The document provides guidance on a systematic approach to problem solving with 4 steps: 1) Examine the problem carefully to understand requirements and available information, 2) Consider different approaches to solving it such as using diagrams or looking for patterns, 3) Choose an approach to implement, and 4) Check that the solution meets what was asked. It then provides examples of problems to solve using this approach and records the steps taken to find the solution.

1. Problem-solving

2. Examine the problem carefully:
 What does it tell me?
 What does it ask me to do?
 Have I all the information I
need?
 Is there any information that is
not helpful?

3. How will I solve it?
I could:
 Use concrete materials
 Draw diagram/picture
 Make a chart/table of information
 See if there are any patterns to spot?
 Try to guess and test (trial and error)
 Break it down and solve each part

4. Have I done what I was asked?
 Have I arrived at a solution/solutions?
 Have I shown this answer clearly?
 Have I expressed my answer in the
correct units?
 Have I shown clearly how I arrived at
this answer?

5. Summary: Problem-solving
 Examine the problem carefully:
 How will I solve it?
 Have I done what I was asked?

6. Problems to solve
 Mary’s age is a multiple of 2;  A furniture store sold 16 tables,
next year it will be a multiple of some with 3 legs and some with
3. What age will she be when 4.
this happens again? How often The tables had 52 legs in total;
does it happen? how many of each did they sell?
 How many times from midnight  My 9 coins look identical but
to noon does a digital clock one is lighter than the rest. How
show 3 or 4 consecutive can I use a balance twice to find
numbers. Remember, zeros are the counterfeit coin?
not shown before a 3-digit time.  Cut a pizza with 4 straight cuts.
Record your answers carefully
to help you look for a pattern. What is the fewest possible
number of pieces?
How long is it between these
times? What is the most possible?

7. Problem-solving
I am sitting in company at a round
table. I want to share out my 25
sweets, one at a time around the table,
so that I get the first and the last sweet.
How many are sitting at the table?

8. Problem-solving
 A farmer rears free-range pigs in a large
walled field; she wants to keep them in
a pen some of the time, but she has just
24 fence panels, each 1 metre long.
Investigate possible arrangements to
give the pigs as much space as
possible?