Dividing with Arrays: Visualizing Groups

Mathematics Grades 4th Grade 2:06 Video
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Lesson Description

Learn how to use arrays to understand and solve division problems. See how many equal groups you can make!

Video Resource

Visualizing division with arrays

Khan Academy

Duration: 2:06
Watch on YouTube

Key Concepts

  • Division as equal groups
  • Arrays as a visual representation of division
  • Relationship between multiplication and division

Learning Objectives

  • Students will be able to identify arrays that represent a given division problem.
  • Students will be able to determine the quotient (answer) of a division problem using arrays.
  • Students will be able to explain how an array models division.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what division means – sharing equally into groups. Ask students for examples of when they might use division in their daily lives (e.g., sharing snacks, dividing toys).
  • Video Viewing (5 mins)
    Watch the Khan Academy video 'Visualizing division with arrays'. Encourage students to pay attention to how the arrays are used to represent division problems.
  • Guided Practice (10 mins)
    Work through example problems together. Draw arrays on the board and ask students to identify the corresponding division problem. For instance: * Draw an array with 12 circles arranged in 3 rows of 4. Ask: "What division problem does this array show? (12 ÷ 3 = 4 or 12 ÷ 4 = 3)"
  • Independent Practice (10 mins)
    Provide students with division problems and ask them to draw arrays to represent and solve them. Examples: * 15 ÷ 5 = ? * 24 ÷ 6 = ? * 30 ÷ 5 = ?
  • Wrap-up (5 mins)
    Review the key concepts of the lesson. Ask students to explain in their own words how arrays help visualize division. Discuss the relationship between multiplication and division.

Interactive Exercises

  • Array Building with Manipulatives
    Provide students with counters (e.g., beans, buttons, small blocks). Give them a division problem (e.g., 18 ÷ 3) and ask them to create an array using the counters to solve the problem.
  • Online Array Tool
    Use an online array maker tool (search for "array maker") to create and manipulate arrays interactively. This allows students to experiment with different division problems and see the corresponding arrays.

Discussion Questions

  • How does an array help you understand division?
  • Can you think of a multiplication problem that the array also shows?
  • How is division like sharing?

Skills Developed

  • Visualizing division
  • Problem-solving
  • Connecting multiplication and division

Multiple Choice Questions

Question 1:

Which array shows 12 divided by 3?

Correct Answer: 3 rows of 4

Question 2:

If you have 20 stickers and want to put them into 4 equal groups, how many stickers will be in each group?

Correct Answer: 5

Question 3:

Which division problem does an array with 5 rows of 3 circles show?

Correct Answer: 15 ÷ 3 = 5

Question 4:

What does division mean?

Correct Answer: Sharing equally into groups

Question 5:

An array has 6 rows of 2. What is the total number of items in the array?

Correct Answer: 12

Question 6:

Which of these is NOT a way to think about division?

Correct Answer: Adding repeatedly

Question 7:

You have 24 cookies and want to divide them among 4 friends. How many cookies does each friend get?

Correct Answer: 6

Question 8:

An array can help us understand division because it shows...

Correct Answer: Equal groups

Question 9:

If you divide 16 by 4, what number do you get?

Correct Answer: 4

Question 10:

Which array shows 21 divided by 7?

Correct Answer: 3 rows of 7

Fill in the Blank Questions

Question 1:

Division means to share equally into __________.

Correct Answer: groups

Question 2:

An __________ is a way to show division using rows and columns.

Correct Answer: array

Question 3:

The answer to a division problem is called the __________.

Correct Answer: quotient

Question 4:

In the problem 10 ÷ 2 = 5, the number 5 is the __________.

Correct Answer: quotient

Question 5:

Arrays help us see that division is the opposite of __________.

Correct Answer: multiplication

Question 6:

If you have 15 candies and divide them into groups of 3, you will have __________ groups.

Correct Answer: 5

Question 7:

Dividing 12 by 4 means putting 12 into __________ equal groups of 4.

Correct Answer: 3

Question 8:

When you create an array, you are making sure each group has the __________ number of items.

Correct Answer: same

Question 9:

An array with 4 rows and 5 columns has a total of __________ items.

Correct Answer: 20

Question 10:

If you divide 25 by 5, the answer is __________.

Correct Answer: 5

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

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