Unit 4, Lesson 8
How Much in Each Group? (Part 1)
Grade 6
8.1
Warm-up
Here is a tape diagram.
- Think of a situation with a question that the diagram can represent. Describe the situation and the question.
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Trade descriptions with your partner. Answer your partner’s question.
8.3
Activity
Here are three diagrams and three descriptions that represent situations about filling containers of water.
3 fraction bar diagrams. Diagram A, diagram B, and diagram C. Diagram A 2 equal parts. 1 and the fraction 1 over 2 parts shaded. 1 part labeled unknown quantity and 1 container. One and the fraction 1 over 2 parts labeled 15 cups. Diagram B, 2 equal parts. Both parts shaded. 1 part labeled unknown quantity and 1 container. Total labeled 15 cups. Diagram C, 3 equal parts. 1 part shaded and labeled 15 cups. Total labeled the unknown quantity and 1 container.
- Tyler filled 2 equal-size bottles with 15 cups of water. How much water was in each bottle?
- Kiran filled pitchers with 15 cups of water. How much water was in the full pitcher?
- Priya needed 15 cups of water to fill pail. How much water is needed to fill 1 pail?
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Match each situation to a diagram. Be prepared to explain how you know.
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Tyler:
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Kiran:
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Priya:
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- Choose one situation. Write a multiplication equation and a division equation to represent the situation. Then answer the question.
8.4
Activity
Here are three diagrams and three descriptions that represent situations about sections of highways.
3 fraction bar diagrams. Diagram E, diagram F, and diagram G. Diagram E, 2 equal parts both shaded. 1 part labeled unknown quantity and 1 section. Total labeled the fraction 3 over 4 mile. Diagram F, 3 equal parts. 1 part shaded. 1 part labeled the fraction 3 over 4 mile. Total labeled unknown quantity and 1 section. Diagram G, 2 equal parts. One and the fraction 1 over 2 parts shaded. 1 part labeled unknown quantity and 1 section. One and the fraction 1 over 2 parts labeled the fraction 3 over 4 mile.
- Priya’s class has adopted two equal sections of a highway to keep clean. The combined length is of a mile. How long is each section?
- Lin’s class has also adopted some sections of a highway to keep clean. If sections are mile long, how long is each section?
- A high school adopted a section of highway to keep clean. If of the section is mile long, how long is the section?
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Match each situation to a diagram. Be prepared to explain how you know.
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Priya’s class:
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Lin’s class:
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High school:
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- Choose one situation. Write a multiplication equation and a division equation to represent the situation. Then answer the question.
Student Lesson Summary
Sometimes we know the amount for multiple groups, but we don’t know how much is in one group. We can use division to find out.
For example, if 5 people share pounds of cherries equally, how many pounds of cherries does each person get?
We can represent this situation with a multiplication equation, a division equation, and a diagram:
A fraction bar diagram. 5 equal parts. Each part labeled “unknown quantity.” 1 part labeled “1 person.” Total labeled “8 and one half pounds” and “5 people.”
can be written as . Dividing by 5 is equivalent to multiplying by , and . Each person gets pounds.
Other times, we know the amount in a fraction of a group, but we don’t know the size of 1 group. We can also use division to find out.
For example, Jada poured 5 cups of iced tea in a pitcher and filled of the pitcher. How many cups of iced tea fill the entire pitcher?
Here are equations and a diagram that can represent this situation:
A fraction bar diagram. 3 equal parts. 2 parts shaded and labeled “5 cups” and “the fraction 2 over 3 pitcher.” Total labeled “unknown quantity cups” and “1 pitcher.”
If of a pitcher is 5 cups, then of a pitcher is half of 5, which is . Because there are 3 thirds in 1 whole, there would be or cups in one whole pitcher. We can check our answer by multiplying: , and .
Notice that in the first example, the number of groups is greater than 1 (5 people) and in the second, the number of groups is less than 1 ( of a pitcher), but the division and multiplication equations for both situations have the same structure.
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