Problem Solving

1. Problem Solving

2. This package is designed to promote the teaching of and raise the awareness of problem solving in schools. It is an outline for an Inset day that lends itself to adaptation to suit the needs of any school.

3. Programme of the day9:00 Coffee and Introduction9:15 Skills pupils need to solve problems10:15 Problem solving strategies10:45 Coffee11:00 Act it out11:30 Draw it out11:45 Use Equipment12:15 Using a diagram12:45 Lunch1:30 Use a list1:50 Trial and Improvement2:10 Draw a table2:30 Working backwards2:45 Why use stories3:00 Problem Solving within a Story4:00 Tea and Plenary

4. Checklist of Problem Solving SkillsInput / Seeing • Systematically searches and looks for information • Is precise in gathering information • Can consider information from more than one source • Recognises patterns • Understand stability of characteristics

5. Elaboration / Thinking • Understands the spatial relationships of elements of a problem • Understands events and their relationships in time • Identifying there is a problem • Understands the relationships between the terms • Understands when something is missing from these terms • Understands what terms are relevant

6. Elaboration / Thinking • Can summarise relevant terms • Can compare like terms or attributes • The ability to organise information • Good short term memory • Can summarise experience and comment on relationship to goal • Can give logical reasons for opinions and relates information to possible outcomes • Can test a hypothesis • Can plan future actions • Understands logical multiplication

7. Output / Generating • Can give clear unambiguous instruction • Understands the vocabulary for the task • Plans responses not just the first thing that comes into their head • Has the confidence to fail • Understands the importance of the process as well as the outcome

8. In pairs or small groups fill in the checklist of the Problem Solving Skills used by two particular pupils you teach. It would be useful to consider two very different pupils.

9. Helpful Hints relating to Problem Solving Checklist • In your pairs read and discuss the activities relating to the Thinking Skills. • How could these or alternative activities be used to improve the skills of your chosen pupils?

10. How to Solve Problems • Understand and explore the problem • Find a strategy • Use the strategy to solve the problem • Reflect on the solution and how useful the strategy was

11. Problem Solving Strategies • Act it out • Draw it out • Use equipment • Draw a diagram • Make a list • Trial and Improvement • Draw a table • Work backwards • Thinking

12. ThinkingThe final strategy on the list is a ‘catch all’ because it contains the strategies that are not generally used in isolation but in combination with other strategies. • Being Systematic • Visualise • Looking for patterns • Using known skills • Testing the answer

13. Act it out Strategy 1 Act the problem out to help you solve it.

14. Boris Versus Freddie Boris the spider has noticed Freddy the Fly stuck on the opposite side of his web. (the four by Four grid) Boris has to move along the lines of his web and cannot travel across the gaps. What is the shortest route Boris must take to reach Freddy Fly. How many different ways can he get there? What would be the longest route?

15. Draw it out Strategy 2 Draw a picture to help you solve the problem.

16. Lots of Legs Boris and Norris decided to have a party. They wanted to ask all their friends who lived at the end of the garden. They sent invitations to three ants, four bees and two spiders. As a result of Maurice the Moth’s dive bombing, their web was rather delicate and they wanted all their friends to wear slippers. How many slippers do they need to have to give slippers to all their friends?

17. Use equipment Strategy 3 Use equipment to help you solve a problem How can I solve this problem?

18. Holly's Big Adventure Holly the dog was out for a walk in the woods when she saw a leprechaun sitting on a log crying. Holly asked 'What is the problem?' the Leprechaun replied that his wife had ordered him to collect some chestnuts. Holly looked around the forest floor and saw all the chestnuts that had fallen from the trees in the gales. 'So pick them up said Holly' 'No' replied the leprechaun, 'you don't understand. I have to collect exactly 50g of chestnuts. Not one more or one less!' Holly noticed in the clearing the see-saw that the elves had left behind. Holly asked the leprechaun if he had anything in the bag. He produced a 400g tin of soup. 'Ah ah!!!' said Holly, 'Now we can solve the problem.' What did Holly do?

19. Draw a diagram Strategy 4 Draw a diagram to show the problem and help you solve it

20. Day at the Races Five horses ran in a race against each other every day. Red horse always won when it was sunny. Green horse always won when it was windy. Blue horse and Black horse won on alternate days. In one month there had been five rainy days at the beginning of the month followed by 26 days where four had been windy. Blue horse had won six races. On how many days did red horse win?

21. Strategy 5 Make a list Be organised and write things down as you solve a problem

22. Pizza Parlour Sam visited the Pizza Parlour. On the menu there were ten different choices of toppings: Cheese tomato pepperoni ham chicken onions peppers pineapple mushroom beef Sam decided to choose three toppings to go on his pizza. How many different pizzas could he make?

23. Strategy 6 Trial and improvement If at first you don’t succeed try try again

24. On the Farm In the farmyard there are some pigs and some chickens. There are 87 animals and 260 legs. How many pigs are there in the farmyard?

25. Strategy 7 Draw a table Put your information in a table so you can spot any patterns and solve the problem

26. On the Farm In the farmyard there are some pigs and some chickens. There are 87 animals and 260 legs. How many pigs are there in the farmyard?

27. Strategy 8 Working backwards Sometimes it’s easier to start at the answer and work backwards to find the solution

28. Hare and Tortoise Hare arrived five minutes after Tortoise at the finish line. It had taken him 30 minutes to run the last 3 km of the race. He had stopped off at the cake shop just before that and had spent 10 minutes buying and eating some doughnuts. Before this he had been talking to Lucy bunny for 20 minutes. He had run all the way from the start before he saw Lucy, who was standing on the halfway point outside the cake shop. It had taken him twice as long to run the first half of the race compared to the second half. (Probably because he had fallen asleep under a tree) What time had Hare started the race? What time did Tortoise finish the race? If Tortoise had been travelling at a steady speed, who had reached the cake shop first?

29. Problem Solving within a Story

30. Why use Stories? • Stories help to put the child into the context of the problem • Stories are often an easier way to remember a type of problem for future reference • Stories aid children’s ability to explain • Stories can be used to contextualise problems of any kind

31. Now it's your turn!