Mastering Integer Multiplication: A Trio of Numbers!

PreAlgebra Grades High School 5:23 Video
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Lesson Description

Learn how to confidently multiply three integers, whether positive or negative, using the associative property and the rules of integer multiplication. This lesson builds a solid foundation for pre-algebra skills.

Video Resource

How to Multiply Three Integers | Multiplying Integers | Math with Mr. J

Math with Mr. J

Duration: 5:23
Watch on YouTube

Key Concepts

  • Integer Multiplication Rules (same signs = positive, different signs = negative)
  • Associative Property of Multiplication
  • Product (result of multiplication)

Learning Objectives

  • Students will be able to correctly multiply three integers, applying the rules for positive and negative numbers.
  • Students will be able to apply the associative property of multiplication to simplify calculations.
  • Students will be able to explain why the order of operations can be altered in multiplication problems.

Educator Instructions

  • Introduction (5 mins)
    Briefly review the rules for multiplying two integers (positive x positive = positive, negative x negative = positive, positive x negative = negative, negative x positive = negative). Highlight that these rules are the foundation for multiplying three or more integers.
  • Video Viewing (7 mins)
    Watch the "How to Multiply Three Integers | Multiplying Integers | Math with Mr. J" video. Encourage students to take notes on the examples and the explanation of the associative property.
  • Guided Practice (10 mins)
    Work through example problems similar to those in the video, emphasizing the step-by-step process. Include examples with various combinations of positive and negative integers. Solve each problem using left-to-right multiplication AND by using the associative property, showing students how to compare the two different processes.
  • Independent Practice (10 mins)
    Provide students with a set of practice problems to solve individually. Circulate to provide support and answer questions.
  • Review and Wrap-up (3 mins)
    Review the key concepts and address any remaining questions. Briefly introduce how these skills will be used in more complex algebraic expressions.

Interactive Exercises

  • Integer Multiplication Game
    Play an online game (e.g., on Math Playground) that involves multiplying integers. This provides a fun and engaging way to practice the skill.
  • Whiteboard Challenge
    Divide students into groups and assign each group a multiplication problem with three integers. Have each group solve the problem on a whiteboard using both left-to-right multiplication and the associative property. Then have each group present the solution.

Discussion Questions

  • How does knowing the rules for multiplying two integers help you multiply three or more?
  • Explain, in your own words, what the associative property of multiplication allows us to do.
  • Can you think of a real-world situation where you might need to multiply three or more integers?

Skills Developed

  • Procedural Fluency (multiplying integers)
  • Conceptual Understanding (associative property)
  • Problem-Solving

Multiple Choice Questions

Question 1:

What is -2 x 3 x -4?

Correct Answer: 24

Question 2:

Which property allows you to change the grouping of factors in multiplication without changing the product?

Correct Answer: Associative Property

Question 3:

What is a 'product' in mathematics?

Correct Answer: The answer to a multiplication problem

Question 4:

A negative times a negative always equals a:

Correct Answer: Positive

Question 5:

What is -1 x -1 x -1?

Correct Answer: -1

Question 6:

Which expression is equivalent to 5 x (-2 x 3) using the associative property?

Correct Answer: (5 x -2) x 3

Question 7:

What is 4 x -1 x 0?

Correct Answer: 0

Question 8:

When multiplying three integers, if there are an odd number of negative integers, the product will be:

Correct Answer: Negative

Question 9:

What is the product of -6, 2, and -1?

Correct Answer: 12

Question 10:

If you multiply a positive integer by a negative integer by another positive integer, the answer will be what?

Correct Answer: Negative

Fill in the Blank Questions

Question 1:

A negative number multiplied by a negative number is always a ______ number.

Correct Answer: positive

Question 2:

The answer to a multiplication problem is called the ______.

Correct Answer: product

Question 3:

According to the ______ property, the grouping of factors does not change the product.

Correct Answer: associative

Question 4:

When multiplying -5 x 2 x -3, you can first multiply -5 x 2 to get -10, then multiply -10 x -3 to get ______.

Correct Answer: 30

Question 5:

If you have three integers, and one of them is zero, the product is always ______.

Correct Answer: zero

Question 6:

A positive integer times a negative integer equals a _______ integer.

Correct Answer: negative

Question 7:

-2 x -2 x -2 = ______

Correct Answer: -8

Question 8:

In the expression (-3 x 4) x 2, the parentheses indicate we should perform -3 x 4 ______.

Correct Answer: first

Question 9:

When multiplying three integers, if all three are negative, the result will be ________.

Correct Answer: negative

Question 10:

6 x -5 x -2 is equal to ________.

Correct Answer: 60

Educational Standards

PA.N.1:Read, write, compare, classify, and represent real numbers, and use them to solve problems in various contexts. PA.A.3.2:Justify steps in generating equivalent expressions by combining like terms and using order of operations (to include grouping symbols). Identify the properties used, including the properties of operations (associative, commutative, and distributive).

Teaching Materials

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