Math 7 Unit 4

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This chapter continues to build the big idea of proportional relationships in the context of real-world situations. Students begin in Section 4.1 by looking at similar figures in order to determine how the figures change when the sides are enlarged or reduced uniformly. Then students investigate how to use and make scale drawings.

In Section 4.2, students begin comparing relationships in the context of bank accounts, bulk food purchases, and gas mileage in cars. They also revisit the million-penny tower problem from Chapter 1. Students will examine tables, graphs, and situations to identify characteristics of proportional relationships. Students will use informal strategies to solve proportional situations.

In Section 4.3, students will use a concrete manipulative (called “algebra tiles”) to build shapes that have an unknown dimension. That specific but unknown dimension will be represented with a variable, most often x. Students write expressions to represent the perimeter and area of these shapes. Because students will “see” the shapes and build their expressions differently, they will generate multiple expressions, creating the need to decide if expressions are equivalent. This motivates the use and practice of combining like terms in an expression.

As students move into Chapter 4, they should be starting to use some of the Mathematical Practices with more regularity. It should only take a gentle reminder from you to attend to precision in their communication with each other. They should be more comfortable constructing viable arguments and critiquing the reasoning of others as you encourage discourse during class. Students should now want to make sense of the problems that you ask them to attempt and they should be starting to show more and more perseverance in solving them.

In this chapter, you will guide students to look for and make use of more mathematical structures as they make connections and build understanding. They will also spend a lot of time modeling with mathematics.

7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.GG.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.

7.RP.2. Recognize and represent proportional relationships between quantities.

a) Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b) Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c) Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d) Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

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