Chapter 1 Introduction and Representation
Welcome to math class! This chapter will introduce you to the mathematical practices that you will be using and working with throughout this course and beyond. You will start by working with your classmates to solve a series of challenging problems. These problems preview some of the mathematics that you will be learning throughout the year.
In Section 1.1 you will work on several challenging investigations with your team, some of which you will revisit later in this course. The main purpose of these problems is to introduce some of the big concepts of this math course, such as organizing data and using mathematical reasoning to make predictions.
Then in Section 1.2, you will develop multiple ways to represent (or show) mathematical ideas. You will represent your ideas using numbers, symbols, diagrams, words, and various kinds of graphs and tables.

Section 1.1 In this section, you will get to know the members of your class and your study team. You will work with your classmates on challenging problems and activities. You will find ways to explain your thinking and you will learn from the thinking of others. 

Section 1.2 Next, you will find multiple ways to represent mathematical ideas: using words, numbers and symbols, diagrams, and different kinds of graphs. You will explain your ideas to your team and listen carefully to their ideas. 
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Chapter 2 Arithmetic Strategies and Area
In the beginning of this chapter, you will continue your focus on representation from Chapter 1. You will do experiments and learn several ways to display and understand the results of your experiments.
Then, in Section 2.2, you will investigate area and how to measure it. You will also explore the relationship between area and perimeter and think about how changing one affects the other.
In Section 2.3, you will focus on multiplication. You will use your understanding of our base ten number system to visualize multiplication in new ways. This will allow you to calculate products efficiently.
In this chapter, you will learn how to:
• Analyze the strengths and weaknesses of various graphical representations of data.
• Define and measure the area of rectangles and shapes that can be broken into rectangles.
• Use a generic rectangle to multiply, both on paper and mentally.
• Find the greatest common factor of selected numbers.

Section 2.1 To begin the chapter, you will learn several ways to represent data that you collect. You will learn to make mathematically justified statements about how accurately your class was able to determine the length of one minute without using a clock! 

Section 2.2 Section 2.2 focuses on area. You will learn how to measure area using a variety of units, and why standard units are useful. You will also learn about perimeter and its relationship to area.


Section 2.3 In this section, you will take a closer look at multiplication and how it relates to area.

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Chapter 3 Portions and Integers
This chapter begins with a focus on multiple ways to represent portions, such as percents, decimals, and fractions. You will use 100% blocks as a tool to explore the relationships between the equivalent representations of portions. You will also connect portions to ratios.
In Section 3.2, you will describe how a point moves on a number line by adding integers. You will also learn about absolute value and how to find the length of a line segment on a coordinate graph.
In this chapter, you will learn how to:
• Use a powerful new tool for finding equivalent fractions.
• Use percents, decimals, and fractions to describe a portion of a whole.
• Represent portions as percents, decimals, and fractions with pictures, symbols, and words.
• Find the decimal form of a number when it is given as a percent or fraction.
• Connect ratios to portions as ways to represent comparisons of parts.
• Add positive and negative integers and rational numbers.
• Find the absolute value of a number.
• Find the length of horizontal and vertical line segments on a coordinate graph.

Section 3.1 In the first section, you will develop a useful tool for finding equivalent fractions and verifying that they are equivalent. You will also represent portions of wholes as percents, decimals, and fractions. Then you will work to find efficient ways to move between equivalent representations of the portions. 

Section 3.2 In this section you will describe motion on a number line using integers. You will learn how addition can help you predict the starting or ending point of a series of moves. Then you will relate this movement to finding distance. Finally, you will connect your understanding of movement along a number line to distance on a coordinate graph. 
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Chapter 4 Variables and Ratios
Are you ready to strengthen your prealgebra skills? One skill that is essential for algebra is figuring out unknown amounts. In Section 4.1, you will begin to think about how to do so. You will use variables to represent unknown quantities and will use what you know about a problem to find the value of these variables.
In Section 4.2, you will move from mystery numbers to a mystery mascot. With your class, you will work to enlarge the mystery mascot. Then you will learn how to enlarge or reduce figures while keeping their shapes the same. You will use ratios to compare the side lengths of figures to determine if they are the same shape.
In this chapter, you will learn how to:
• Use variables to generalize and to represent unknown quantities.
• Write multiple expressions to describe a pattern and recognize whether the expressions are equivalent.
• Find the value of an algebraic expression when the value of the variable is known.
• Enlarge and reduce figures while maintaining their shapes.

Section 4.1 You will write expressions with variables and learn about equivalent expressions. You will work with your team to find strategies for representing and finding unknown lengths. 

Section 4.2 In this section, you will learn how to enlarge and reduce figures while maintaining their shapes. You will also learn about using ratios to describe relationships between shapes of different sizes. 
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Chapter 5 Multiplying Fractions and Area
You know about multiplying, and you know about fractions; in this chapter, you will learn about multiplying fractions!
In Section 5.1, you will calculate portions of fractions, or “parts of parts.” You will use these ideas to develop strategies for multiplying fractions and mixed numbers.
In Section 5.2, your new knowledge of multiplying fractions will help you understand decimal multiplication. You will also investigate how multiplying by a number close to, much larger than, or much smaller than 1 affects size of the product.
Section 5.3 focuses on the question, “How can we use what we know about the areas of basic shapes to find the areas of complex shapes?” As you develop new strategies for finding the areas of shapes, you will be able to solve new problems that involve more complex areas.
In this chapter, you will:
• Learn how to calculate a part of another part.
• Discover how to multiply fractions, mixed numbers, and decimals.
• Find the areas of shapes, including rectangles, triangles, parallelograms, and trapezoids.

Section 5.1 You will learn how to multiply fractions by examining portions of fractions. Then you will connect this process to finding the products of mixed numbers. 

Section 5.2 In the second section, you will extend what you learned in the first section to find products of decimals. This will also help you understand how multiplication by a number greater than or less than 1 affects the product. 

Section 5.3 You will find the areas of different shapes such as parallelograms, triangles, and trapezoids by rearranging them into rectangles. 

Section 5.4 Finally, you will reflect about what you have learned in Chapters 1 through 5. 
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Chapter 6 Dividing and Building Expressions
In the previous chapter, you worked with multiplication. Now you will turn your attention to division. In Section 6.1, you will find ways to divide different amounts of licorice among different numbers of people. You will gain a deep understanding of division by using diagrams and pictures to model it. The strategies that you develop in this chapter will help you in Chapter 7 when you will work further with division.
You will begin Section 6.2 by building expressions with a new tool called “algebra tiles.” You will use variables to describe the perimeters and areas of shapes built with tiles when one dimension is unknown or can represent various lengths.
In this chapter, you will learn how to:
• Represent division of fractions using diagrams. • Divide whole and mixed numbers by fractions. • Use the Order of Operations to find the correct value of a numerical expression. • Combine like terms and simplify algebraic expressions. • Use a variable to represent any number.

Section 6.1 In this section, you will begin by looking at integer division by dividing different amounts of licorice among different numbers of people. You will use diagrams and other strategies to divide the licorice equally. Then you will divide fractions and mixed numbers and use your knowledge of division to solve problems. 

Section 6.2 This section introduces algebra tiles and uses their areas and perimeters to develop the skills of building expressions and combining like terms. You will simplify and evaluate algebraic expressions for given values. 
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Chapter 7 Rates and Operations
In Japan, speedlimit signs on the highway read, “Speed Limit 100.” Are people in Japan allowed to drive faster than people in the United States? In Section 7.1, you will explore questions involving rate, like this one. You will also learn how to find unit rates to make comparisons. You will examine races called triathlons to discover when rates will be the same and when they will be different.
In Section 7.2, you will extend your previous understanding of division with fractions to include division with mixed numbers and decimals. You will discover efficient methods to divide with these portions.
In Section 7.3, you will use mathematical operations to do mathematical “magic” tricks. You will also learn how the tricks work and be able to create your own tricks using variables and algebra tiles.
In this chapter, you will learn how to:
• Calculate rates, including unit rates.
• Compare ratios and rates with different units.
• Divide more efficiently with fractions, mixed numbers, and decimals.
• Rewrite expressions by combining like terms and using the Distributive Property.
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Chapter 8 Statistics and Multiplication Equations
Do you remember learning about the famous Calaveras County frogjumping contest in Chapter 1? In Section 8.1, you will return to the data from the frogjumping contest. This time, you will use new tools to analyze and compare groups of frogs. You will also look at more ways to display and interpret the data.
In Section 8.2, you will transition to the subject of statistics. Your work in this section will build on your knowledge of statistics to look at statistical questions.
Then, in Section 8.3, you will work with more reallife situations, revisiting math ideas you have already studied and learning new strategies to apply to new contexts. When traveling in a car, for example, have you ever asked, “When are we going to get there?” Did you know that you could use mathematics to answer that question?
In Section 8.3, you will use diagrams like the ones you used for percents to find the relationship between distance, rate, and time. You will also learn how to compare quantities that are very different.
In this chapter, you will learn how to:
• Use measures of central tendency, histograms, stemandleaf plots, and box plots to represent and compare data.
• Consider the shape and spread of data both through a visual display and through calculations.
• Decide if a question is a statistical question.
• Solve problems involving distance, rate, and time.
• Convert units so that they are the same and then use them to compare rates.

Section 8.1 This section introduces another method of representing data, the box plot. You will decide which of the representations you have learned and which measure of central tendency will best help you compare sets of data. You will also look at the shape and spread of data. 

Section 8.2 In this section, you will investigate statistical questions and learn how to write them. 

Section 8.3 You will identify the relationship between distance, rate, and time and will use it to solve word problems. You will compare rates that do not involve the same units and determine when unit conversion is necessary. 
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Chapter 9 Volume and Percents
Congratulations on reaching the last chapter of this math course! Now you get to extend your thinking about various topics you have studied this year.
You will begin this chapter by extending your work with measuring lengths and area. Here you will measure the surface area and volume of threedimensional objects. You will practice visualizing threedimensional solids and how their parts fit together. You will use “flattened” shapes, called nets, to do this.
In Section 9.2 you will extend your work with percents to calculate percent discounts, tips, and interest earned. Percents are all around you, such as 20% off at clothing stores, 8.75% sales tax, and 20% tips in restaurants, and now you get to explore them in even more detail.
Finally, in the course closure and reflection (Section 9.3), you will work with your team to solve challenging problems that allow you to reflect about your learning from this entire course.
In this chapter, you will learn how to:
• Find the volume of threedimensional solids, known as right prisms.
• Find the surface area and volume of a rectangular prism.
• Calculate percents using pencil and paper as well as mental math strategies.

Section 9.1 In this section, you will learn about volume and surface area of threedimensional solids. You will develop strategies for calculating the volume and the surface area of a prism. Then you will compare how surface area and volume are related by building threedimensional rectangular prisms. Finally, you will visualize shapes using nets.


Section 9.2 Here, you will calculate percents to solve problems involving tips, interest, sale prices, and discounts. 

Section 9.3 You will work with your team to solve challenging problems using what you have learned throughout the entire course. You will reflect about your learning and how you have been thinking as you have solved problems this year. 
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