Transcript If I know ……. , then

Creative thinking in
mathematics
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
Problem solving target boards
A 2-digit
A multiple of 5
An even
Between 10
An odd
and 16
number
Less than 10
number
number
16
20
More than 19
6
18
10
Even and more Between 6 and
than 16
12
15
3
17
12
What’s my rule?
This pair of numbers is connected by a simple
rule.
2,8
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.
4
1
2
3
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?
10
Again, this is an addition wall.
Working backwards, what could the numbers
be in the bottom row of bricks.
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
31 14 20 16
24 6
5 25
30 29 18 36
11 7 13 1
Comparing metric capacities
0
1
2
Stay standing if the capacity you have on your card is:
less than
1500 ml
greater
than ¾
litre
greater than
0.4 litres
greater than
500 ml but less
than 1¼ litres
Questions as tools for
teaching and learning
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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.
‘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?
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Lay out cards ‘Ace’ to ‘King’ (face down);
Turn over every 1st,2nd,3rd,4th … 13th 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
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Targeted questioning;
Support (resources, adult);
Providing time;
Through outcome;
Type of questioning;
By chosen strategy(ies);
Visual/display;
Using maths ‘buddies’;
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.
Odd one out?

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Tell yourself;
Tell a friend;
Tell a ‘pen friend’;
11
16
5
Odd One Out?
What’s the Question?
What is one
quarter of 28?
How many
years until
you’re 13?
How many
days are there
in 1 week?
Nine take
away two
The
answer
is 7
What is 3
plus 4?
How much
more is 10 than
3?
How old will
your brother
be next week?
I have 1 square & 1
triangle. How many
sides are there
altogether?
‘Guardian of the Rule’
15
19
28
34
1
11
7
16
4
3
61
100
9
14
8
10
12
True
True or False?
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.
If I know ……. , then …..
3 × 8 = 24
If I know ……. , then …..
24 ÷ 16 = 1.5
240 ÷ 16 = 15
8 × 3 = 24
15 × 16 = 240
240 ÷ 8 = 30
3 × 8 = 24
30 × 8 = 240
15 × 8 = 120
24 ÷ 3 = 8
0.3 × 8 = 2.4
24 ÷ 8 = 3
15 × 4 = 60
3 × 4 =12
100% is
£320
3p
2p
Double 5
is 10
4p
5p
100g cost
40p
If I know ……. , then …..
8+2=10
7+3=10
5+4=9
50+50=100
6+4=10
5+5=10
Double 5
is 10
10-5=5
5+3=8
4+4=8
5+2=7
6+6=12
11-5=6
If I know ……. , then …..
2% is
£6.40
1% is
£3.20
60% is
£192
10% is
£32
5% is
£16
50% is
£160
100% is
£320
15% is
£48
25% is
£80
12.5%
is £40
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:
3+2=6−1
6÷3=4÷2
6+2=4+3+1
6=3×4÷2
Can each number (or digit) be used in the
same number sentence?
Links to different types of problems
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Story/context
‘The boy with 3 bossy sisters’ / ‘On the bus’ / ‘Clara’s pocket money’
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Finding all possibilities
Target number problems
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Logic/deduction
“My total is 15. What could my difference be?”/ “I have two different
coins in my hand …”
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Diagram/visual
Mental imagery (bus queue, shapes)
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Finding patterns/describing rules
Counting stick / ‘Pause it’ /