Real World Problems
Most teachers can agree that students, beginning in elementary, must be exposed to math problem solving with steps. That is the entire point of teaching mathematics. We want our students to be able to solve real world math problems. The reach of math problem solving goes far beyond the classroom. The goal is to produce people who are able to apply problem solving strategies in their homes and careers. On our end as teachers, tutors and parents we must show students the natural progression of math problem solving steps. Let’s take a dive into each of the steps of math problem solving and how we can apply them to a variety of problems.
Step 1: Read and Understand
Reading the problem sounds like the most trivial of the math problem solving steps, but it can be the most crucial. Students must be able to read, understand and interpret the words in the word problem. Some students will be able to read the words, but not understand what the problem is saying. Others will be able to read and understand, but not be able to interpret. There are many strategies that can be used if a student is struggling to read the problems. Those include having the student read and interpret the problem in chunks and reading the problem aloud to the student. There are some activities that have students put the word problems together like puzzle pieces which allow for teachers to get a better understanding of well students are engaging with the problems.
To prove their understanding, have students box or highlight the action words in the problems and mark them with what operations they think go along with the action words. Students should underline the question they are being asked to solve. In addition, if working with students in small group settings ask them to explain the problem in their own words.
Step 2: Plan
If your students are able to accurately determine what the actions are in the problem, here is the step where they get to choose a math problem solving strategy to plan how they will solve the word problem. Here is a list of common math problem solving strategies:
- Draw a model
- Act it out
- Work backwards
- Write a number sentence
- Look for a pattern
- Make a table or list
- Guess and check
This step offers lots of flexibility for students who have different learning styles. Math problem solving with steps does not require that all students solve problems in the same way. In my classroom I explain to students that I am their coach and just like any other coach, I teach them the skills during practice, but in the game it’s up to the player to determine the best strategy.
Step 3: Solve
Based on the math problem solving strategy that the student chose, it is now time to work to determine their final answer. During this step students will show all of their thinking whether they are using number sentences or guessing and checking. As an educator, this step in the math problem solving strategy gives you a look into how your students are thinking. This step often takes some sort of counting or computation and many mistakes can take place.
Step 4: Check
If I had to guess, this is one of the most highly skipped steps when students are math problem solving with steps that are not written down for them on paper or in a graphic organizer. However, this is the step where students will see if their answers make sense. I often recommend for my students to check their computations in this step or choose another math problem solving strategy to see if they get the same answer. For example, if they multiplied to find the answer, have them divide to check the multiplication. If they drew a model, have them write a number sentence to accompany the model.
Step 5: Communicate
After checking their work in step four, students should be able to communicate their answer to others. I have students practice this by writing their answer in a complete sentence using the context of the word problem. If the problem asks, “how many bowties does Sam have in each drawer?” an appropriate sentence would be, “Sam has ___ bowties in each drawer.” I think this step is important in becoming a real world problem solver. This is what leads to conversations amongst children once they hear each other’s ideas and can offer feedback.
Summing It All Up (pun intended)
Students will receive the best opportunity to become lifelong problem solvers if the steps of math problem solving are used with fidelity. Additionally, consistency from grade-to-grade further allows students to own math problem solving with steps. You have an important role to ensure that students are practicing math problem solving with steps on a daily basis. If you would like to give your students some practice please check out these multiplication and division word problems in my store.
