1. Glosmaths www.glosmaths.org mathematics@gloucestershire Session 3 Exploring aspects of ‘problem solving’ within PSRN Aims: To consider the development of ‘reasoning, decision making and communication skills’ To explore different problem types and the skills and strategies pupils may need to solve them To reflect on organisational approaches for supporting the development of ‘problem solving’

2. Glosmaths What do we mean by ‘problem solving’? Reasoning Using what you know to deduce something else, making generalisations and being able to apply what you have learnt in a range of contexts; Making decisions What to find might not be obvious, too much/little information, many methods are possible, may be no answer; Communicating Listening carefully, explaining what you have done, being aware of what is happening inside your head and communicating using a mix of media;

3. Glosmaths Classification of Problems Story/context problems – usually involving computation; Finding all possibilities; Logic/deductive problems; Diagram problems and visual puzzles; Finding rules and describing patterns;

4. Glosmaths Finding all possibilities Have a system for finding the possibilities, e.g. start with the smallest number; Check for repeats; Know when all possibilities have been found; Organise the recording of possibilities, e.g. in an ordered list or table; Sandcastles 1,2,3 oops

5. Glosmaths Logic/deductive problems Identify the given facts and prioritise them; Look for any relationships and patterns in the information given; Use one piece of information in the problem and see what effect it has; Choose and use a recording system to organise the given information; Check that the answer meets all the criteria; Goldilocks Car parking

6. Glosmaths Diagram/visual problems Identify the given information and represent it in another way; Use a systematic approach to solve the problem and a way of recording if necessary; Use drawings or annotations to help; Visualise the problem using familiar shapes or patterns; Try other possibilities to check the solution; Shape hunt

7. Glosmaths Describing rules and finding patterns Decide on the information you need to describe and continue the pattern; Give examples to match a given statement and ones which don ’ t; Describe a rule of a pattern or relationship in words or pictures; Predict the next few terms in a sequence to test the rule; Use a rule to decide whether a given number will be in the sequence or not; Please Mrs Gate lady… Convince me …

8. Glosmaths Story/context problems Ben had 9 balloons. 2 popped. How many were left? Rosie had a beautiful sparkly purse. She had a 5p, a 2p and a 1p coin. How much did she have in total? identify the key words; discard redundant/irrelevant information; translate the problem into a mathematical model; understand the language in the problem; identify stages/steps required to solve the problem; develop estimation skills; Problem solver Open stories

9. Glosmaths Spring is coming!

10. Glosmaths Can you count the flowers growing in the field? How might you count them? www.glosmaths.org mathematics@gloucestershire

11. Glosmaths Can you follow these instructions to help the Easter Bunny hide this Easter egg? -The egg should not be hidden behind the smallest tree. -The flowers need lots of water. -The egg should be hidden somewhere between the tallest tree and the wheelbarrow. -The egg should be hidden behind something with four legs. -Where should the egg be hidden? www.glosmaths.org mathematics@gloucestershire

12. Glosmaths The farmer says “ I only want eight baby lambs in this field”. Are there enough lambs here? www.glosmaths.org mathematics@gloucestershire

13. Glosmaths This Easter egg has three stripes. The stripes can be red or yellow. How many different ways could the egg be decorated? www.glosmaths.org mathematics@gloucestershire

14. Glosmaths Sally was making an Easter bonnet. She wanted to put the following pattern on her bonnet. What object would come next? What would the twelfth object in the pattern be? How did you work it out? Would this object appear in the pattern? How could you change the pattern so that you could have the chocolate bunny in it too? www.glosmaths.org mathematics@gloucestershire

15. Glosmaths Mum bought three Easter eggs. They cost £3, £2 and £1. How much money did Mum spend altogether? www.glosmaths.org mathematics@gloucestershire £3 £2 £1

16. Glosmaths Convince me that 7 tadpoles and 5 tadpoles total 12 tadpoles. www.glosmaths.org mathematics@gloucestershire

17. Glosmaths What is the same and what is different about these two Easter eggs? www.glosmaths.org mathematics@gloucestershire

18. Glosmaths I put 10 chocolate bunnies in my basket. My friend ate 3 of them. How many chocolate bunnies were left? www.glosmaths.org mathematics@gloucestershire

19. Glosmaths On Monday 3 baby chicks hatched out of their eggs. On Tuesday 5 baby chicks hatched. How many baby chicks were there altogether? What if another 6 chicks hatched on Wednesday? www.glosmaths.org mathematics@gloucestershire

20. Glosmaths Give me an example of a flower that is taller than the daffodil …. and another… and another. Give me an example of a flower that is shorter than the tulip… and another…. and another. www.glosmaths.org mathematics@gloucestershire

21. Glosmaths Last week we planted some bulbs. There were twelve bulbs in total. We planted half of the bulbs in one pot and half in another pot. How many bulbs were in each pot? www.glosmaths.org mathematics@gloucestershire

22. Glosmaths Some of the baby lambs were playing ‘hide and seek’ with the farmer. The farmer spotted twelve legs behind a bush. How many of the lambs had he found? www.glosmaths.org mathematics@gloucestershire

23. Glosmaths www.glosmaths.org mathematics@gloucestershire The Easter Bunny needs help to deliver the egg to the house. Can you help him find a way to get there? How many different routes could he take?

24. Glosmaths The Easter bunny left an Easter egg for Peter, Megan, Jack, Jill, Sam and their Mummy and Daddy. How many eggs did he leave? www.glosmaths.org mathematics@gloucestershire

25. Glosmaths The Easter bunny is trying to sort out some Easter gifts. Could you help decide how to sort them? www.glosmaths.org mathematics@gloucestershire

26. Glosmaths The Easter Bunny is filling some Easter baskets for Andy, Maisie and Freddie. He puts four eggs in Andy’s basket, six in Maisie’s and five in Freddie’s. He wants to make sure that all three baskets have the same amount of eggs in. Can you help him to sort out the problem? www.glosmaths.org mathematics@gloucestershire

27. Glosmaths Spring has arrived! Today is March the 21st. It is the first day of Spring! Easter Sunday is on the 4 th of April. How many more days is it until Easter Sunday? www.glosmaths.org mathematics@gloucestershire 21 22232425262728 293031 March 1234 April

28. Glosmaths The farmer has been organising his new born animals. Can you work out his rule for sorting them into these groups? Could you sort the animals in a different way? www.glosmaths.org mathematics@gloucestershire

29. Glosmaths Session 4 – Next steps Further resources available Reflect on the planning process and resources to support Consider next steps back in school Evaluations