Teacher confession time:

I did not create this poster, but I could have. In fact I had one very similar hanging in my classroom from 2007-2012. I even wrote one of my National Board portfolio entries about a lesson designed around

This brings be to CUBES. A problem solving strategy I've seen quite a few times in classrooms. I never used it, but mostly because I didn't hear about it. I probably would have been all over that. If you aren't familiar, here is the strategy:

C- circle the numbers

U- underline the question

B- box the keywords, or math action words

E- evaluate the steps you should take

S- solve and check

You might be wondering why I stopped using keywords in math class in 2012. Honestly, I was pretty stubborn. I mean, kids

The big deal is we no longer want students to just get answers. We want students to make meaning, understand concepts, and generally know what the heck they are doing!

If I haven't convinced you yet, consider this: We tend to give students problems that fall in line with keywords and CUBES and work out pretty neatly and nicely. Here's an example:

The keyword indicated subtraction, the numbers are 10 and 3... so, 10-3=7. See, it seems to work!

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But there are many non-examples. Take, for instance, this one:

The keyword indicates subtraction, the numbers are 7 and 3. So, 7-3=4.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

And there are lots of these non-examples. Check out these:

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What

One idea for getting kids better at solving problems is to try numberless word problems. You might be thinking, how is this math if there are no numbers?! Well, trust me, taking the calculation part out, at first, helps students generalize and plan a strategy without having to worry about computation.

Giving students non-routine problems helps them develop problem solving strategies. They also get used to the idea that you might not be able to solve a math problem in 2.5 seconds, and that is okay!

Model solving problems for students and think-aloud as you do it so they know what it looks and sounds like.

We do need to help students understand math terms. Sometimes teachers push back a bit and ask, "If I don't teach keywords, how will students know the terms product, sum, quotient, and difference?"

I think it's important for students to know, for example, that the product is the result of multiplying. However, just because the word product is in a word problem, it does not mean you should automatically multiply whatever numbers you see! Consider my example above: "The product of 3 and another number is 15. What is the other number?" Certainly multiplication is implied with the term product, but you are actually solving 3x=15, not doing 3 times 15.

The bottom line is we need to help students make sense of what is going on in a problem. This is not an easy task and there is no one anchor chart that is going to work. It takes time, but is worth it. So join me in making keywords a practice to leave in the past!

**I used to teach my students about keywords in math class.**I did not create this poster, but I could have. In fact I had one very similar hanging in my classroom from 2007-2012. I even wrote one of my National Board portfolio entries about a lesson designed around

*keywords*!This brings be to CUBES. A problem solving strategy I've seen quite a few times in classrooms. I never used it, but mostly because I didn't hear about it. I probably would have been all over that. If you aren't familiar, here is the strategy:

C- circle the numbers

U- underline the question

B- box the keywords, or math action words

E- evaluate the steps you should take

S- solve and check

You might be wondering why I stopped using keywords in math class in 2012. Honestly, I was pretty stubborn. I mean, kids

*got the right answers*when I taught key words! I thought I was helping them. Students liked them. Parents understood them. There are actually several reasons I decided to stop using keywords. At the time, I was being coached as part of the West Cook Math Initiative (thanks, Margie!). I also started to learn more about the Common Core State Standards and what students should be expected to do.**So, why shouldn't we use keywords and CUBES? What is the big deal?**The big deal is we no longer want students to just get answers. We want students to make meaning, understand concepts, and generally know what the heck they are doing!

If I haven't convinced you yet, consider this: We tend to give students problems that fall in line with keywords and CUBES and work out pretty neatly and nicely. Here's an example:

Natalie had 10 cookies. Her brother, Juan, takes away 3. How many cookies does Natalie have?

The keyword indicated subtraction, the numbers are 10 and 3... so, 10-3=7. See, it seems to work!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

But there are many non-examples. Take, for instance, this one:

Annie takes away 3 cookies from her brother. She puts the cookies in her pile that originally had 7. How many cookies does Annie have?

The keyword indicates subtraction, the numbers are 7 and 3. So, 7-3=4.

__But wait! That's not right!__Annie actually has 10 cookies. This is an addition problem?!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

And there are lots of these non-examples. Check out these:

The product of 3 and another number is 15. What is the other number?

Lizzy buys some groceries. All together her bill is $17. She pays with a $20, how much change does she get?

Michelle wonders how many groups she can make. She figures she can make 4 if there are 6 students in each. How many total students are there?

Bob has twice as many pets as Sarah. Bob has 10 pets, how many does Sarah have?

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What

*can*we do to help students solve word problems? I do have a few ideas:**Numberless Word Problems**One idea for getting kids better at solving problems is to try numberless word problems. You might be thinking, how is this math if there are no numbers?! Well, trust me, taking the calculation part out, at first, helps students generalize and plan a strategy without having to worry about computation.

**Non-routine Problems**Giving students non-routine problems helps them develop problem solving strategies. They also get used to the idea that you might not be able to solve a math problem in 2.5 seconds, and that is okay!

**Think-Alouds**Model solving problems for students and think-aloud as you do it so they know what it looks and sounds like.

**Vocabulary in Context**We do need to help students understand math terms. Sometimes teachers push back a bit and ask, "If I don't teach keywords, how will students know the terms product, sum, quotient, and difference?"

I think it's important for students to know, for example, that the product is the result of multiplying. However, just because the word product is in a word problem, it does not mean you should automatically multiply whatever numbers you see! Consider my example above: "The product of 3 and another number is 15. What is the other number?" Certainly multiplication is implied with the term product, but you are actually solving 3x=15, not doing 3 times 15.

The bottom line is we need to help students make sense of what is going on in a problem. This is not an easy task and there is no one anchor chart that is going to work. It takes time, but is worth it. So join me in making keywords a practice to leave in the past!

Great post Annie! I managed to stay away from key words, but did use strategies like CUBES. I especially like the part on vocabulary in context and hadn't thought of it in this light before. So many teachers want to focus on math vocabulary - which is good - but they want to do it outside of any context.

ReplyDeleteHi Chris!

DeleteAgree, vocab means so much more to students when used in real math situations!

I am actually surprised that some teachers use the idea of keywords like this, I had never seen it before, but it is definitely a dangerous way of teaching problem solving. I think that you really give some good examples of this and bring these issues to light. I am going to make sure to not focus on keywords when I enter a classroom full time. I really like the idea of Numberless Word Problems because that really digs at making sure the students are understanding what operations and concepts are key in solving various problems.

ReplyDeleteThe picture you posted at the end makes me think of the book ‘Nix the Tricks’ by Tina Cardone and MTBoS, I saw this book mentioned on Dan Meyer’s Blog. After seeing so many posts on various blogs about getting rid of mathematical tricks, I am really interested in reading this book, just thought I’d share it here in case no one else had heard of it!

Hi Mathew,

DeleteYes, I love Nix the Tricks! :)

http://showyourthinkingmath.blogspot.com/2013/12/nix-tricks.html

I really appreciate this post, Annie. As I was growing up, I was involved with vocabulary charts, and your examples that you posted of problems that seems like it uses one operation, but is actually meant for another operation, can be confusing when focusing on these vocab charts.

ReplyDeleteAs Mathew stated above, I want to try to stay away from keywords as well, and do my best to have students understand the concepts. Along with the numberless word problems, I really enjoyed reading through the post on the Think Aloud. Word problems are always the bane of any student in math, and can be difficult to comprehend no matter how short or long the problem is. However, when the teacher became the student, it shows the rest of the class that it takes thinking to understand what a word problem is saying. It takes that extra effort on myself to encourage students to think in and out of the classroom, and I want to display that mentality to my future students.

Andrew,

DeleteBest of luck as you are starting your teaching journey! Thanks for visiting my blog!

I'm still stuck on Annie taking those cookies away from her brother. Haha! ☺️

ReplyDeleteDon't worry, mom, it is just a hypothetical situation. ;)

Delete