Maths WorkshopKS1

Aims in KS1

• To have a secure knowledge of number facts and a clear understanding of the four operations.

• To be able to use their knowledge and understanding to carry out calculations mentally and to apply appropriate strategies when using larger numbers.

• To have an efficient, reliable written method of calculation for each operation that can applied with confidence.

Strategies for Mental Calculations

• Number bonds to 10 and 20• Counting forwards and backwards in

1s and 10s• Doubles and near doubles• Partitioning and recombining

numbers• Adjusting near multiples of 10 • Bridging through 10• Inverse relationships

Addition

Progression in Addition

Recording calculations in pictures

4 + 2 = 6 3 + 3 = 6

Bead strings or beads / counters to illustrate addition

8 + 2 = 10

Using a number line to count on in units

12 + 6

+1 +1 +1 +1 +1 +1

12 18 12 + 6 = 18

12 + 6 =

12 + 6 = 18

+

1

+

1

+

1

+

1

+

1

+

1

1812

Using a number line to count on in tens

+ 10 + 10 + 10

24 + 30 =

24 + 30 = 54

+

10

+

10

+

10

24 34 44 54

Partition a number to bridge through a multiple of ten

I can partition a number to bridge through a multiple of ten 16 + 7

+ 4 + 3

16 20 23

16 + 7 = 23

15 + 8 =

+ 5

15 20 23

+ 3

15 + 8 = 23

Use a number line to count on in tens and units by partitioning

I can partition a number to bridge through a multiple of ten 16 + 7

+ 4 + 3

16 20 23

16 + 7 = 23 48 + 14 =

62

48 + 14 =

+

10

48 58 62

+ 4

Adding near multiples of ten by adding in tens and adjusting

+ 20

35 54 55

-1

25 + 19 =

25 + 19 = 44

+ 20

454425

Partitioning to solve more complex addition

265 + 177 =

265 = 200 + 60 + 5177 = 100 + 70 + 7 __________ 300 + 130 + 12 = 442

Using the partitioned method to add in columns

215 + 176 11 ( 5 + 6) 80 (10 + 70) 300 (200 + 100) 391

215 + 176 =

215 + 176 = 391

Column method including carrying digits

217 + 179 =

2 1 71 7 9

217 + 179 = 396

1

3 9 6

Bead strings or beads / counters to illustrate subtraction

10 – 2 = 8

Using a number line to count back in units 12 + 6

+1 +1 +1 +1 +1 +1

12 18 12 + 6 = 18

18 - 6 =

18 – 6 = 12

-1-1-1-1-1-1

12 18

Progression in Subtraction

Recording calculations in pictures

9 – 5 = 4

To find the difference by counting on the number line

+ 10 + 10 + 10

32 - 18 =

2 + 10 + 2 = 14

+ 2 +

10

+ 2

18 20 30 32

32 - 18 = 14

To bridge through a multiples of ten when counting back

42 – 25 =

+ 10 + 10 + 10

42 – 25 = 17

- 3

17 20 22 42

- 2 - 20

To subtract near multiples of ten by subtracting in tens and adjusting

I can subtract near multiples of ten by subtracting in tens and adjusting 45 - 19

-20

+1

25 26 45

45 – 19 = 26

- 20

35 36 55

55 – 19 =

55 – 19 = 36

To partition numbers and subtract using decomposition

81 – 57 =

81 – 57 = 24

50 780 1

70 1

420

To partition numbers and subtract using decomposition

534 - 218 =

534 - 218 = 316

218 = 200 10 8

534 = 500 30 4

20 1

300 10

6

To use a number line to find the difference between decimals

+ 10 + 10 + 10

6.2 – 1.6 =

6.2 – 1.6 = 4.6

+ 0.4 + 4 + 0.2

1.6 2.0 6.0 6.2

0.4 + 4 + 0.2 = 4.6

Subtraction using the column method

561 – 146 =

561 – 146 = 415

561

146

15

4 15

Counting objects in equal groups

Count how many in each group

3 groups /lots of 5

To understand multiplication as repeated addition

5 x 2

2 + 2 + 2 + 2 + 2

5 x 2 = 10

5 lots of 2 =

2 + 2 + 2 + 2 + 2 =

5 x 2 = 10

Multiplication as arrays(arranging the counters in equal

rows – an array)

Repeated addition on a number line

4 x 5

+5 +5 +5 +5

0 5 10 15 20 4 x 5 = 20

4 lots of 5 =

4 lots of 5 or 4 x 5 = 20

5 + 5 + 5 + 5 = 20

To count in 2s, 5s and 10s

2s 5s 10s

To simplify multiplication by partitioning

14 x 3 = (14 = 10 + 4)

10 x 3 = 30

4 x 3 = 12

14 x 3 = 42

(30 + 12 = 42)

To multiply by 10, 100 and 100 using place value (Y3)

  Th H T U

      1 2

    1 2 0

  1 2 0 0

1 2 0 0 0

12 x 10 = 120

12 x 100 = 1200

12 x 1000 = 12000

To multiply using multiples of 10, 100, 1000

3 x 20 = 3 x 2 x 10 = 60

7 x 300 = 7 x 3 x 100 = 2100

To multiply using grid method (Y4)

24 x 6 =

x

6 120

24

420

24 x 6 = 144

120 + 24 = 144

Multiply by expanded multiplication

42 x 8 16 (2 x 8) 320 (40 x 8) 336

42 x 8 =

42 x 8 = 336

Multiplication using column method (Y5)

24 x 37 =

24 x 37 = 888

24 x 37

168

720

888

Sharing items into groups

6 shared between 2 is 3

Division by repeated subtraction

4 x 5

+5 +5 +5 +5

0 5 10 15 20 4 x 5 = 20

20 ÷ 5 =

20 ÷ 5 = 4

-5 -5 -5 -5

Division by chunking (Y4-5)

63 ÷ 5 =

6350 (10 X 5)

13 ( 2 x 5 ) 10 3

63 ÷ 5 = 12 r 3

Division by semi-compact division (Y6)

357 ÷ 6 =

357 ÷ 6 = 59 r 3

6 3 5 7

5

30

57

54

9

3

Division by compact method (Y6)

357 ÷ 6 =

5

6 3 5 759 r 3

357 ÷ 6 = 59 r 3

Questions