# Writing a Multiplication Word Problem

Word problems are typically not students’ or teachers’ favorite part of the math lesson. When I talk with teachers, they are frustrated with teaching multiplication word problems.

I think one of the things we have been missing is teaching students the structure of what is involved in any multiplication word problem. “Look for and make use of structure” is the Common Core Mathematical Practice Standard 7. I have seen time and time again this practice playing a significant role in how a student is able to understand the content being taught. With a good understanding of the structure of multiplication in the context of a story, word problems can be created and understood.

I went into a fourth grade class and tested this idea out. We began the lesson brainstorming different scenes that would be engaging for the students. I gave the students cards that were labeled: group, in each group, and total. I explained that in every multiplication problem there are three numbers involved: what is in each group, how many groups, and what is in the total. Then we walked through as a class one of the scenes.

I modeled writing a word problem using students on a bus. At the end of the lesson, the students got into groups and wrote one or two problems themselves. Here are a few examples of what they wrote.

**There were 2 malls. They each had 10 stores. How many stores were there altogether?**

**There were 4 trailers. Each trailer holds 14 cows. How many cows were there?****There were 8 kids in the candy store. They each ate 32 pieces of candy. How many pieces of candy were eaten?**

**There were 5 stores. Each shopper bought 500 shirts in each store. How many shirts did they buy in all?**

And so teaching multiplication word problems becomes easier. Once students understand how to brainstorm their own groups and what is in each group, they will write endless word problems–all about things they are interested in. Students will become engaged and build word problems through the lens of the structure of multiplication.

This is also a great way to teach writing equations for word problems. I have used it with my 7th graders. We do several examples together on the board, and show how the pattern of the word problem can be turned into an equation that represents it. Then I give them simple equations, like 7+4 = 11 and have them do the reverse and write the word problem for that equation. (It also requires a higher level of Bloom’s Taxonomy when they are creating their own word problems.) I have often taken their word problems that they write and used them on the equations test at the end of the unit. They are really thrilled when they see their own work on an assessment!

Have you done this with fractions? I have done this also and it is awesome to watch how they create their problems.

What about multi step word problems, how would you structure teaching that? Our kids struggle so much with them.

I have done this and called it ‘Create a question’ The groups write out questions during warm up time. I do this a couple of days and then I pick 10 and shrink them or retype them and give as a quiz at the end of the week. I have animal figures, and that is how I group them, when they enter they randomly grab an animal and that is their think tank group.

This is a great idea…why limit it to multiplaction? I almost did not read the article because it was about mulitplcation and I teach 2nd grade. This would be great for addition and subtraction. Look into Thinking Math I think you will like it.

This is amazing!

I have a question…Did the children answer the problems they created?

I love having kids do the word problems themselves. I would do this with my third graders, and it gave them so much ownership in the experience. And they want to try and stump their classmates, so they tend to write more challenging problems than I would necessarily give them, which is great.