🔢 MathGrade 3Lesson 15
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Use Arrays and Models

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

Learning Objectives

  • 1Draw an array to represent a multiplication expression with rows and columns
  • 2Write a multiplication sentence from a given array or area model
  • 3Use arrays to explain why the order of factors does not change the product
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Mini Lesson

An array is a set of objects arranged in equal rows and columns. Arrays are a powerful way to visualize multiplication and show why changing the order of the factors does not change the product. Area models are rectangles divided into unit squares that show the same idea.

Reading an Array

  • Count the number of rows (horizontal lines of objects).
  • Count the number of columns (vertical lines of objects).
  • Write the multiplication sentence: rows × columns = total.
  • Example: 3 rows of 4 dots → 3 × 4 = 12.

Commutativity: Rows and Columns Can Swap

  • Rotate the array 90 degrees: 3 rows of 4 becomes 4 rows of 3.
  • Both give the same total: 3 × 4 = 4 × 3 = 12.
  • This is the commutative property of multiplication.

Area Models

  • An area model is a rectangle split into a grid of unit squares.
  • The dimensions (length × width) give the multiplication sentence.
  • Count the squares to check: a 4 × 6 rectangle has 24 unit squares.
What is an Array? 3 rows of 4 dots showing commutativityA 3 by 4 array of dots with rows and columns labeled. Below: 3 times 4 equals 12 and 4 times 3 equals 12.What is an Array?3 rows4 columns3 \u00d7 4 = 124 \u00d7 3 = 12Same total \u2014 commutative property
Area Model: 4 rows times 6 columns equals 24A rectangle divided into a 4 by 6 grid of unit squares. The dimensions are labeled 4 and 6. Below: 4 times 6 equals 24 square units.Area Model4 rows6 columns4 \u00d7 6 = 24 sq unitsCount the squares to check!
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If you forget a multiplication fact, draw a quick array and count the dots. The array never lies!

Vocabulary
Array
A grid of equal rows and columnse.g. A 4 × 3 array has 4 rows and 3 columns.
Row
A line of items going acrosse.g. The array has 4 rows.
Column
A line of items going up and downe.g. Each column has 4 squares.
Model
A picture or drawing that shows a math probleme.g. I drew a model to show 4 × 3.
Area model
A rectangle drawn to show multiplicatione.g. My area model is 4 squares wide and 3 squares tall.
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