Recently I had a guest on my vlog, Ann Elise Record, who talked about addition and subtraction word problems. Now, anytime people learn about math problem types, one thing that they want to go do is to go right back and teach the problem types to their students.

Watch the video or read the transcript below:

Here are links to products/activities mentioned in this vlog. (Some may be affiliate links which just means that if you do purchase using my link, the company you purchased from sends me some money. Find more info HERE about that.)

• Ann Elise’s Video on Addition & Subtraction Word Problems
• Introduction to Problem Solving by Susan O’Connell
• Teacher’s Guide to CGI from the University of Wisconsin Oshkosh
• Children’s Mathematics book by Thomas Carpenter, et. al

Knowing the Names of the Problem Types is Just for Teachers

Now, one of the things I want to start off with is the chart of the story problem types.

Now, this chart may look different from one you’ve seen before. I personally love the one that was started by Cognitively Guided Instruction because that’s the first place I ever learned about it. And I like the terminology that they used.

On this chart, we don’t have to go back and help the kids realize which ones are join-change-unknown, and which ones are separate-result-unknown. The idea is for us as teachers to know these different math problem types exist, and be able to make sure that our textbooks are giving kids exposure to those. And if the textbook isn’t doing this, then we have to create opportunities for kids to have the chance to be able to solve these kinds of problems.

Solving Math Problem Types Should Not Be A Procedure

Now, the big reason I do not want you to go back and try to teach the math problem types to your students is that often when we teach each problem type, along with that comes instruction on how to solve that problem type. Then students are seeing all these different rules and procedures for solving all the different problem types, and it becomes too much for them to remember. The idea is to just let kids solve it any way they can.

Cognitively Guided Instruction found this nice progression that kids went through as they tried to solve problem types without any instruction from their teacher. If you want more info, here’s a link to the teacher’s guide to CGI, which is a great summary that was put together by the University of Wisconsin at Oshkosh. It doesn’t say who did it, but there’s where I found the link.

If you want all the details about CGI and how to implement that into your classroom, and learn more about that progression that students go through, then I highly recommend the book Children’s Mathematics by Thomas Carpenter and his whole group there.

But the big idea is that you give kids a story problem, and just let them solve it any way that they can without us telling them, “This is this kind of a problem, here are the steps that you do.” Or without us saying, “Underline the important information.” Or, “Circle the numbers, then look for keywords.”.

Help Kids Look For The General Structure Of The Problem

We want kids to make sense of the problems and solve it in a way that is natural to them. Which leads me into my last point. The big idea that we want kids to take-away when solving math problems is that we want them to find the structure of the problem.

What’s happening in the problem? It’s not about finding keywords and then numbers and then figuring out the operation. It’s about understanding what’s actually happening. Can we act this out? Is there action in the problem? Or is there no action?

Sometimes there’s actual action like “I had $7, and then I lost $5. Now how much do I have?” That’s where things are actually going away. And sometimes there’s just no action. Another example would be, “I have 7 chocolate chip cookies on the counter, and I have 5 oatmeal cookies on the counter. How many cookies do I have?”

There’s no action, I’m not eating any, I’m not baking more. There’s just that amount there. There’s nothing really telling the kids to put them together except for the question that I asked. And that’s where we fall into that keyword trap. We want to be able to help kids to use a keyword to figure out what operation to do.

But instead, we should be using the big idea or what I love, is Susan O’Connell’s idea of key concepts. This is a chart that she mentions in her book, An Introduction to Problem Solving.

And I love this idea!!! We really need to help kids be able to understand the key concept that when you’re doing addition you are putting things together. Now, sometimes there’s action in the problem that tells you, “Put them together.” Like the example, “I had $7 and then I earned eight more dollars.” That is saying put those together. Kids can have had that experience where they get more money. It gets added to the pile of money that they had.

But there are times, like the cookie problem, where you aren’t, there’s no action, you just have what you have. But the idea is, hey, if we’re being asked to put things together, that could mean addition. But, if you notice in that chart, it could also mean multiplication.

When you’re doing multiplication, you’re putting things together, but the things you’re putting together are of equal sets. So, “I have seven chocolate chip cookies and seven oatmeal cookies.” I could solve that with addition, but I can also solve it with multiplication because they’re both put together types of problems.

IF the question that I ask is, “How many do I have all together?” I could also take that beginning part of, “I have seven chocolate chip cookies…” And this one wouldn’t really work if I have the same amount. But let’s say the original question, “I had seven chocolate chip cookies and five oatmeal cookies.” I could ask the question, “How many do I have all together?” Which means I’m going to put these together.

But I could’ve asked, “How many more chocolate chip cookies do I have than oatmeal?” Now when I’m comparing, guess what? It’s a comparison problem and according to this chart, we need to subtract. So we can help kids understand these key concepts. Because those key concepts always last. Whereas keywords don’t.

Alright, so the big things I want you to understand when you’re trying to get kids to understand the math problem types, is:

The problem types are not for the kids. They’re for us, to be able to understand and make sure we’re giving kids lots of exposure to all of them.

The other thing is that we don’t teach the problem types because then we end up teaching procedures. Instead we want kids to have the understanding, and use their own natural strategies.

Then the last thing is help kids understand the structure. Not keywords, not procedures, but to understand the structure.

I hope that this video has helped you build your math mind, so you can go build the math minds or your students.

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