When I first learned about the different types of word problems (many, many years ago) I thought that we were overcomplicating the issue. Our program had students spending a lot of time reading word problems and identifying which problem type they were. Students were spending days writing “situation equations” and “solution equations” based on these word problem types.
I wasn’t a fan.
Over the years I have discovered that while my instincts were correct in some respects (my special education students with a tentative understanding of word problems were not best served spending their time writing a variety of equations as a means of understanding word problems) I really underestimated the importance of understanding word problem types.
What Are Word Problem Types
Given an addition or subtraction or multiplication or division word problem, we see consistent structures in the action of the problems.
For addition and subtraction this means:
- Put Together and Take Apart Problems
- Add to and Take Away Problems
- Comparison Problems
For multiplication and division this means:
- Equal Groups Problems
- Array Problems
- Comparison Problems
Why Do Word Problem Types Matter
Word problem types are important both in terms of your instruction and assessment. So often as teachers we lament the fact that word problems seem to be more of a “reading and comprehension” issue than a “math” issue. Recognizing word problem types can help to bridge the gap.
As a teacher, recognizing word problem types can help to determine what your students do understand and comprehend in terms of a math story and what they still need support with.
For example, your student is given the following two problems. They quickly and easily solve the first problem but struggle and ultimately give up when trying to solve the second.
5 red fish and 8 yellow fish are swimming in the pond. How many fish are in the pond altogether?
5 red fish and 8 yellow fish are swimming in the pond. How many fewer red fish than yellow fish are in the pond?
By recognizing that the first problem is a “put together” type problem and that the second is a “comparison” type problem, you can focus your teaching to support your student in understanding comparison problem structures.
Rather than simply stating that your student “struggles with word problems” you can identify exactly which structures your students understand and where they need additional support and instruction.
How Can We Support Our Students?
- When using word problems in your instruction, be mindful of the types of problems you are using. Note which problem types your students are successful in and where they need more support.
- If your students need support understanding how to solve a word problem type, use hands-on manipulatives and visual models to model the problem so that your students can more easily understand the context.
- Use explicit practice to solve a variety of word problems within the word problem type your students are practicing.
- Mix word problem types together. Hand your students a variety of word problems on task cards. Ask your students to find all of the problems of a given type. Can they distinguish, for example, all of the comparison problems from the group?
- Use numberless word problems to help your students focus on the action or context of word problems.
Word Problem Resources
Using different types of word problem resources can help you to support your students in different ways.
Word Problem Task Cards can be a useful tool when you want your students to attend the the structure of math problems. You can use the cards to create sorting activities.
Word Problem Notebooks are a useful tool when you want your students to draw models and visual representations of word problems and to connect these models to an equation.
Numberless Word Problems help get to the heart of the action or context of a word problem. Because you start with no numbers and employ a great deal of conversation these problems are simple to differentiate and give all students a point of access into the activity.
