Seventh Grade · Math · week 1

Testing for proportionality

Determine whether a relationship shown in a table is proportional by testing whether the ratio between the two quantities stays constant.

Two quantities are in a proportional relationship when their ratio is always the same number, no matter which pair of values you pick. If x is the amount of one thing and y is the amount of the other, you test proportionality by computing y/x for every pair in the table. If every pair gives the exact same number, the relationship is proportional. If even one pair gives a different number, it is not.

This matters because plenty of real relationships are NOT proportional. A taxi ride with a flat pickup fee plus a per-mile charge is not proportional, since part of the cost is not tied to the miles at all. Testing every pair, not just one, is the only way to be sure.

📋 For the teacher
Teach it (10–15 min):
  • Write the table on paper and compute y/x underneath every single pair before deciding anything -- no shortcuts this week.
  • Show one clearly non-proportional table (like a flat fee plus a rate) so the contrast is obvious, not just abstract.
  • Keep the division consistent: always y/x (output over input), never mixing the order between pairs.
  • Connect it to shopping: if the price per item is always the same, the cost is proportional to the quantity bought.
Talk about it:
  • How do you test a table to see if it is proportional?
  • Why does a flat fee ruin a proportional relationship?
  • Can you think of something you buy where the price is NOT simply proportional to the amount?

Mastery looks like: They test every pair in a table by computing the same ratio and correctly conclude whether the relationship is proportional.

Common stumbles: Testing only one pair instead of every pair; dividing in an inconsistent order (x/y for one pair, y/x for another).

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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