Same Math › Grade 7 › Proportional relationships
What is a proportional relationship?
Two quantities are proportional when one is always the same multiple of the other. If 1 cup of flour makes 12 cookies, 2 cups make 24 and 3 make 36: cookies ÷ cups is always 12. That number is the constant of proportionality, k, and the equation is y = 12x.
- Same ratio every row: y ÷ x = 12.
- k is the unit rate: cookies per cup.
- Its graph is a straight line through (0, 0).
Why schools teach it
It connects ratios to algebra
Seventh graders decide whether two quantities are proportional, find the constant of proportionality in tables, graphs and equations, and write equations like y = kx (7.RP.A.2). It's the bridge from sixth-grade ratio tables to eighth-grade slope.
The test is simple: divide y by x in every row. If you always get the same number, it's proportional.
At the kitchen table
What to say, and what to skip
Say this
What do you get when you divide y by x?
Is it the same in every row?
What does k mean in this story?
Cookies per cup.Does the graph go through zero?
Skip this
- Calling any straight line proportional.It must also go through (0, 0).
- Cross-multiplying without understanding.It works, but k explains what's going on.
- Mixing up x and y.k = y ÷ x, the second quantity per one of the first.
See it in action
Is $3 for 2 apples, $6 for 4, $10 for 6 proportional?
Divide cost by apples in each row
1.5 · 1.5 · 1.67Compare
not all the sameConclude
not proportional
Real prices often aren't proportional: bulk deals change the unit price.
Free practice sheet
Make a proportional relationships sheet
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Parents also ask
What's the difference between k and unit rate?
They're the same number here: the amount of y for 1 of x.
How does this relate to slope?
k is the slope of the line y = kx. Eighth grade builds on this.
What does a non-proportional graph look like?
A curve, or a straight line that doesn't go through (0, 0).
Why does (0, 0) matter?
Zero cups make zero cookies. If zero of one gives some of the other, it's not proportional.