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

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

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

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

Ways to promote reasoning

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

TALK PICTURES Talk pictures

Low Threshold High Ceiling Task

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

Ways of supporting or extending the problem https://established1962.wor dpress.com Find products Get the children to write their own problems Numbers 0-20

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

Spikey and Curly’s problem

What did you notice about the task?

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

White Rose Hub: Problem of the day

Kagen Structures

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

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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.

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? http://nrich.maths.org/6708

Handshakes…introduction to algebra Number of Number of Number of people hands handshakes 1 2 0 2 4 1 3 6 3 4 8 6

I have just spent £9. What could I have bought? fish £2 chips £1 Solution Fish 0 1 2 3 4 Chips 9 7 5 3 1

Using algebra to work out times tables X6 2n + 4n = 6n Double, double again and then add the two answers: ( twice the number and 4 times the number make 6 times the number) X8 10n – 2n = 8n Arithmogons

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?

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, 1 + 2 = 3, 4 + 3 = 7 and 8 + 0 = 8. Some of us did it the other way round, making the smallest totals first, with the smallest numbers: 1 + 2 = 3, 4 + 3 = 7, 8 + 0 = 8, 7 + 6 = 13 and 9 + 5 = 14. We could also come up with pairs randomly but it's quicker to use a strategy. 7 + 0 = 7, 5 + 3 = 8, 9 + 4 = 13, 6 + 8 = 14 and 1 + 2 = 3. What numbers could be inside the "8" envelope? Now have a go at this one below ' Make 37' http://nrich.maths.org/1885

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?

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.