Plan Comparisons Answer Key
About This Worksheet
This worksheet helps seventh-grade students compare two proportional plans by finding and comparing their rates. Each problem presents Plan A and Plan B in different forms, such as equations and tables, and students must determine the rate for each one. They then decide which plan has the greater rate and show how they know. This gives students practice comparing relationships even when the information is represented differently. The activity connects proportional reasoning with decision making in situations such as points, costs, tickets, data use, rewards, and credits.
What Students Practice
Students find the constant of proportionality for each plan by reading an equation or analyzing a value table. They record the rate for Plan A and Plan B, then compare the two values directly. In some problems, k can be read from an equation, while in others students must divide y by x using a pair from the table. This requires them to move comfortably between different representations. Students also practice explaining which plan is greater based on the rate rather than on the size of a single number.
Why This Matters
Students sometimes compare tables or equations by looking only at the largest visible values. That can be misleading because the important question is how quickly one quantity changes compared with the other. Finding k gives students a fair way to compare two proportional relationships. This idea is closely related to comparing slopes in later algebra. It also has practical uses in comparing prices, rewards, rates, and service plans.
Teaching Tips
Have students find both rates before choosing which plan is greater. Encourage them to write the rate with units when the context provides them. If a table is involved, remind them that larger y-values do not automatically mean a larger rate. Instead, compare y/x for each plan. Asking students to justify the choice with one sentence can help make sure they are comparing the rates rather than guessing.
Curriculum Standards
This worksheet supports CCSS.MATH.CONTENT.7.RP.A.2.B by asking students to identify constants of proportionality from equations and tables. It also reinforces CCSS.MATH.CONTENT.7.RP.A.2 by having students compare proportional relationships using those constants. The cross-representation comparisons build important preparation for later work with slope and linear functions. This worksheet works especially well for independent practice, assessment, enrichment, or review near the end of a proportional relationships unit.