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The ability to solve word problems doesn’t necessarily come easily to all students. We can improve our students’ ability to solve story problems with a few simple word problem-solving strategies. When it comes to comprehending, understanding, and solving word problems, sometimes it is helpful to move beyond traditional word problems and try a new word problem type that is designed to support students in tackling these tricky skills!
In order to solve word problems, students need to be able to:
- Comprehend the action or context of a word problem
- Understand the question or missing piece of information
- Develop a mathematically sound plan for solving for the missing information.
- Accurately calculate to find their solution.
It’s a balance between comprehension, an understanding of math concepts, and an ability to carry out math concepts. Identifying which of these steps are strengths or needs for your students can help you to choose a strategy that will best improve their word problem performance.
Word Problem Solving Strategy #1: Numberless Word Problems
Who is this strategy for? If your students are struggling to understand the action, context or question in a story problem, discussion and numberless word problems will be a word problem-solving strategy that can help your students tremendously! This strategy also helps your “number pluckers” who see numbers, pluck and add together regardless of context! Numberless word problems slow your students down!
Using a tool such as numberless word problems can help your students in their understanding precisely because the numberless word problem strategy emphasizes discussion every step of the way!
How do I use this strategy? As you solve numberless word problems you begin with a problem with no numbers at all and ask a variety of questions as you discuss and slowly add information back into the problem.
Reagan picked flowers for a bouquet! She picked both roses and carnations.
When you initially present the problem, ask your students questions such as
- Who is the story problem about?
- What is happening in this story?
- What are you wondering about?
Reagan picked flowers for a bouquet! She picked 7 roses and also some carnations.
- What new information do we have?
- What do you think we might learn next?
- What *could* be the number of carnations in the bouquet? What might make sense?
Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations.
- What new information do we know?
- What do you know about the story?
- What happened in the story?
- Could we draw a picture or diagram to match the story?
- What might we be wondering about the bouquet?
- What questions could we answer about the bouquet?
Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations. How many flowers are in the bouquet in all?
- What is the question wondering?
- Do we have enough information to answer that question?
- Could we draw a picture or diagram to match the story?
- Where do we see the 7 roses in our diagram?
- Where do we see the 8 carnations in our diagram?
- How can we use the diagram to answer the question of how many flowers are in the bouquet in all?
DONE FOR YOU NUMBERLESS WORD PROBLEMS
Kindergarten | 1st Grade | 2nd Grade | 3rd Grade | 4th Grade
Word Problem Solving Strategy #2: Guided Visual Models
Who is this strategy for? Visual models help your students to organize the information they know as well as to visualize the missing piece of information. Drawing visual models helps lead your students to an equation. This strategy is ideal for students who understand what a word problem is asking but have difficulty connecting the action of a word problem to an equation.
A visual model might include:
- A math drawing (simple circles or an organic representation)
- A number bond (number bonds can be used beyond addition and subtraction! Adding more “parts” can help to visualize multiplication and division as well!)
- Tape diagrams
How can I use this strategy? As you are supporting your students in using these visual models, continually ask questions and draw connections between the word problem and their diagram.
Frank built a tower using 16 blocks. He took 7 blocks off of his tower and gave them to Declan so he could build a tower as well. How many blocks does Frank have left?
- What is happening in this story?
- Could you draw a picture that shows what happened?
- Let’s create a number bond that matches the story.
- Frank had 16 blocks. Was that all of the blocks in the story or part of them? Where would we put the total in our number bond?
- Frank gave away 7 blocks. Was that all of the blocks or a part of the blocks? Where would we put the part in our number bond?
- And we’re wondering how many blocks Frank has left. Where is the missing part in our number bond? Could we write a question mark in that part?
If your students are familiar with number bonds or tape diagrams, knowing that they are missing a part will lead them to writing a subtraction equation or a missing addend addition equation to solve.
**If your students are not familiar with how to find a missing part or missing whole in an equation this is a topic that needs to be addressed as well! Your students are missing foundational math understandings that are critical to their word problem-solving strategy. Additional practice with both fact families and missing numbers in an equation will be helpful to your students!
Word Problem Strategy #3: Problem Sorts
Who is this strategy for? This strategy is for ALL students! When your students examine problems to help understand the underlying structures and problem types, solving word problems becomes easier.
If you were to be asked to cook dinner for a group of people at the drop of a hat, you would likely have a much easier time putting together a pizza than you would a complicated curry dish. You understand the underlying structure of a pizza- crust, sauce, cheese, toppings- and because you know this structure, given any different type of pizza (BBQ, Traditional, Garlic, Buffalo Chicken) you would be able to use the structure to come up with a recipe quickly and easily.
Understanding and recognizing problem types can do the same thing for our students! Understanding that in a “put together” problem there are going to be parts and that those parts can be put together using addition makes these problems much easier to solve!
How can I use this strategy? One way to help your students to recognize and understand problem types is to sort word problems. In a problem sort, you aren’t attending to the matter of solving the problem at all. Instead, you are reading the problems and sorting them based on whether the problem is missing a part or missing the total. If you are working on multiplication and division word problems you might sort based on whether the problem is missing the total, missing the number of groups or missing the group size. Other problem types will lend themselves to different sorting activities.
Additional Word Problem Resources
Using different types of word problem resources can help you to support your students in different ways.
Word Problem Sort Cards can be a useful tool when you want your students to attend to the structure of math problems. Sort the cards based on problem type or based on the operation your students would use to solve. After sorting, solve the problems together. Reuse the sort as a math center!
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.
