Seventh Grade · Math · week 2

The constant of proportionality

Identify the constant of proportionality (the unit rate k) from a table, an equation, or a verbal description, and write the equation y = kx.

Once you know a relationship is proportional, one single number describes the WHOLE thing: the constant of proportionality, usually called k. It is the unit rate -- how much y you get for exactly one unit of x. Find it by computing y/x for any pair (they all give the same answer, since the relationship is proportional).

Once you know k, you can write the whole relationship as one short equation: y = kx. Plug in any x and multiply by k to get y instantly, without needing the rest of the table.

📋 For the teacher
Teach it (10–15 min):
  • Say it plainly: "k is just the unit rate -- what one single x is worth in y."
  • Practice finding k from at least two different pairs in the same table to build the habit of checking.
  • Once k is found, have them write y = kx immediately and use it to predict a value NOT already in the table.
  • Point out that k can be a whole number, a decimal, or even a fraction -- the method never changes.
Talk about it:
  • What does the constant of proportionality actually tell you in real life?
  • Once you know k, how can you find y for any x without a table?
  • Why should finding k from two different pairs give you the same answer?

Mastery looks like: They correctly compute k from a table, equation, or description, and write the matching equation y = kx.

Common stumbles: Flipping the division (computing x/y instead of y/x); forgetting to write the final equation after finding k.

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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