1) This document provides examples and explanations of different types of problem solving strategies including creating organized lists, working sequentially, filling in gaps by finding patterns, combinations of numbers, and determining possible outcomes of events. 2) Examples include determining the number of ways to choose a school captain from 7 prefects, the combinations of animal tops and bottoms that can be created by splitting animals in half, and the number of 3-digit numbers that can be made using the digits 1, 2, and 3. 3) The document asks the reader to determine the number of ways 4 people can line up, the number of double scoop ice cream cones that can be made from 3 flavors, and the possible outcomes of

1. Problem SolvingCreating an Organised List

2. Creating an Organised ListThis strategy is similar to drawing a table but it is normally used when there is more information available.You need to follow a procedure or sequence to make sure or all possibilities are listed an not repeated.When creating a list, one item should be kept the same or constant while the others change.

3. Work SequentiallyDecide on a starting point then work in an order.Example:The school captain and vice-captain are to be chosen from 7 prefects. How many different choices can be made?Let the symbols A B C D E F and G stand for the seven prefects.

4. Filling In The Gaps After Working Out A PatternExample:Various animals are split in half and different combinations of the tops and bottoms are created. The animals used are a fish, dog, cat, mouse, guinea pig and rabbit. How many different combinations can be made?

5. There are five combinations for every top of an animal.What would the answer be?

6. Combinations of NumbersSometimes you will be given problems that ask you to combine a series of numbers.Example:Using the digits 1, 2 and 3 how many 3 digit numbers can you make?

7. Problem 1David, Brett, Jenna and Carmel are lining up to go to the cinema. How many different ways can they line up?

8. Problem 2How many different double scoop ice cream cones can be made using the flavours vanilla, chocolate and strawberry?Vanilla on top and choc on bottom is the same as choc on top and vanilla on bottom.

9. Problem 6If you toss two coins in the air, what are all the possible outcomes when they land?