1. Fluency, Problem solving and Reasoning Maths for NQTs Mark Hattersley Mark.hattersley@bradford.gov.uk @MarkAHattersley Philipa Varley Philipa.varley@bradford.gov.uk @philipav

2. Aims To develop an understanding of the new mathematics curriculum To develop ideas for fluency, problem solving and reasoning

3. Starter- Strike it out How to play ‘Strike it out’ NRich

4. Player 1 2+3 = 5

5. Player 2 Must start where player 1 finished 5 + 10 = 15

6. Player 1 Must start where player 2 finished 15 – 1 is and so on The loser is the person who can not complete their go Play again collaboratively– can you use as many numbers as possible?

7. Starter- Factors and multiples a collaborative game Rules of the game Player 1 chooses a number Player 2 must choose a number that is a factor or multiple of player 1’s number Player 1 must choose a number that is a factor or multiple of player 2’s number And so on… How many numbers can you get in your sequence? NRich

8. 2 Minute task What is important?

9. What do these mean?

10. What does it look like?

11. What is the meaning of Fluency? http://www.nctm.org/about/content.aspx?id=34 791 Fluency Is it simply fast and accurate? Read the article Agree a definition for Fluency

12. What else do you know? 7x3=21 3x7=21 21÷7=3 21÷3=7 70x3 =210 3x70=210 210÷70=3 210÷3=70 17 x 3 = 57

13. KS1 What else do you know? 10 = 7 + 3 10 – 3 = 7 10 = 3 + 7 10 – 7 = 3 70+ 30 = 100 30 + 70 =100 100 = 70 + 30 100 – 30 = 70 3 + 7 = 10 7 + 3 = 10 17 + 3 = 20

14. What does problem solving mean? Does it mean word problems?

15. Problem solving and reasoning Word Problems Representing  analyse  record  do  check  confirm Enquiring  plan  decide  organise  Interpret  reason  justify Reasoning create deduce apply explore predict hypothesise test Communicating Explain methods and solutions choices decisions reasoning

16. NCETM – new curriculum resources

19. What does reasoning mean? Close your eyes and think of ….

20. Reasoning Mat This reminded me of...so I... When I looked at the table/result/grap h I noticed that... What if… This worked so... Using the numbers in my table I looked at..... I can see a pattern... I already know that... so.... I tested I used... method because... I noticed a connection between... This didn’t work so... I noticed that... I decided to......... because........ This is true here because… This is always true because… I wondered why...

21. Reasoning Mat KS1 What if… This worked so... I can see a pattern... I tried … This didn’t work so... I noticed that... I decided to......... because........ I wondered why…

22. NCETM - Reasoning Progression documents with reasoning questions www.ncetm.org.uk/resources/44672

23. Reasoning question styles Spot the mistake / Which is correct? True or false? What comes next? Do, then explain Make up an example / Write more statements / Create a question / Another and another Possible answers / Other possibilities What do you notice? Continue the pattern Missing numbers / Missing symbols / Missing information/Connected calculations Working backwards / Use the inverse / Undoing / Unpicking Hard and easy questions The answer is… Visualising What else do you know? / Use a fact Fact families Convince me / Prove it / Generalising / Explain thinking Make an estimate / Size of an answer Always, sometimes, never Making links / Application Can you find? What’s the same, what’s different? Odd one out Complete the pattern / Continue the pattern Another and another Ordering Testing conditions

24. Estimation/ Range of answers What is 432 - 175 ? Discuss these “answers” using estimation to decide which could be right and which are wrong. 607, 257, 343, 238,

25. Estimation/ Range of answers Key stage 1 example 63 + ? = 100 Discuss these “answers” using estimation to decide which could be right and which are wrong. 47 46 37 36

26. Sometimes, always, or never true? The difference between any two odd numbers is an even number If you add three consecutive numbers together the answer is always even The sum of three odd numbers is divisible by 5

27. KS1 Sometimes, always, or never true? When I add two numbers together I get an even answer. Adding 10 to a 2 digit number changes both digits. When I add two lots of odd numbers, the answer is always odd.

28. Using your reasoning mat, discuss these sequences or number sentences 10, 8, 5, 1, -4 3, 6, 10, 16, 22, 29 Questioning techniques – right or wrong? 7 – 10 = -7 7 – 10 = -3

29. Using your reasoning mat, discuss these sequences or number sentences 2, 4, 6, 8, 10 5, 10, 16, 20, 23 KS 1 Questioning techniques – right or wrong? 7 + 4 = 11 7 – 4 = 11

30. Doing and Undoing Doing Find the area of these rectangles 4cm 8cm 2cm 6cm 8cm 7cm

31. Doing and Undoing The area of a rectangle is 48cm. What could the dimensions be? 2

32. Doing and undoing KS1 Doing +=

33. Doing and undoing KS1 Undoing – How many teddies are hiding in each pot? + =

34. Fluency, problem solving and reasoning every day Look at the two examples of worksheets. Which allows for problem solving and reasoning? Closed, closed, open

35. Where to go for ideas Opening up questions documents Pitch and Expectations (year group) Reasoning mat Levelopaedia Nrich Website NCETM

36. Where to go for ideas Opening up questions documents Reasoning mat NCETM reasoning documents Levelopaedia Available on B radford S chools O nline

37. New sample questions July 2014 Fluency Reasoning Problem Solving

38. New sample questions July 2014 Fluency Reasoning Problem Solving

39. Aims To develop an understanding of the new mathematics curriculum To develop ideas for fluency, problem solving and reasoning