Rate Comparisons
About This Worksheet
This worksheet helps seventh-grade students compare two proportional relationships and decide which one has the greater rate. Students work with situations involving streaming downloads, bike rentals, game points, trail distance, snack packs, and water filling. Some relationships are shown with equations, while others are shown with tables, so students must find the rate from different kinds of representations. They then compare the constants of proportionality and explain which relationship changes faster. This gives students a strong bridge between proportional reasoning and later slope work.
What Students Practice
Students identify the constant of proportionality for each relationship by reading an equation or calculating y/x from a table. They then compare the two k-values and decide which plan or situation has the greater rate. The worksheet asks students to explain why, which helps them connect the numerical comparison with the meaning of the relationship. Because equations and tables appear side by side, students practice moving between different representations. This builds flexibility and helps them recognize that the same rate idea can be shown in several forms.
Why This Matters
Students need a dependable way to compare relationships that do not look alike on the page. Finding k gives them one common measure that works whether the relationship is shown in words, tables, equations, or graphs. This is important because larger values in a table do not always mean a larger rate. Learning to compare constants of proportionality prepares students directly for comparing slopes of linear functions. It also helps with real-world decisions involving speed, cost, production, and growth.
Teaching Tips
Have students find both rates before making any comparison. For equations in the form y = kx, remind them that k is the number multiplying x. For tables, have them divide one y-value by its matching x-value and then check another pair. Encourage students to explain their choice using the actual k-values rather than saying one option “looks bigger.” This helps keep the comparison mathematical and precise.
Curriculum Standards
This worksheet directly supports CCSS.MATH.CONTENT.7.RP.A.2.B by asking students to identify constants of proportionality from equations and tables. It also supports CCSS.MATH.CONTENT.7.RP.A.2 by having students compare proportional relationships. The explanation component strengthens mathematical reasoning and prepares students for later work with slope and linear functions. The worksheet is a strong fit for independent practice, homework, review, or enrichment.