Teaching Problem Solving Strategies

A number of years ago I was introduced to the concept of teaching formalized problem solving strategies to elementary aged children. This mathematics program was a tremendous success and dramatically improved the mathematical reasoning and problem solving of the students I taught. Most importantly the students enjoyed it and looked forward to it each week. The problem solving strategies included:

Acting it Out or Using Concrete Materials
Create an Organized List
Creating a Tree Diagram
Drawing a Diagram
Drawing a Table
Guess and Check (Guess and Checking)
Look for a Pattern
Using Logical Reasoning (Logical Reasoning)
Using Simpler Numbers (Solve a Simpler Problem)
Work Backwards (Working Backwards)

Once I began to look, I found a  number of problem solving resources online and in book stores. However, not all of the resources were easy to find. The purpose of this post is to bring these resources together so you can introduce problem solving into your classroom or school or further develop your program if you have one in place.

The program we taught was based on books published in Australia by Blake Education called Solve that Problem by Sharon Shapiro. There are two books in the series Upper Primary and Middle Primary. These books are available in the UK via Badger Publishing. US residents are able to purchase these books via Amazon in the UK.

A good starting point is to use resources offered online.  A number of the strategies explored in Solve that Problem are available free in .pdf format via the Blake Education website under the Problem Solving heading. Samples of another great problem solving book, “Mathematics Problem Solving Coach” are also offered in .pdf format online.

There are a number of books and online resources available to help you teach problem solving including:

Online Resources

Bogazici University Faculty of Education
Figure This Challenges
MathStars Newsletter
Math Stories (paid subscription)
New Zealand Ministry of Education
Port Angeles School District
Thinkquest 1
Thinkquest 2
Thinkquest 3


Mathematics Problem Solving Coach
Maths Problem Solving Series by Val Morey
Problem Solving Strategies by Steck Vaughn
Solve that Problem by Sharon Shapiro
Targeting Maths Problem Solving by Judy Tertini & Gloria Harris
Problem-Solver’s Math Journal by Teacher Created Materials

How do student layout the problems?

The students would paste a copy of the problem at the top of a page in their workbook and then set out the problem as following:

What? The students write a full sentence explaining what they are trying to find out.
Strategy: The students write the strategy they are going to use.
Working: The students set their work out as taught for each particular strategy.
Answer: The students write a full sentence answer.

Problem Solving Layout Example.pdf


To reduce the emphasis on just the final answer each problem is given a mark out of five.  This encourages the students to set their work out in a clear and systematic way and take care when planning and formulating their answers.

What? One mark for explaining what they are looking for.
Strategy: One mark for choosing the correct strategy to solve the problem.
Working: Two marks for demonstrating the working for the strategy they chose and setting the working out in a clearly.
Answer: One mark for finding the correct answer and explaining the answer in a full sentence.

Problem Solving Unit

I have created a unit of work containing 56 problems using problems from the invaluable Port Angeles School District WASL website. The unit contains eight questions and answers for each of the following strategies, Act it Out, Draw a Diagram, Guess and Check, Logical Reasoning, Look for a Pattern, Using Simpler Numbers and Work Backwards.  Please download, modify and use this unit to suit your needs.

Problem Solving Unit of Work.zip