How to use the bar model/strip diagram to help you solve multi-step word problems
The bar model (also called a strip diagram) is my go-to in math! I don't know how I would teach math without it. It's such a natural way to model a problem. My students in intervention are really responding to it because the bar model is a great visual.
Now, I'm going to walk you through a problem. Take a look at problem #29. If you can't read it, the problem states:
Denise and 12 friends are going to the movies. Denise buys all the tickets in advance. Each ticket is $9.75. She also has an $8 off coupon. What is Denise's total for the tickets?
I help my struggling readers by reading the problem aloud while they whisper read along with me. Then, I have them read it one more time on their own.
Next, we discuss the problem in depth. I ask my students to do the following 3 things. Students can use highlighters or underline.
1) Find a sentence that is important and explain why it is important to the group.
2) Find a phrase that is important and explain why it is important to the group.
3) Find a word that is important and explain why it is important to the group.
We have had some great math discussions from doing this! It also helps me better understand their misconceptions.
Now, it's bar model time! Since this is a multi-step problem, the bar model is perfect because it visually shows each step. This is so helpful for kids.
Since Denise and 12 friends are going to the movies, the students will need to know that 12 + 1 = 13 people in all, so we will need to draw 13 parts. You can see below I used p to represent person and I only drew 4 parts and ...13 p for shorthand (not 13p). This shorthand means that there are 13 people who Denise will need to buy tickets for. (My students have been practicing this for quite some time, so they understand this shorthand. If you need to draw a whole divided into 13 equal parts, go for it!) Then, I labeled each part $9.75 since this is the cost per movie ticket or cost per person.
Below the labeled parts, I drew what I like to call "the grabber", which represents all the parts you need in order to solve for the total. We also added " - $8" after discussing the coupon will deduct $8 off the original total. While I am drawing the bar model on the whiteboard, my students are talking through the problem with me and they are drawing the same one on their small whiteboards.
Now, we are able to solve the first step. It's helpful to organize your work by numbering each step as you go. The first step is to multiply $9.75 by 13 people. I allow some time for my students to work on this step and look out for any computation or fact errors. Don't forget the decimal!
Then, we numbered the next step. The second step is to subtract $8 from the total. Again, my students worked independently and then, I guided them through the same step on the whiteboard. The final total with the coupon is $118.75.
After we solved the problem, my students and I collectively wrote a detailed sentence about the answer. Our sentence was: Her total with a coupon is $118.75.
We agreed that "with a coupon" was important to this sentence because it distinguishes that the final total was different from the original total since Denise used an $8 off coupon.
Don't be scared to try out bar models! Once you get used to them, you'll definitely keep it in your instructional tool box. You can use this problem as an example. Hope this helps you!
Here's another resource to help you. It's scaffolded and they're task cards! You can do a few a day and then, add it to your math centers or use as a small group lesson.
Solving Problems using a Strip Diagram Task Cards
Now, I'm going to walk you through a problem. Take a look at problem #29. If you can't read it, the problem states:
Denise and 12 friends are going to the movies. Denise buys all the tickets in advance. Each ticket is $9.75. She also has an $8 off coupon. What is Denise's total for the tickets?
I help my struggling readers by reading the problem aloud while they whisper read along with me. Then, I have them read it one more time on their own.
Next, we discuss the problem in depth. I ask my students to do the following 3 things. Students can use highlighters or underline.
1) Find a sentence that is important and explain why it is important to the group.
2) Find a phrase that is important and explain why it is important to the group.
3) Find a word that is important and explain why it is important to the group.
We have had some great math discussions from doing this! It also helps me better understand their misconceptions.
Now, it's bar model time! Since this is a multi-step problem, the bar model is perfect because it visually shows each step. This is so helpful for kids.
Since Denise and 12 friends are going to the movies, the students will need to know that 12 + 1 = 13 people in all, so we will need to draw 13 parts. You can see below I used p to represent person and I only drew 4 parts and ...13 p for shorthand (not 13p). This shorthand means that there are 13 people who Denise will need to buy tickets for. (My students have been practicing this for quite some time, so they understand this shorthand. If you need to draw a whole divided into 13 equal parts, go for it!) Then, I labeled each part $9.75 since this is the cost per movie ticket or cost per person.
Below the labeled parts, I drew what I like to call "the grabber", which represents all the parts you need in order to solve for the total. We also added " - $8" after discussing the coupon will deduct $8 off the original total. While I am drawing the bar model on the whiteboard, my students are talking through the problem with me and they are drawing the same one on their small whiteboards.
Now, we are able to solve the first step. It's helpful to organize your work by numbering each step as you go. The first step is to multiply $9.75 by 13 people. I allow some time for my students to work on this step and look out for any computation or fact errors. Don't forget the decimal!
Then, we numbered the next step. The second step is to subtract $8 from the total. Again, my students worked independently and then, I guided them through the same step on the whiteboard. The final total with the coupon is $118.75.
After we solved the problem, my students and I collectively wrote a detailed sentence about the answer. Our sentence was: Her total with a coupon is $118.75.
We agreed that "with a coupon" was important to this sentence because it distinguishes that the final total was different from the original total since Denise used an $8 off coupon.
Don't be scared to try out bar models! Once you get used to them, you'll definitely keep it in your instructional tool box. You can use this problem as an example. Hope this helps you!
Here's another resource to help you. It's scaffolded and they're task cards! You can do a few a day and then, add it to your math centers or use as a small group lesson.
Solving Problems using a Strip Diagram Task Cards
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