Often mathematics is about probability and prediction. By using this strategy(an extension of the tabling and organised list strategies) and visually presenting the information, a pattern often emerges. If a pattern can be established, it becomes relatively easy to predict what comes next. Once a pattern is able to be verified and checked it can be applied at any stage throughout the problem.

This strategy underlines the fact that problem solving strategies are interrelated and interwoven. Students will be using at least two or three sub skills simultaneously as they approach the higher levels of problem solving.

Teaching Strategy

Read the problem thoroughly.
Organise the information given into a grid to show up any patterns.
In this case the number appears to grow by a factor of 4.
Project this fact through to day 8 and day 10.

Complete the chart

Often it is difficult for students to deal in the abstract and visualise patterns and solutions. By providing real materials that can physically symbolise an element of a problem, students can move, manipulate and present solutions to problems more easily: 3-D doodling!

Use six matches to create four equilateral triangles

Teaching Strategy

Use any manipulatives that are of equal size and length to avoid inserting an extra dimension to the problem.

Define the term 'equilateral'.

This strategy is also called the if/then approach. Logical reasoning forms the basis of a great many problem solving techniques. In this strategy, statements or information can be used or extrapolated to create the next part of the solution (unlike guess and check where it is an all or nothing statement). Each piece of information should confirm the previous hypothesis or lead to a new hypothesis, hence the if/then label. Students steadily progress through the statements. Often, eliminating an option can be as useful as solving a piece of the puzzle.

At the sports carnival, five students ran in a mixed 100 metre race. Use the clues below to complete the table.

Teaching Strategy

Set up the labels and categories. Work out all the names.
Read each clue thoroughly.
Do not always start with the first clue because others may provide more information, e.g. John being the first boy to finish doesn't mean he finished first, although he may have.
Make a statement and use the clue to confirm or dismiss it.
Use named counters if required and see if the order fits the clues.

This strategy is useful for problems which are presented by a range of events that have occurred. Each stage or piece of information affects the next stage. Students start at the end point and work backwards to ascertain the original situation, as if they were rewinding a video tape.

In an all-in wrestling championship, all the wrestlers entered the ring together. Within three minutes, half were thrown over the top ropes and eliminated. In the next four minutes, half of those remaining in the ring were eliminated. By the ten minute mark, the number in the ring had dropped by half again. Fifteen minutes after the start of the competition, half of these remaining competitors had been tipped over the rope, and in the last five minutes, one more wrestler was tossed to the floor, leaving only one wrestler standing - the winner!
How many wrestlers entered the ring at the start of the match?

Teaching Strategy

Start with the winner and double at each recognisable time lapse:
  end of match = 1 wrestler
  5 minutes before end = 2 wrestlers
15 minutes into the match = 4 wrestlers
10 minutes into the match = 8 wrestlers
  4 minutes into the match = 16 wrestlers
  3 minutes into the match = 32 wrestlers