Lesson 2Meanings of Division
Learning Goal
Let’s explore ways to think about division.
Learning Targets
I can explain how multiplication and division are related.
I can explain two ways of interpreting a division expression such as
. When given a division equation, I can write a multiplication equation that represents the same situation.
Warm Up: A Division Expression
Problem 1
Here is an expression:
What are some ways to think about this expression? Describe at least two meanings you think it could have.
Activity 1: Bags of Almonds
A baker has 12 pounds of almonds. She puts them in bags, so that each bag has the same weight.
Clare and Tyler drew diagrams and wrote equations to show how they were thinking about
Problem 1
How do you think Clare and Tyler thought about
Problem 2
Explain what each division expression could mean about the situation with the bags of almonds. Then draw a diagram and write a multiplication equation to show how you are thinking about the expression.
Are you ready for more?
Problem 1
A loaf of bread is cut into slices.
If each slice is
of a loaf, how many slices are there? If each slice is
of a loaf, how many slices are there? What happens to the number of slices as each slice gets smaller?
What would dividing by 0 mean in this situation about slicing bread?
Lesson Summary
Suppose 24 bagels are being distributed into boxes. The expression
24 bagels are distributed equally into 3 boxes, as represented by this diagram:
24 bagels are distributed into boxes, 3 bagels in each box, as represented by this diagram:
In both interpretations, the quotient is the same (
These two ways of seeing division are related to how 3, 8, and 24 are related in multiplication. Both
can be read as “3 groups of 8 make 24.” can be read as “8 groups of 3 make 24.”
If 3 and 24 are the only numbers given, the multiplication equations would be:
In both cases, the division