7th Grade, CC2, Unit 4
Proportions and expressions
Section 4.1: You will examine several similar shapes to determine how those shapes are related. You will use the patterns that you identify to find missing lengths and areas on shapes and to make scale drawings.
Section 4.2: This section introduces the idea of a proportional relationship through tables, graphs, equations, and real-life situations. You will learn strategies for solving proportional situations.
Section 4.3: Here, you will be introduced to algebra tiles. You will use their areas and perimeters to build expressions and combine like terms. You will work with algebraic expressions, simplifying and evaluating them for given values.
combining like terms
constant of proportionality
What's the relationship?
How can I solve it?
What is being compared?
Which shapes are similar?
Are these representations equivalent?
Find solutions to problems involving proportional relationships.
Identify proportional relationships in tables, graphs, and equations.
Calculate unit rates.
Combine like terms and simplify algebraic expressions.
Rewrite expressions by combining like terms and using the Distributive Property.
Simplify and compare two algebraic expressions.
- 7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.G.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.2a. 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.
- 7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- 7.RP.2c. 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.
- 7.RP.2d. 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.