Multiplying Made Easier: Properties and Patterns!

Mathematics Grades 4th Grade 8:34 Video
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Lesson Description

Learn how to use properties like the commutative and distributive properties to simplify multiplication problems. Discover how to break down numbers to make multiplying easier!

Video Resource

Properties and patterns for multiplication | 3rd grade | Khan Academy

Khan Academy

Duration: 8:34
Watch on YouTube

Key Concepts

  • Commutative Property of Multiplication
  • Distributive Property of Multiplication
  • Decomposing Numbers for Easier Multiplication

Learning Objectives

  • Students will be able to apply the commutative property to simplify multiplication.
  • Students will be able to use the distributive property to break down multiplication problems into smaller, manageable parts.
  • Students will be able to decompose numbers to make multiplication easier.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of multiplication as repeated addition. Show examples of arrays to visually represent multiplication. Ask students if the order of numbers matters in multiplication (leading to the commutative property).
  • Video Viewing (10 mins)
    Play the Khan Academy video "Properties and patterns for multiplication | 3rd grade | Khan Academy." Encourage students to take notes on the commutative and distributive properties as they are explained in the video.
  • Commutative Property Discussion (5 mins)
    Discuss the commutative property: a x b = b x a. Give examples like 3 x 5 = 5 x 3. Practice with simple examples on the board.
  • Distributive Property Explanation (10 mins)
    Explain the distributive property using the video's example (4 x 7 = 4 x (5+2) = (4 x 5) + (4 x 2)). Work through a few examples together, showing how to break down larger numbers.
  • Practice Problems (15 mins)
    Provide students with practice problems involving both commutative and distributive properties. Start with easier problems and gradually increase the difficulty. Encourage students to work in pairs.
  • Wrap Up (5 mins)
    Review the key concepts of the lesson. Ask students to explain in their own words how the commutative and distributive properties can help them with multiplication. Preview the next lesson.

Interactive Exercises

  • Array Building
    Provide students with manipulatives (e.g., counters, blocks) to build arrays that demonstrate the commutative property (e.g., build a 3x4 array and then a 4x3 array to show they have the same total).
  • Distributive Property Game
    Create a game where students have to break down larger multiplication problems using the distributive property. For example, a card might say 'Solve 6 x 12 using the distributive property.' Students could break it down as 6 x (10 + 2) = (6 x 10) + (6 x 2).

Discussion Questions

  • How does knowing the commutative property help you solve multiplication problems faster?
  • Can you think of a time when using the distributive property would be helpful in real life (e.g., calculating the cost of multiple items)?
  • Why is it important to understand the properties of multiplication?

Skills Developed

  • Multiplication Fluency
  • Problem-Solving
  • Mathematical Reasoning

Multiple Choice Questions

Question 1:

Which property says that you can change the order of numbers when multiplying?

Correct Answer: Commutative Property

Question 2:

What is 5 x 8 the same as?

Correct Answer: 8 x 5

Question 3:

Which expression shows the distributive property correctly for 3 x 9?

Correct Answer: 3 x (5 + 4)

Question 4:

What is 4 x (3 + 2) the same as?

Correct Answer: (4 x 3) + (4 x 2)

Question 5:

If 6 x 7 = 42, what is 7 x 6?

Correct Answer: 42

Question 6:

Using the distributive property, how can you break down 7 x 11?

Correct Answer: 7 x (10 + 1)

Question 7:

What is 2 x 15?

Correct Answer: 30

Question 8:

Which property makes it easier to solve 9 x 2?

Correct Answer: Commutative Property

Question 9:

Which number sentence is the same as 8 x 6?

Correct Answer: 8 + 8 + 8 + 8 + 8 + 8

Question 10:

How can you use the distributive property to solve 5 x 13?

Correct Answer: 5 x (10 + 3)

Fill in the Blank Questions

Question 1:

The ___________ property says you can multiply numbers in any order.

Correct Answer: commutative

Question 2:

4 x 9 is the same as 9 x ____.

Correct Answer: 4

Question 3:

The ___________ property helps you break down a multiplication problem.

Correct Answer: distributive

Question 4:

3 x (5 + 2) = (3 x 5) + (3 x ____)

Correct Answer: 2

Question 5:

Using the distributive property, 6 x 10 = (6 x 5) + (6 x ____)

Correct Answer: 5

Question 6:

Multiplying 7 x 8 gives you the same answer as multiplying 8 x ____.

Correct Answer: 7

Question 7:

5 x (4 + 1) = (5 x 4) + ____

Correct Answer: (5 x 1)

Question 8:

If 2 x 6 is 12, then 6 x 2 is _____.

Correct Answer: 12

Question 9:

6 x 12 can be solved by breaking it down to 6 x (10 + ___)

Correct Answer: 2

Question 10:

Changing the order of factors does not change the ____.

Correct Answer: product

Educational Standards

4.N.2.1:[Objective] Demonstrate fluency with multiplication and division facts with factors up to 12. 4.N.2.2:[Objective] Multiply 3-digit by 1-digit and 2-digit by 2-digit whole numbers, using various strategies, including but not limited to standard algorithms. 4.A.2.1:[Objective] Use the relationships between multiplication and division with the properties of multiplication to solve problems and find values for variables that make number sentences true.

Teaching Materials

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