1. Aims of the meeting
understanding of what is reasoning and problem solving in curriculum 2014
Reasoning and problem solving at greater depth
Bank of activities to support reasoning
Ways to evidence reasoning and problem solving

3. Research has shown that the ability to reason mathematically is the most important factor in a pupil’s success in mathematics.
NCETM 2015

4. Got it http://nrich.maths.org/1272
It is a version of a well known game called Nim.
Start with the Got It target 23.
The first player chooses a whole number from 1 to 4 .
Players take turns to add a whole number from 1 to 4 to the running total.
The player who hits the target of 23 wins the game.
Play the game several times.
Can you find a winning strategy?
Can you always win?
Does your strategy depend on whether or not you go first?
What happens if you change the number of participants
Low threshold high ceiling tasks NRich

5. Small steps are easier to take
Teaching for Mastery
Number Facts
Table Facts
Making Connections
Procedural
Conceptual
Chains of Reasoning
Access
Pattern
Representation
& Structure
Mathematical Thinking
Fluency
Variation
Coherence
Small steps are easier to take

7. Ways to promote
reasoning

8. Further Activities to promote reasoning
WAGOLL
Sometimes, never, never true
Prove it in three ways
Convince me
Find all the possibilities
Explain this in two ways: which is the most efficient and least efficient?
Number talk
Empty box calculations – more open ended
Kagen Structures
Group solutions
Talk for maths
Draw it

9. TALK PICTURES
Talk pictures

10. Low Threshold High Ceiling Task

13. WAGOLL
How could support or challenge the children with this activity?

14. Ways of supporting or extending the problem
dpress.com
Find products
Get the children to write their own problems
Numbers 0-20

15. It is better to solve one problem 5 times than 5 different problems.
Polya – a Standford University professor
One anchor task and vary it over several sessions to get more deepening.
The importance of exploring through talk and through the concrete resources

16. Spikey and Curly’s problem

17. What did you notice about the task?

18. No numbers- no mathematical symbols
One word at a time so the students had time to process the information
Resources to visualise the problem
Focus on the relationship between Spikey and Curly
Low threshold high ceiling
Qualitative relationship rather than the quantitative relationship

19. White Rose Hub: Problem of the day

20. Kagen Structures

21. Deepening Understanding
Another website Ben Mayoh – you have to subscribe
A bank of resources

22. Check my paper
From the same website -

23. Transum

25. 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.

27. Handshake challenge How many handshakes will 5 people make? 10 15?
Ext: 6 children out
One of those 6 to become the person who shakes the hand of the others, how does this effect the mathematical outcome?

28. Handshakes…introduction to algebra
Number of Number of Number of
people hands handshakes

29. I have just spent £9. What could I have bought?
fish £2
chips £1
Solution
Fish Chips

30. Using algebra to work out times tables
X n + 4n = 6n
Double, double again and then add the two answers:
( twice the number and 4 times the number make 6 times the number)
X n – 2n = 8n
Arithmogons

31. Target board Which of these are:
An odd prime number < 20? Three numbers which total 20?
Half of one less than 3 x7? How many are prime numbers?
Can you find any square numbers?

32. Sealed solution What numbers could be inside the "8" envelope?
A set of ten cards, each showing one of the digits from 0 to 9, is divided up between five envelopes so that there are two cards in each envelope. The sum of the two numbers inside it is written on each envelope: 7 8 13 14 3
We started off by thinking of all the possible ways of making the totals. This took a long time.
We thought that it would be best to make the biggest totals first, using the bigger numbers to make them:
14 = 9 + 5, 13 = 6 + 7, = 3, = 7 and = 8.
Some of us did it the other way round, making the smallest totals first, with the smallest numbers:
1 + 2 = 3, = 7, = 8, = 13 and = 14.
We could also come up with pairs randomly but it's quicker to use a strategy.
7 + 0 = 7, = 8, = 13, = 14 and = 3.
What numbers could be inside the "8" envelope?
Now have a go at this one below ' Make 37'

33. Heads and feet On a farm there were some hens and sheep.
Altogether there were 8 heads and 22 feet.
How many hens were there?

34. Fill in the missing numbers☼ 8 $
& ♣ 17 ♥ 16 € 11 9 14 18
Individually have a go at solving the puzzle. You need to work out the value of each symbol, so that when you add each row or column you get the total at the end.
How did you start the puzzle?
Once you found the value of the sun what did you do next?
Give an example of how you worked out one of the other symbols?
Discussion less about the different calculation strategies the children are using and more about the problem solving strategies that they are using however the children are still using and applying a number of different mental mathematics strategies.