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Here is a tape diagram.
Trade descriptions with your partner. Answer your partner’s question.
For each question:
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.
Match each situation to a diagram. Be prepared to explain how you know.
Tyler:
Kiran:
Priya:
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.
Match each situation to a diagram. Be prepared to explain how you know.
Priya’s class:
Lin’s class:
High school:
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.