# 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!

What a fantastic idea! Students love when you use their work and create is the highest level of Bloom’s Taxonomy. Creating problem is very engaging for students because they are using things that they know and are relevant to them.

Thanks. It also gives me a chance to do some formative assessment about whether or not they really understand the meaning of the equation.

Yes I agree. Moments where students create their own word problem really allows you to see if they understand the concept.

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

Great idea to use fractions! I would guess that it would be harder to come up with scenes for the fractions to happen, but as long as the class brainstorms scene possibilities, it would be great. Students can be so creative, and they love to solve problems that come from their peers instead of the text book. I would love to see pictures and word problems your students write. Who knows, maybe we could consolidate the word problems students wrote from all over and publish it.

I am not sure how to load a picture into this program. I will look into it. I have a google account with the district I work in, maybe I can send it to you that way. I would love to share this idea. I started it when I learned it from another teacher 15 years ago.

Great! You could email it to me, or my email is also linked with google. You could just share it with me on google drive. Thanks! I can’t wait to see your students in action.

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

I think you just game me a future blog idea. What grade level do you teach? I can find a local classroom to field test some ideas with it. I agree that multi step word problems can be especially challenging for students. In my experience part of their struggles goes back to not solving one step problems easily and the other lies in their struggle to understand the concept and picture it. What is important is that they recognize their are multiple steps to the problem and the procedures they need to use to solve it. One thing that I have done that was successful is to do lessons where the students job was to simply tell me the procedure and NOT solve the problem. You could collect some multi step problems and single step problems and do a sorting task. The focus would be on if they recognize when there are multiple steps. Another task would be to have them draw or act out the multi step problems. You could even come up with a cute sign or sound that the class would do when they need to solve step one. Most of students experience is with single step problems, so we just have to give them more engaging experiences, so they know it is a possibility.

I am a math coach in a large urban district. I work with all grade levels. All good ideas, thanks. I’ll keep an eye out for that blog post. 🙂

Sounds good! I know with Performance Tasks being a big part of Common Core, students are going to need to become better with multi step word problems. I’ll have to see what works best with the students.

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.

That sounds great! I like they way you randomly group your students. 🙂 Have you done it with other procedures like division? How easy was it for you students to have the unknown in different places?

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.

Thanks! I would agree that it doesn’t have to be limited to multiplication. I haven’t used it with addition and subtraction yet, but I plan to in the future. If you try it please send pictures and some examples of the story problems the kids wrote. What I think is powerful is the way students recognize the parts that build a multiplication problem. The students love to write their own problems. I looked into the Thinking Math and watched a video about it. I think that kind of thinking is so powerful for students as they build a strong mathematical knowledge base.

I will get some pictures when they do it. You are absolutely correct, the students need to have a strong mathematical sense so they can continue on to more difficult math. I think if I was given the mathematical foundation I am trying to give my students I would be a mathematical genius. I think that is true for most people, limits were put on us… let’s not do that to our students!

This is amazing!

Thanks! I find it so exciting to watch kids engaged and excited to do word problems, since most of the time they find them so frustrating!

I teach College students and most of them hate word problems :). They get amazed when word problems are broken down!

My experience has been that very few people enjoy word problems, but this experience can help change that. When you can see the structure of the problems, you can create problems from a context that is in your world. (I would be interested to hear what college students write about. 🙂 )This is what engaged the students. Hearing the problems their peers wrote, really excited them and applied multiplication to their world.

I’ve tried an exercise with some of my students where they create problems from a context that is in their world, it was fun and I got a lot of ‘beer keg’ word problems :). Hey, it helped, so I can’t complain.

Helping them see the math in their world can be interesting and informative. Long term memory is supported when they can make a connection to their world, so keep giving them opportunities to connect math and the real world.

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

Great question! Yes each group answered their own questions. This kept the questions challenging and realistic for their peers to answer. As a class we had time to answer one question from each group. The more advanced students wrote more problems, but I made sure every group of students was able to write two problems.

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.

Yes, some of the students I worked with were really trying to challenge the others. It was really exciting to see the EL students successful with this as well. Each student was able to write a problem and feel successful.