• Free
  • Grade 8
  • Tables, x steps vary

Finding the rate of change worksheets

How much does y move for every one x? These free printable worksheets read the rate of change off a table, including tables whose x steps by more than one.

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Ready to printFinding the rate of change
Finding the rate of change worksheet — Tables, x steps vary, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Rate of change is a division, and the whole difficulty is the denominator. When a table's x column steps by one, the rate is just the difference in y — and a child who has only seen those tables reads 12 off a column that steps by 3, because 12 is what the subtraction gave them. It is the right subtraction and the wrong answer.

Why this sheet works

So every question makes the division visible. Find how far y moved, find how far x moved, and divide the first by the second — even when x steps by one, where the division leaves no trace. Writing it down every time is what builds the habit before it is needed, which is the reason the walks divide by 1 out loud.

How this one works

One question from this sheet, worked through a step at a time.

x: 6, 7, 8, 9 y: 68, 77, 86, 95

x6789y68778695
x steps111y steps999
9÷1=9
rate of change9
  1. Rate of change means how much y moves for every ONE x. So it is a division, and the two things being divided are both differences: how far y went, over how far x went.
  2. Take both rows of steps. x moves 1, 1, 1 — the same each time — and y moves 9, 9, 9. They are steady, so this table really does have one rate rather than a different one in every gap.
  3. Now divide: 9 ÷ 1 = 9. Dividing by one changes nothing, which is exactly why it is worth writing down — on a table whose x steps by more, it will not.
  4. So the rate of change is 9: y moves 9 while x moves 1, and 9 ÷ 1 = 9.