Creating Word Problems With Division

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SWBAT write and solve division stories involving sharing objects equally.

Big Idea

Writing in math develops problem solving skills because, as a writer, the student must organize and describe their mathematical thinking.


15 minutes

You already know how to write and solve addition, subtraction, and multiplication stories. Today you will be learning to write and solve division stories!

On the board write 3 x 2  =____

What are some multiplication stories you could write about this number sentence? Students should be able to produce answers that involve creating equal groups ie: Three teams are playing a game. There are two players on each team. How many players are there in all? 

Well, number stories provide information and ask a question, which we have practiced doing all year. Now we will work on creating and solving division problems of our own.  

It is useful to create an anchor chart with the essential parts of a problem to provide a scaffold for struggling students to refer to. The pieces of a problem that I introduced are: -The problem must have a total number of objects -The problem must involving sharing them equally or dividing them up equally. I did not provide additional guidance beyond this because I didn't want to over complicate the process for them. I wanted to see what they produced with limited restrictions.

I write a student created problem on the board, and then I call on a student to help us identify if it has all of the parts we need to solve it.

On the board write ____.

Work with your partner to write a division story for this number sentence. Just remember that we have to share equally so nobody gets their feelings hurt when we divide! 

I pair students up quickly on the carpet so that they can get straight to work. It is important here to give groups time to discuss so they can justify their ideas to one another (MP6). I give students time to write their stories and when finished they raise their hands so that I can pair them with another group that is finished so that they can share their work. This is important because the common core expects students to be able to explain themselves, construct arguments and critique one another’s work (MP3). 

Guided Practice

20 minutes

I’m going to give each group a division card so start thinking now about some good stories you could tell to help explain it. I need you to work with your partner to write a division story for the number sentence on your card, and we are going to try solving each others stories when we are finished.

Give groups a division card (flash card or hand make them on index cards). I use flash cards because they are already made, but if students were struggling with division I would hand make cards with smaller numbers on index cards until they mastered the concept. Students must determine which use of tools, including pencil and paper and concrete models, they might need in order to create and solve their problem (MP5). I lean in on group conversations to make sure they’re all on the right track.

Collect the stories and re-hand them out to groups. I want you and your partner to solve the division story you were given. Remember to show all of work by writing a number sentence and drawing a model to match your work (MP4). 

Independent Practice

20 minutes

You guys are great authors of math problems! I think you are ready to write your own problems now, without a partner! I’m going to put division problem cards out, so choose one carefully, because you’re going to write a division problem for the rest of us to solve. We will use these problems as we continue to study division, so please put the problem on 1 side of the paper and solve it on the back. We don’t want to give the answer away!

I often allow students to spread out around our room, write in crayon and write in markers, just to make it more fun. It's amazing how excited they get about writing a math problem with crayon or marker. As students work I take my iPad around and take videos of students working. I will play the videos at the end of the lesson so students are able to hear the thinking of their classmates while they were creating problems, looking for solutions and recognizing relationships (MP1). My goal with all lessons is for students to develop a range of strategies in solving multiplication and division problems so that they become more fluent problem solvers (3.OA.7). This goes beyond memorization of facts to create a deeper understanding of the relationships between multiplication and division.