Today is rung 9 of 15 on this topic
Proportional relationships and the constant of proportionality
Can do: Recognises proportionality in tables, graphs and equations, and identifies k in y = kx.
Why it matters
It is the central idea of the year and the direct ancestor of slope, gradient and linear functions in Grade 8.
What it looks like when it's wobbly
Calls any increasing relationship proportional, including ones with a starting fee.
โฑ๏ธ Two-minute check
"Is this proportional?" with two tables, one with a fixed fee. "What's k in each?"
Solid looks like: Only the one through the origin, with k identified as the constant ratio.
The full activity for this topic ยท 25 minutes
Three Ways to Spot It
- 1Take a real pay rate and build a table of hours and earnings.
- 2Check every row for the same y รท x. That constant is k.
- 3Graph it โ it must be a straight line through the origin.
- 4Now do a phone plan with a monthly fee. Same straightness, no origin, not proportional.
- 5Write both as equations and compare y = kx with y = kx + b.
If it's too hard
Tables only, checking the ratio row by row.
If it's too easy
Given a graph, extract k and write the equation, then predict beyond the data.
Say this
"Divide y by x in every row. Same answer every time? Then it's proportional โ and that number is k."