Multiplication as scaling worksheets

Is 3/4 × 20 more than 20, less than 20, or the same? These free printable worksheets ask that and nothing else: no product is ever calculated, because the whole skill is knowing the answer before you would have one.

Multiplication as scaling
Multiplication as scaling worksheet — Whole and fractional factors, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

“Multiplying makes it bigger” is true for every multiplication a child meets until fifth grade, and then it stops being true. This page is where it stops. A factor above one stretches the number, a factor below one shrinks it, and the sheet asks for that judgement on its own so the belief has somewhere to break.

Why this sheet works

Some factors are worth exactly one and are written as fractions — 4/4, 6/6, 10/10. A bare 1 would give itself away, and “the same” has to be a real option rather than the one nobody picks. Noticing that a fraction is a whole is part of the reading.

How this one works

Bigger or smaller?

5/4?1
5/4>1
5/4×60>60
5/4 × 60ismore than60
  1. Do not work it out. The only thing that decides the answer is how the factor compares with 1.
  2. 5/4 is top-heavy: 5 is bigger than 4, so it is more than 1.
  3. Multiplying by something bigger than 1 stretches a number.
  4. So 5/4 × 60 is more than 60.