Montana Math MT.5.NF.5

Math5th GradeNumber and Operations – Fractions

The Standard

Interpret multiplication as scaling (resizing), by: 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, and Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number 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 q/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

2026 Montana Mathematics Content Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students predict whether multiplying by a fraction makes a number bigger or smaller, without calculating the product. They explain what happens when the fraction is less than or greater than 1. They also explain why multiplying the top and bottom of a fraction by the same number leaves its value unchanged.

What Mastery Looks Like

A student can say 8 × 3/4 is less than 8 and 8 × 5/4 is greater than 8 without finding either product. They can show that 2/3 equals 6/9 because multiplying by 3/3 does not change its value.

Common Misconceptions

Some students think multiplication always makes a number bigger. Others assume every fraction is less than 1, or think multiplying 2/3 by 3/3 triples its value.

How to Assess It

Exit ticket: Without calculating, tell whether 12 × 3/4 and 12 × 5/4 are greater or less than 12, and explain why. Show why 2/3 equals 6/9 using multiplication by 1.

Lesson moves

Ways to Teach It

  1. Fold a paper strip into thirds and shade two parts, then fold each third in half to show why 2/3 equals 4/6.

  2. Ask students to write why 9 × 7/6 exceeds 9 while 9 × 5/6 falls short, without calculating either product.

  3. Give pairs cards with expressions such as 6 × 2/3, 6 × 1, and 6 × 4/3 to sort by product size.

  4. Use a recipe for four servings and ask whether multiplying each ingredient by 3/2 or 1/2 makes more or less food.

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Printable MT.5.NF.5 Worksheet

Preview of the MT.5.NF.5 printable worksheet

A ready-to-print activity worksheet aligned to MT.5.NF.5, with an answer key for the teacher on its own page. No account needed.

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