Solving Measurement Word Problems with Addition Strategies

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With textbooks having students use different strategies to solve addition problems, I wanted to do a short series all about what the strategies are and how they are useful even as students start solving time and measurement and money type of addition problems.

I’m Christina Tondevold, The Recovering Traditionalist, and I hope you’ll stick around because in this video we are going to take a look at solving measurement word problems using 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 from this series

Number Sense Courses

Free Training – Components of Number Sense in PreK-2

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

As I said, this is part of a series. This is actually the 3rd video. And if you’ve missed the other two, I will link to them below this video. But we started off with a video that just explains the 5 strategies. And then the 2nd video was about how students can use those 5 strategies to help them when they’re solving elapsed time problems. In this video we’re going to take a look again at those same 5 strategies, but what they look like when students are solving measurement problems.

Now I always have these warnings, but I want to remind you of them in case you didn’t see the other videos.

#1 These strategies are not, are not to be directly taught to your students. These strategies happen naturally when students have a sense of numbers. So the numbers that we’re working with in these problems though are measurement type stuff. Kids need a sense of how inches relate to feet and how feet relate to yards. And if you’re working with things like ounces, they need to understand how many ounces it takes to create a pound. So before they will ever use these strategies, you need to focus on relationships. What are the relationships around the different measurement types? And help kids get really solid in those. 

If they don’t have those relationships built, they won’t do these strategies. And you trying to teach them will be a complete waste of your time. So I’m going to link below this to a couple of free trainings’ that I have about what kind of relationships we should be bringing out around numbers. Now these trainings’ do talk about whole numbers. But as you’re watching those numbers, I want you to think about, how do they relate to measurement ideas? And the types of numbers that we’re working with with measurement. 

#2 is that I have certain names that I call them. You might call them something different. But what we call them honestly does not matter. I prefer to use a name for the strategy that highlights what kind of mathematics they are doing. What are they doing mathematically? That is how I decide what the name is. So the strategy is different than how they model it. I can model a strategy in different ways. I can take the same strategy and model it on a number line. I can model it using an equation. It doesn’t make the strategy different. It’s the same strategy, I’m just modeling it differently. 

Now even though I say that there is this base of 5 strategies, there are times when things will look the same or even there will be combinations of these strategies, because kids will combine. They’ll like this part and this part. So it’s not like these are the only ways to do it. Kids naturally derive these strategies and there might be a combination of them that kids create.

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

Sierra wants to build some shelves for her room. She wants one shelf to be two feet, 7 1/2 inches. The other shelf is going to be 3 feet, 10 3/4 inches. What is the minimum length of a board that Sierra needs to buy to be able to build those shelves?

Traditional Algorithm

Just starting off with kind of the traditional way that we would solve that problem is to just set it up and do 2 feet, 7 1/2 inches, plus 3 feet, 10 3/4 inches. And then we teach kids to get their common denominator. So the 1/2 would become 2/4, right? And this is something that if kids have number sense around fractions, understanding that 1/2 is the same as 2/4 is one of those fundamental things around number sense of fractions that we need kids to have. 

So they go through and they add this up. And hopefully when they see 5/4, they know to regroup that. Because 5/4 is more than one. But a lot of kids don’t, because they’re so used to regrouping things when you have 10 of something. So if kids understand all of this stuff, they have to understand regrouping it, and they would know they could get 1 whole inch and they would be left with 1/4. 

Now they have 18 inches. And again, they’re regrouping a different base system here. Because it’s not 10, it’s the 4s that we just did. They have to understand that they regroup at 12, because 12 inches makes the next foot. So if we have 18 inches, that is a foot, but we have 6 inches left over. So we end up with 6 feet, 6 1/4 inches. 

So that’s a perfectly fine way. And it’s a way that, yeah, you want kids to be able to get there and understand all of those things. But leading up to it, kids might have other ways that they approach this problem that are still viable, and dare I say darn cool. 

Compensating

So let’s take a look at a couple other strategies that kids would use to solve that measurement problem. Okay, as we’ve talked about before, compensating is when a kid does something that they shouldn’t have done in the problem and they have to come back and compensate for it. So in this scenario we might see a kid who, instead of adding 3 feet, 10 3/4 inches, just says that’s almost like 4 feet. So I am just going to add the 4 feet and I’m going to get 6 feet, 7 1/2 inches. But then they have to come back and compensate for what they did. She doesn’t want one that’s 4 feet. She wants one that’s 10 3/4 inches. 

So how much extra did they tack on? Well, they added an extra 1 1/4 inches, so they have to come back and take that away. Again, kids still will need to be able to instantly think in their minds, okay, 1/2 is really 2/4. So if I’m taking away 1/4, I’m going to be left with 1/4 there. 6 inches. So we still get 6 feet, 6 1/4 inches.

Give & Take

So the give and take method is really similar to that compensating. It’s the kid who wants to make that 3 feet, 10 3/4 inches, 4 feet. They’re like, gosh, that is really close to 4. But they just do it up front. They’re going to chunk off 1 1/4 inches here to be able to make that 4 feet. But then what are they left with? Well, they’re left with 2 feet, 6 1/4 inches. So we put that together and we still get our 6 feet, 6 1/4 inches.

Decomposing

Decomposing is where the kids will leave one of the numbers the same, but then they’ll break down or decompose the other number that they’re adding. So I am decomposing mine into bigger chunks because that’s the way I see it. 

Your kids might need to break it down into smaller chunks. But right away I see that I could do 4 1/2 inches right here so that I could get to 3 feet. That’s nice and friendly for me. And once I’m there, I’m just like, well let me add the 3 feet to it. Now I know, I’m at 6 feet, then I have to stop and think. Okay, what have I added so far? And what do I still need to add? 

Well, out of my 3 feet, 10 3/4 inches, I still have to add 6 1/4 inches. So now I’ve got 6 feet, 6 1/4 inches. So again, they’re breaking it down into chunks that make more sense to them and trying to get to friendly numbers. But again, they need to have this base understanding of what is friendly when they’re dealing with measurement.

Like Values/Place Value

In the beginning of the series, I called this strategy place value. But the more I’m doing it with all kinds of problems, I’ve tended to like more of the like values. Because I’m not always just adding my ones with my ones and tens with my tens and hundreds with my hundreds. It really just means like values. 

You’re going to add your tens with your tens, yes, but as you move into measurement stuff, you’re adding your inches with inches, feet with feet, whatever it might be. You have to have ‘like values’ to add them together. Right? You have to have the same measurement type to be able to put those together and add them. 

So in this scenario, you’re adding your feet together. So you might see the kids do that over here. They’ve got the 5 feet, then they move into their inches here. 3/4 inches.  And when they get to this 17 inches, they’re automatically off to the side. The cool part about this strategy is that often kids are adding up as they go. So they had their 5 feet. They have 17 inches. And they know that that is 1 foot and 2 inches. Again, this is all dependent upon them having some number sense, some measurement sense about what the benchmark numbers are when they’re dealing with measurement. 

So, now they’re already up to 6 feet, 5 inches here. Right? And then when they do their 1/2 plus their 3/4, again, they might say it’s 5/4 and then move that around into 1 1/4. But you also might get a kid who says, well, 3/4 is really 1/2 and 1/4. So 1/2 and 1/2 gives me the one. They automatically know it’s 1 1/4.  So then we can put those together and we’d get out 6 feet, 6 1/4 inches.

Kids don’t need to do every strategy

After you’ve seen all 5 of these ways, a final reminder. Don’t teach them all to your students and don’t have them solve every problem 5 different ways. There are types of problems, and the numbers in those problems, that elicit kids to want to use one of these strategies. If I had created this problem and one of them was 2 feet, 3 inches, and the other one was 3 feet, 4 inches, you would not have used any of those strategies. We would have just stacked it and solved it. Right?  There is a time and a place for these different strategies. And that time and place is personal to your students. They will decide what strategy to use based upon their understanding of the numbers in that problem. 

We really need to focus on helping them understand the numbers and the quantities and how quantities relate to each other. The byproduct of that is kids naturally will do these strategies. You don’t need to spend months trying to teach these strategies to students. You need to focus on helping them build a relationship about these measurement quantities and then the strategies will naturally come from that. All right. I hope that this video has 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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