Numberless Word Problems

Transcript
You may have heard about numberless word problems. They’re interesting. A numberless word problem is just what it sounds like: a word problem with no numbers in it. I think you’ll find that they can be really useful at all kinds of grade levels, so let me give you a couple of examples.

So, imagine we have younger students and instead of a question like “There were 4 cats and 3 dogs. How many animals were there?” which has numbers, we ask a question like this one: “There were some cats and there were some dogs. You decide how many cats, you decide how many dogs, and then you tell me how many animals there are.” So, all we did was take the numbers out of a more traditional problem. Now, I just said, “There were some of these and some of these.” You could, instead, put blanks: “There were blank cats and blank dogs.” You could do it that way instead, but what is consistent is that you take the numbers out of a more traditional problem and let students choose the numbers to work with.

Here’s an example for some older elementary students. It’s a percent question. So, instead of saying, “You went to a store and there was a jacket that cost $50, and it was 20% off. How much did you spend?” I would say, “You went to a store and there was a sale, and there was a percent off. You decide how much the jacket you want to buy costs. You decide how much you would save by choosing the appropriate percent that you like. And then you tell me how much you’ll pay for your jacket.” So, again, we could’ve used blanks. The percent discount was blank percent, or the jacket cost blank dollars. But, in both cases, what we’re doing is removing the numbers from a traditional problem and letting students make choices and work with their own numbers.

Now obviously these are what I’ve been calling, for many years now, open questions. They’re just a particular style of open questions because the numbers were removed, and what we know is that when we do these kinds of questions with students, they concentrate more on the underlying ideas, e.g., “What kind of operation should I do, and why should I do it?” because they’re not distracted by the actual values that they might see in the problem. There’s a lot of experience now that people have had that suggests that these are really great for kids.