Solving Money Word Problems with Addition Strategies

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Well since our standards and textbooks are having students solve addition problems using strategies, I wanted to do this little mini-series all about what the addition strategies are and how they apply as kids are solving time and measurement and money addition problems. 

I’m Christina Tondevold, The Recovering Traditionalist and I hope that you’ll stick around for our last video in this series where we’re going to take a look at Solving Money Word Problems with Addition Strategies. In our quest to build our math minds so we can build the math minds of our students.

Watch the video or read the transcript below:

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The 4 videos in this series

Number Sense Courses

Free Training – Components of Number Sense in PreK-2

Free Training – Components of Number Sense in 3rd-5th

Now as I’ve said, this is the last video, if you’ve missed the other videos that talk about what the five strategies are, how they apply to solving elapsed time problems and measurement word problems, I’ll link below this video to all of those videos. So I always like to start off though with my warnings, in case you haven’t seen the previous videos. 

#1 When we’re talking about using strategies and having kids use strategies, when I first learned of this I wanted to go back and teach my students all of these ways that you could solve addition problems because all I knew was just the traditional “stack it and solve.” And once I learned these other ways I’m like, oh my goodness I want to share this with all of my students but what ended up happening was I would teach them and then it was like kids were just thoroughly confused. They didn’t understand any of the strategies, so the idea behind this is that I’m sharing these strategies because I want you to know what they are because your students will naturally do these without you directly teaching it. 

So it’s not something you directly teach, I want you to be aware of and watch for these and help illicit them in your students. The way that we do that is by laying a solid foundation of the numbers first and then kids naturally will want to use that foundation of what they know about numbers to help them solve these problems. 

So when we’re dealing with issues of money, kids need to understand how money relates to other types of money, like how does a dime relate to a quarter? Like all of those kinds of things we need to spend time developing, and how many cents does it take to make a dollar? All of that stuff is at that foundation, the number sense around the numbers that we use when we’re talking about money. You have to spend time developing that first and then these strategies start to come out. So I will link, below this video also, to a couple of free videos that I have about number sense and how we develop it for students. And it’s not about money numbers it’s just regular numbers but I want you to watch that and think about how it applies to helping your students understand more about money. 

#2 Is that I use specific names for these strategies, you may call them something different. The name really doesn’t matter. The only reason I think the name matters, is so that when we say the name we want it to illicit the strategy, like what’s the mathematics that the kids are doing? So the strategy is different than how we model it, I could do the strategy and I could write it down on paper differently than how you wrote that same strategy. I might show it on a number line, you might show it as an equation, it’s the same strategy we’re just modeling it different. So name the strategies based upon the mathematics that’s happening not the model, not the student’s name. You may need to pick your own strategy names but I’m going to give you the ones I use. If you like them, if they make sense to you, use those But I think it’s also beneficial to make sure that your whole school is in agreement about what you’re calling them. 

#3 The last warning, is that there is this base of five strategies but kids will do a combo of them. So if you see kids who are kind of like doing bits and pieces of it, it’s okay we don’t need to directly teach it. Kids naturally do these things and they will naturally combine strategies to do something that makes sense to them. That’s the big idea of this, is that these strategies happen when kids are trying to make sense of the problem using the knowledge that they have about the numbers. All right, so let’s dig in to looking at these strategies through the lens of money word problems. We are going to use the same problem and look at all five strategies using this one problem. 

So the problem that we are going to use to show all of these strategies is:

Jaeger has $73.86. He mows some lawns and makes $48.50.  How much money does he have now? 

Traditional Algorithm

We’re going to start with just the traditional algorithm of stacking it and solving it and then we’re going to look at the other strategies that kids might potentially use to solve this problem. Okay, so traditionally the way we were taught was to just stack these numbers and add, which is totally fine and kids will get the answer. As long as they remember all the rules and procedures right but the problem that I have with the traditional algorithm, not that I don’t want kids to be able to do this but that so many kids can do this without any understanding of the numbers or of money. 

So we’re going to take a look at the other strategies for addition and they may, to you, seem more complicated. Like why would I want kids to do this when they could just do this traditional algorithm and it’s so easy? But part of this series, we are also going to be looking at these strategies when kids are subtracting and I got to tell ya, when you get to subtraction with money this is the number one area where kids struggle. Heck, even adults struggle right? When we’re trying to get back change in a real life setting, when you’re out at the store so many people don’t know how to figure out how much money they get back. So we’re going to take a look at these strategies with addition because if kids are doing them with addition problems, they will be more likely to do them when we get to subtraction.

Compensating

Okay so the first one I want to take a look at is a kid who says, man that $73.86 is really close to $74. So I’m just going to do $74 plus the 48.50 and that gets me to $122.50. But they did not have $74 they only had $73.86 so that’s why I like to call this compensating because the kid did something they weren’t supposed to do, so now they need to come back and compensate for that. 

Well, the difference between what they had versus what they actually added back here with the 74 is that 14 cents. So they need to come back and take out that 14 cents. Now some of you are sitting there thinking, well my kids are struggling with subtraction, how are they going to subtract 14 right here? Well that’s one of the things that we work on when kids are doing whole numbers, you don’t have to just subtract the 14 if we think back to other strategies we’ve talked about like decomposing. When kids see this they can be like, okay $122.50, well if I take away 10 cents that would get me to 40 cents and then another 4 cents gets me to the 36 cents. 

They will start doing combinations of these and you feel like, well that’s a lot of steps but again, man think about all the number sense that kids are doing if they’re doing these strategies. Again, that’s why we don’t directly teach them because you cannot teach number sense. My saying is Number Sense is Caught, It’s Not Taught. So if kids don’t already have this number sense, trying to teach this strategy will be pointless, they will just become more frustrated. Again, these videos are just to expose you to ways that kids might potentially think about it beyond the traditional way that we were taught.

Give & Take

As we’ve talked about in prior videos, this next one of give and take is really similar to the compensating. It’s the kid who really wants to make the $73.86 a $74 but instead of just saying it’s $74 they just come over here and take the amount that they would need to be able to make this $74 and decompose this one to what’s left over. And then they can add those to get the $122.36.

Decomposing

Okay our next strategy is one I call decomposing because the kids will leave one of the numbers whole but then they’ll decide to break apart the other number to make it easier to add to the $73.86. 

So instead of adding $48.50 all at once, they say well if I just had the 14 cents that would be easy because we know what gets us to the $74. And then I’m going to add the additional 36 cents because I needed to add 50 cents but I’ve only done the 14 so I got to do the additional 36. $74.36 now I can work with the dollar amount, well $48 isn’t very friendly to add right here but for some kids $26 sounds really friendly because they know that that will get them to the $100 and 36 cents and then all they have left if the additional $22. 

So again, they’re leaving one of the numbers the same and then they are breaking up the other number along the way and they are still adding the $48.50, they’re just decomposing it into friendlier chunks that are easier for them to add.

Like Values/Place Value

Okay, our last strategy for addition looks like we’ve set it up like the traditional algorithm but kids kind of like to do math from left to right just like they read. This strategy is often called like expanded form or partial sums, I like to call it place value or I kind change that to like values because it doesn’t matter what kind of addition problem you’re doing, you always need to add together the like values. You add your ones with your ones, your tenths with your tenths, thousandths with your thousandths. It doesn’t matter what you’re adding but you have to have like values. 

In this case, kids can start with adding their tenths together and then we get 110 right off the bat. The cool part about this strategy is right off the bat they are thinking about how big their answer is, is this even reasonable.  Often times when kids start at the right side and work their way over, they aren’t thinking about how much it is at, they’re just kind of going through the motions. So instantly I know my answer is going to be bigger than 110, and then they go to their ones and now they’ve got 11 that they’re adding. And typically what kids will do is off to the side they are already adding this up as they go. So they already know they’re at 121, they’re not waiting until the end to do all of this addition. So when they get over to their tenths or their dimes they have 80 cents and 50 cents and that’s $1.30. So again, off to the side they’re thinking here I’m already up to 122 and 30 cents and then when they get to their pennies, they just have 6 cents to add and they get to their 122 and 36 cents. 

In this kind of a strategy typically the kids who are doing it on their own, they are adding up as they’re going. The way that this tends to be taught in the textbooks is they do all of this addition and then they stack it and add. That’s not what we recommend because then it’s like so many steps but really they’re just keeping track along the way and then when they get to that final amount they’ve already got their answer.

Kids don’t need to do every strategy

As we wrap this up, you’ve seen all five strategies, I want to remind you again that we don’t teach these and we don’t make kids solve one problem, five ways. I’m showing you one problem five ways just so you can see the potential ways but you don’t have your students do that. I intentionally picked a problem that worked nicely, you could solve them any of the ways. 

If I had picked a different problem, different numbers you wouldn’t have wanted to use those strategies. If I had said Jaeger had $12 and 25 cents and he earned $15.50 you wouldn’t have used those strategies. I picked the numbers intentionally. So don’t force your kids to solve a problem using these different strategies if it doesn’t make sense to solve using those strategies. 

This again is just to help you see what your students could use to solve it, not that they have to solve them in this way. All right, I hope that this video helped you build your math mind so you can go build the math minds of your students, have a great day!

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