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6-8 Grade 6 Unit 4 Lesson 5

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Lesson 5

5.1 Warm-up 5.2 Activity 5.3 Activity Student Lesson Summary

Unit 4, Lesson 5

How Many Groups? (Part 2)

Grade 6

5.1

Warm-up

Reasoning with Fraction Strips

Write a fraction or whole number as an answer for each question. If you get stuck, use the fraction strips. Be prepared to share your reasoning.

How many s are in 2?
How many s are in 3?
How many s are in ?

Fraction strips depicting 2 in 8 different ways.

Are You Ready for More?

5.2

Activity

More Reasoning with Pattern Blocks

Your teacher will give you pattern blocks. Use them to answer the questions.

Four pattern blocks: One large yellow hexagon, one blue rhombus, one red trapezoid, and one green triangle.

If the trapezoid represents 1 whole, what does each of the other shapes represent? Be prepared to show or explain your reasoning.
1. 1 triangle
2. 1 rhombus
3. 1 hexagon
Use pattern blocks to represent each multiplication equation. Use the trapezoid to represent 1 whole. Sketch or trace the blocks to record your representation.
Diego and Jada were asked “How many rhombuses are in a trapezoid?”
- Diego says, “. If I put 1 rhombus on a trapezoid, the leftover shape is a triangle, which is of the trapezoid.”
- Jada says, “I think it’s . Since we want to find out ‘How many rhombuses . . . ?’ we should compare the leftover triangle to a rhombus. A triangle is of a rhombus.”
Do you agree with either of them? Explain or show your reasoning.
Select all the equations that can be used to answer the question: “How many rhombuses are in a trapezoid?”

5.3

Activity

Drawing Diagrams to Show Equal-size Groups

For each situation:

Draw a diagram to represent the situation.
Answer the question.
Write a multiplication equation or a division equation for the relationship between the quantities.

The water hose fills a bucket at gallon per minute. How many minutes does it take to fill a 2-gallon bucket?
The distance around a park is miles. Noah rode his bicycle around the park for a total of 3 miles. How many times around the park did he ride?
You need yard of ribbon for one gift box. You have 3 yards of ribbon. How many gift boxes do you have ribbon for?

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Student Lesson Summary

Suppose one batch of cookies requires cup of flour. How many batches can be made with 4 cups of flour?

We can think of the question as being: “How many s are in 4?” and represent it using multiplication and division equations.

Let’s use pattern blocks to visualize the situation and say that a hexagon is 1 whole.

Diagram of 4 hexagons. Each hexagon is made up of 3 rhombuses using pattern blocks.

Since 3 rhombuses make a hexagon, 1 rhombus represents , and 2 rhombuses represent .
We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.

Other kinds of diagrams can also help us reason about equal-size groups involving fractions. This example shows how we might reason about the same question asked earlier: “How many -cup are in 4 cups?”

Diagram with 4 rectangles, partitioned into thirds.

We can see each “cup” partitioned into thirds, and that there are 6 groups of -cup in 4 cups. In both diagrams, we see that the unknown value (or the “?” in the equations) is 6. So we can now write:

Glossary

None

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