Modifying Math Word Problems to Encourage Curiosity
Have you wondered about something so intensely that you just had to grab your phone and search for the answer right then and there (even if it was in the middle of a staff meeting…)?
Curiosity is a powerful thing. We want to see that desire in our students! We want our kids so invested in the math that they are doing that they can’t stop until they figure it out. Kids are naturally curious, even if it isn’t always what we would like them to be curious about.
This post is part of a collaboration with other fantastic teachers about inspiring wonder and curiosity throughout all content areas in upper elementary. Don’t miss out on the other posts linked at the bottom of this post!
If we can peak students’ curiosity in our math classrooms, then we’ve got them hooked. When students are curious, they are engaged. When they are engaged in meaningful tasks, they learn. That sounds like a win all the way around, right?
So how can we open up our math problems to wonder and curiosity so that students are motivated and engaged in the math they are doing? Here are two of my favorite strategies for encouraging mathematical curiosity through word problems!
Throw out the question!
Yes, you read that right. Get rid of the question. Give students all the context of the story problem, but leave off the question. When we as teachers are always giving students the question, we are always telling students what they should be wondering about, whether they are genuinely interested or not. When we remove the question from a problem, we leave it open for students to ask their own questions.
There are times when we can truly let students wonder whatever it is they are wondering about the information we’ve given them. But let’s be real. Most of us have standards and pacing guides and time constraints and tests. We feel the pressure of “staying on topic” before we have to move on to teaching the next concept.
Most of the time we need students actively working through the concept that we are focused on. For this reason, I like to give some direction to the task to focus students’ thinking a bit.
To keep students headed in the direction that I would like them to head while still giving them the freedom to wonder, I first take an ordinary word problem and I remove the question:
“Derek practiced the drums for 1.5 hours this afternoon. Tonight he practiced the piano for 1 3/4 hours.”
Notice there is no question at the end for students to solve. Then I ask a question like:
“What question could you ask Derek that would require you to use fractions or decimals to solve it?”
Sometimes it’s okay to simply ask, “what question could you ask about this situation?” but know you will get a whole lot of responses, some of which will not be focused on the math in the problem. This is why I added “…that would require you to use fractions to solve it” to the question. Now students can come up with their own questions, but they will need to use their understanding of fractions or decimals in some way.
Possible student-created questions are: Did Derek practice more than 4 hours? How much time did Derek spend practicing his instruments today? How much longer did Derek practice piano than he did drums? If Derek practiced the same amount every day, how many hours does he spend practicing instruments in a week?
Do you see how each of these questions has a different level of complexity? I like this strategy because it requires students to think about the context and consider what they might be wondering about the situation, while also allowing them to solve a problem that is appropriate for their own level of understanding about the concept.
The more sophisticated the task/story problem is, the greater students’ level of curiosity will be. Whether you are using a rich task or a word problem from your math curriculum, this strategy is an easy tool to immediately open up a problem to give students choice.
Give students the answer.
So instead of only giving students the problem or context, this strategy requires only giving students the answer. When we only give students the answer, now it is up to them to come up with the context for the solution. In order to do that, they have to think about how they might work with or use that solution in their own lives. They cannot come up with the context without making real world connections to the math!
Instead of giving students the problem:
“The new rug in the library is 10 feet long and 15 feet wide. What is the area of the rug?”
Which, by the way, is a very low-level question, I’d give students the following question:
“If the answer is 150 square feet, what could the problem be?”
With this strategy, I like to add units to the solution so that students have some sort of starting place. By adding units, students now begin thinking about area, how big 150 square feet is, where they have experienced a space that big… is it in a house? A school? The playground?
When you give students the answer instead of the problem, you are leaving room for students to be curious and creative. This instantly increases engagement but also demands a deeper level of thinking. Coming up with the problem requires students to make real world connections and do whatever math would lead to that specific answer.
Some students will struggle with the open-ended-ness (is that a word?) of this task. That’s okay. Productive struggle is good. For those who are struggling and not making forward progress, it may be necessary to modify the task a bit, especially if this is a new strategy you are trying with your students. To modify, try combining the two strategies by giving students the context and then asking them to figure out what question would lead to a specific answer.
An example of this modification would be:
“The old rug in the library had an area of 275 square feet. The area of the new rug is 425 square feet. What question might someone ask about this situation that would lead to an answer of 150 square feet?”
Students will need to figure out that the answer comes from subtracting 275 sq. ft. from 425 sq. ft. Then they will need to come up with a question that would be answered by using subtraction.
A possible student-created questions is, “how much larger is the new rug than the old rug?”
This does shift the focus away from students’ own wonderings a bit. Instead, it provides two challenges for students that are less open-ended but still mathematically meaningful because students have to 1) figure out what math actions lead to the solution and 2) create the context for a question that would represent that specific math action.
Not only do these strategies give students space to wonder about math, but they also build students’ problem solving skills in a way that is so very different from the repetitive practice of solving a page full of word problems. I just love these strategies because they require connections, creativity, and critical thinking. I don’t need to tell you how different that is from the typical problem solving practice ;)
If you’re ready to try one or both of these strategies in your own classroom, be sure to download this problem solving activity FREE!
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