1. NQT KS1 and KS2 Mathematics Course Event Code: LIS 13/253 Tutors: Kathryn Roper and Simon Nortcliffe Venue: Kesgrave High School, Ipswich

3. Aims of the course To develop a clearer understanding of children’s progression in mathematics To know some of the key hard to teach, difficult to learn aspects of the mathematics curriculum Understand how to transfer knowledge gained from assessment and tracking data into practical teaching to impact on learning

4. Session 1

5. Key principles to help with the teaching of mathematics  Every day is a mental mathematics day  Hands-on learning is still important  Seeing mathematics through models and images supports learning  Talking mathematics clarifies and refines thinking  Make mathematics interesting  Learning from mistakes should build up children’s confidence

6. Progression Activity Working with a partner can you put the objectives in order starting with Reception and ending with Progression to Year 7. Consider whether your children are working at age related expectations; where they are doing well and areas where more support is required. What is the progression from the previous year group to your year group?

7. Teaching children to calculate mentally How do you support children in your school to progress with their mental calculations? Turn to ‘Progression in mental calculations’ beginning on page 4 of the document. Work with someone on your table to devise an activity, using practical resources, to support the skills required for your year group focusing on addition and subtraction or multiplication and division. Share your activity with another pair.

8. Tea/Coffee

9. Reflection Reflecting on your mathematics teaching to date consider the following questions: What is working well? What would you like to have more support in moving your mathematics teaching forward? Please write your comments on sticky notes and put them on the flip chart sheets.

10. Session 2

11. Strategies to promote speaking and listening in mental mathematics Visualisation / mathematical imaginings Always, sometimes, never true True or false Negotiation of meaning Using one of the above strategies plan an activity to address the objectives in Block B, Unit 3.

12. Lunch

13. All four band members need to cross a bridge. They start on the same side of the bridge. A maximum of two people can cross at any time. It is night and they have just one lamp. People that cross the bridge must carry the lamp to see the way. A pair must walk together at the rate of the slower person: Bono: - takes 1 minute to cross Edge: - takes 2 minutes to cross Adam: - takes 7 minutes to cross Larry: - takes 10 minutes to cross The second fastest solution gets the friends across in 21 minutes. The fastest takes 17 minutes. Can you work out how it is done? U2 Bridge Crossing Problem

14. Solutions 1 and 2 cross over first. 2 minutes Then 1 goes back. 1 minute Then 7 and 10 cross over. 10 minutes Then 2 crosses back. 2 minutes Then 2 and 1 cross together. 2 minutes Total Time: 17 minutes! 1 and 2 1 2,7 and 10 7 and 10 2 1 and 2 1 1,2,7 and 10

15. Interim task Carry out your planned activity and reflect on the children’s responses and the impact on pupil learning. Be ready to discuss the outcomes of the planned activity and anything else you have undertaken as a result of attending day 1. Day Two – Monday 10 th June 2013

16. Why teach problem solving? Children need to be able to analyse everyday situations and apply their maths to real life problems Children enjoy problem solving activities - Maths is enjoyable! Children with a wide range of attainment can participate Children learn not to expect immediate answers Develops children’s skills of co-operation and collaboration Encourages children to check their answers and use mathematical language Develops thinking and reasoning skills Numeracy framework has been revised to include renewed emphasis on Speaking and Listening and Using and Applying Mathematics

17. Two aspects to teaching problem solving Teaching specific strategies to solve particular types of problem, for example in units on reasoning about number or shape; Posing questions in ‘everyday’ teaching for children to practise and develop their general mathematical thinking and reasoning skills across the full mathematics curriculum, not just in the units on problem solving.

18. Problem Solving Two methods of approach Approach A Approach B

19. Approach A Start with a problem or investigative task during an initial whole-class discussion. Children then continue the same task or activity, often in pairs or small groups, developing it to a level appropriate to their attainment. Collect together children’s responses and set similar problems. Open-ended problems are useful for this.

20. Approach B Complete an activity during an initial whole-class discussion and highlight the strategies used. Follow this by providing different, but related, tasks. Most children will work on a task; however some could work on a simplified task and some on a harder task.

21. Problem solving materials

22. Research shows that… Mayher (1985) identified the following factors as contributing towards problem solving performance: Practice in recognising problem types. Practice in representing problems – whether concretely, in pictures, in symbols, or in words. Practice in selecting relevant and irrelevant information in a problem. Extract taken from ‘Primary Mathematics – Teaching for understanding’ Barmby et al, 2009.

23. Classification of problems Finding all possibilities; Logic problems; Finding rules and describing patterns; Diagram problems and visual puzzles; Word problems.

24. Finding all possibilities

25. Children’s strategies Have a system for finding the possibilities Organise a way of recording ideas/strategies Use a method of tracking what has been included and what has not Have a way of deciding when all possibilities have been found

26. Logic problems

27. Children’s strategies Identify the given facts and prioritise them Look for any relationships and patterns in the information given Use one piece of information at a time and see what effect it has, then keep one fixed and test the other Choose and use a recording system to organise the given information Check that the answer meets all the criteria

28. Finding rules and describing patterns

29. Children’s strategies Decide on the information you need to describe and continue the pattern Give examples to match a given statement and ones which do not 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

30. Diagram problems and visual puzzles

31. Children’s strategies 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

32. Word problems Nadia is working with whole numbers. She says: ‘If you add a two-digit number to a two-digit number you cannot get a four-digit number.’ Is she correct? Explain why.

33. Word problems Children’s strategies Read and make sense of the problem Recognise key words, relevant information and redundant information Decide which number operations to use and in which order Choose an efficient way to calculate Check their work to see whether it makes sense

34. Other resources to support the teaching and learning of problem solving Problem solving pack - DCSF Mathematical challenges for able children in Key Stages 1 and 2 - DCSF Developing the Mathematical Challenges for able children - Suffolk We can work it out! – ATM It makes you think! – ATM NRICH website – www.nrich.maths.orgwww.nrich.maths.org Talk Maths – Camden Maths Learning Network Targeting Level 4 through Problem solving

35. Questioning ‘Good questioning techniques have long being regarded as a fundamental tool of effective teachers.’ Jenni Way, October 2001.

36. Changing the mind-set When we ask a question, we’re not only interested in the correct answer but in what children think.

37. What makes questioning effective? Prepare key questions to ask. Ask fewer but better questions. Use appropriate language and content. Give pupils “thinking time” to respond to questions, and pause between them. Prompt pupils, give cues. Listen, and acknowledge pupils’ responses positively. From 'How do they walk on hot sand', Suffolk Publication, 2001.

38. Bloom’s taxonomy

39. Odd one out Which is the odd one out? Why?

40. Odd one out Which is the odd one out? Why? The only shape with curved sides?

41. Odd one out Which is the odd one out? Why? The only shape with curved sides? The only shape with three sides?

42. Odd one out Which is the odd one out? Why? The only shape with curved sides? The only shape with three sides? The only shape with four equal sides?

43. Odd one out Which is the odd one out? Why? The only shape with curved sides? The only shape with three sides? The only shape with four equal sides? ?

44. Odd one out Which is the odd one out? Why? 6, 15, 28, 36, 66

45. Odd one out Which is the odd one out? Why?

46. Hide the hand…….. I have 5 coins totalling 22p in my hand. What are the coins?

47. Hide the hand…….. I have 5 coins totalling 22p in my hand. What are the coins?

48. Hide the hand…….. I have 5 coins totalling 22p in my hand. What are the coins?

49. Hide the hand…….. I have 5 coins totalling 22p in my hand. What are the coins?

50. Hide the hand…….. I have 5 coins totalling 22p in my hand. What are the coins?

51. Hide the hand…….. I have 5 coins totalling 22p in my hand. What are the coins?

52. Give me…… and another…..and…. A multiple of 2 The dimensions of a polygon with a perimeter of 36 centimetres 3 numbers with a mean of 12 A net of a cube A fraction bigger than 1/2

53. Convince Me That this isn’t a square? ?

54. Convince Me The hidden shape is a yellow triangle

55. Convince Me The hidden shape isn’t a yellow triangle

56. What is wrong with the statement …? How can you correct it? When I count in 2s, the numbers will always be even. If I count on in 10s from 15, the units digit will change each time.

57. What is the same and what is different about...? 27 227 37272 237 22

58. Sometimes, always, never true? Helen says that when you add two consecutive numbers the answer is always odd. Is she right? Explain your answer. eg 26 and 27

59. POGs Providing pupils with a structure of answering questions; a peculiar, obvious and general example. Can you think of an example for numbers with a product of 60. Peculiar – 240 x 0.25 Obvious – 10 x 6 General rule – two numbers that make 60 when multiplied together

60. The Suffolk Hub – www.suffolklearning.co.uk

61. Contact Information By phone: Office - (01473) 263962 Liz Rivett E-mail: Kathryn.Roper@suffolk.go.uk Simon.Nortcliffe@suffolk.gov.uk Website: www.suffolklearning.co.uk