Distributive Property - Array Model

Examples, solutions, and videos to help Grade 3 students learn how to model the distributive property with arrays to decompose units as a strategy to multiply.

Common Core Standards: 3.OA.1, 3.OA.5, 3.OA.3, 3.OA.4

New York State Common Core Math Grade 3, Module 1, Lesson 10

Distributive Property Array Model

The following diagram shows the distributive property using the array model. Scroll down the page for more examples of the distributive property using the array model.

NYS Math Module 1 Grade 3 Lesson 10 Concept Development

A guitar has 6 strings. How many strings are there on 3 guitars?
Draw an array to represent the total number of guitar strings.
8 × 2 = _____

NYS Math Module 1 Grade 3 Lesson 10 Problem Set

  1. 7 × 3 = (5 × 3) + (2 × 3) = _____
    (5 × 3) + (2 × 3) = 15 + __________
    15 + ______= __________

Is (3 × 4) + (2 × 4) = 12 + 8 = 20 the same as 5 × 4?

Joe planted 6 rows of carrots in his garden. There are 6 carrots in each row. How many carrots did he plant?

NYS Math Module 1 Grade 3 Lesson 10 Homework

  1. 6 × 3 = __________
    12 + ______ = ______
    6 × 3 = ______
  2. 8 × 2 = ___
    (     × 2) = __
    (     × 2) = ______
    (4 × 2) + (4 × 2) = ______ + ______
    ____ × 2 = ________
  3. Adriana is organizing her books on shelves. She puts 3 books in each row.
    a. Use the multiplication sentences on the right to draw arrays to show the books on Adriana’s top and bottom shelves.
    __________× 3 = 15
    __________× 3 = 3

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