James Clear has many memorable quotes in his book Atomic Habits, but my favorite by far is, “You do not rise to the level of your goals. You fall to the level of your systems.”
Prior to practicing the daily word problem routine I currently use in my classroom, I used a system that relied heavily on keyword identification with a word problem strategy called CUBES..
I taught my students to circle numbers, box keywords, underline the question, and begin their solution sentence before we had solved the question.
If this is your current system, it was once my own as well. But, I know that if you are here reading this post, then you need a way to help your students solve word problems accurately. I am going to go out on a limb and say the system you are currently using isn’t working. It’s time to throw it away, sister!
Good, you’re ready for a change. So was I. You may have been told that if you improve your students’ reading levels, then their math understanding will improve also. I was told the same.
But, I challenged this idea. I presented my admin with data that showed my at level readers also failing at word problems. I knew that the problem wasn’t reading (at least for ALL of my students). The problem was the system I was using to teach word problems.
How does our brain solve word problems?
This realization guided my research into how the brain goes about solving a new problem. I learned about cognitive load theory. This theory states that the more we can reduce the brain’s workload for lower level thinking tasks, the more brain power is left for higher level thinking.
It makes sense. If students can spend less time thinking about what 9 + 6 is, the more energy they have to think if their answer was reasonable.
I thought if we could expand students’ knowledge of word problem types and build their experiences in solving these problems, the less energy they would have to use thinking about what operation they needed to solve. What follows is the daily procedure I use in my own classroom with great success!
How to Solve Word Problems Daily Routine:
Step #1: Numberless Word Problem of the Day
Every morning I start our math block time with a daily numberless word problem. Why numberless? We all have students that either rush into solving, grabbing any and all numbers possible, and solve without thinking about the problem context. Chances are you also have students that when they see a word problem, automatically shut down. They know from past experience that this type of problem is too difficult for them.
Numberless word problems take the focus out of solving the problem and replace it with discussing the story of a word problem. Just like all stories, word problems have characters, settings, and a plot that includes a conflict requiring a solution. My students and I check our understanding, a common reading comprehension skill. We identify the common story elements, focusing on the characters, setting and what is happening in the problem.
This step is accessible to ALL students, and the result is that even my reluctant students participate in the discussion. If you want students to know how to solve word problems, they do need to be able to understand the story. So, have them check their understanding by looking for common story elements.
Step #2: Visualize
By focusing on the story of the word problem, students start to discuss what they might do to solve it. They start talking about math operations like addition, subtraction, multiplication, and division. They bring in their prior knowledge from their own experiences that are similar to the story. Again, these are all skills we teach students to use as readers. It flows naturally for our students to apply those same concepts to math word problem stories. Stop reinventing the wheel.
I encourage my students to draw pictures with the information, using our problem type models to support their ideas. We fill in these models with the information we know from the problem, adding labels to support their thinking. When it comes to how to solve word problems, having a visual model helps validate student ideas and claims.
Step #3: Substituting Numbers
The reason I love using numberless word problems is that it allows students to suggest their own numbers for the problem. This approach improves student engagement in the process as the problems feel uniquely their own.
Likewise, it allows for easily differentiated learning in a whole class setting. Some students choose to use larger numbers or numbers with fractions or decimals, while other students choose small numbers that they are more comfortable with.
The importance here is not arriving at the same solution with one answer. Instead, it is the discussion and confidence building that is taking place with solving word problems at each individual student’s level.
Step #4: Writing equations:
Writing equations is a higher level thinking skill. The visual models support students in writing equations to match both the situation of the problem and the solution to solve it.
Students are able to substitute their own numbers into the equations and solve in a way that is MOST comfortable for them. We discuss their solutions and if their answers made sense using the numbers that they selected.
STEP #5: Writing their own problems
Lastly, it is important to go over the type of problem your students just worked with. I use digital anchor charts from our classroom website. From this, students write their own word problem in a journal, or if it is October, December, or February, we make paper chains to decorate the classroom.
Giving students the opportunity to write their own word problems strengthens their understanding of the problem types. In turn, this increases their confidence through guided experience.
When they come across a problem that is similar, they are MORE likely to recall what they did to solve it before and apply that knowledge to a new problem they encounter.
As James Clear also said, “Every action you take is a vote for the type of person you want to become.”
I want my students to become confident word problem solvers. This means that we practice word problems daily. The result of this habit is that my students don’t just solve word problems, they are problem solvers. Daily practices and habits like this become a part of students math identities.
In summary, by:
- Discussing problem structure through numberless word problems
- Connecting to students’ life experiences and prior knowledge
- Encouraging students to visualize problems and organize information in models
- Evaluating solutions
- Increasing their background knowledge and experience by writing their own similar word problems..
…you are creating a daily practice that removes the stigma around word problems. Because my students encounter word problems daily, the problems are no longer new and scary. My students, and your will too if you use this strategy regularly, will know what to expect and how to approach word problems.
If your students aren’t rising to the level of your goals in math class, it’s either because you either:
- Don’t have a system
- Use a system that relies on keyword identification
It’s time to change the system. Learn more by taking my Making Sense of Math: Word Problems class over on PopPD.
