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Math Problem Solving 101

images of Mr Elementary Math problem solving strategies

Have you ever given your students a money word problem where someone buys an item from a store, but your students come up with an answer where the person that bought the item ends up with more money than he or she came in with?

Word problem solving is one of those things that many of our children struggle with.  When used effectively, questioning and dramatization can be powerful tools for our students to use when solving these types of problems.

I came up with this approach after co-teaching a lesson with a 3rd grade teachers.  Her kids were having extreme difficulty comprehending a word problem she presented.  So we devised a lesson that would help students better understand problem solving.

The approach we took included the use of several literacy skills, like reading comprehension and writing. First, we started the lesson with a “think aloud” modeled by the teacher.We read and displayed the problem below but excluded ALL of the numbers. See the images below:

The purpose of reading the problem without the numbers is to get the students to understand what is actually happening in the problem.  Typically some students focus solely on keywords when solving word problems, but I do not advise using this approach exclusively.  With math problems, the context of the problem and actions in the problem determine how the child should go about solving it.

Read the Problem Without Numbers & Ask Questions:

After reading the problem (without numbers) to the students, I asked the following questions:

  • Can you describe what is happening in your own words?
  • What is the main idea of the problem?
  • How could you act this out?

Make a Plan & Ask Questions:

After the students articulated what was happening in the problem, we made a plan to solve the problem.  I used the following guiding questions:

  • What information do we know?
    • Sample Answers include- We know that Kai has some goldfish. Kai donated or gave away some of the goldfish.
  • What information do we need?
    • Sample Answers includeWe need to know how many goldfish Kai has.  We also need to know how many he gave anyway.  We also need to know how many bowls there are.
  • Ultimately, what are we trying to find out? (What is the question wanting you to find?)
    • Sample Answers include- We need to find out how many fish belong in each bowl.

The class discussed the answers to the questions above. As we discussed the questions above the responses were written out on a problem solving template.

As part of this process, we clarified student understanding of the problem and determined what we needed to find and do to solve the problem.  Next, we walked the students through the process of showing their work using pictures.  Lastly, we checked our answers by writing an equation that matched the pictures to finally solve the problem.

Team Work Counts

After going through the process with the class, we decided to split the students into small groups of 3 and 4 to solve a math problem together.  The groups were expected to use the same process that we used to solve the problem.  It took a while but check out one of the final products below.

images of Mr Elementary Math problem solving strategies

Benefits to Using this Process:

  • Students understood what the problem is asking them to do
  • Students are required to think and communicate as a team
  • Students avoid making errors that can come with only using keywords
  • Students are required to record their math reasoning using the problem solving template
  • After using this process a couple of times, students get used to explaining and justifying their answers
  • You become the facilitator of the learning by asking more questions, thereby making students independent thinkers

Things to Consider Include:

  • This process in NOT quick.  It requires TIME.  You should not rush the process and expect to have it completed in 20 – 30 minutes in one day.
  • This process is not a one time lesson.  Students may not get it the first time.  It should be seen a routine that can be used when solving word problems.

If students are still having problems, I would strongly recommend having students quickly act some of these problems out. Sometimes students are so focused on the numbers, they only want to add/subtract/multiply/divide but have no clue what is happening in the problem.

Before I wrap up this post,  I want to remind that using questioning throughout this process is so important. I go into more detail about the exact steps to take in my guest post Problem Solving Made Simpler.

Be sure to let me know how this process works in your classroom in the comments below.