5th grade multiplication as scaling worksheets

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Multiplication as scaling worksheets for 5th grade ask your child to predict the size of a product without working it out. Each of the 8 problems shows a fraction multiplication such as 3/2 × 2/3. Your child compares one factor with 1, then compares the product with the other factor, and writes a comparison sign for each. No computing, only reasoning about size.

Free printable PDF worksheet, aligned to Common Core 5.NF.B.5.

Each print is a different sheet with its own answer key. You don't need to sign up.

The kind of problems you'll get

Complete each problem. Use the models and show your reasoning where asked.

  1. 3/2 × 2/3 2/3 1 3/2 × 2/3 3/2

    Answer: Below 1: smaller.

  2. 4/3 × 1 1 1 4/3 × 1 4/3

    Answer: 1: unchanged.

  3. 1 × 3/2 3/2 1 1 × 3/2 1

    Answer: Above 1: larger.

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on each sheet

Every version prints on US Letter or A4, with its answer key after the problems.

This sheet is one of the versions on the 5th grade multiply fractions page, with its own difficulty choices and its own answer key.

How to teach this

Cover the answer line and ask one question first: is this factor smaller than 1, equal to 1, or bigger than 1? That answer decides the whole problem. A factor below 1 shrinks the other number, a factor above 1 grows it, and a factor of exactly 1 leaves it alone. Have your child say the size word out loud before writing the sign, then write both comparisons in the same order every time: factor against 1, product against the other factor. The trap is a product like 3/2 × 2/3, which equals 1 and looks small on its own. It is still smaller than 3/2, and that is what the second comparison asks. To check one answer, pick a friendly number such as 8, multiply it by the same factor, and see which way it moved.

Watch for: Kids assume multiplying always makes a number bigger, because it did with whole numbers. Multiplying by a fraction below 1 takes a part of the number, so 1/2 × 8 is 4, which is smaller than 8. Kids compare the product with 1 instead of with the other factor. The sheet asks two separate questions, and the second one is whether the product is smaller or larger than the number that got scaled.

Common questions about 5th grade multiplication as scaling

What does my child write on this sheet?
Two comparison signs per problem, not a product. The first sign compares one factor with 1. The second compares the product with the other factor. The answer key also names the size in words: a factor below 1 makes it smaller, above 1 makes it larger, and exactly 1 leaves it unchanged.
Why doesn't the sheet ask for the answer to the multiplication?
Because standard 5.NF.B.5 is about reasoning about size before computing. If your child can say that 4/3 × 1 stays at 4/3 and that 1/2 × 8 lands below 8, the arithmetic on the multiply fractions sheet makes more sense afterward.
How many problems are there, and is there an easier version?
Eight problems per print, all at one level. This sheet has no easier or harder setting. If eight feels like a lot, do the first four together and let your child finish the rest alone, then compare answers with the key.

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Aligned to Common Core 5.NF.B.5. Reviewed by the One more sheet team. Content version 241, updated September 2026.

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