What are some ways to think about this expression?
Describe at least two meanings you think it could have or two questions it could be used to answer.
2.2
Activity
Bags of Clay
An art teacher has 12 pounds of clay. 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 in this situation.
Clare's tape diagram and equation. 2 equal parts labeled 6. Total, 12. Equation blank times 6 = 12.
Tyler's tape diagram and equation. 6 equal parts labeled 2. Total, 12. Equation 6 times blank = 12.
How do you think Clare and Tyler thought about ? Explain what the parts in each diagram and each equation (including the unknown number) could mean in the situation.
Pause here for a class discussion.
What could each division expression mean in the situation with the bags of clay? Draw a diagram and write a multiplication equation to show how you are thinking about each of these expressions.
Student Lesson Summary
Suppose 24 books are being distributed into boxes. The expression can be understood in two ways:
24 books are distributed equally into 3 boxes, as represented by this diagram:
In this case, the quotient, 8, is the number of books in each box.
24 books are distributed into boxes, 3 books in each box, as represented by this diagram:
In this case, the quotient, 8, is the number of boxes used.
These two ways of seeing division are connected to the way 3, 8, and 24 are related by multiplication.
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 can be used to find the unknown value, and the “?” can mean one of two things:
The size of a group (as in “3 groups of what number make 24?”)
The number of groups (as in “How many groups of 3 make 24?”)
Glossary
None
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