Lesson 5How Many Groups? (Part 2)
Learning Goal
Let’s use blocks and diagrams to understand more about division with fractions.
Learning Targets
I can find how many groups there are when the number of groups and the amount in each group are not whole numbers.
Warm Up: Reasoning with Fraction Strips
Problem 1
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 ?
Activity 1: More Reasoning with Pattern Blocks
Use pattern blocks to answer the questions.
Problem 1
If the trapezoid represents 1 whole, what do each of the other shapes represent? Be prepared to show or explain your reasoning.
1 triangle
1 rhombus
1 hexagon
Print Version
If the trapezoid represents 1 whole, what do each of the other shapes represent? Be prepared to show or explain your reasoning.
1 triangle
1 rhombus
1 hexagon
Problem 2
Use pattern blocks to represent each multiplication equation. Use the trapezoid to represent 1 whole.
Problem 3
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.
Problem 4
Select all the equations that can be used to answer the question: “How many rhombuses are in a trapezoid?”
Activity 2: Drawing Diagrams to Show Equal-sized Groups
Problem 1
For each situation, draw a diagram for the relationship of the quantities to help you answer the question. Then write a multiplication equation or a division equation for the relationship. Be prepared to share your reasoning.
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? The water hose fills a bucket at
gallon per minute. How many minutes does it take to fill a 2-gallon bucket?
Are you ready for more?
Problem 1
How many heaping teaspoons are in a heaping tablespoon? How would the answer depend on the shape of the spoons?
Lesson Summary
Suppose one batch of cookies requires
We can think of the question as being: “How many
Let’s use pattern blocks to visualize the situation and say that a hexagon is 1 whole.
Since 3 rhombuses make a hexagon, 1 rhombus represents
Other kinds of diagrams can also help us reason about equal-sized groups involving fractions. This example shows how we might reason about the same question from above: “How many
We can see each “cup” partitioned into thirds, and that there are 6 groups of