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

 

20

 

10 

15

 

6

18

 

17

 

3

 

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

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

34 21This 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.

31 14 20 16

24 6 5 25

30 29 18 36

11 7 13 1

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.

Comparing metric capacities

0 1 2

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

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.

‘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 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?

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’;

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?

Tell yourself; Tell a friend; Tell a ‘pen friend’; 16

11 5

Odd One Out?

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

‘Guardian of the Rule’15

11

16

9

14 812

4

19

10

1

7

3

28

34

10061

True or False?TrueFals

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 …..

3 × 8 = 2415 × 8 = 120

15 × 4 = 60

240 ÷ 16 = 15

30 × 8 = 240240 ÷ 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

Double 5 is 10

100% is £320

100g cost 40p

3p

4p

5p

2p

If I know ……. , then …..

Double 5 is 10 10-

5=5

11-5=6

7+3=10

5+5=10

6+4=10

50+50=100

5+4=9

5+3=8

8+2=10

5+2=74+4=8

6+6=12

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

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 + 13 + 2 = 6 − 1

Can each number (or digit) be used in the same number sentence?

6 ÷ 3 = 4 ÷ 2 6 = 3 × 4 ÷ 2

Links to different types of problems

Story/context ‘The boy with 3 bossy sisters’ / ‘On the bus’ / ‘Clara’s 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’ /