# Teaching Tape Diagrams for Math Word Problems

As teachers, we know that tape diagrams, which are also known as bar models or strip diagrams, can be excellent tools for making sense of math word problems. But to our students sometimes they just seem impossible! (And if they’re new for you, too, don’t worry! I’ve got examples of tape diagrams below).

Never fear. I’ve got a trick that will help every student master using tape diagrams for word problems. And once they get it, they’ll be able to solve tricky grade-level word problems independently!

At this point in my career, I’ve taught every grade from K-5, and this trick works with all of them. I’ve used it successfully in 1st grade, 2nd grade, 3rd grade, and even for intervention or special education students in 4th grade and 5th grade. No student is too old or too young! (Well, kindergarteners might be too young).

## What is a tape diagram?

First things first. A tape diagram is just a specific way of representing the parts and total in a math word problem or story problem. Is it the only model you can draw? No. Is it the only way to solve a word problem? No. But can it be a really effective tool for thinking about and solving word problems, once you’ve mastered it? Yes!

## How to teach tape diagrams for word problems so that students actually get it

Here’s the trick: you need to teach your students the types of word problems. When they read a word problem, instead of circling the numbers or searching for key words, they should be thinking first and foremost about what type of word problem it is. And for addition and subtraction, there are only three types!

• Missing total problems
• Missing part problems
• Comparison problems

That’s it! Three types!

Here’s what they are and how to teach them:

### Missing Total Word Problems

A missing total word problem is any problem that gives you the parts, and asks you to find the total, or whole. Examples:

Sophia has 3 pencils and she buys 5 more. How many pencils does Sophia have in total?

In the aquarium, there are 2 clownfish and 4 angelfish. How many fish are there in total?

### Missing Part Word Problems

A missing part word problem is any problem that gives you the total and one of the parts, and asks you to find the other part. Examples:

A pet store had 9 bags of pet food, but 3 bags were sold to customers. How many bags of pet food are left in the store?

In a fruit basket, there are 9 apples and oranges. If 5 of them are apples, how many oranges are there?

5 kittens were in the basket. Some more kittens joined. Then there were 8 kittens. How many kittens joined?

### Comparison Word Problems

A comparison word problem is any problem that gives you both parts, and asks you to compare them in some way. Examples:

Grace ran 9 meters. This is 6 more than Oliver ran. How many meters did Oliver run?

In a box, there are 7 red pens and 6 blue pens. How many more red pens are there than blue pens?

A bottle can hold 2 fewer liters of water than the tank. The tank can hold 9 liters. How many liters can the bottle hold?

The trick is getting your students to identify the type of word problem before they start to solve. This requires lots of modeling and guided practice. Read the problem through with the students, and after reading think aloud. Something like: “Hmmmmm, do we know the total or the parts here? I notice that we know the number of clownfish and the number of angelfish, but not how many fish there are in all. It seems like the clownfish are one part, and the angelfish are the other part, and the total is all of the fish. We know both parts, but are still looking for the total. It must be a missing total problem!”

As you model, teach the tape diagram that goes with each kind of problem. You can even have examples of the different tape diagram types posted in the classroom for quick reference. This way, once the students know which kind of problem they have in front of them, they can draw the tape diagram, write an equation, and solve, no problem! The hard work is done!

## Tape diagram examples

Here are the only 3 tape diagrams that students will need for addition and subtraction story problems:

## How to get students to draw tape diagrams and solve word problems independently

As time goes on, fade out your modeling and start to ask students: Do we know the parts here? Do we know the total? What are we trying to find?

And then ask students to tell you what kind of problem it is! I like to have each student just write in shorthand on the paper or whiteboard what kind of problem they think it is: MP for missing part, MT for missing total, C for comparison.

The students who know are good to solve on their own. They can reference the posted tape diagrams as needed, but the way is clear once they know the problem type. I pull students who don’t have it down yet into a small group for more support, where we talk about the parts and total further. Once they understand the problem type, I send them off onto their own, as well.

And just like that, your students are independently problem solving! No more getting operations mixed up or getting stuck on tape diagrams.