Tips for Teaching Addition and Subtraction Word Problems (EP9)

Teaching Tips for Addition and Subtraction Word Problems

Hey, everyone, and welcome to another episode of Elementary Math Chat. Today’s episode is another content-specific episode, and we’re going to talk about how to help our students overcome the challenges that they experience with word problems, and we’ll be specifically talking about addition and subtraction word problems.

Today, I’ll start by taking you through the six problem-solving steps that I had my students use when it came to addition and subtraction word problems. I’ll then go into a few different ways that you can incorporate word problems into your daily instruction, weekly instruction, and monthly, and then I’ll end by sharing a few different strategies that helped my students who were struggling.

I think teaching students how to solve word problems is one of the most, if not the most challenging parts of being a math teacher. And I remember struggling with word problems when I was a student as well. So, it’s not like this is something new that we’re all of a sudden dealing with.

The problem for me was that I don’t ever remember being taught how to solve word problems, and students need to be taught how to solve them. They can add and subtract all day long. But if we don’t teach them when to add, or when to subtract, they are going to fall short when it comes to solving word problems.

Now for many students, their struggles with reading can play a big role in this. But there’s a little more to it than just reading the problem. The biggest struggle students have with word problems is not knowing what the question is asking, and therefore not knowing which operation they should use. So, the struggle is not in reading the problem, the struggle is in understanding it.

So, let’s talk about some ways that we can help them with that. I’ll start by sharing a few dos and don’ts when it comes to word problems. I do think schools should be as consistent as possible with the way they approach problem-solving, especially within your lower grades K-2 and then upper grades 3-5. This would be a great topic for a professional development session or something to discuss during a math vertical team meeting if you have those.

Vertical teams are where you would have one math teacher per grade level, and they meet together and discuss things that can be implemented across the grade levels. So, problem-solving would be a great topic for vertical teams.

If you can discuss problem-solving with your entire staff, then that’s even better. My school was lucky enough to have Greg Tang visit our school the week before students came, and problem-solving was a huge focus of his presentation. So, a lot of tips I’m sharing today come from what I learned through his presentation.

Here’s another do I’m going to add to this list. If you ever get the chance to attend a Greg Tang presentation, do everything you can to make that happen. He really is the best, and I’ve actually been lucky enough to see him twice. He has so many great ideas and a lot of them are around problem-solving.

Let’s move on to the don’ts when it comes to teaching word problems. This first one involves acronyms. I know there are a lot of cute acronyms out there. I literally Googled math problem-solving acronyms, and there are a bunch of them. I’ve heard of a few of them. I’ve heard of the CUBES strategy and the RACE, R-A-C-E strategy. But there’s also the IDEAL strategy and the RISE, R-I-S-E strategy, or even the CLEAR strategy.

I’m not saying acronyms don’t work. Clearly, they do if you think about PEMDAS. I know a lot of ELA teachers use acronyms for writing prompts that work really well. But the big difference with those acronyms is they are consistent between all of the grade levels in the school. Anytime you are working with the order of operations, you are going to use PEMDAS, and that is why it works.

So, if every teacher in your school uses the same acronym to teach word problems, then you might have some success with it. But what happens if, in second grade, the teachers use the CUBES strategy, and then in third grade, those teachers use the RACE strategy, and then in fourth grade, they use the CLEAR strategy? Do you see how that could be confusing for students?

 My honest opinion is that we need to take the focus off of the acronyms and put it toward consistent school-wide steps that focus more on comprehension and understanding of the problem, rather than following an acronym.

So, here are my recommendations for how you can do just that. The first thing we need to make sure all students do is to read the entire problem. It sounds like an obvious first step, but it means that we don’t want them to skim and only focus on keywords. It’s not that you can’t discuss keywords, they can help in some situations. But that can’t be your only approach because sometimes words have more than one meaning.

For example, the word each can mean both multiply and divide. The word more can mean both add and subtract, depending on the context. So, some keywords can be tricky, and we don’t want to rely on them alone.

My recommendation for helping address these misconceptions is to do a series of number talks around them. You’ll want to do addition and subtraction separately, and then by the end of the number talk, you will have a word web that you can turn into an anchor chart and post around your room.

The focus of your number talks should be on discussing the meaning behind addition and subtraction, and how we use addition and subtraction in our lives outside of school. For example, you can ask them to think about a time when they had to add something together. This could be when they were cooking, playing a video game, or when they put up a lemonade stand. Depending on your grade level, you may need to prompt them a little bit, and that’ll get them on the right track.

So, they may think about a situation where they had to combine two or more things together, like when they were cooking, or another time when they had to find a total, or they had to add their points together to figure out their score. As they begin to share their examples, then what you want to do is to create a word web and then add these words to the word web.

So, your word web for addition could have the keywords for addition, but then also have your student’s connection to this word. For example, you would have the word total on the word web, and then underneath that word total, you could have something like, “Marcus found the total when he added up his points from both games.” This is going to help them make a real-world connection with every single word on your word web that means addition.

Then do the same thing with subtraction. This will be a little more challenging to think of. So, you may need to prompt them a little bit more with this one. You could ask them when they had something taken away, or when they sold something, maybe it was Girl Scout cookies, or compared the difference between two things. That’s a big one for upper elementary.

Again, each example that is named is then supported by a real-world example, and this way, their focus is on that real-world connection to the math term, and not just the key word that they’re trying to memorize. Now you have these anchor charts that they can refer to when they get stuck and they’re unsure if they should add or subtract.

So again, step number one is to teach our students to read the entire problem. Let’s move on to step number two.

Step number two is to ask yourself these two questions, and the point of these questions is just to get to know the problem a little bit better. Who or what is the problem about? And are you missing the part, or are you missing the total?

For example, the question might be about Casey’s dogs, or it might be about Marion’s coin collection. That’s all you’re asking them to think about. They might struggle a little bit to answer the question of are you missing the part or the total, but we’ll take care of that in the next step.

One thing Greg Tang reinforced over and over was that we should be teaching our students to take notes as they solve word problems. So, as they ask themselves the questions of who is this about, what is this about, am I missing the part or the whole, they can jot that down. It’s similar to when they annotate the text in reading, but they’re doing it with a math problem. So, it does make sense.

Another example would be if a question is about how much Kristen’s dog has grown over the years, and she wants to know how much it weighs now. Well, they might write down that it’s about Kristen’s dog and that they’re missing the total in the problem, and they don’t have to write it in a sentence. It can just be Kristen’s dog, total. That’s it, and this will prepare them for step number three, which is to write an answer statement.

Answer statements are where you take the question and rewrite it as a statement. For example, if the question is, how many total pounds does Kristen’s dog weigh now, the answer statement could be Kristen’s dog weighs _____ pounds. What answer statements do really well is they help focus their attention on exactly who or what they need to solve for. It’s obvious that they need to find the total weight of this dog.

Now, you’ll notice a lot of times in your math textbook, the answer statements are written there. They’re usually at the bottom. But it’s also important that we teach our students how to write their own. So, after they’ve written their answer statement, they move on to step four, which is to draw and label a model.

Drawing a model is part of the note-taking process. It’s just more of a visual way to take notes. For addition and subtraction, these could be part-part-total models or comparison models. It sounds kind of strange to call them part-part-total models, you probably call them part-part-whole, and that’s what I did too. But Greg Tang made a good point. He said you should only refer to them as part-part-whole if you’re talking about fractions. Otherwise, it’s a total, and that makes so much sense.

Think about if you looked in your closet at your shoes, and you counted up all the shoes that you had. You would say you have a total of 20 pairs of shoes. You wouldn’t call them a whole. Or if you had a total number of points at the end of a game, you wouldn’t call that your whole. You would call your total. So, it makes a lot of sense.

Anyway, going back to step number three, which is to draw a model. Once they have this model drawn, then they go back through the story and start labeling the model. And then by the end, they’ll be able to decide whether they should add or subtract. If they’re missing the total, they know they need to add. If they’re missing a part, they know they need to subtract.

And that takes us to step number five, which is to write an equation to solve. So, this would be either an addition equation or a subtraction equation. Once they have their answer, then they’re ready for the final step, which is step number six, fill in the answer statement to check for reasonableness, and make sure you’re reading this answer statement. Don’t just put it in there and move on.

This is where a lot of them will realize that they made a mistake because they’ll have something like, Kristen’s dog weighs 500 pounds. And of course, that does not make sense. So, putting their answer within their answer statement, and reading it out loud really does force them to check their answer for reasonableness.

Let’s do a quick recap of these problem-solving steps before we move on. Step number one is to read the entire problem. Step number two is to ask yourself who or what the problem is about, and are you missing the part or the total. Step number three is to write an answer statement. Step number four is to draw a model and label it with information from the story. Step number five is to write an equation and solve, and step number six is to fill in your answer statement with your answer to check for reasonableness.

Now, I know every single chapter has a problem-solving lesson. So, you’re going to get this in at least once a chapter. But for them to really become efficient and comfortable with this process, you’ll want to provide additional activities for them to practice, and I have three suggestions for how you can do this.

I’m going to circle back to Greg Tang one more time for my first suggestion. On his website, there is a word problem generator that will create word problems for all four operations within 1000. You can customize the problem by selecting what range of numbers you want.

I always chose between one and 1000 for fourth grade, but you can stay within 100 if you teach the lower grades. I don’t believe it goes above 1000 though, but for me, my focus was always on helping them decide whether to add or subtract. So, I didn’t really care about how challenging the numbers were.

You can also select what part of the problem you want to be unknown. For example, whether the starting number is unknown, or the change is unknown, and it will generate a word problem for you. Then if you select hint, a bar model will appear to help students decide whether to add or subtract. And then when you’re finished, you hit check, and the answer is revealed.

This is a great activity to do a couple of times a week. I would even suggest daily while you’re in your addition and subtraction unit, and you can do this with a vertical team of students. I know I talked about vertical teams of teachers a little bit earlier, but vertical teams of students was something that I discovered when I was subbing last year. I never did this in the classroom.

The reason they’re called vertical teams of students is because literally, students are standing vertically while they solve these problems. Their vertical team is a really small team, so it’s only two to three students, and you spread them around the room and they solve the problems using either portions of your whiteboard, or just boards that are placed around the room.

They really enjoyed solving the problems in their vertical teams, and I liked that they were standing and interacting with each other. It got them up and moving, and it allowed them to work together with other peers. This was something they did every single day. So, this is another way you can give your students extra practice with word problems.

I will have the link to the word problem generator in the show notes and that way you can play around with it a little bit.

Another recommendation is to do a problem of the month. When I did this. I had a whole problem-solving bulletin board in the back of my room, and each month I picked eight students who showed exceptional work and I displayed them on this bulletin board.

I also did not make up these word problems on my own. I would go through the textbook and any question that we didn’t get to that I felt like they needed practice with, I would type them up in my template, and then that would be their problem of the month.

If you’re interested in doing a problem of the month, I will put my free and editable problem-solving template in the show notes, and you can download that, type in your problems, and you can do this with your students each month.

The third and final way you can practice word problems is with choice boards. You can put in a worksheet that you find that has word problems, or you can make one on your own by using the word problems from the generator I talked about. You would just have to copy and paste them in a document, and then put them on your choice board. So, the word problem generator can be a daily practice, the problem of the month can be a monthly practice, and your choice board can be a weekly practice. 

Finally, I want to leave you with some suggestions to try if your students are having a hard time with word problems. It can be difficult to keep track of everything going on within a word problem, especially if it’s multi-step. So, in those cases, I always have students draw a t-chart. One side of the t-chart is for step one, and the other side is for step two. You’ll even see in my problem of the month template, I have it set up that way.

So, if they are supposed to add on step one, have them draw a bar model and write an equation under the left side of the t-chart. If they need to subtract for step two, have them do this on the right side of the t-chart. It’s the simplest idea, but it really does help organize their thoughts.

Another tip that helped my strugglers was to replace the numbers with very basic numbers. I’m talking single-digit numbers. Sometimes those large numbers in addition and subtraction problems become a real barrier for them, and the smaller numbers can help them focus more on the meaning of the story and make more sense of it. A lot of times, this helps them figure out whether they should add or subtract. So, that is one I recommend trying.

My final tip for today is to post these problem-solving steps in your classroom, and that way you can refer to them when you’re teaching, and your students can refer to them when they’re solving their word problems. I know there’s no acronym to follow, but they will become routine for you and for your students if you make them a part of your routine, so make sure you read through them every single time you solve a word problem.

If you want more information about these problem-solving steps, I will have a copy of these in the show notes that you can download, and I’ll also link to an editable PowerPoint lesson on problem-solving with addition and subtraction. You can grab that if you’re looking for even more practice.

I hope you’re excited to try some of these new ideas, either the new problem-solving steps, the word problem generator, or even the problem of the month. A little practice really does go a long way when it comes to word problems.

All right, well, let’s get to today’s teaching Tip of the Week. Today I am sharing a tip for how to have a little fun with your students when it comes to word problems. Although, this one might be a little more fun for you!

My very funny and creative teammate came up with this idea when we were putting together a worksheet that had a whole bunch of word problems for our students to practice before an upcoming benchmark test.

Often, we would put their names in the word problems. But this time, we decided to do something a little different. This was in the month of December, so we decided to take all of the characters from the Christmas Vacation movie and put their names in the story problems. We wanted to see if our students would notice, and some of them did.

It was really funny to look around the room and see their expressions as they started to catch on to what we were doing, and it helped lighten the mood because nobody wanted to sit there and solve word problems all day.

We did this another time with task cards where all of the word problems had names like Zach, Jessie, Kelly, and Slater. I’m sure you can guess this one. It’s Saved By the Bell. We did it one more time with Full House names. So, have a little fun with your students and give this one a try.

Well, that is all for today’s episode. Have a great week, and I will see you next Tuesday.