Area Models and the Distributive Property
Print 3rd grade area model worksheets: split rectangles into 5 + n columns and write a × (5 + n) = a × 5 + a × n. 12 versions with answer keys.
Worksheet version 1 of 12. The answer key matches the current version.
Find the area of each small rectangle, then add them to find the area of the whole rectangle.
Part A. Each rectangle is split into 5 columns and the rest. Fill in the blanks.
4 × 6 = 4 × (5 + 1)
= ___ × ___ + ___ × ___
= ___ + ___ = ___
7 × 9 = 7 × (5 + 4)
= ___ × ___ + ___ × ___
= ___ + ___ = ___
7 × 8 = 7 × (5 + 3)
= ___ × ___ + ___ × ___
= ___ + ___ = ___
6 × 7 = 6 × (5 + 2)
= ___ × ___ + ___ × ___
= ___ + ___ = ___
Part B. Draw a line after the fifth column to split the rectangle, then fill in the blanks.
3 × 9 = 3 × (5 + ___)
= ___ × ___ + ___ × ___
= ___ + ___ = ___
5 × 6 = 5 × (5 + ___)
= ___ × ___ + ___ × ___
= ___ + ___ = ___
About this worksheet
An area model shows why the distributive property works. A rectangle 7 squares tall and 8 squares wide has an area of 7 × 8. Split the 8 columns into 5 and 3, and you get two smaller rectangles: 7 × 5 = 35 and 7 × 3 = 21. Together they make 35 + 21 = 56, so 7 × 8 = 7 × (5 + 3) = 7 × 5 + 7 × 3.
Splitting off 5 works well because facts with 5 are easy to count, and the leftover part is a small fact from 1 to 4. Each version has four rectangles that are already split, one for each width from 6 to 9, and two that students split themselves by drawing a line after the fifth column.
Practice aligned to CCSS 3.MD.C.7c.
Before this: area by counting unit squares. Next: 4th grade composite area and missing sides. More practice: area and perimeter worksheets, multiplication worksheets and 3rd grade math worksheets.
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