Montana Math MT.5.NF.4

Math5th GradeNumber and Operations – Fractions

The Standard

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction by: Expressing the product a/b × q as "a" parts of a partition of q into b equal parts, equivalently, as the result of a sequence of operations a × q ÷ b, and Finding the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, showing that the area is the same as would be found by multiplying the side lengths, multiplying fractional side lengths to find areas of rectangles, and represent representing fraction products as rectangular areas.

2026 Montana Mathematics Content Standards

Teacher's field guide

What This Standard Means

What Students Need to Do

Students find a fraction of a number by splitting it into equal parts, then taking some parts. They tile rectangles with fractional side lengths and multiply the sides to find the area.

What Mastery Looks Like

A student can show 3/4 × 8 as three groups of 8 ÷ 4, then get 6. For a 2/3-by-3/4 rectangle, they count six tiles worth 1/12 square unit each and give the area as 1/2 square unit.

Common Misconceptions

Students may multiply 8 by 4 instead of dividing it into fourths. They may count six tiles in a rectangle and call the area 6 square units, forgetting that each tile is smaller than one square unit.

How to Assess It

On an exit ticket, ask students to draw 3/4 of 8 and find its value. Then have them draw a 2/3-by-3/4 rectangle on a grid and label its area.

Lesson moves

Ways to Teach It

  1. Give pairs a unit-square grid divided into thirds across and fourths down; shade a 2/3-by-3/4 rectangle and count its 1/12-square-unit tiles.

  2. Ask, 'Why does 3/4 of 8 equal 3 × (8 ÷ 4)?' Have students sketch their answer and write two sentences.

  3. Play fraction-area match with cards showing side lengths, shaded grids, and products; partners match three cards and check by counting tiles.

  4. Draw a garden bed 2/3 meter wide and 3/4 meter long on graph paper; find its area in square meters.

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Printable MT.5.NF.4 Worksheet

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