Maryland Math 5.NOS.D.12.c

Math5th GradeNumber and Operation Sense

The Standard

5.NOS.D.12
Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths and show that the area is the same as would be found by multiplying the side lengths.

Maryland College and Career Ready Standards for Mathematics (2025) · APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF MULTIPLICATION AND DIVISION TO MULTIPLY AND DIVIDE FRACTIONS.

Teacher's field guide

What This Standard Means

What Students Need to Do

Students draw rectangles with fractional side lengths on a unit grid. They cover each rectangle with equal squares, count the area of those squares, and check it by multiplying the side lengths.

What Mastery Looks Like

A student draws a rectangle 2/3 unit wide and 1/2 unit tall on a grid marked in sixths. They count twelve squares with 1/6-unit sides, find an area of 12/36 or 1/3 square unit, and get the same result by multiplying.

Common Misconceptions

Some students count twelve small squares and call the area twelve square units, rather than 12/36 of a square unit. Others add the side lengths instead of multiplying them.

How to Assess It

Exit ticket: On a unit square divided into a 6 by 6 grid, shade a rectangle 2/3 unit wide and 1/2 unit tall. Count the small squares, give the area in square units, and check it by multiplying.

Lesson moves

Ways to Teach It

  1. Give pairs a 6 by 6 unit grid; have them cut squares with 1/6-unit sides and tile a 2/3 by 1/2 rectangle.

  2. Ask, "Why do twelve small squares cover 1/3 square unit rather than twelve square units?" Have students explain with a labeled grid.

  3. Play grid match: draw two fraction cards, shade their rectangle on a 6 by 6 grid, and match its area to a product card.

  4. Sketch a floor mat 3/4 meter by 1/2 meter on quarter-meter grid paper; count the tiles and check its area by multiplying.

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