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?
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.
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.
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!