Grouping Fun: Discovering the Associative Property of Multiplication!

Mathematics Grades 4th Grade 3:35 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how changing the grouping of numbers in a multiplication problem doesn't change the answer! This lesson explores the associative property of multiplication with fun examples and activities.

Video Resource

Associative property of multiplication

Khan Academy

Duration: 3:35
Watch on YouTube

Key Concepts

  • Associative Property of Multiplication
  • Grouping in Multiplication
  • Order of Operations

Learning Objectives

  • Students will be able to define the associative property of multiplication.
  • Students will be able to apply the associative property to solve multiplication problems with three or more factors.
  • Students will be able to recognize that changing the grouping of factors does not change the product.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students if they think the order in which we multiply numbers matters. Present a simple example like 2 x 3 x 4. Without explicitly stating the rule, ask half the class to solve (2 x 3) x 4 and the other half to solve 2 x (3 x 4). Discuss the results and introduce the idea that maybe grouping doesn't matter.
  • Video Viewing (7 mins)
    Play the Khan Academy video: 'Associative property of multiplication'. Encourage students to take notes on the examples provided.
  • Guided Practice (10 mins)
    Work through examples similar to those in the video on the board. Emphasize the use of parentheses to show different groupings. For example: (3 x 2) x 5 = 3 x (2 x 5). Have students solve each side of the equation to verify they are equal.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing multiplication problems with three or more factors. Instruct them to solve each problem using two different groupings to demonstrate the associative property. Include a mix of easier and slightly more challenging problems.
  • Wrap-up and Discussion (3 mins)
    Review the concept and answer any remaining questions. Briefly discuss real-world examples where the associative property can be useful.

Interactive Exercises

  • Group It Up!
    Divide students into small groups and give each group a set of number cards (e.g., 2, 3, 4, 5, 6). Have them create multiplication problems using three numbers and then solve the problem using different groupings. Each group can present their findings to the class.

Discussion Questions

  • Can you think of a time when changing the grouping of numbers might make a multiplication problem easier to solve?
  • Does the order you multiply the numbers change the final answer? Why or why not?
  • Why is it important to understand the associative property of multiplication?

Skills Developed

  • Multiplication fluency
  • Problem-solving
  • Mathematical reasoning

Multiple Choice Questions

Question 1:

What does the associative property of multiplication tell us?

Correct Answer: Changing the grouping of numbers doesn't change the answer.

Question 2:

Which of these shows the associative property of multiplication?

Correct Answer: (4 x 5) x 1 = 4 x (5 x 1)

Question 3:

Solve: (2 x 4) x 3 = ?

Correct Answer: 24

Question 4:

Which expression is equal to 5 x (2 x 3)?

Correct Answer: (5 x 2) x 3

Question 5:

What is the value of 1 x (5 x 4)?

Correct Answer: 20

Question 6:

Which grouping would make this equation easier to solve? 2 x 5 x 9 = ?

Correct Answer: (2 x 5) x 9

Question 7:

Solve: 3 x (3 x 2) = ?

Correct Answer: 18

Question 8:

Which of these is NOT an example of the associative property?

Correct Answer: (1 x 2) x 3 = 3 x (1 x 2)

Question 9:

Is (3 x 4) x 2 = 3 x (4 x 2) true or false?

Correct Answer: True

Question 10:

Which number goes in the box to make this true: (2 x 1) x 5 = 2 x (1 x ?)

Correct Answer: 5

Fill in the Blank Questions

Question 1:

The ___________ property of multiplication says that changing the grouping of numbers does not change the answer.

Correct Answer: associative

Question 2:

In the equation (2 x 3) x 4, we multiply 2 and 3 first because they are in ___________.

Correct Answer: parentheses

Question 3:

(1 x 2) x 3 is equal to 1 x (2 x _______).

Correct Answer: 3

Question 4:

2 x (5 x 1) = ___________

Correct Answer: 10

Question 5:

If we have 4 x 2 x 5, we can group it as (4 x 2) x 5 or as 4 x (2 x _______).

Correct Answer: 5

Question 6:

When we group numbers, we put them in ____________.

Correct Answer: parentheses

Question 7:

True or False: The associative property works for addition but not multiplication.

Correct Answer: false

Question 8:

To make solving easier, sometimes we change the _______ in a multiplication equation.

Correct Answer: grouping

Question 9:

(3 x 1) x 2 = 3 x (1 x __)

Correct Answer: 2

Question 10:

1 x (3 x 2) equals _____.

Correct Answer: 6

Educational Standards

4.N.2.5:Use strategies and algorithms (e.g., mental strategies, standard algorithms, partial quotients, repeated subtraction, the commutative, associative, and distributive properties) based on knowledge of place value, equality, and properties of operations to divide a 3-digit dividend by a 1-digit whole number divisor, with and without remainders. 4.N.2.1:Demonstrate fluency with multiplication and division facts with factors up to 12.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans