Creative thinking in mathematics

1
Creative thinking in mathematics
2
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

3
Problem solving target boards
  20
  16
  6
  17
18
  12
  10
  15
  3
4
Whats 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, dont say what it
  is. Just provide further examples to confirm your
  conjecture.

2 , 8
5
3
4
2
1
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?
6
10
Again, this is an addition wall. Working
backwards, what could the numbers be in the
bottom row of bricks.
7
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.
14 20 21 34 39 45 50
8
Comparing metric capacities
0
1
2
Stay standing if the capacity you have on your
card is
greater than 0.4 litres
less than 1500 ml
greater than ¾ litre
greater than 500 ml but less than 1¼ litres
9
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 1st,2nd,3rd,4th 13th card
  (irrespective whether its 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 childrens capacity to think about
  their own learning.

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Odd one out?

• Tell yourself
• Tell a friend
• Tell a pen friend

16
11
5
14
Odd One Out?
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Whats the Question?
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Guardian of the Rule
15
19
28
34
1
11
4
7
16
3
61
100
9
12
14
10
8
17
True or False?
False
True

• 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
19
If I know . , then ..
15 16 240
24 16 1.5
240 16 15
30 8 240
240 8 30
3 8 24
8 3 24
15 8 120
24 3 8
0.3 8 2.4
15 4 60
24 8 3
3 4 12
20
100 is 320
3p
2p
4p
Double 5 is 10
5p
100g cost 40p
21
If I know . , then ..
5050100
8210
7310
5510
6410
549
Double 5 is 10
10-55
538
448
11-56
527
6612
22
If I know . , then ..
2 is 6.40
60 is 192
1 is 3.20
50 is 160
10 is 32
100 is 320
25 is 80
5 is 16
12.5 is 40
15 is 48
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Missing Operation(s)

• Give children some numbers to balance a number
  sentence.
• eg 6 , 3 , 5 , 4 , 1 , 2
• There could be more than one answer

6 2 4 3 1
3 2 6 - 1
6 3 4 2
6 3 4 2
Can each number (or digit) be used in the same
number sentence?
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Links to different types of problems

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