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Visualizing in Math- Strip Diagrams

Visualizing in math is a crucial thinking skill students need in order to be successful in math. There are many approaches in how we can make thinking visible but today we are going to focus on using strip diagrams.

As a teacher, one of the things I see my students struggle with the most is knowing when they should add, subtract, multiply, or divide. A lot of times I would tell my students to visualize the problem in their head but the problem is I couldn't see what my students were visualizing. Were they breaking apart the problem in their head to help them decide if they would add, subtract, multiply, or divide? Or were they thinking about what they were going to do once school was over? I needed a way to make their thinking more visible not only for me but for them as well.

I tried several different approaches but what I have found works the best are strip diagrams. Strip diagrams are a concrete way to help students break down problems to decide what operation(s) they need to solve the problems. Two of my main questions I ask my students as we begin this process are:

  1. Do we have a total or need a total? If we need a total, we are adding or multiplying. If we have a total, we are subtracting or dividing.

  2. Are we joining or seprating? If we are joining we are adding or multiplying. If we are separating we are subtracting or dividing.

These two questions prompt my students on where they should begin to solve the problem. From there we will use the appropriate strip diagrams to solve the problem. Using a strip diagram will help students visualize and reason through the problem.

In the next half of this post I am going to share with you how to use strip diagrams for each type of operation. In my next post I will share with you some different activity ideas you can use in your classroom to help your students practice this skill.

Addition- Joining

Addition and subtraction strip diagrams are the most commonly used in the classroom. Below you will find an example of an addition strip diagram. The top box represents the total or the whole Since we do not have a whole we place a question mark in this box.

The two addends or parts that we are joining go in the bottom two boxes. We join these two parts to get the whole. The parts equals the whole.


Subtraction- Separating

Let's talk subtraction strip diagrams. When we are subtracting we know that we have a total and we are going to seprate or subtract a part from that total.

In the strip diagram below we have a total of 57 and we are going to separate the part 33 from the total. The question mark represents the missing part that when added to 33 will give your whole 57.



A comparison strip diagram does not have a total bar.

If I have 13 cookies and my sister has 4 cookies, how many more cookies do I have than my sister?

In this case I do not have a total bar in my strip diagram because I am not joining or separating. I am simpy comparing to see how many more cookies I have than my sister.


Multiplication Strip Diagram

13 groups of 9 or

13 x 9

A multiplication diagram shows the groups and how many are in each group. The question mark shows we are missing the total, or we need a total. When students are creating or reading a multiplication strip diagram I have them write "___ groups of ___ " off to the side and then fill it in. Again the boxes represent the number of groups and number inside the box represents how many are in each group. In the problem above it would be 13 groups of 9 or 13 x 9.


Division Strip Diagram

In division we have a total and we are wanting to seprate or divide the total into equal groups. In the strip diagram we know we have a total of 48 and based on the picture we are wanting to divide the 48 into 8 groups. The problem will be 48 divided by 8.

Students will solve the problem and will find that 48 divided by 8 is 6, as shown in the completed strip diagram below.


In my next post we are going to look at different activities we can use in the classroom to help students practice using strip diagrams for addition, subtraction, multiplication, and division. Stay Tuned!

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