Unit 4, Lesson 4
How Many Groups? (Part 1)
Grade 6
4.1
Warm-up
Equal-size Groups
Write a multiplication equation and a division equation for each sentence or diagram.
- Eight $5 bills are worth $40.
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- There are 9 thirds in 3 ones.
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Write a multiplication equation and a division equation for each sentence or diagram.
Your teacher will give you pattern blocks as shown here. Use them to answer the questions.
If a hexagon represents 1 whole, what fraction does each of the following shapes represent? Be prepared to show or explain your reasoning.
1 triangle
1 rhombus
4 triangles
3 rhombuses
Here are Elena’s diagrams for
Two diagrams of pattern blocks: The first is of one red hexagon composed of two red trapezoids. The diagram is labeled with the equation 2 times one half equals 1. The second diagram is of two blue hexagons where each hexagon is composed of three blue rhombuses. The second diagram is labeled with the equation 6 times, one third, equals 2.
Use pattern blocks to represent each multiplication. Sketch or trace the blocks to record your representation. Remember that a hexagon represents 1 whole.
Answer each question. If you get stuck, consider using pattern blocks.
Some problems that involve equal-size groups also involve fractions. Here is an example: “How many
Pattern-block diagrams can help us make sense of such problems. Here is a set of pattern blocks.
If the hexagon represents 1 whole, then a triangle must represent
Twelve triangles make 2 hexagons, which means there are 12 groups of
If we write the 12 in the place of the “?” in the original equations, we have:
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