Lesson 4How Many Groups? (Part 1)
Learning Goal
Let’s play with blocks and diagrams to think about division with fractions.
Learning Targets
I can find how many groups there are when the amount in each group is not a whole number.
I can use diagrams and multiplication and division equations to represent “how many groups?” questions.
Warm Up: Equal-sized Groups
Problem 1
Write a multiplication equation and a division equation for each statement or diagram.
Eight $5 bills are worth $40.
There are 9 thirds in 3 ones.
Activity 1: Reasoning with Pattern Blocks
Use pattern blocks to answer the questions.
Problem 1
If a hexagon represents 1 whole, what fraction do each of the following shapes represent? Be prepared to show or explain your reasoning.
1 triangle
1 rhombus
1 trapezoid
4 triangles
3 rhombuses
2 hexagons
1 hexagon and 1 trapezoid
Print Version
If a hexagon represents 1 whole, what fraction do each of the following shapes represent? Be prepared to show or explain your reasoning.
1 triangle
1 rhombus
1 trapezoid
4 triangles
3 rhombuses
2 hexagons
1 hexagon and 1 trapezoid
Problem 2
Here are Elena’s diagrams for
Problem 3
Use pattern blocks to represent each multiplication equation. Remember that a hexagon represents 1 whole.
Problem 4
Answer the questions. If you get stuck, consider using pattern blocks.
How many
s are in 4? How many
s are in 2? How many
s are in ?
Lesson Summary
Some problems that involve equal-sized 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: