Unit 4, Lesson 6
Using Diagrams to Find the Number of Groups
Grade 6
6.1
Warm-up
We can think of the division expression as the question: “How many groups of are
in 10?” Complete the tape diagram to represent this question. Then find the answer.
Complete the tape diagram to represent the question: “How many groups of 2 are in 7?” Then find the answer.
6.2
Activity
To make sense of the question “How many s are in 1?” Andre wrote equations and drew a tape diagram.
A tape diagram with three equal parts. The first two parts are shaded and are each labeled one third, total 1. A bracket is labeled 1 group of two thirds, and contains the first two parts.
- In an earlier task, we used pattern blocks to help us solve the equation .
Explain how Andre’s tape diagram can also help us solve the equation. -
Write a multiplication equation and a division equation for each question.
Then draw a tape diagram and find the answer.-
How many s are in 1?
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How many s are in 3?
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How many s are in 5?
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Student Lesson Summary
One batch of a recipe calls for kg of flour. If a baker used 2 kg of flour, how many batches did she make?
We can think of the question as “How many groups of kg make 2 kg?” and represent it with the equations:
To help us make sense of the question, we
can draw a tape diagram. This diagram shows 2 whole kilograms, with each kilogram partitioned into fifths.
Fraction bar diagram. 10 equal parts. Each part labeled "the fraction 1 over 5." Total labeled "2 kilograms" and "question mark batches." Every two parts labeled "1 batch."
We can see that there are 5 groups of in 2. Multiplying 5 and gives or 2, so is 5.
Sometimes the number of groups or the result of dividing is not a whole number. Suppose one serving of rice is cup. How many servings are there in cups?
Here are two equations and a diagram that represent the situation:
Fraction bar diagram. 16 equal parts. 14 parts shaded. 14 parts labeled “unknown number of groups” and “3 and one half cups.” Each part labeled the fraction 1 over 4. First 3 parts labeled “1 serving.”
The diagram shows 4 full groups of , plus 2 extra s, which make of a group. So is . We can check this quotient by multiplying and .
, and , which is or .
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