Multiplying with Groups: Discovering Different Ways to Reach the Same Answer!

Mathematics Grades 4th Grade 4:19 Video
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Lesson Description

Learn how to use groups of objects to understand multiplication and find different ways to get the same answer!

Video Resource

Multiplication as groups of objects | Multiplication and division | Arithmetic | Khan Academy

Khan Academy

Duration: 4:19
Watch on YouTube

Key Concepts

  • Multiplication as repeated addition
  • Arrays and grouping
  • Factors and products
  • Commutative property of multiplication

Learning Objectives

  • Students will be able to represent multiplication as groups of objects.
  • Students will be able to identify different factor pairs for a given product.
  • Students will be able to understand that the order of factors does not change the product (commutative property).

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they already know about multiplication. Ask them to give examples of when they use multiplication in everyday life. Introduce the idea that multiplication is like adding the same number multiple times.
  • Video Viewing (7 mins)
    Play the Khan Academy video 'Multiplication as groups of objects'. Encourage students to pay attention to how the video uses groups of balls to represent multiplication.
  • Guided Practice (10 mins)
    After the video, work through a few examples on the board. Use manipulatives (e.g., counters, blocks) to physically create groups and demonstrate the concept. For example, ask: 'How can we show 3 x 5 using groups of objects?'
  • Independent Practice (10 mins)
    Provide students with worksheets or drawing paper. Have them draw different ways to represent a given number as groups. For example: 'Show 18 as groups of objects in at least two different ways.'
  • Wrap-up and Discussion (3 mins)
    Review the key concepts of the lesson. Ask students to share their drawings and explain how they represent multiplication as groups. Reinforce the idea that the same product can be obtained through different combinations of factors.

Interactive Exercises

  • Array Building
    Give students a set of small objects (e.g., beads, buttons). Ask them to create different arrays to represent various multiplication facts (e.g., create an array for 4 x 6).
  • Grouping Game
    Divide the class into small groups. Give each group a number (e.g., 24). Have them brainstorm and draw all the different ways they can represent that number as groups of objects.

Discussion Questions

  • Can you think of a time when using groups would help you solve a multiplication problem?
  • Why can we arrange objects in different ways and still get the same total when multiplying?
  • How does understanding groups help you learn your multiplication facts?

Skills Developed

  • Visual representation of multiplication
  • Problem-solving
  • Critical thinking
  • Multiplication fluency

Multiple Choice Questions

Question 1:

Which of these shows 3 groups of 4?

Correct Answer: 4 + 4 + 4

Question 2:

If you have 5 groups of 2 cookies, how many cookies do you have in total?

Correct Answer: 10

Question 3:

Which multiplication sentence is shown by 2 groups of 8?

Correct Answer: 2 x 8 = 16

Question 4:

Which of the following is another way to write 6 x 3?

Correct Answer: 6 + 6 + 6

Question 5:

You have 4 groups of pencils, and each group has 5 pencils. How many pencils do you have?

Correct Answer: 20

Question 6:

What number is the same as 2 groups of 7?

Correct Answer: 14

Question 7:

Which of these shows 4 x 2 using groups?

Correct Answer: 4 + 4

Question 8:

If you have 3 groups of 6 toy cars, how many cars do you have?

Correct Answer: 18

Question 9:

Which multiplication sentence represents 5 groups of 3?

Correct Answer: 5 x 3 = 15

Question 10:

What is another way to write 7 x 2?

Correct Answer: 7 + 7

Fill in the Blank Questions

Question 1:

4 groups of 5 is the same as 4 _____ 5.

Correct Answer: times

Question 2:

3 x 7 means 3 groups of _____

Correct Answer: 7

Question 3:

If you have 2 groups and each group has 9 items, you have _____ items total.

Correct Answer: 18

Question 4:

5 groups of 4 equals _____.

Correct Answer: 20

Question 5:

8 times 2 is the same as 8 groups of _____.

Correct Answer: 2

Question 6:

6 groups of 3 is written as 6 _____ 3

Correct Answer: x

Question 7:

If you have 4 groups of 6, you have a total of _____ items.

Correct Answer: 24

Question 8:

7 x 3 means 7 groups of _____.

Correct Answer: 3

Question 9:

9 times 2 equals _____

Correct Answer: 18

Question 10:

2 groups of 6 is the same as _____.

Correct Answer: 12

Educational Standards

4.N.2.1:Demonstrate fluency with multiplication and division facts with factors up to 12. 4.N.2.2: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: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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