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Creative thinking in mathematics

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Objectives To consider the importance of mathematical thinking and reasoning To explore a range of thinking skills activities that promote reasoning in the daily mathematics lesson

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20 10 15 66 666 18 17 33 333 12 16 A 2-digit number A multiple of 5 An even number Between 10 and 16 An odd number Less than 10 More than 19 Even and more than 16 Between 6 and 12 Problem solving target boards

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What’s my rule? This pair of numbers is connected by a simple rule. Suggest another pair of numbers that satisfies the same rule. If you think you know the rule, don’t say what it is. Just provide further examples to confirm your conjecture. 2, 8

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3421 This is an addition wall. This is an addition wall. [NB could also be subtraction/difference wall] The value of each brick can be found by adding the pair of numbers on the row below. What is the number that needs to be put into the brick at the top?

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10 Again, this is an addition wall. Working backwards, what could the numbers be in the bottom row of bricks.

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31142016 246525 30291836 117131 14 20 21 34 39 45 50 Three in a row Choose two numbers from the row of numbers above the grid. Find the difference between these numbers. If the answer is on the grid, cover that number with a counter.

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Comparing metric capacities 012 Stay standing if the capacity you have on your card is: greater than 500 ml but less than 1¼ litres greater than ¾ litre less than 1500 ml greater than 0.4 litres

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Questions as tools for teaching and learning Questions prompt pupil to inspect their existing knowledge and experience to create new understandings. Questioning models for pupils how experienced learners seek meaning. Questioning is a key method of differentiation. Answering questions allows pupils who have difficulties communicating through writing the opportunity to contribute orally. Questions are useful tools for assessment. Questions can reveal misconceptions.

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‘Card activity’ (to demonstrate how questioning can promote reasoning skills) Lay out 2 sets of red & black ‘Ace’ to ’King’ cards. Can you pair all cards (ie one black & one red) to make the same total? Pair each black card with a red one to make a square number; Now can you pair them to make prime/triangular numbers? Lay out cards ‘Ace’ to ‘King’ (face down); Turn over every 1 st,2 nd,3 rd,4 th … 13 th card (irrespective whether it’s been turned over or not); What cards are left facing up? What do you notice? What number would come next in the sequence? Why?

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Differentiation in whole class oral work Targeted questioning; Support (resources, adult); Providing time; Through outcome; Type of questioning; By chosen strategy(ies); Visual/display; Using maths ‘buddies’;

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Thinking Skills Thinking skills are a key part of the National Curriculum & an essential tool for learning. They help children to develop the understanding as well as the knowledge required for each subject. Activities can be used across the curriculum to help develop children’s capacity to think about their own learning.

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Odd one out? Tell yourself; Tell a friend; Tell a ‘pen friend’; 16 115

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Odd One Out?

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What’s the Question? How much more is 10 than 3? How old will your brother be next week? How many days are there in 1 week? Nine take away two What is one quarter of 28? What is 3 plus 4? How many years until you’re 13? I have 1 square & 1 triangle. How many sides are there altogether? The answer is 7

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‘Guardian of the Rule’ 15 11 16 9 14 8 12 4 19 10 1 7 3 28 34 100 61

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True or False? True Fals e I can make four different numbers with two different digits. All triangles have three sides. If a number ends in a 3 then it is even. I can make 10p using four different coins. There are 100cm in 1 metre. If I subtract 10 from any whole number (integer), the units digit always remains the same.

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If I know ……., then ….. 3 × 8 = 24

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If I know ……., then ….. 3 × 8 = 24 15 × 8 = 120 15 × 4 = 60 240 ÷ 16 = 1530 × 8 = 240 240 ÷ 8 = 30 15 × 16 = 240 8 × 3 = 24 24 ÷ 3 = 8 24 ÷ 16 = 1.5 24 ÷ 8 = 3 0.3 × 8 = 2.4 3 × 4 =12

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Double 5 is 10 100% is £320 100g cost 40p 3p 4p 5p 2p

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If I know ……., then ….. Double 5 is 10 10-5=5 11-5=6 7+3=105+5=106+4=10 50+50=100 5+4=9 5+3=8 8+2=10 5+2=7 4+4=8 6+6=12

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If I know ……., then ….. 100% is £320 25% is £80 12.5% is £40 1% is £3.20 50% is £160 10% is £32 60% is £192 5% is £16 15% is £48 2% is £6.40

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Missing Operation(s) Give children some numbers to ‘balance’ a number sentence. eg 6, 3, 5, 4, 1, 2 eg 6, 3, 5, 4, 1, 2 There could be more than one answer: 6 + 2 = 4 + 3 + 13 + 2 = 6 − 1 Can each number (or digit) be used in the same number sentence? 6 ÷ 3 = 4 ÷ 26 = 3 × 4 ÷ 2

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Links to different types of problems Story/context ‘The boy with 3 bossy sisters’ / ‘On the bus’ / ‘Clara’s pocket money’ ‘The boy with 3 bossy sisters’ / ‘On the bus’ / ‘Clara’s pocket money’ Finding all possibilities Target number problems Target number problems Logic/deduction “My total is 15. What could my difference be?”/ “I have two different coins in my hand …” “My total is 15. What could my difference be?”/ “I have two different coins in my hand …” Diagram/visual Mental imagery (bus queue, shapes) Mental imagery (bus queue, shapes) Finding patterns/describing rules Counting stick / ‘Pause it’ / Counting stick / ‘Pause it’ /

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