MAISA CCSS Mathematics Curriculum Grades 6-8

Transcription

1 A Correlation of Grades To the MAISA CCSS Mathematics Curriculum Grades 6-8

2 A Correlation of envisionmath2.0 Grades 6-8, 2017 Introduction The most successful elementary program is now available for middle school. envisionmath2.0 brings the power of engagement, effectiveness, and efficiency to Grades 6-8. Invite students to explore, collaborate, and visualize math. Welcome to envisionmath2.0 Grades 6-8! It s BIG for middle school, because it gets the small things right. Course organization focuses on Common Core Clusters, giving students time to dive deeper and make connections. Coherence and rigor promote higher achievement. Students experience an environment full of interactive learning aids with personalized practice and feedback. Built-in RtI ensures support for all students. Actionable data helps you prepare learners for Next-Generation Assessments. Flexibility allows you to make the program your own. Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved.

3 A Correlation of envisionmath2.0 Grades 6-8, 2017 Table of Contents Overview Overview Grade 8 Overview Grade Copyright 2016 Pearson Education, Inc. or its affiliate(s). All rights reserved.

4 Overview Unit 1 Using Factors and Multiples Unit 2 Rate and Ratio Reasoning Lessons Lesson 3-1 Understand and Represent Exponents Lesson 3-2 Find Greatest Common Factor and Least Common Multiple Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane Lesson 4-8 Understand Dependent and Independent Variables Lesson 4-9 Use Patterns to Write and Solve Equations Lesson 4-10 Relate Tables, Graphs, and Equations Lesson 5-1 Understand Ratios Lesson 5-2 Generate Equivalent Ratios Lesson 5-3 Compare Ratios Lesson 5-4 Represent and Graph Ratios Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units Lesson 6-1 Understand Percent Lesson 6-2 Relate Fractions, Decimals, and Percents Lesson 6-3 Represent Percents Greater Than 100 or Less Than 1 Lesson 6-4 Estimate to Find Percent Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent 1

5 Overview Unit 3 Using Fraction Operations Lessons Lesson 1-3 Multiply Fractions Lesson 1-4 Understand Division with Fractions Lesson 1-5 Divide Fractions by Fractions Lesson 1-6 Divide Mixed Numbers Lesson 1-7 Solve Problems with Rational Numbers Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 4-1 Understand Equations and Solutions Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Lesson 4-6 Understand and Write Inequalities Lesson 4-7 Solve Inequalities Lesson 6-2 Relate Fractions, Decimals, and Percents Lesson 7-8 Find Volume with Fractional Edge Lengths Unit 4 Extending Representations of Rational Number Lesson 1-7 Solve Problems with Rational Numbers Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane 2

6 Overview Unit 5 Univariate Data Unit 6 Computing with Decimals and Percents Lessons Lesson 8-1 Recognize Statistical Questions Lesson 8-2 Summarize Data Using Mean, Median, and Mode Lesson 8-3 Display Data in Box Plots Lesson 8-4 Display Data in Frequency Tables and Histograms Lesson 8-5 Summarize Data Using Measures of Variability Lesson 8-6 Choose Appropriate Statistical Measures Lesson 8-7 Summarize and Compare Data Distributions Lesson 1-1 Fluently Add, Subtract, and Multiply Decimals Lesson 1-2 Fluently Divide Whole Numbers and Decimals Lesson 1-3 Multiply Fractions Lesson 1-4 Understand Division with Fractions Lesson 1-5 Divide Fractions by Fractions Lesson 1-6 Divide Mixed Numbers Lesson 1-7 Solve Problems with Rational Numbers Lesson 5-1 Understand Ratios Lesson 5-2 Generate Equivalent Ratios Lesson 5-3 Compare Ratios Lesson 5-4 Represent and Graph Ratios Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units Lesson 6-1 Understand Percent Lesson 6-2 Relate Fractions, Decimals, and Percents Lesson 6-3 Represent Percents Greater Than 100 or Less Than 1 Lesson 6-4 Estimate to Find Percent Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent 3

7 Overview Unit 7 Introduction to Algebraic Thinking Lessons Lesson 3-1 Understand and Represent Exponents Lesson 3-2 Find Greatest Common Factor and Least Common Multiple Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 4-1 Understand Equations and Solutions Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Lesson 4-6 Understand and Write Inequalities Lesson 4-7 Solve Inequalities Lesson 4-8 Understand Dependent and Independent Variables Lesson 4-9 Use Patterns to Write and Solve Equations Lesson 4-10 Relate Tables, Graphs, and Equations Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons Lesson 7-5 Represent Solid Figures Using Nets Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Lesson 7-8 Find Volume with Fractional Edge Lengths Unit 8 Two and Three Dimensional Measurement Lesson 2-6 Represent Polygons on the Coordinate Plane Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 4-1 Understand Equations and Solutions 4

8 Overview (Continued) Unit 8 Two and Three Dimensional Measurement Lessons Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Lesson 4-6 Understand and Write Inequalities Lesson 4-7 Solve Inequalities Lesson 4-8 Understand Dependent and Independent Variables Lesson 4-9 Use Patterns to Write and Solve Equations Lesson 4-10 Relate Tables, Graphs, and Equations Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons Lesson 7-5 Represent Solid Figures Using Nets Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Lesson 7-8 Find Volume with Fractional Edge Lengths 5

9 Unit 1 - Using Factors and Multiples Content Expectations The Number System 6. NS.B. Compute fluently with multi-digit numbers and find common factors and multiples. 6. NS.B.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2). Lesson 3-2 Find Greatest Common Factor and Least Common Multiple Expressions & Equations 6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.A.1. Write and evaluate numerical expressions involving whole-number exponents. Lesson 3-1 Understand and Represent Exponents Lesson 3-3 Write and Evaluate Numerical Expressions 6.EE.A.2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Lesson 3-1 Understand and Represent Exponents Lesson 3-2 Find Greatest Common Factor and Least Common Multiple Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Unit Level Standards 6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.A.2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations) Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions 6

10 Unit 2 - Rate and Ratio Reasoning Content Expectations Ratios & Proportional Relationships 6.RP.A. Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.A.1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak. For every vote candidate A received, candidate C received nearly three votes. Lesson 5-1 Understand Ratios Lesson 5-2 Generate Equivalent Ratios Lesson 5-3 Compare Ratios Lesson 5-4 Represent and Graph Ratios Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units 6.RP.A.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship. For example, This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar. We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger. 6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-2 Generate Equivalent Ratios Lesson 5-3 Compare Ratios Lesson 5-4 Represent and Graph Ratios Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units Lesson 6-1 Understand Percent Lesson 6-2 Relate Fractions, Decimals, and Percents 7

11 (Continued) 6.RP.A.3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Lesson 6-3 Represent Percents Greater Than 100 or Less Than 1 Lesson 6-4 Estimate to Find Percent Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent 6.RP.A.3a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. Lesson 5-2 Generate Equivalent Ratios Lesson 5-3 Compare Ratios Lesson 5-4 Represent and Graph Ratios Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates 6.RP.A.3b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems 6.RP.A.3c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Lesson 6-1 Understand Percent Lesson 6-2 Relate Fractions, Decimals, and Percents Lesson 6-3 Represent Percents Greater Than 100 or Less Than 1 Lesson 6-4 Estimate to Find Percent Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent 6.RP.A.3d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units 8

12 Unit Level Standards The Number System 6.NS.C. Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.C.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.C.6c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane Expressions & Equations 6.EE.C. Represent and analyze quantitative relationships between dependent and independent variables 6.EE.C.9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Lesson 4-8 Understand Dependent and Independent Variables Lesson 4-9 Use Patterns to Write and Solve Equations Lesson 4-10 Relate Tables, Graphs, and Equations 9

13 Unit 3 - Using Fraction Operations Content Expectations Number & Operations Fractions 5.NF.A. Use equivalent fractions as a strategy to add and subtract fractions. Grade 5 Standard 5.NF.A.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2. For related content, please see: Lesson 1-1 Fluently Add, Subtract, and Multiply Decimals Lesson 1-3 Multiply Fractions Lesson 1-4 Understand Division with Fractions Lesson 1-5 Divide Fractions by Fractions Lesson 1-6 Divide Mixed Numbers Lesson 1-7 Solve Problems with Rational Numbers Grade 5 Standard 5.NF.B. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Lesson 1-3 Multiply Fractions Lesson 1-4 Understand Division with Fractions Lesson 1-5 Divide Fractions by Fractions Lesson 1-6 Divide Mixed Numbers Lesson 1-7 Solve Problems with Rational Numbers Grade 5 Standard 5.NF.B.6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Lesson 1-3 Multiply Fractions Lesson 1-7 Solve Problems with Rational Numbers Grade 5 Standard 5.NF.B.7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Lesson 1-4 Understand Division with Fractions Lesson 1-5 Divide Fractions by Fractions Lesson 1-6 Divide Mixed Numbers Lesson 1-7 Solve Problems with Rational Numbers 10

14 The Number System 6.NS.A. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 6.NS.A.1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Lesson 1-4 Understand Division with Fractions Lesson 1-5 Divide Fractions by Fractions Lesson 1-6 Divide Mixed Numbers Lesson 1-7 Solve Problems with Rational Numbers Expressions & Equations 6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers. Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions 6.EE.A.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions 11

15 6.EE.B. Reason about and solve one-variable equations and inequalities. 6.EE.B.6. Use variables to represent numbers Lesson 4-1 Understand Equations and and write expressions when solving a realworld or mathematical problem; understand Lesson 4-2 Apply Properties of Equality Solutions that a variable can represent an unknown Lesson 4-3 Write and Solve Addition and number, or, depending on the purpose at Subtraction Equations hand, any number in a specified set. Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Lesson 4-6 Understand and Write Inequalities Lesson 4-7 Solve Inequalities 6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Unit Level Standards ** Indicates items in 5th grade CCSS-M that are further developed through this unit. Due to recent changes in the grade levels of the standards, as well as the complex nature of developing students understanding of fraction operations, it is advised that 6th grade teachers assess students current understanding of fraction operations and determine whether the listed 5th grade standards need further development. Unit 4 - Extending Representations of Rational Number Content Expectations The Number System 6.NS.C. Apply and extend previous understandings of numbers to the system of rational numbers. 6.NS.C.5. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line 12

16 6.NS.C.6. Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. 6.NS.C.6a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., ( 3) = 3, and that 0 is its own opposite. 6.NS.C.6b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane 6.NS.C.6c. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane 6.NS.C.7. Understand ordering and absolute value of rational numbers. Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers 13

17 6.NS.C.7a. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret 3 > 7 as a statement that 3 is located to the right of 7 on a number line oriented from left to right. Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers 6.NS.C.7b. Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write 3 C > 7 C to express the fact that 3 C is warmer than 7 C. Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers 6.NS.C.7c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of 30 dollars, write 30 = 30 to describe the size of the debt in dollars. Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers 6.NS.C.7d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than 30 dollars represents a debt greater than 30 dollars. Lesson 2-1 Understand Integers Lesson 2-2 Represent Rational Numbers on the Number Line Lesson 2-3 Absolute Values of Rational Numbers 6.NS.C.8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Lesson 2-4 Represent Rational Numbers on the Coordinate Plane Lesson 2-5 Find Distances on the Coordinate Plane Lesson 2-6 Represent Polygons on the Coordinate Plane Unit Level Standards Not Applicable 14

18 Unit 5 - Univariate Data Content Expectations Statistics & Probability 6.SP.A. Develop understanding of statistical variability. 6.SP.A.1. Recognize a statistical question as Lesson 8-1 Recognize Statistical Questions one that anticipates variability in the data related to the question and accounts for it in the answers. For example, How old am I? is not a statistical question, but How old are the students in my school? is a statistical question because one anticipates variability in students ages. 6.SP.A.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.A.3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6.SP.B. Summarize and describe distributions. 6.SP.B.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Lesson 8-1 Recognize Statistical Questions Lesson 8-2 Summarize Data Using Mean, Median, and Mode Lesson 8-5 Summarize Data Using Measures of Variability Lesson 8-6 Choose Appropriate Statistical Measures Lesson 8-7 Summarize and Compare Data Distributions Lesson 8-1 Recognize Statistical Questions Lesson 8-2 Summarize Data Using Mean, Median, and Mode Lesson 8-6 Choose Appropriate Statistical Measures Lesson 8-7 Summarize and Compare Data Distributions Lesson 8-3 Display Data in Box Plots Lesson 8-4 Display Data in Frequency Tables and Histograms 6.SP.B.5. Summarize numerical data sets in relation to their context, such as by: Lesson 8-2 Summarize Data Using Mean, Median, and Mode Lesson 8-3 Display Data in Box Plots Lesson 8-4 Display Data in Frequency Tables and Histograms Lesson 8-5 Summarize Data Using Measures of Variability Lesson 8-6 Choose Appropriate Statistical Measures Lesson 8-7 Summarize and Compare Data Distributions 15

19 6.SP.B.5a. Reporting the number of observations. Lesson 8-3 Display Data in Box Plots Lesson 8-4 Display Data in Frequency Tables and Histograms 6.SP.B.5b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. Lesson 8-3 Display Data in Box Plots Lesson 8-4 Display Data in Frequency Tables and Histograms 6.SP.B.5c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Lesson 8-2 Summarize Data Using Mean, Median, and Mode Lesson 8-3 Display Data in Box Plots Lesson 8-4 Display Data in Frequency Tables and Histograms Lesson 8-5 Summarize Data Using Measures of Variability Lesson 8-6 Choose Appropriate Statistical Measures Lesson 8-7 Summarize and Compare Data Distributions 6.SP.B.5d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Lesson 8-5 Summarize Data Using Measures of Variability Lesson 8-6 Choose Appropriate Statistical Measures Lesson 8-7 Summarize and Compare Data Distributions Unit Level Standards Not Applicable Unit 6 - Computing with Decimals and Percents Content Expectations Number & Operations in Base Ten 5.NBT.A. Understand the place value system. Grade 5 Standard 5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Lesson 1-1 Fluently Add, Subtract, and Multiply Decimals Lesson 1-2 Fluently Divide Whole Numbers and Decimals This standard is also met in envisionmath Grade 8. Please see: Lesson 1-6 Understand Integer Exponents Lesson 1-7 Use Properties of Integer Exponents 16

20 (Continued) Grade 5 Standard 5.NBT.A.2. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Lesson 1-8 Understand Scientific Notation Lesson 1-9 Use Scientific Notation to Estimate Quantities Lesson 1-10 Perform Operations with Numbers in Scientific Notation 5.NBT.B. Perform operations with multi-digit whole numbers and with decimals to hundredths. Grade 5 5.NBT.B.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Lesson 1-1 Fluently Add, Subtract, and Multiply Decimals Lesson 1-2 Fluently Divide Whole Numbers and Decimals Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent Ratios & Proportional Relationships 6.RP.A. Understand ratio concepts and use ratio reasoning to solve problems. 6.RP.A.3c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. Lesson 6-1 Understand Percent Lesson 6-2 Relate Fractions, Decimals, and Percents Lesson 6-3 Represent Percents Greater Than 100 or Less Than 1 Lesson 6-4 Estimate to Find Percent Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent The Number System 6. NS.B. Compute fluently with multi-digit numbers and find common factors and multiples. 6. NS.B.2. Fluently divide multi-digit numbers using the standard algorithm. Lesson 1-2 Fluently Divide Whole Numbers and Decimals 6. NS.B.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Lesson 1-1 Fluently Add, Subtract, and Multiply Decimals Lesson 1-2 Fluently Divide Whole Numbers and Decimals Lesson 1-7 Solve Problems with Rational Numbers 17

21 Ratios & Proportional Relationships 7.RP.A. Analyze proportional relationships and use them to solve real-world and mathematical problems. Standard 7.RP.A.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Lesson 5-1 Understand Ratios Lesson 5-2 Generate Equivalent Ratios Lesson 5-3 Compare Ratios Lesson 5-4 Represent and Graph Ratios Lesson 5-5 Understand Rates and Unit Rates Lesson 5-6 Compare Unit Rates Lesson 5-7 Solve Unit Rate Problems Lesson 5-8 Ratio Reasoning: Convert Customary Units Lesson 5-9 Ratio Reasoning: Convert Metric Units Lesson 5-10 Relate Customary and Metric Units Lesson 6-1 Understand Percent Lesson 6-2 Relate Fractions, Decimals, and Percents Lesson 6-3 Represent Percents Greater Than 100 or Less Than 1 Lesson 6-4 Estimate to Find Percent Lesson 6-5 Find the Percent of a Number Lesson 6-6 Find the Whole Given a Part and the Percent The Number System 7.NS.A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Standard 7.NS.A.2d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. Lesson 6-2 Relate Fractions, Decimals, and Percents Unit Level Standards Not Applicable 18

22 Unit 7 - Introduction to Algebraic Thinking Content Expectations Expressions & Equations 6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.A.1. Write and evaluate numerical expressions involving whole-number exponents. 6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers. Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions 6.EE.A.2a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation Subtract y from 5 as 5 y. 6.EE.A.2b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. 6.EE.A.2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2. Lesson 3-4 Write Algebraic Expressions Lesson 3-1 Understand and Represent Exponents Lesson 3-2 Find Greatest Common Factor and Least Common Multiple Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Lesson 7-8 Find Volume with Fractional Edge Lengths 19

23 6.EE.A.3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 6.EE.A.4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Reason about and solve onevariable equations and inequalities. Lesson 3-3 Write and Evaluate Numerical Expressions Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions 6.EE.B. Reason about and solve one-variable equations and inequalities. 6.EE.B.5. Understand solving an equation or Lesson 4-1 Understand Equations and inequality as a process of answering a Solutions question: which values from a specified set, if Lesson 4-6 Understand and Write any, make the equation or inequality true? Inequalities Use substitution to determine whether a Lesson 4-7 Solve Inequalities given number in a specified set makes an equation or inequality true. 6.EE.B.6. Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions Lesson 4-1 Understand Equations and Solutions Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Lesson 4-6 Understand and Write Inequalities Lesson 4-7 Solve Inequalities 20

24 (Continued) 6.EE.B.6. Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Lesson 4-8 Understand Dependent and Independent Variables Lesson 4-9 Use Patterns to Write and Solve Equations Lesson 4-10 Relate Tables, Graphs, and Equations Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons Lesson 7-5 Represent Solid Figures Using Nets Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Lesson 7-8 Find Volume with Fractional Edge Lengths Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers 6.EE.C. Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.C.9. Use variables to represent two Lesson 4-8 Understand Dependent and quantities in a real-world problem that Independent Variables change in relationship to one another; write Lesson 4-9 Use Patterns to Write and Solve an equation to express one quantity, thought Equations of as the dependent variable, in terms of the Lesson 4-10 Relate Tables, Graphs, and other quantity, thought of as the independent Equations variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. 21

25 Unit Level Standards Not Applicable Unit 8 - Two and Three Dimensional Measurement Content Expectations Expressions & Equations 6.EE.A. Apply and extend previous understandings of arithmetic to algebraic expressions. 6.EE.A.2. Write, read, and evaluate expressions in which letters stand for numbers. Lesson 3-4 Write Algebraic Expressions Lesson 3-5 Evaluate Algebraic Expressions Lesson 3-6 Generate Equivalent Expressions Lesson 3-7 Simplify Algebraic Expressions 6.EE.A.2c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2. Lesson 3-5 Evaluate Algebraic Expressions Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons Lesson 7-5 Represent Solid Figures Using Nets Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Lesson 7-8 Find Volume with Fractional Edge Lengths 6.EE.B. Reason about and solve one-variable equations and inequalities. 6.EE.B.6. Use variables to represent numbers Lesson 3-4 Write Algebraic Expressions and write expressions when solving a realworld or mathematical problem; understand Lesson 3-6 Generate Equivalent Expressions Lesson 3-5 Evaluate Algebraic Expressions that a variable can represent an unknown Lesson 3-7 Simplify Algebraic Expressions number, or, depending on the purpose at Lesson 4-1 Understand Equations and hand, any number in a specified set. Solutions Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers Lesson 4-6 Understand and Write Inequalities Lesson 4-7 Solve Inequalities 22

26 (Continued) 6.EE.B.6. Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Lesson 4-8 Understand Dependent and Independent Variables Lesson 4-9 Use Patterns to Write and Solve Equations Lesson 4-10 Relate Tables, Graphs, and Equations Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons Lesson 7-5 Represent Solid Figures Using Nets Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Lesson 7-8 Find Volume with Fractional Edge Lengths 6.EE.B.7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. Lesson 4-2 Apply Properties of Equality Lesson 4-3 Write and Solve Addition and Subtraction Equations Lesson 4-4 Write and Solve Multiplication and Division Equations Lesson 4-5 Write and Solve Equations with Rational Numbers 6.EE.C. Represent and analyze quantitative relationships between dependent and independent variables. 6.EE.C.9. Use variables to represent two Lesson 4-8 Understand Dependent and quantities in a real-world problem that Independent Variables change in relationship to one another; write Lesson 4-9 Use Patterns to Write and Solve an equation to express one quantity, thought Equations of as the dependent variable, in terms of the Lesson 4-10 Relate Tables, Graphs, and other quantity, thought of as the independent Equations variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. 23

27 Geometry 6.G.A. Solve real-world and mathematical problems involving area, surface area, and volume. 6.G.A.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Lesson 7-1 Find Areas of Parallelograms and Rhombuses Lesson 7-2 Solve Triangle Area Problems Lesson 7-3 Find Areas of Trapezoids and Kites Lesson 7-4 Find Areas of Polygons 6.G.A.2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Lesson 7-8 Find Volume with Fractional Edge Lengths 6.G.A.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving realworld and mathematical problems. Lesson 2-6 Represent Polygons on the Coordinate Plane 6.G.A.4. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Lesson 7-5 Represent Solid Figures Using Nets Lesson 7-6 Find Surface Areas of Prisms Lesson 7-7 Find Surface Areas of Pyramids Unit Level Standards Not Applicable 24

28 Overview Unit 1 Two Dimensional Geometry Unit 2 Operations w/ Positive and Negative Rational #s Lessons Lesson 4-1 Write and Evaluate Algebraic Expressions Lesson 4-2 Understand Linear Expressions Lesson 4-3 Simplify Linear Expressions Lesson 4-4 Expand Linear Expressions Lesson 4-5 Factor Linear Expressions Lesson 4-6 Add Linear Expressions Lesson 4-7 Subtract Linear Expressions Lesson 4-8 Analyze Equivalent Expressions Lesson 5-1 Write Two-Step Equations Lesson 5-2 Solve Two-Step Equations Lesson 5-3 Solve Equations Using the Distributive Property Lesson 5-4 Solve Inequalities Using Addition or Subtraction Lesson 5-5 Solve Inequalities Using Multiplication or Division Lesson 5-6 Graph Solutions of Inequalities Lesson 5-7 Write Two-Step Inequalities Lesson 5-8 Solve Two-Step Inequalities Lesson 5-9 Solve Multi-Step Inequalities Lesson 8-1 Solve Problems Involving Scale Drawings Lesson 8-2 Draw Geometric Figures Lesson 8-3 Draw Triangles with Given Conditions Lesson 8-4 Solve Problems using Angle Relationships Lesson 8-5 Solve Problems Involving Circumference of a Circle Lesson 8-6 Solve Problems Involving Area of a Circle Lesson 1-1 Understand Integers and Absolute Value Lesson 1-2 Understand Rational Numbers Lesson 1-3 Add Integers Lesson 1-4 Subtract Integers Lesson 1-5 Add and Subtract Rational Numbers Lesson 1-6 Multiply Integers Lesson 1-7 Multiply Rational Numbers Lesson 1-8 Divide Integers Lesson 1-9 Divide Rational Numbers Lesson 1-10 Solve Problems with Rational Numbers 25

29 Overview Unit 3 Proportional Reasoning and Similarity Unit 4 Ratio, Proportion, and Percent Lessons Lesson 2-1 Connect Ratios, Rates, and Unit Rates Lesson 2-2 Determine Unit Rates with Ratios of Fractions Lesson 2-3 Understand Proportional Relationships: Equivalent Ratios Lesson 2-4 Describe Proportional Relationships: Constant of Proportionality Lesson 2-5 Graph Proportional Relationships Lesson 2-6 Apply Proportional Reasoning to Solve Problems Lesson 3-1 Analyze Percents of Numbers Lesson 3-2 Connect Percent and Proportion Lesson 3-3 Represent and Use the Percent Equation Lesson 3-4 Solve Percent Change and Percent Error Problems Lesson 3-5 Solve Markup and Markdown Problems Lesson 3-6 Solve Simple Interest Problems Lesson 6-1 Populations and Samples Lesson 6-3 Draw Inferences About Populations Lesson 8-1 Solve Problems Involving Scale Drawings Lesson 1-10 Solve Problems with Rational Numbers Lesson 2-1 Connect Ratios, Rates, and Unit Rates Lesson 2-2 Determine Unit Rates with Ratios of Fractions Lesson 2-3 Understand Proportional Relationships: Equivalent Ratios Lesson 2-4 Describe Proportional Relationships: Constant of Proportionality Lesson 2-5 Graph Proportional Relationships Lesson 2-6 Apply Proportional Reasoning to Solve Problems Lesson 3-1 Analyze Percents of Numbers Lesson 3-2 Connect Percent and Proportion Lesson 3-3 Represent and Use the Percent Equation Lesson 3-4 Solve Percent Change and Percent Error Problems Lesson 3-5 Solve Markup and Markdown Problems Lesson 3-6 Solve Simple Interest Problems Lesson 4-2 Understand Linear Expressions 26

30 Overview (Continued) Unit 4 Ratio, Proportion, and Percent Unit 5 Algebraic Expressions and Equations Lessons Lesson 4-3 Simplify Linear Expressions Lesson 4-4 Expand Linear Expressions Lesson 4-5 Factor Linear Expressions Lesson 4-6 Add Linear Expressions Lesson 4-7 Subtract Linear Expressions Lesson 4-8 Analyze Equivalent Expressions Lesson 6-1 Populations and Samples Lesson 6-2 Biased and Unbiased Samples Lesson 6-3 Draw Inferences About Populations Lesson 6-4 Compare Populations Using Data Displays Lesson 6-5 Compare Populations Using Statistical Measures Lesson 7-1 Understand Likelihood and Probability Lesson 7-2 Connect Relative Frequency and Experimental Probability Lesson 7-3 Represent Sample Spaces Lesson 7-4 Find Probabilities of Simple Events Lesson 7-5 Determine Outcomes of Compound Events Lesson 7-6 Find Probabilities of Compound Events Lesson 7-7 Simulate Compound Events Lesson 8-1 Solve Problems Involving Scale Drawings Lesson 2-3 Understand Proportional Relationships: Equivalent Ratios Lesson 2-4 Describe Proportional Relationships: Constant of Proportionality Lesson 2-5 Graph Proportional Relationships Lesson 2-6 Apply Proportional Reasoning to Solve Problems Lesson 3-1 Analyze Percents of Numbers Lesson 4-1 Write and Evaluate Algebraic Expressions Lesson 4-2 Understand Linear Expressions Lesson 4-3 Simplify Linear Expressions Lesson 4-4 Expand Linear Expressions Lesson 4-5 Factor Linear Expressions Lesson 4-6 Add Linear Expressions Lesson 4-7 Subtract Linear Expressions Lesson 4-8 Analyze Equivalent Expressions Lesson 5-1 Write Two-Step Equations Lesson 5-2 Solve Two-Step Equations Lesson 5-3 Solve Equations Using the Distributive Property 27