Division

Division

Divide Objects into Groups

Opening

Divide Objects into Groups

You can find 12 ÷ 4 by dividing 12 objects into 4 equal groups.

  • How can you use a similar method to find 89÷4?
  • Discuss this question with your partner.

12 divided by 4 = 3

Math Mission

Opening

Devise strategies for dividing a fraction by a whole number.

Mia’s Models

Work Time

Mia’s Models

Mia wants to divide 89 by 4. She draws two different models to represent the fraction 89.

Use one of Mia’s models of 89, or make your own model of the fraction, to help you solve the problem.

  • Divide 89 by 4.
  • Write a division equation to represent what you did.
  • Use multiplication to check your answer.

Can you divide your model into 4 equal parts? What is the size of each part?

 

Juice

Work Time

Juice

There is 34 quart of juice left in a carton. If the 6 members of the Nelson family share the juice equally, how much (in quarts) will each person get?

  • Write the division expression that you need to solve this problem.
  • Make a model.
  • Use your model, or use a method that does not involve a model if you prefer, to solve the problem.
  • Use multiplication to check your answer.

Can you find an equivalent fraction for 3 4 that is easy to divide into 6 equal parts?

Carlos’s Method

Work Time

Carlos’s Method

Carlos knows that division and multiplication are inverse operations. He knows, for example, that dividing by 4 is the same as multiplying by 14. He thinks that he can use this inverse relationship to help him divide a fraction by a whole number.

To solve 89 ÷ 4, Carlos writes the expression 89 × 14. He multiplies to get 836, and then simplifies 836 to the equivalent fraction 29. Carlos writes this answer: 89 ÷ 4 = 29.

  • Use Carlos’s method to solve 95 ÷ 3.
  • Use multiplication to check your answer.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Explain how you solved each problem.
  • Provide a comparison of the three problems.
    • What is similar about the problems?
    • What is different about the problems?

Challenge Problem

  • Create a real-world problem that can be solved by finding 23÷5.

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ methods for dividing a fraction by a whole number.

As your classmates present, ask questions such as:

  • Where in your model do you see the total amount that you divided into equal groups?
  • Where in your model do you see the number of equal groups?
  • Where in your model do you see the size of each group?
  • How can you use what you know about equivalent fractions to make the problem easier?
  • What do you know about the relationship between multiplication and division? How can this relationship help you solve the problem?

Divide Fractions by Whole Numbers

Work Time

Divide Fractions by Whole Numbers

Solve the problems using the method of your choice.

  1. 56÷5
  2. 37÷6
  3. 58÷8
  4. 158÷5

Use one of the following strategies or one of your own.

  • Visualize the problem.
  • Draw a model.
  • Use the fact that division is the inverse of multiplication. For example, dividing by 2 is the same as multiplying by 1 2 .

Divide a Fraction by a Whole Number

Formative Assessment

Summary of the Math: Divide a Fraction by a Whole Number

Write a summary about how to divide a fraction by a whole number.

Check your summary.

  • Do you describe at least one way that you can use a model to divide a fraction by a whole number?
  • Do you explain how to use the inverse relationship between multiplication and division to divide a fraction by a whole number?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

One thing that still confuses me about dividing a fraction by a whole number is …