What’s your go-to strategy for teaching word problems? I always encourage my students to use models. Modeling helps students make sense of a problem and catch mistakes before they happen.

Until recently, I didn’t care what kind of model my kids used. Drawings, tally marks, symbols were all fair game. But lately, I’ve found myself returning over and over again to tape diagrams in math. They are a nearly fail-proof way to work through a story problem and have helped my students become problem solving masters!

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## What exactly are tape diagrams in math?

A tape diagram is a drawing that looks sort of like a labeled segment of tape. It is used to illustrate number relationships. Tape diagrams in math are also known as strip diagrams, bar models, fraction strips, or length models.

In practice, tape diagrams in math look like this…

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Tape diagrams have become my go-to model when teaching math. They work for any type of word problem, but I especially love them for solving multiplication and division. These are new concepts for third graders, and tape diagrams are a wonderful way to visualize them.

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## How do you solve problems using tape diagrams in math?

To solve math word problems using tape diagrams, students must first ask, “Do I know the whole amount or total?”

If that number is supplied by the problem, fill it in. If not, put a question mark at the bottom of the diagram. Then look for other information in the problem and fill that in. The question mark always represents whatever the question is asking you to find.

Here is an example of how I use tape diagrams to teach division word problems:

Students will quickly begin to see a pattern… the bottom number is always the product of the top two numbers.

Therein lies the beauty of this model: It is self-correcting. If the top two numbers, when multiplied, do not equal the bottom, you’ve done something wrong.

A tape diagram is a great way for students to see how multiplication and division are related.

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When teaching students to use tape diagrams in math, it’s a good idea to have them write all four possible equations. So in the above example, we would also write ? x 4 = 32 and 32 ÷ ? = 4. This is important because it reinforces the concept of inverse operations and fact families. It also gives students a tool to use when they encounter problems with a missing factor or divisor.

Once my students are able to interpret word problems and solve them using tape diagrams, I teach them to analyze a tape diagram and write their own story problems to go with it. This requires higher-order thinking and really develops their mathematical minds.

Take a look at the tape diagram below. What could it represent?

As you can see, the tape diagram has seven sections. Each section contains three of something. The total amount is unknown and is represented by a question mark.

Here are some of the word problems my students created based on this tape diagram:

- I read 3 pages in my book every day. How many pages did I read in 7 days?
- There are 7 cars. There are 3 people in each car. How many people are riding in cars?
- Mom made a really big pizza. She gave each of her kids 3 pieces of pizza. How many pieces of pizza did the 7 kids eat?
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What about this one?

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Here we have a tape diagram with four sections. We don’t know how much is in each section, but we do know that the total is 32 as indicated at the bottom.

My third graders’ answers included:

- I made 32 brownies. If I share them with 4 friends, how many brownies can each friend have?
- I got 4 packs of gum. There were 32 pieces of gum in all. How many pieces were in each pack of gum?
- 32 kids wanted to play kickball at recess. They got into teams. If there were 4 teams, how many kids were on each team?
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These are some pretty good interpretations of the tape diagrams for a group of 9-year olds! As you can see, tape diagrams in math can be used for more than just solving a problem. They are a great way to build your students’ critical thinking skills.

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If you want to try some structured tape diagram activities with your students, this resource includes task cards and worksheets for solving multiplication and division word problems: