Problem Solving in Math

What is non-routine problem-solving?

Also referred to as creative problem-solving, non-routine problem-solving requires some degree of creativity or originality.  Non-routine problems typically do not have an immediately apparent strategy for solving them.  Oftentimes, these problems can be solved in multiple ways and with a variety of strategies.  Just like computational exercises (e.g long division), non-routine problem-solving must be explicitly taught to students.

Why non-routine problem-solving will always be a part of my instruction:

  • It prepares students for real-life problem-solving.  Real-life problems do not come with prescribed steps on how to solve them. People must think creatively and logically to solve them.
  • It allows students the gift of choice.  I use the word “gift” however, for many students, this aspect is very overwhelming to them.  They are used to being told what to do and how to do it.  This literally cripples students when it comes time to solve a problem that doesn’t follow a learned algorithm.   With non-routine problems, students must choose how they will tackle them.  Over time, they learn to trust themselves to determine appropriate strategies and solve these challenges confidently.
  • As mentioned above, it builds student confidence.  Students soon realize that they can independently choose an appropriate strategy (or strategies) and successfully apply it.
  • It presents students with a healthy dose of “struggle.”  I am all for teaching within students’ instructional levels.  However, I firmly believe that students must also feel a little uncomfortable, even frustrated, at times.  Non-routine problem-solving will frustrate some of your students, especially at first.  Don’t give up!  Talk to your students about how they are feeling.  Provide the appropriate scaffolding needed to help them get through these problems.  In time, your students will amaze you with what they are able to do.
  • It’s fun!!! I am not just saying that because I am a math geek.  It really is fun, and your students will love the variety it offers.  Even my students who do not get the correct answer enjoy the process.
  • It fosters student communication skills.  Students must document and explain the strategies they use.
  • It’s for EVERYONE.  I never reserved these activities for my “higher-achieving” students.  In fact, many students who struggled with computational concepts THRIVED with non-routine problem-solving.

Steps for non-routine problem solving:

There are four widely used steps that must be modeled for your students to give them a framework when working with these problems.

  1. Understand
  2. Plan
  3. Execute
  4. Review

For a detailed breakdown of these four steps and a free flip-book printable (pictured above), please check out this blog post: Steps for Non-Routine Problem Solving.

Instructional Applications:

You have a number of options on how you can present these problems to your students.

  • Whole Group: You can project a problem for the whole class to see using an LCD or overhead projector.  Students may work on whiteboards, or simply use paper and pencil to solve the problem.  The work can be done independently, or you can have students work together in pairs or small groups.  In the latter option, I would require all students to write down the work on their own whiteboard or paper.  This whole group option can follow with a few students presenting their plan for solving the problem; this is a nice opportunity for the class to see multiple strategies that can be used to solve the same problem.
  • Independent Work: Students can have their problem ready anytime they need to be working independently (i.e. fast-finishers, centers, morning work, etc.)
  • Cooperative Learning:  Pair up students to work on a problem together.  This is a valuable option because it adds the instructional benefits of communication and collaboration to the process.


One last thing to consider: In addition to the above applications, think about how you would like your students to share or present their work.  This is an important component for a number of reasons:

  • It holds students accountable for their work.
  • It provides students with an important opportunity to explain their problem-solving processes.
  • It allows other students to see a variety of ways to solve a problem.
  • It provides students with a “time to shine” as they present their work to others.

Students can present in a number of ways:

  • They can present their work to the whole class, basically conducting their own “think aloud” similar to what the teacher has done when he/she directly modeled the process to the class.
  • They can present their work to another student or a small group of students.
  • They can present their work to a parent or an older sibling.
  • They can present their work on an online forum (i.e., Edmodo, etc.) hosted by the teacher.

Some examples (and solutions) that you can try today with your students:

The problems above are from my Brain Power Math Books.  If your kids are “hungry” for more, check them out!