Finding Success Teaching Math Word Problems

Math word problems can be vexing. How many times have you heard someone say, “I hated those word problems when I was in school!” Although we’ve come a long way from trying to figure out how long it will take for two trains to meet if they travel at different speeds (ugh), math textbooks still pose word problems that have contexts that are uninteresting, unrelatable, and inauthentic. Kids respond to problems they care about and are interested in solving, not contrived situations they don’t relate to. 

 

Why are Word Problems so Tricky?

Math word problems can be difficult to solve. First, you have to read the story, which can be tricky especially if you are an English language learner, and if there are unfamiliar academic terms to understand. Then, you have to figure out what the numbers mean, choose the numbers to work with, and then decide what to do with them (add, subtract, multiply, or divide). In other words, solving math word problems involves problem solving. In this post, I’ll share 3 things that helped me find success in teaching a math word problem: an interesting and relatable context, an authentic audience for students to share their math thinking, and strategic teacher support. 

 

Nino’s Pills

A few weeks ago I was driving home from the beach with Lynn, my body surfing buddy. As we were driving, she told me that her dog Nino was sick and the vet had given her 21 pills, directing her to give Nino 1 ½ pills each day. Lynn was wondering how many days she’d have to give her dog the pills. Before you read on, try to figure out the problem mentally. 

Lynn and I struggled a bit without paper and pencil, but we finally figured out the answer (in different ways). The problem intrigued me. Over the next few days I posed the ‘Nino’s Pills’ problem to several friends and everyone thought about it differently. Some divided, some multiplied, others added or skip-counted, while a few just estimated. When I asked them what they visualized, I got different responses. Some saw a collection of whole pills and half pills, others saw charts, a few thought of equations.  Nino’s Pills, I realized, was a good problem because it was interesting and relatable, elicited multiple perspectives, and it was definitely a problem worth solving, especially if you’re an animal lover!

 

Trying Out Nino’s Pills in Fifth Grade

Soon after Lynn shared Nino’s Pills with me, I visited Kathy Seckington’s fifth grade class in Poway, California to try it out. I had previously interviewed Kathy for our blog post Helping Students Become Better Listeners in Math Class, so I knew she would be open to letting me come in and co-teach the lesson with her. I’m glad I did because I learned a lot.

I began the lesson by structuring the launch using the Three Reads Protocol, or what I call a ‘slow reveal.’ 

 

Step 1

I began by showing the students my first slide.  Notice the picture of Nino in his halloween costume–he was dressed up as a banana and the students loved it! They were immediately drawn into the word problem. 

This was our first read of the problem, without numbers. A numberless word problem allows students to focus their attention on the context without having to start worrying about a solution (check out this numberless word problem slide deck for examples). 

Students wondered what was wrong with Nino. They noticed there weren’t any numbers in the problem yet, and wondered how many pills Lynn was given and how many pills she would have to give her dog each day. They also wondered how many days Lynn would have to give the pills to Nino.

 

Step 2:

Next, I showed the word problem but this time it included the numbers:

 

Lynn’s dog Nino is sick. The vet gave Lynn 21 pills to give Nino so 

that he will get better. Lynn must give Nino 1 ½ pills every day until 

the pills are all gone. 

 

After reading the problem, we had a class discussion about what new information students learned, and what they visualized when reading the story. 

 

Step 3: For step 3, we read the problem a third time and I asked the students what math questions they might have to answer. 

 

Step 4: 

For step 4, I revealed the math question students would have to answer, and we discussed diagrams they might use to help them solve the problem.

Lynn’s dog Nino is sick. The vet gave Lynn 21 pills to give Nino so that he will get better. Lynn must give Nino 1 ½ pills every day until the pills are all gone. For how many days does Lynn have to give Nino the pills?

Write a letter to Lynn that explains your thinking using a diagram, words, and numbers/equations.

 

Structuring the Classroom for Success

The way Kathy structures her math lessons is really impressive. It sets up students for success by providing opportunities for both independent work as well as for group support . Kathy has the students start at their own desks, thinking and writing on their desktops individually. 

Then, Kathy has the students move to a whiteboard at the perimeter of the room to work on the problem in groups of three.

 

Students’ Letters to Lynn

After Kathy led a class discussion in which groups shared their thinking, she sent them back to their seats to work on their letters to Lynn. From reading their letters, it was apparent that students benefited from opportunities to work alone, then with a group of three, and then hear other groups’ thoughts during the class discussion. When they were ready to write their letters to Lynn, they had lots of ideas to share. Following are just a few examples of the different ways  Kathy’s fifth graders approached Nino’s Pills. 

Like many of Kathy’s students, this boy created a diagram showing  pills and half-pills with the corresponding number of days. He’s also able to show an equation representing the problem.

 

Here, see how this fifth grader shows how she uses repeated addition to arrive at the answer.

 

Below, see how the student uses a T-Chart to reveal a pattern.

Finally, here’s one of Kathy’s students explaining how his group solved the problem. Notice how they used trial and error starting with 15 days, multiplying 1 ½ x 15 by first multiplying 1 x 15, then ½ x 15. That resulted in 22 ½ days– too high. Then they tried 13 days, then finally were successful with 14 days. 

An Authentic Audience for a Problem Worth Solving

One of the things I noticed from teaching this lesson is the power of posing a problem that students care about solving. The other thing I came to appreciate  is the importance of having an authentic audience for students to communicate their math thinking.  When Kathy’s fifth graders realized that Lynn would actually be reading (and later responding-see the end of the post) to their letters, there was a shift in the room. The students were motivated to not only solve the problem, but to also communicate what they’d learned– to a real person. This changed everything. 

Another big take-away from teaching this lesson is how important it is to provide strategic teacher support. Using the Three Reads Protocol for example, helped Kathy’s fifth graders wrap their brains around the word problem, slowly revealing information, allowing students to understand the context and the meaning of the numbers and their relationships, as well as identify the question they were asked to answer. And the last take-away for me was learning how Kathy sets up her room for success by providing structures for individual work, group collaboration, and time for discussion. 

Our students deserve problems that are relatable, interesting, and that are worth solving. By posing  problems like Nino’s Pills, we send the message that math is important and used to solve real world conundrums, not just contrived problems from the textbook page. 

We know that teachers are busy and don’t always have the time to replace what’s in their textbooks. But posing an engaging word problem just once during a math unit, or adjusting and editing what’s already in the teachers edition to make problems more relatable can make a big difference. There’s a world of real math problems out there for our students to solve. We just have to find them!

Thank you Kathy, and thanks to all of your fifth graders who helped Lynn answer her question!

 

Lynn’s Email Response to the Students