So, the fun and games of learning how to make arrays, skip counting on number lines and using models to solve multiplication problems has lead to the equally exciting task of solving division problems. Everyone seems to be making great progress and making meaning of multiplication and division in real world problems, UNTIL … wait for it … wait for it … We mix the two together!
And here the real “fun” begins … A few students usually have an intuition about the structure of the problems and just “get it” with out much help, but the majority of students need direct, systematic instruction paired with hands on or pictorial examples to really, truly, deeply, understand the difference between multiplication and division in word problems. But where can we start?
Start with The Same Story!
I like to take the same story and write 3 word problems that use the same story, but ask 3 different questions. This really helps my students to see how multiplication and division can be the same and different in a word problem and help them to see to importance of analyzing the question. How many times have you had a student choose multiplication to solve a division problem because they “saw the word each”? Solving similar problems and then discussing the problems in relation to each other can really get students thinking deeper about problem solving.
For example, my 3 word problems might be:
- Jeff had 4 plates of cookies to take to his neighbors. He put 6 cookies on each plate. How many cookies was Jeff giving his neighbors?
- Jeff had 4 plates of cookies to take to his neighbors. He had 24 cookies and put an equal number of cookies on each plate. How many cookies did he put on each plate?
- Jeff had 24 cookies to take to his neighbors. He put the cookies on plates. Each plate had 6 cookies. How many plates did he use?
The three problems have the same story, but different clues are given and different questions are asked for each problem. (Get this FREEBIE here)
As we work through the problems, I ask my students these questions:
- What is the question asking me to find?
- Does the story tell me the total?
- Does the story tell me the number in each group?
- Does the story tell me the number of groups?
Draw pictures or make diagrams!
We write down the question and clues. Then draw a picture …
After discussing how we made our picture we make our number sentence.
Write a number sentence and label the answers.
Compare and Reflect!
Continue to have meaningful discussion as you practice!
As you continue working guided problems with students ask them to explain why they are choosing to multiplication or division. Encourage students to question each other when working in small groups or with partners. Have them write their own examples of word problems using the same story, but different questions.
3 thoughts on “Understanding Multiplication and Division in Word Problems”
These are great ideas for the interchangeable nature of multiplication and division. I know for me, as a kid, word problems were the bane of my existence. My brain seemed to go “offline” once I realized I was attempting to solve a math problem. It’s neat to see you offer your students those questions as ways to assist them in figuring the problem out for themselves.
Great ideas for teaching a hard concept!