Teaching math word problems without keywords? Yes, you can! In this blog post, I share how I use operation situations to help with math word problems.
“Who can tell me a word that tells us to add when we solve a word problem?”
At least fifteen hands shot into the air, some waving that oh-so-familiar “pick-me” wave.
One by one, students proudly shared their words . . .
“What an amazing list of words you came up with, but what about subtraction? What words signal a subtraction problem?”
Again, the students raised their hands to respond.
“how many more”
“how many less”
Once the words were neatly recorded on chart paper, the students divided themselves into groups of two and completed a set of addition and subtraction task cards.
While the students created an impressive list of words, I wondered if all the students would be able to remember them when solving word problems.
So, what’s wrong with using math keywords?
An Alternative to Keywords
If we can’t expect students to recognize these signal words to know what to do, how do we help with math word problems?
Great question– I can answer it with two simple words– operation situations.
Now, don’t get me wrong, I have been guilty of expecting my students to pick up on these keywords when solving problems too; however, a conference session I attended many moons ago changed my way of thinking.
At the time, I taught fourth grade and dedicated a portion of my math instruction to help my students develop word problem analysis skills with a word problem of the day program.
When we read each day’s word problem, I noticed something interesting . . . each problem fell in a specific category for each operation.
I couldn’t believe it!
In the beginning, I referred to the set of operation situations I learned about at the summer conference session. They included:
- Addition: part-part-whole, joining
- Subtraction: something leaves, comparing, missing part
- Multiplication: groups of something
- Division: how many groups, how many in each group
Using Operation Situations to Help with Math Word Problems
Each time we encountered a new word problem, I asked the students to describe what was happening in the word problem. From there, we then discussed what action (operation) was taking place.
From the beginning, most students could connect the picture they created in their heads with an operation. Then I helped them connect the situation illustrated in the story problem with the more formal language of the corresponding operation situation.
Consider the following problem:
The Lions finished the 400-meter freestyle relay race in 3.83 minutes. The Ravens finished in 3.72 minutes. The Knights finished in 4.05 minutes. What is the difference between the finish times for the first and third place teams?
For this problem, students might say we are looking for the difference between the finish time for the Ravens (first place) and the Knights (third place) relay race team. Students might also say we need to find out how much faster the first-place team (the Ravens) finished the race than the third-place team (the Knights).
During this discussion, if not mentioned by a student, I would add we need to compare the Ravens time to the Knights time and state, “when we compare two numbers, we determine the difference between the two quantities”. I might even follow with a visual to help the students understand what it means to find the difference between two numbers. (See the image below.)
Okay. I know what you’re thinking . . . what about multiple-step problems?
That’s a great question.
Let’s consider another problem.
When Brandon and Kelly arrive at the BrightStar campground, they begin preparing dessert to eat after their campfire cookout. There are eight people on the camping trip. Brandon and Kelly prepare three smores for each person. Each smore has one marshmallow. If the bag of marshmallows they used had 4 dozen marshmallows, how many marshmallows are leftover?
For this problem, students will call it a subtraction situation because they need to determine the leftover amount. I would revoice their thinking and call this a “something leaves” situation because they started with a bag of 4 dozen marshmallows, then some left, and there is now a specific amount remaining.
Now, the only missing piece of information from this situation is the quantity removed. So we go back to the problem to look for clues.
When we return to the problem, we see there are eight people on the camping trip. We also know Brandon and Kelly (Hello 90210 fans!) prepare three smores for each person and each smore has one marshmallow. So, to determine how many marshmallows Brandon and Kelly need, we use the “groups of something” situation– which means to multiply 8 people x 3 smores (marshmallows).
Hopefully, students will also notice the conversion. It’s not necessarily an operation situation we need to flesh out, but students need to acknowledge it. After working through the pieces of information needed to solve the problem, students can articulate they need to subtract the number of marshmallows used (8 groups of 3) from the total in the bag (4 dozen).
Wait . . . There’s a Keyword Here
You might be saying to yourself, “This problem has a keyword, so why is all of this necessary?”
This problem could have been written without the use of the words “leftover.” In fact, it could say, “If the bag of marshmallows they used had 4 dozen marshmallows, how many marshmallows were in the bag when Brandon and Kelly put the supplies away after dessert.” Notice there isn’t a keyword here, so some students might feel discouraged before even starting.
The Bottom Line
We want our students to engage with story problems so they can see the story in their heads. Can you see Brandon, Kelly, Brenda, Dylan, Andrea, Steve, Donna, and David around the campfire after their high school graduation making smores? (Yes, you guessed it . . . I’m an 80s child and loved watching 90210. I’m even into the current version of it!)
When students can visualize the situation, they begin to make sense of the actions taking place, such as someone counting the number of marshmallows they need and removing them from the bag. After this action, we can easily determine the quantity remaining.
More Operation Situations
During the first year I implemented this strategy to help with math word problems, my students and I noticed some situations didn’t quite fit, such as money situations where we know the amount spent and the change received but need to know the amount given to the cashier.
These types of problems made me curious to look for more situations I could use to address all of the types of problems we encountered; however, these initial eight situations were a great starting place and helped my students become proficient at solving math word problems for a great number of years.
Ready to use the operation situations to help with math word problems? Download a free set of posters using the form below!
What strategies do you use to help with math word problems? Respond in the comments below.