About This Worksheet
This worksheet helps seventh-grade students decide whether a table shows a proportional relationship by checking the ratio y/x. Students examine ten different value tables and determine whether the same constant appears for every pair. If the ratio stays the same, the table is proportional; if it changes, it is not proportional. Students also write the value of k when the relationship is proportional. This makes the activity a clear and direct way to connect tables with the constant of proportionality.
What Students Practice
Students divide each y-value by its matching x-value and compare the results across the table. They decide whether the ratio remains constant and label the relationship as proportional or not proportional. When the relationship is proportional, students record k as the constant of proportionality. Some tables use whole-number patterns, while others include decimals, which gives students practice with different numerical forms. This strengthens their ability to analyze tables rather than just notice that numbers are increasing.
Why This Matters
A table can look like it has a pattern without actually being proportional. The key test is whether the same multiplicative relationship connects every x-value to its y-value. Learning to check y/x helps students distinguish true proportional relationships from other patterns. This idea carries directly into equations and graphs, where the same constant k describes the relationship. It is also an important step toward understanding slope in later algebra.
Teaching Tips
Have students calculate y/x for the first pair and write that result beside the table. Then ask them to check one or two more pairs before deciding whether the relationship is proportional. If the ratios do not match, remind them that even one different pair means the table is not proportional. For proportional tables, have them explain what k means in words. This helps connect the number to the relationship instead of treating it like a label.
Curriculum Standards
This worksheet strongly supports CCSS.MATH.CONTENT.7.RP.A.2.A, which asks students to decide whether two quantities are in a proportional relationship. It also aligns with CCSS.MATH.CONTENT.7.RP.A.2.B by having students identify the constant of proportionality from tables. The repeated y/x checks help students build a dependable method for analyzing proportional data. It works well for independent practice, homework, intervention, or a quick formative assessment.