Unit 3, Lesson 2
Meanings of Division
Accelerated 6
2.2
Activity
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.
-
2.3
Activity
Mai is making a bubble mixture. The recipe says to add sugar to help the bubbles last longer.
-
To make one batch of mixture, 14 grams of sugar is needed. To get that amount, Mai uses 4 packets of sugar.
- In this situation, what does the value of represent?
- Find the quotient. Show your reasoning. If you get stuck, consider drawing a diagram
-
Mai needs 26 fl oz of water to make a larger amount of the mixture. The only measuring tool she has is a 4-fl oz scoop. How many scoops will it take to measure 26 fl oz of water?
- Will the answer be more than 1 or less than 1?
- Write a multiplication equation and a division equation that represent this situation.
Use “?” to represent the unknown quantity. - Find the unknown quantity. If you get stuck, consider drawing a diagram.
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?”)
None