CCSS.Math.Content.7.RP.A

CCSS.Math.Content.7.RP.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.7.RP.A.1

  Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

• CCSS.Math.Content.7.RP.A.2

  Recognize and represent proportional relationships between quantities.

• CCSS.Math.Content.7.RP.A.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 observ...

• CCSS.Math.Content.7.RP.A.2b

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

• CCSS.Math.Content.7.RP.A.2c

  Represent proportional relationships by equations.

• CCSS.Math.Content.7.RP.A.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) ...

• CCSS.Math.Content.7.RP.A.3

  Use proportional relationships to solve multistep ratio and percent problems.

01

What Students Need to Do

Students decide whether tables, graphs, equations, and written situations show proportional relationships. They find unit rates and constants of proportionality, write equations, and solve ratio and percent problems.

02

What Mastery Looks Like

Students can find and explain the constant of proportionality in a table, graph, equation, or context. They can write an equation in the form y = kx and use it to find missing values. They can solve percent problems involving tax, tips, discounts, markups, and percent change.

03

Common Misconceptions

Students may use additive differences when a constant multiplier is needed. They may assume every straight-line graph is proportional, even when it does not pass through the origin. They may reverse units when finding unit rates or apply percent change to the wrong starting amount.

04

How to Assess It

Give an exit ticket with the table (2, 6), (5, 15), and (8, 24). Ask students to find the constant, write an equation, and calculate a 20 percent discount on $45.

1. 01

   Have pairs mix colored water using different concentrate-to-water ratios, then record totals and identify mixtures with the same constant ratio.

2. 02

   Ask students to explain why a straight line through the origin represents a proportional relationship, using one labeled point as evidence.

3. 03

   Play a matching game with cards showing tables, graphs, equations, and situations that represent the same proportional relationship.

4. 04

   Use grocery ads to calculate unit prices, compare package values, and determine final prices after discounts and sales tax.

• CCSS.Math.Content.8.EE.B

  Understand the connections between proportional relationships, lines, and linear equations.