followed by the quadratic formula, laws of exponents, exponential functions, and functions of inverse variation. Algebra I: A Function Approach Part 2 is presented as a semester-long high school course. All lessons contain a study guide and practice and mastery test. Many lessons include graphing calculator activities designed to expand students' understanding of functional relationships and data representation. A virtual, fully functional graphing calculator designed specifically for this course is included. A graphing calculator tutorial is also included. Enriched interactive features include Reflect and Apply worksheets, drag and drop activities, layered sequence activities, and other processes that allow the student to respond to the material in a variety of ways. Each feature is designed to fully engage the student with the course content and provide varied methods to help the student master the skills presented. Study guides contain practice problems with immediate feedback and additional explanation of algebraic applications, allowing the students to self-correct their learning as the course progresses. 65

70 Algebra I: A Function Approach Part 2 Grade Levels 9 10 This course is enriched by National Library of Virtual Manipulatives (NLVM) applets. The content in this course addresses many objectives of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics. The Algebra I: A Function Approach Part 2 course is designed to help students understand that functions represent a relationship of dependence that can be represented in a variety of ways, including tabular, graphical, and symbolic. Students will integrate the mechanics of algebra with real-life applications and gain an appreciation of the many ways algebra is used in everyday situations. Students will write and solve equations for real-world situations. Students will learn to analyze the slope and y-intercept for linear functions in the context of real-life applications and to translate a real-life application problem into an equation. Students will develop a point-slope linear equation given a rate and a data point and identify which linear equation form is most appropriate for a given situation. They will solve and graph inequalities and compound inequalities. Students will develop a system of equations, generate a table of values for a linear system, and solve a system of equations by graphing. They will solve a system of equations by graphing from slope-intercept form and from standard form. Students will understand the process used when solving a system of equations by matrices. Students will identify the graph and parameters of a quadratic function. They will understand monomials and polynomials and how to arrange polynomials in ascending and descending order. Students will find the greatest common factor for a set of terms, factor a trinomial into two binomial factors, and solve a quadratic equation by using the quadratic formula. Students will use the product rule and the power rule of exponents to simplify exponential expressions. They will simplify expressions using the quotient rule for exponents and those with negative exponents. Students will identify an exponential growth or decay function and the graph of an inverse variation function. They will analyze data and situations involving inverse variations. 66

71 Algebra I: A Function Approach Part 2 Grade Levels 9 10 The National Library of Virtual Manipulatives is a library of uniquely interactive, web-based virtual manipulatives or concept tutorials for mathematics instruction supported by the National Science Foundation. Each applet provides interactive math lessons and activities. The launch icon for NLVM objects is located on the study guide pages of the GC lesson. Software Web Browser Third Party Content NLVM Recommendation Software Requirements Microsoft Internet Explorer 6.0 or higher or Safari 2.0 or higher Adobe Flash Player Adobe Shockwave Player Adobe Reader Java 1.41 or higher Link for Download (select Get ADOBE FLASH PLAYER) Plug-ins NLVM, PDFs (select Get SHOCKWAVE PLAYER) (select Get ADOBE READER) normally installed with your GlobalCourseware client For further exploration, resource links to the Internet may be provided in some lessons. An Internet connection is required to utilize the EB components of the GlobalCourseware. 67

72 Algebra I: A Function Approach Part 2 Grade Levels 9 10 The lessons in Algebra I: A Function Approach Part 2 are divided into four units of study. These units are designed to guide the student through mastery of algebra concepts. Each lesson contains a primary skill and utilizes multiple skills from the group skill set. Algebra I: A Function Approach Part 2 Units Lessons Unit 1: Linear Functions Lessons: 1 9 Unit 2: Linear Systems Lessons: Unit 3: Quadratic Functions Lessons: Unit 4: Introduction to Other Functions Lessons: The following lessons contain Reflect and Apply worksheets: Linear Inequalities Applications 1, Applications of Linear Systems 2, Solving Systems Using Matrices, Solving Inequalities by Graphing, and Solving Systems of Inequalities and Applications. These worksheets provide additional problems that can be completed independently or presented for whole-class instruction. A Solutions Manual for instructor use is provided as a separate document in.pdf form. This manual contains the questions and answers for all Reflect and Apply worksheet problems. 68

73 Algebra I: A Function Approach Part 2 Grade Levels 9 10 Unit 1: Linear Functions 1 Linear Models: Write a linear equation model given the slope and the y-intercept and use the Function Notation model to solve problems Study: Layered Sequence 2 Linear Models Write a linear equation model given the slope and the y-intercept and use the model to solve problems; express linear functions as equations Study: Layered Sequence 3 Writing Equations Write linear equations to solve word problems; solve multi-step equations Study: Layered Sequence 4 Real-World Models Write a slope-intercept equation for real-world models using two data points; Study: Layered Sequences Using 2 Points use a slope-intercept equation to answer questions about real-world models (3) 5 Real-World Models Generate a point-slope equation for real-world models using the slope and Using Point-Slope point; use the equation to answer questions about the model Study: Layered Sequence Choosing a Linear Model Solving Two-Step Equations Linear Inequalities Applications 1 Linear Inequalities Applications 2 Introduction to Linear Systems Solving Linear Systems Using a Table Solving Systems by Graphing 1 Solving Systems by Graphing 2 Writing Systems of Equations Determine an appropriate linear form (slope-intercept, point-slope, or standard form) to model a situation Write and solve 2-step equations for real-world situations; solve equations with variables on both sides of an equation Use linear inequalities to represent situations and solve problems; use compound inequalities to represent situations Use linear inequalities to represent situations and solve problems, graph linear inequalities; write and graph compound inequalities Unit 2: Linear Systems Write a system of linear equations for an applied situation; understand the meaning of the solution; interpret the system's data represented in a graph or table Write and solve a system using a table; identify a solution to a linear system from a table; generate a table of values for a linear system Solve systems by graphing; determine the number of possible solutions for a system of equations Solve systems by graphing; convert the equations in the system to y = or slope-intercept form Write a system to solve a problem; assign variables for a system of equations, write a system of equations Study: Drag and Drop Activity, Layered Sequences (4) Study: Graphing Calculator Drag and Drop Activity, NLVM Activity Study: Reflect and Apply Worksheet Study: Drag and Drop Activity Study: Graphing Calculator, Layered Sequences (4) Study: Graphing Calculator, Layered Sequences (3) Study: Graphing Calculator Study: Drag and Drop Activity, Fill-in Chart 69

74 Algebra I: A Function Approach Part 2 Grade Levels Applications of Linear Systems 1 Write a system to solve a problem; translate a problem with two unknowns into a system of equations Study: Graphing Calculator Applications of Linear Systems 2 Review: Solving Systems by Graphing Solving Systems by Substitution Solving Systems by Elimination Solving Systems Using Matrices Exploring Systems of Linear Inequalities Solving Inequalities by Graphing Solving Systems of Inequalities and Applications Exploring Quadratic Functions Write a system to solve a problem; translate an application problem with two unknowns into a system of equations Solve systems by graphing using slope-intercept form and x- and y-intercepts for standard form Write a system and solve by substitution; algebraically determine the number of solutions to a system Write a system and solve by elimination using addition and multiplication; use the elimination method to solve a system of equations Write a system in matrix notation; identify the matrix product that will produce the solution to a system if solved by matrices Write a system of linear inequalities and explore reasonable solutions; determine if an ordered pair is a solution of linear inequalities Graph a linear inequality on a coordinate plane; determine the solution region for an inequality in slope-intercept and standard form Write and solve linear systems of inequalities; write and solve a system of inequalities for an application problem Unit 3: Quadratic Functions Identify a parabola; analyze graphs of quadratic functions in real-life applications; identify the graph of a quadratic function Study: Layered Sequence, Reflect and Apply Worksheet Study: Graphing Calculator, Layered Sequences (5), Plot the Lines (3) Study: Drag and Drop Activity, Layered Sequences (5) Study: Layered Sequences (4), Fill-in Chart Study: Drag and Drop Activity, Layered Sequence Study: Drag and Drop Activity Study: Plot the Lines (3), Layered Sequences (2), Reflect and Apply Worksheet Study: Plot the Line, Reflect and Apply Worksheet Study: Graphing Calculator, Layered Sequence 70

75 Algebra I: A Function Approach Part 2 Grade Levels Graphs of Quadratic Functions Adding Polynomials Naming Polynomials Polynomials in Perimeter and Area Multiplying Polynomials Factoring Polynomials: GCF and Difference of Squares Factoring Trinomials Roots, Factors, Zeros, and Solutions of Quadratics Examine the effects of parameter changes for a, b, and c on the graph of a quadratic function Define monomial and polynomial; add and subtract polynomials; write polynomials in descending order Identify degree of a monomial and polynomial; arrange polynomials in descending or ascending order by specific variable Multiply polynomials; find perimeter and area of plane figures where length of a side is represented as a polynomial expression Multiply polynomials using the distributive property in a linear and box format Factor quadratic polynomials by the greatest common factor and by difference of squares Factor quadratic trinomials; factor quadratic trinomials to solve area problems Define and make connections between roots, factors, zeros, and solutions of quadratics; solve quadratic equations by factoring and graphing Study: Graphing Calculator Drag and Drop Activities (3), Layered Sequences (3) Study: Drag and Drop Activity, Layered Sequences (2) Study: Drag and Drop Activities (5), Layered Sequences (2) Study: Graphing Calculator Drag and Drop Activity, Fill-in Charts (2), Layered Sequences (6), Study: Drag and Drop Activities (2), Layered Sequences (5), Study: Drag and Drop Activity, Fill-in Chart, Layered Sequences (2) Study: Fill-in Charts (4), Layered Sequences (8) Study: Graphing Calculator Drag and Drop Activities (2), Layered Sequences (5) 71

76 Algebra I: A Function Approach Part 2 Grade Levels The Quadratic Formula Laws of Exponents 1 Laws of Exponents 2 Introduction to Exponential Functions Inverse Variation Functions Find solutions of a quadratic equation by the quadratic formula; identify, write and solve quadratic equations Unit 4: Introduction to Other Functions Use laws of exponents to find the product of monomial expressions; simplify monomial expressions raised to a power Use laws of exponents to simplify and combine monomial expressions; learn quotient rule, definition of negative exponent and definition of zero as an exponent Introduce exponential functions in practical applications; define, write, and recognize functions Introduce inverse variations functions in practical applications; identify equations for inverse variation; identify graph of inverse variation functions Study: Graphing Calculator Drag and Drop Activity, Layered Sequence Study: Layered Sequence Study: Graphing Calculator, Drag and Drop Activity, Layered Sequences (3) Study: Graphing Calculator 72

77 Algebra II: Part 1 and 2 Grade Levels GlobalCourseware Algebra II: Part 1 and 2 introduces students to the following concepts and functions and more: Algebra II: Part 1 rational numbers rules for combining and multiplying real numbers order of operations connecting words and numbers through expressions grids quadrants defining linear equations three-variable equations matrix multiplication polynomial types Algebra II: Part 2 review of square roots radicals solving and factoring identifying and evaluating the discriminant of a quadratic equation graphing parabola circle parts and formulas hyperbola graphing quadratic relations and inequalities 73

78 Algebra II: Part 1 Grade Levels Review of the real number system including rational numbers, integers, whole 1 Rules of Algebra numbers, counting numbers, and irrational numbers; rules for combining and multiplying real numbers and order of operations. 2 Review of properties of real numbers; associative property of multiplication and Real Number division, distributive property, substitution property; terms associated with real Properties NLVM Activities (2) number properties and operations, and review of inequalities. 3 Algebraic Connecting words and numbers through expressions, students practice writing Expressions and simplifying expressions. 4 Algebraic Equations Difference between expressions and equations, symbols used in writing equations, identifying unknowns. 5 Solving Equations Rules for solving equations, combining like terms, step-by-step examples of simplifying and solving equations. 6 Problem Solving 1 Developing equations to solve for unknowns, developing a plan to solve problems, and working related problems that develop from one original problem and checking answers for reasonability. 7 Rewriting Formulas Solving for variables with more than one unknown, converting Celsius to Fahrenheit and vice versa, isolating variables, multiplying by reciprocals. Study: 8 Solving & Graphing Definition and examples of ordered pairs, x and y axes, and the coordinate plane, students write equations from information on grids, positive and negative slope. 9 Properties of Rules and properties of inequalities, review of divisibility and multiplication Inequality properties. 10 Inequalities Relating inequalities to variables, intersection and union, examples of solving and graphing inequalities Absolute Value Equations Absolute Value Inequality 13 Problem Solving Relations & Functions Graph Linear Functions Review of absolute values, determining absolute values as related to equations, comparing absolute values as solutions to equations, checking answers for reasonableness. Examples of positive and negative numbers in inequalities, inequalities having no solution. Converting words in problems into symbols, converting answers to similar terms, various problem solving examples and strategies. Review of coordinate plane, quadrants, identifying origin, abscissa, ordinate, domain, range, and function, representing relations on graphs. Defining linear equations, rise, run, slope, writing linear equations in standard form, graphs as linear functions, constant functions, x and y intercepts. NLVM Activities (3) 74

79 Algebra II: Part 1 Grade Levels Slope of a Line Identification of positive, negative, zero, and undefined slopes, rise, run, relating slope to graphs. 17 Graph Linear Half planes and boundaries, writing equations and graphing in slope-intercept Inequalities form, double-checking linear equality graphs. 18 Parallel & Defining and graphing parallel and perpendicular lines on the coordinate plane, Perpendicular solving for parallel lines from points and slope, negative reciprocals as slopes. Study: NLVM Activities (2) 19 Difference of slope-intercept form and standard form for linear equations, Identify Linear determining when to use point-slope, slope-intercept, x-intercept or y-intercept Equations to graph linear equations, review of relations and functions, Identifying relationships between variables, checking answers for 20 Problem Solving 3 reasonableness, using equations to solve problems, using charts or other visual 21 Direct Variation 22 Graphing Equation Systems 23 Graphing Systems 24 Addition & Substitution 25 Solving Inequalities 26 Linear Programming 27 Three-Variable Equations 28 Data in Matrices tools as aids in solving problems. Definition of direct variations and examples of graphs of direct variations, proportionality constants, means as a product of extremes, using proportions to solve problems. Characteristics of intersecting, coinciding, and parallel planes and systems of equations for each, comparing equations that have same slope, different slope, and different intercepts, Solving equations by graphing intersecting, coinciding, and parallel lines in planes, equations with infinite solutions, equations that have no solution. Solving linear systems by addition and substitution, comparing solutions to problems worked using both methods, practicing using linear equations to solve everyday problems, hints for evaluating problems to find the best way to solve. Illustrating inequalities with graphs and using them to find solutions, the effect of absolute value on graphs, adding and subtracting numbers inside and outside absolute value symbols. Identifying variables, various constraints, and feasible regions in graphs, determining maximum and minimum values within feasible regions, the importance of linear programming as it relates to various careers, Using matrices, Cramer s rule, and/or addition to solve equations with three variables, graphing ordered triples, three-dimensional thinking in solving problems. Identifying and labeling data in matrices, performing operations using matrices, dimensions of matrices. Study: Study: NLVM Activities (2) Study: NLVM Activities (3) Essay: Logic Essay: Writing Equations 75

80 Algebra II: Part 1 Grade Levels Matrix Multiplication Checking the dimensions of matrices before multiplication, products of matrices, step-by-step examples of multiplying matrices. 30 Size & Reflections Changes in size or magnitude and scale factor, examples using matrices in everyday life situations, coordinates of reflected images, graphing reflections. Study: NLVM Activities (2) Definition of transformation, formula, point, and matrix transformations, 31 Transformation commutative, associative, and identity properties with matrix multiplication, closed sets. 32 Rotation Definition and examples of rotation, relating rotation to angles, negative and positive magnitude, algebraic formulas for rotation, finding the images of rotations. 33 Matrix Addition 34 Exponents 35 Polynomial Types 36 Polynomial Operations 37 Factoring Quadratics 38 Polynomial Equations 39 Negative Exponents 40 Scientific Notation Rational Operations 1 Rational Operations 2 Discussion of rules of matrix addition and subtraction of elements, addition properties in matrices, adding three matrices, multiplying elements in matrices, subtracting matrices, using matrices to solve problems in everyday life. How to utilize exponents as a shortcut method when multiplying variables and simplifying fractions. Definition and examples of monomials, binomials and polynomials, examples of like and unlike terms, determining the degree of polynomials. Graphing and factoring quadratic trinomials, linear terms, ascending and decreasing order of polynomials. Graphing and factoring quadratic trinomials, linear terms, ascending and decreasing order of polynomials. Solving problems using polynomials equations. 5-step approach to solving problems. Formulas and computations for solving problems. Review of exponents and their uses, zero as an exponent, negative exponents, simplifying problem using positive and negative exponents. Definition and examples of scientific notation, using negative and positive exponents. Converting expressions from decimal form to scientific notation, significant digits. Common denominators, finding higher variables, step by step factoring and solving, adding subtracting, rationals by simplifying. Products of rational expressions, factoring numerators, and denominators of polynomials solving problems using rational expressions to solve practical problems. Essay: Writing Equations 76

81 Algebra II: Part 1 Grade Levels Simplifying Rationals Formula for quotient of 2 polynomial, factoring polynomials review of ACF, quadratic trinomials, perfect squares and difference of squares. 44 Complex Rationals Definition and examples of complex rationals using shortcuts to simplify and solve complex rationals. 77

82 Algebra II: Part 2 Grade Levels Roots and Radicals Review of square roots and perfect squares and radicals; solving problems containing radicals; inverse of squaring numbers, irrational numbers, principal Essay: Draw and Label square roots 2 Real Number Multiplication and division of radicals, simplifying radical expressions, radical Properties 1 exponents, irrational numbers, product property of rationals 3 Real Number Addition and subtraction of radicals, like radicals and like terms, using the Properties 2 distributive property to solve problems 4 Rational Exponents Using addition, subtraction, multiplication, and division and combinations of operations to solve problems with rational exponents 5 Equations Identify radicals and solving equations with radicals 6 Imaginary Numbers Identification and problem solving using imaginary numbers 7 Complex Numbers 1 Solving addition and subtraction problems of complex pure and imaginary numbers 8 Complex Numbers 2 Multiplication and division of complex numbers, using the commutative property to solve problems, the FOIL method of factoring and solving 9 Quadratic Equations Solving quadratic equations by completing the square, solving and factoring, 1 completing the square to solve equations 10 Quadratic Equations Using the quadratic formula to solve problems, checking for reasonableness of 2 all solutions Essay: Logic 11 The Discriminant Identifying and evaluating the discriminant of a quadratic equation; using the discriminant to determine the number of solutions to an equation 12 Roots Equations involving the sum and products of roots and their connection to the coordinate plane 13 Quadratic Equations 3 Rewriting equations in quadratic form to solve 14 Problem Solving Solving problems using quadratic equations 15 Quadratic Relations Identifying and illustrating distance and midpoint, solving problems with number lines, absolute value, the Pythagorean Theorem 16 Parabolas Characteristics and definition of parabola 17 Graphing Parabola Plotting parabola on the coordinate plane 78

83 Algebra II: Part 2 Grade Levels Circles Circle characteristics; solving problems involving identification of circle parts and formulas 19 Ellipses Characteristics of ellipses; plotting ellipses on the coordinate plane, identification and illustration of fixed points 20 Hyperbola Characteristics of hyperbola, visual illustrations of hyperbola, intersection of planes and cones, identifying the difference between ellipses and hyperbola 21 Graphing Relations Identifying relations; identifying functions; graphing quadratic relations and inequalities 22 Graphing Intersections of graphs of quadratic relations, graphing conic inequalities and Inequalities intersections 23 Variations Inverse and joint variations of linear functions; combined variation 24 Exponential Functions 25 Inverse Functions Logarithmic Functions Exponential Equations 28 Arithmetic Sequence 29 Arithmetic Series 30 Geometric Sequence 31 Geometric Series 32 Infinite Geometric Series 33 Binomial Theorem Different strategies for simplifying and solving equations and expressions with rational positive and negative exponents Ordered pairs, coordinates, the domain, identification and illustrations of the inverse function Identification and explanation of logarithmic functions, the exponential/logarithmic scale, definition and examples of logarithms Definition and examples of exponential equations, solving problems using the graphing calculator, properties of logarithms, significant digits, compound interest problems Definition and examples of arithmetic sequences, difference of numbers, finite sequences of numbers Definition and examples of arithmetic series in real world situations, identification of sigma, solving problems using arithmetic series Definition and examples of geometric sequence, geometric progression, terms of geometric sequences Definition and examples of geometric series, formulas for solving problems with geometric series Examples and definition of common ratios, formulas, convergent geometric series, solving problems with geometric series Identification of patterns and integral powers, finite series, coefficients, variable powers, factorials, solving factorial problems NLVM Activities (2) Essay: Logic Essay: Writing Equations Essay: Writing Equations 79

84 Geometry Grade Levels 9 11 GlobalCourseware Geometry introduces students to the following concepts and functions and more: introduces basic geometric terms angles perpendicular and parallel lines rays and transversals measuring line segments lines segments sides and vertices of angles acute, obtuse, and right angles parallel and skew lines acute, obtuse, and right triangles calculating perimeter volume and area of trapezoids polygons proportional ratios pyramids cones spheres chords circumference tangents angle measurement 80

85 1 Geometry Grade Levels 9 11 Introduces basic geometric terms commonly used throughout the course. Foundation of Postulates, theorems, hypotheses, and other definitions. Review of geometric Geometry problems. 2 Geometric Concepts Geometric Measurement Points, Lines, and Planes Segments, Rays, and Angles 6 Angles 7 Transversals 8 Parallelism 9 Triangles 10 Congruent Triangles 11 Triangles Inside and Out A review of geometric concepts including all types of angles, intersecting, perpendicular and parallel lines, rays and transversals. The use of a protractor in the measurement of angles and circles is discussed. A review of the measurement of line segments utilizing a pop-up ruler that can be displayed in inches or centimeters. Definition of points, lines, and planes, collinear points, points and lines as intersections. Number lines and corresponding points, identification of segments, congruency and segments, averaging endpoints, definition and examples of rays, bisectors. Identification of sides and vertices of angles, interior and exterior angle points, adjacent angles, acute, obtuse, and right angles, complementary and supplementary angles, linear pairs, vertical angles. Parallel and skew lines, parallel segments and planes, identification and examples of transversals, corresponding angles and transversals, alternate interior and exterior angles. Rules for congruency in corresponding angles, alternate exterior and interior angles, transversals and parallelism. Identification and examples of acute, obtuse, and right triangles, scalene, isosceles, equilateral and equiangular triangles, determining angles in triangles. Definition and examples of congruent triangles, comparing lines and angles in triangles, order in labeling angles and triangles, congruence statements, sideside-side, side-angle-side, angle-side-angle, angle-angle-side congruent triangles. Identification and examples of vertices, base angles, and congruent sides in isosceles triangles, comparing isosceles and equilateral triangles, exterior angles and remote interior angles in triangles, comparing angles and drawing conclusions about measurement. / Written Response / Written Response NLVM Activities (2) 81

86 Geometry Grade Levels 9 11 Parts of right triangles, legs, hypotenuse. Focus on degree right 12 Right Triangles 1 / triangles. Using the Pythagorean Theorem to solve geometric problems. Written Response 13 Right Triangles 2 14 Quadrilaterals Common right triangles, degree right triangles, patterns in calculating the hypotenuse of a right triangle. An examination of the properties of quadrilaterals including the concept of opposite, consecutive and adjacent sides, angles and vertices. 15 Parallelograms Definition and examples of quadrilaterals and parallelograms. 16 Special Parallelograms 17 Trapezoids 18 Areas of Polygons 19 Conditional Statements 20 Similar Polygons 21 More About Polygons 22 Area Revisited Rectangles, rhombuses, squares, rectangle diagonals, rhombus diagonals, trapezoids, isosceles trapezoids, base angles and diagonals in trapezoids, finding parallels in triangles, finding medians in trapezoids. Examples of various trapezoids and rhombuses; angles and sides; calculating perimeters, examples of parallelism in trapezoids. Formulas for measuring the perimeter and volume and area of trapezoids, measuring surface area. An examination of statements that can be derived from the manipulation of conditional statements. Topics include converse, inverse, contrapositive and biconditional statements. Testing for congruency of quadrilaterals, similarity in polygons, proportional ratios, determining scale factors, proportionality, perimeters of polygons. Definition and examples of regular and irregular polygons. Identification of vertices and sides. Students identify polygons. Area of squares and rectangles, parallelograms and triangles, trapezoids, and regular polygons. 23 Solids 1 Prisms, pyramids and determining the areas and volumes 24 Solids 2 Cylinders, cones, spheres; areas and volumes of similar solids / Written Response Study: / Written Response Study: Essay: Logic/Written Response / Written Response Study: NLVM Activities (2) / Written Response 82

87 Geometry Grade Levels Circles Arcs, chords, and central angles; circumference and area 26 Circles & Angles Inscribed and interior angles, tangents, and angle measurement / Written Response 27 Circles, Arcs, & Sectors Arc lengths and sector area 28 The focus of this lesson is the basic principles of trigonometry and its relation Trigonometric to geometry, definition and examples of sine, cosine, tangent, and other Functions trigonometric terms. 83

88 Trigonometry Grade Levels GlobalCourseware Trigonometry introduces students to the following concepts, skills, and more: angles and angle terminology reference angles definition of sine, cosine, and tangent definition and value of secant, cosecant, and cotangent calculating sides of right triangles using trig to solve real world problems the Law of Sines and Cosines symmetry identities verifying trigonometric identities sum and difference for sine cosine and tangent using cofunction identities graphing trig functions principal values arclength area of circular sectors simple harmonic motion frequency 84

89 Trigonometry Grade Levels Angles Angles; angle terminology; radians; reference angles 2 Sine, Cosine, and The unit circle; finding values from endpoint, definition of sine, cosine, and Tangent tangent 3 Values of Sin, Cos, Values of sine, cosine, and tangent of various angles; using a calculator to find and Tan values 4 Reciprocal Functions Definition and value of secant, cosecant, and cotangent 5 The Pythagorean The Pythagorean Theorem; calculating sides of right triangles / Theorem Written Response 6 Review 1 7 Inverse Functions Definition and value of inverse trig functions 8 Solving Right Triangles Using trig functions and the Pythagorean Theorem to solve right triangles 9 Trigonometry Applications Using trig to solve real world problems 10 Law of Sines 1 Definition of law of sines and applications 11 Law of Sines 2 Further application of the Law of Sines; determining the number of triangles and solving triangles 12 Law of Cosines Definition of law of cosines and solving triangles 13 Solving Triangles Using trig functions and the Laws of Sines and Cosines to solve triangles 14 Triangle Applications Solving triangles in word problems 15 Areas of Triangles Formulas for areas of triangles 16 Review 2 17 Trigonometric Definition of identity; reciprocal identities; quotient identities; Pythagorean Identities identities; symmetry identities 18 Verifying Trig Identities Verifying trigonometric identities and manipulating identities for verification 19 Sum Difference Identities Sum and difference for sine, cosine, and tangent; using cofunction identities 20 Graphing Trig Graphs of sine, cosine, tangent and reciprocal functions; finding values using Functions 1 graphs 21 Graphing Trig Analyzing amplitude, period, and phase shift; graphing functions and Functions 2 compound functions 22 Graphing Trig Functions 3 Graphs of inverse functions; finding values using graphs 85

90 Trigonometry Grade Levels Review 3 24 Double- and Half- Angles Double-angle and half-angle identities 25 Solving Trig Solving equations involving trig functions; principal values; solving for principal Equations and all values 26 Central Angle Applications of central angles; arclength; linear and angular velocity; area of Application circular sectors 27 Simple Harmonic Writing equations for simple harmonic motion; using equations for information; Motion frequency 28 Review 4 29 Comprehensive Exam Comprehensive exam of course content 86

91 Calculus I and II Grade Level 12 GlobalCourseware Calculus I and II introduces students to the following concepts and functions and more: Calculus I calculating x-values and corresponding values continuous functions asymptotes graphing tangents secants, and cosecants sign graphs antiderivatives with negative exponents Calculus II notations of integrals the fundamental theorem of calculus indefinite integrals and antiderivatives natural logarithms arclength surface area and work hydrostatic force inverse functions including natural exponent functions exponential growth and decay inverse trigonometric functions 87

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