The idea of problem solving activities often conjures up images of numbers
and objects that have no direct meaning for students other than teaching the
basic problem solving strategies. The blackline master activities in this book are designed to
present real-life problems in a realistic context so as to provide children
with situations in which everyday problem solving and comprehension skills are
The activities are based around recurring cartoon characters ? named
Archimedes, Pythagoras and Gaileo ? who find themselves exposed to a range
of problems that need to be solved; the sort of problems that students may one
Most sheets include a challenge activity, usually an extension of the main
problem, which will further consolidate comprehension skills. Included
throughout the book are brainteaser Sheets which focus on a particular problem
solving strategy, highlighted at the foot of the Page. These brainteasers can
be photocopied and individually glued on to card so as to create a set.
Students might like to think up their own brainteasers to add to the set.
Problem Solving Strategies
There are many strategies for solving everyday math problems. Some of the
main problem solving strategies have been explained below. In some cases
examples of problems are given where the particular strategy can be applied.
Guess and check:
Probably the first strategy children might try and definitely the easiest. By
making a guess and checking their answer, children have a point of reference
on which to base all other guesses.
I am thinking of two consecutive numbers that when multiplied give 182. A
guess might be to try 14 x 15 which would give 210. Obviously the next guess
would try lower numbers.
Act it out:
Students quite often need to visualize the problem, especially where people or
objects are concerned. Counters, coins and students can be used to help solve
There are 48 players in the darts championships. Each player stays in the
competition until they lose a game. How many games must be played to find the
A caterpillar crawls 2 m up a tree every day. Every night it slips back 50
cm. The tree trunk is 10.5 m tall. How long will it take for the caterpillar
to reach the top of the trunk?
Make a model:
When problems cannot be acted out the next best thing is to make a model using
cubes, matches, and so on.
Make a drawing, diagram or graph:
Graphs and diagrams are particularly useful for trying different combinations
or clarifying information.
Jack has a rectangular field that has an area of 360 m. What are the possible
dimensions of the rectangle?
Look for a pattern:
This strategy can be used in many number and space activities to help simplify
Number patterns: It takes three matches to make a triangle, 5 matches to
make 2 triangles. How many matches are needed to make 3 triangles?
Spatial Patterns: How many squares are there on a checker board?
Construct a table:
By organizing data in a more meaningful way children can better see
relationships, patterns and possibly missing information. This strategy is
best used where different information is given about each person or object in
the problem. A table can include all the information and eliminate irrelevant
Tim, Peter, Max, Jane, Tarnie and Kelly each play sport over the weekend. They
all play a different sport. Match the person to their sport based on the
Tim doesn?t like swimming but enjoys baseball;
Peter likes tennis more than swimming;
Kelly enjoys netball;
Max won?t play hockey;
Jane doesn?t like baseball or diving;
Tarnie plays the sport that Max doesn?t like.