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;

9. Glosmaths Merry Christmas! 1 2 3 4 5 17 7 23 821 6 9 10 11 12 13 14 15 16 18 19 20 22 24

10. Glosmaths December 1st Can you help Father Christmas count the presents to put on his sleigh? How might you count them? www.glosmaths.org mathematics@gloucestershire

11. Glosmaths December 2nd Can you follow these instructions to help Father Christmas deliver this present: -I need to go to a house that is an even number. -The house is a number more than 5. -The house is two less than 8 Which house should Father Christmas deliver his present to? www.glosmaths.org mathematics@gloucestershire 5432678

12. Glosmaths December 3rd Father Christmas says “ I need six reindeer to pull my sleigh.” Are there enough reindeer here? www.glosmaths.org mathematics@gloucestershire

13. Glosmaths December 4th This Christmas tree has three baubles. The baubles can be red or blue. How many different ways could the tree be decorated? www.glosmaths.org mathematics@gloucestershire

14. Glosmaths December 5th Sam was making some Christmas wrapping paper. He put the following pattern on his paper. What picture would come next? What would the tenth picture in the pattern be? How did you work it out? Would this picture appear in the pattern? How could you change the pattern so that you could have Father Christmas in it too? www.glosmaths.org mathematics@gloucestershire

15. Glosmaths December 6th Mum bought two presents. One cost £5 and the other cost £3. How much did Mum spend altogether? www.glosmaths.org mathematics@gloucestershire £3 £5

16. Glosmaths December 7th Convince me that 3 presents and 2 presents total 5 presents. www.glosmaths.org mathematics@gloucestershire

17. Glosmaths December 8th What is the same and what is different about the numbers on these two houses? www.glosmaths.org mathematics@gloucestershire 38

18. Glosmaths December 9th I put 10 candy canes on the Christmas tree. My little boy ate 2 of them. How many candy canes were left? www.glosmaths.org mathematics@gloucestershire

19. Glosmaths December 10th Rudolph ate 3 carrots on Monday and 2 carrots on Tuesday. How many carrots did he eat altogether? What if he ate another 4 carrots on Wednesday? www.glosmaths.org mathematics@gloucestershire

20. Glosmaths December 11th Give me an example of a house number that is more than 3…. and another… and another. Give me an example of a house number that is less than 9 … and another…. and another. www.glosmaths.org mathematics@gloucestershire 8642 10 1214

21. Glosmaths December 12th We decorated the tree with Christmas lights. There were ten lights in total. We put half the lights on the left side of the tree and half on the right side. How many lights were on each side? www.glosmaths.org mathematics@gloucestershire

22. Glosmaths December 13th Some of the reindeer were playing ‘hide and seek’ with Father Christmas. Father Christmas spotted eight legs behind a bush. How many of the reindeer had he found? www.glosmaths.org mathematics@gloucestershire

23. Glosmaths December 14th www.glosmaths.org mathematics@gloucestershire How many triangles can you spot in this star? Can you spot any other shapes?

24. Glosmaths December 15th Father Christmas filled a stocking for James, Sarah, Mum and Dad. How many stockings did he fill? www.glosmaths.org mathematics@gloucestershire

25. Glosmaths December 16th Father Christmas and his elves are trying to sort some of presents. Could you help them decide how to sort them? www.glosmaths.org mathematics@gloucestershire

26. Glosmaths December 17th Father Christmas is filling some Christmas stockings for Peter, Jane and Sally. He puts five presents in Peter’s stocking, four in Jane’s and three in Sally’s. He wants to make sure that all three children have the same amount of presents in their stockings. Can you help him to sort out the problem? www.glosmaths.org mathematics@gloucestershire

27. Glosmaths December 18th Today is December the 18 th. Christmas day is on December the 25 th. How many more days is it until Christmas? www.glosmaths.org mathematics@gloucestershire 1819202122 232425

28. Glosmaths December 19th Father Christmas has been organising his elves. Can you work out his rule for sorting them into these two groups? www.glosmaths.org mathematics@gloucestershire

29. Glosmaths Merry Christmas! www.glosmaths.org mathematics@gloucestershire Have a lovely Christmas holiday and don’t forget to practise lots of counting. You could also see what shapes and patterns you can spot.

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