Multiplication as Scaling Sort

5th Grade MathOperations with Fractions3 pages

About this worksheet

A card-sort worksheet for 5th grade math on multiplication as scaling (Common Core 5.NF.5.a and 5.NF.5.b). Students take twelve expression cards, from 12 × 3/5 to 25 × 11/8, and place each into a three-column sorting mat by asking one question only: is the scaling factor less than, equal to, or greater than 1? Calculating is banned. Two written prompts follow, asking why 20 × 4/5 must fall below 20 and why multiplying by 6/6 changes nothing, which ties the sort back to fraction equivalence.

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$Multiplication as Scaling Sort: Operations with Fractions - page 1$

$Multiplication as Scaling Sort: Operations with Fractions - page 2$

$Multiplication as Scaling Sort: Operations with Fractions - page 3$

Curriculum objectives covered

5.NF.5.a

“Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.”

The whole sorting mat is this standard: all twelve cards get placed by comparing the product to the starting factor without performing any multiplication.

5.NF.5.b

“Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.”

The two writing prompts carry it: question 1 explains the shrink in 20 × 4/5, and question 2 links factors like 6/6 to the equivalence rule a/b = (n×a)/(n×b).

What's inside this worksheet

Expression Cards

Twelve cards mix proper fractions (24 × 1/2, 16 × 9/10, 30 × 2/3), factors equal to one (8 × 7/7, 10 × 9/9, 21 × 5/5, 14 × 8/8), and factors above one (15 × 4/3, 18 × 7/6, 25 × 11/8, and the mixed number 9 × 1 1/4).

Sorting Mat

Students write each card under one of three headers: product less than the starting number, equal to it, or greater than it, judging only by the scaling factor.

Explain Without Multiplying

Question 1 asks why 20 × 4/5 must be less than 20. Question 2 asks why multiplying by 6/6 leaves any number unchanged and how that connects to fraction equivalence.

Answer key

The key sorts all twelve cards into their columns and states the reason for each column, down to the Identity Property behind the equal-to-1 factors.

How teachers use it

Cut-and-sort station

Cut the twelve cards apart and run the mat as a partner station. Requiring a spoken reason per placement keeps the no-calculating rule honest.

Before teaching fraction multiplication

Run this sort before any procedure lesson. Students who already expect 24 × 1/2 to shrink will catch their own computation errors later in the unit.

Exit writing sample

Collect only question 2. The 6/6 explanation shows who connects scaling to equivalence and who is still quoting the rule from the callout box.

More 5th Grade Math worksheets

Place Value and Decimals Measurement and Data Geometry Order of Operations

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