MENTAL COMPUTATION STRATEGIES - St Hilda's School€¦ · d Z i µ u P Ç ] o } µ ( µ o Á Z v ] v P ] u o X > } } l Z } Á Á } Z ] Á ] Z ï ô X ò = î X ò W 1 First we jump

St Hilda’s Junior School

Years 3 - 6

MENTAL COMPUTATION STRATEGIES

(taken from Mathletics Workbooks D – G)

MENTAL STRATEGIES FOR ADDITION

SERIES TOPIC

D 16Copyright © 3P Learning

Addition and Subtraction

a

b

c

Addition mental strategies – bridge to ten

2

3

a =

b =

c =

a =

b =

c =

10 4 14

SERIES TOPIC



Addition mental strategies – jump strategy

a

b

1

a

b

c

2

SERIES TOPIC

G 12Copyright © 3P Learning


Use the jump strategy to add the decimals:

a 35.4 + 3.1

............. + ............. = .............

b

............. + ............. = .............

c 17.6 + 1.9

............. + ............. = .............

Mental strategies – jump strategy with decimals

1

2 Use the jump strategy to answer the following:

a

b

1 First we jump up by the whole numbers.2 Then we jump up by the tenths.

38.6 + 2.6 = 41.2

+1 +1 +0.6

38.6 39.6 40.6 41.2

SERIES TOPIC



Addition mental strategies – doubles and near doubles

5

a

c

e

b

d

5

6

a

c

e

b

d

7

a 24 b 30 c 32

8

a

c

b

d

DOUBLES AND NEAR DOUBLES

BRIDGING TO TEN

JUMP

SERIES TOPIC



1

a

= units

=

b

= units

=

c

= units

=

d

= units

=

Addition mental strategies – split strategy version 2

265 85 36 23 41

12

34

SERIES TOPIC

F 14Copyright © 3P Learning


Addition mental strategies – split strategy

4

5

Truss

Villa

Kia

385

75

*not to scale

SERIES TOPIC

5G 1Copyright © 3P Learning


1 We split the numbers into whole numbers and decimals.23 We add the 2 answers.

= 24 + 1 = 25

Find the perimeter of each shape. Shapes are not drawn to scale. Use the split strategy to help you:

a whole number. In each grid below, look for 4 pairs that add to give a whole number and colour in

+

+

1

2

3

a b c1.6 1.1 2.3 1.5

1.2 1.4 1.5 2.7

1.7 2.5 2.9 3.3

2.1 3.2 3.5

1.7 1.5 3.1

1.3 1.2 3.2 3.6

6.3 6.4 5.1 5.5

6.2 6.6 5.6 2.5

1.4 0.3 0.7 0.9

2.4 2.6 1.2 3.2

1.5 1.7 3.5 1.5

1.6 1.2 1.1

Solve these problems using the split strategy. Make notes as you go:

Mental strategies – split strategy with decimals

a 32.3 + 2.3 = b c 46.2 + 7.1 =

4.2 cm

2.8 cm

3.3 cm

1.5 cm

1.9 cm

0.7 cm4.2 cm

2.8 cm

3.3 cm

1.5 cm

1.9 cm

0.7 cm

4.2 cm

2.8 cm

3.3 cm

1.5 cm

1.9 cm

0.7 cm

a b c

P: P: P:

SERIES TOPIC

9D 1Copyright © 3P Learning


Addition mental strategies – split strategy version 1

1

2

3

a 20

2b c d

a

b

c

d

21

48

SPLIT

SERIES TOPIC

5F 1Copyright © 3P Learning


a ____________ b ___________ c 232 ____________ d ____________

e ____________ f ___________ g ____________ h ____________

Addition mental strategies – compensation strategy

I rounded up by 1

so I subtract 1.

1

3

2

a b

_____

c d

_____

a b

_____

c d

_____

SERIES TOPIC



a 725 – 39 = b 373 – 49 =

725 – 40

373 – 50

_______ = _____________ _______ = _____________

c d 455 – 43 =

455 – 40

_______ = _____________ _______ = _____________

a b

424 + 70

234 + 20

_______ = _____________ _______ = _____________

c 564 + 132 = d 214 + 141 =

564 + 130

214 + 140

_______ = _____________ _______ = _____________

Mental strategies – compensation strategy review

1

2

303 325 + 41 = 366

We rounded up by 2, We rounded down by 1, which means we added 2 which means we subtracted305 – 2 = 303 too many so we subtract 2. 365 + 1 = 366 1 too few, so we add 1 back.

270 – 59 = 211 350 + 73 = 423

We rounded up by 1 which We rounded down by 3 means we subtracted 1 extra, which means we need210 + 1 = 211 so we need to pay it back. 420 + 3 = 423 to add 3 more.

235 + 70 – 2 325 + 40 + 1

270 – 60 + 1 350 + 70 + 3

SERIES TOPIC

13E 1Copyright © 3P Learning



3

4

a A

c C

b R

d E

Round these numbers down to the closest ten. Compensate by adding.

a

_______

c

________

b

_______

d

________

When we round down we compensate by adding.

When we round up we compensate

SERIES TOPIC

E 112Copyright © 3P Learning



1

2

I rounded up by 1,

so I subtract 1.

a

d

b 39

e

c

199

a

_________

c

_________

b

_________

d

_________

COMPENSATION

SERIES TOPIC



Mental strategies – compensation strategy with decimals

1 Round the number closest to a whole number.2

31.4 + 6 I rounded up by 0.2, I rounded down by 0.3, = 37.4 – 0.2 which means I = 59.4 + 0.3 which means I did not = 37.2 added extra so I = 59.7 add enough so I need need to subtract 0.2 to add 0.3

1

a b 6.4 + 3.1 =

9.5 + 3

6.4 + 3

_______ = _____________ _______ = _____________

c d 2.4 + 0.9 =

2.4 + 1

_______ = _____________ _______ = _____________

1 Round the number closest to the whole number.2 52.5 – 3.9 52.5 – 4 We rounded up by 0.1, We rounded down by 0.3,

which means we = 57.4 – 0.3 which means we did notsubtracted extra so = 57.1 subtract enough so

we need to add 0.1 we need subtract 0.3

2

a b 7.2 – 2.9 =

5.3 – 4

7.2 – 3

_______ = _____________ _______ = _____________

c d

32.5 – 10

_______ = _____________ _______ = _____________

SERIES TOPIC



Read the top of this page again to remember how best to think of the bump strategy. Pretend the

Can you see why?

1of ten. This makes the problem easier to do in our heads.

2 Adjust the other number so the

stays the same. This keeps the problem the same.

3 Solve this easier problem. This then gives us the answer to our original problem.

Mental strategies – bump strategy

+1 –190 + 23 = 113

1

a b c d e f

2

3

a 79 + 15

+1 –1

f 226 + 52

+4 –4

b

+2 –2

g 142 + 13

–2 +2

c 32 + 56

h

d

i 421 + 65

e 61 + 24

j 275 + 32

25 4349 51+ +

She is too bossy.

The bump strategy is when the number closest to ten

process. The other number must adjust to compensate.

Hurry, give me 1 so I can

BUMP

MENTAL STRATEGIES FOR SUBTRACTION

USING RELATED FACTS

BRIDGING TO TEN

COUNTING ON

SERIES TOPIC



Solve these using the jump strategy:

a

b

c

d

Subtraction mental strategies – jump strategy

1

2

1

99

JUMP

SPLIT

SERIES TOPIC



Use the split strategy with these problems:

a

b

Subtraction mental strategies – split strategy

1

2

3

a b c d

a

b

SERIES TOPIC



Work out what the missing number is on each set of balanced scales. Use the jump strategy.

Use the jump strategy to subtract these decimals. Break up the second number in your head:

a 36 – 3.3

............. – ............. = .............

b 51 – 2.9

............. – ............. = .............

c

............. – ............. = .............

We can also subtract decimals using the jump strategy.Look at how we do this with 52 – 2.61 First we jump back by the whole numbers.2 Then we jump back by the tenths.

36

51

68

3

4 the missing numbers. 36 – 8.3 = ?

36 8.3 59 11.8

Mental strategies – jump strategy with decimals

– 0.6 – 1 – 1

5249.4 50

Remember that 2.6 is made up of 2 and 0.6 You need to subtract both parts.

SERIES TOPIC



Use the split strategy to solve these money problems:

a

b

c

5

Baseball $42.15

1 We split the numbers into whole numbers and decimals.23 We add the 2 answers.

31 . 4 – 2 . 3 = (31 – 2) + (0.4 – 0.3) = 29 + 0.1 = 29.1

4 Solve these problems using the split strategy. Make notes as you go:

a b c 33.2 + 13.1 =

Mental strategies – split strategy with decimals

–

–

SERIES TOPIC



Set 1 Set 2

a

b

c

d

the sets.

Subtraction mental strategies – subtraction strategy review

1

2

31 33 34 39

1 3 4 9

11 13 14 19

31 33 34 39

41 43 44 49

91 93 94 99

– 9

– 9

– 9

– 9

– 9

– 9

–

31 –

41 –

–

–

–

REVIEW

SERIES TOPIC



Subtraction mental strategies – compensation strategy

1

2

1 extra so

add 1 back.

I rounded up by 1, which means I subtracted 1 extra so we need to add 1 back.

a

d

g

b

e

h

c

i

80– 2

a

________

c

__________

b

________

d

__________

COMPENSATION

SERIES TOPIC



Mental strategies – compensation strategy with decimals

1 Round the number closest to a whole number.2

31.4 + 6 I rounded up by 0.2, I rounded down by 0.3, = 37.4 – 0.2 which means I = 59.4 + 0.3 which means I did not = 37.2 added extra so I = 59.7 add enough so I need need to subtract 0.2 to add 0.3

1

a b 6.4 + 3.1 =

9.5 + 3

6.4 + 3

_______ = _____________ _______ = _____________

c d 2.4 + 0.9 =

2.4 + 1

_______ = _____________ _______ = _____________

1 Round the number closest to the whole number.2 52.5 – 3.9 52.5 – 4 We rounded up by 0.1, We rounded down by 0.3,

which means we = 57.4 – 0.3 which means we did notsubtracted extra so = 57.1 subtract enough so

we need to add 0.1 we need subtract 0.3

2

a b 7.2 – 2.9 =

5.3 – 4

7.2 – 3

_______ = _____________ _______ = _____________

c d

32.5 – 10

_______ = _____________ _______ = _____________

SERIES TOPIC



1the secondten. This makes the problem easier to do in our heads.

2 Do the same to the other number

2 numbers stays the same. 3 Solve this easier problem. This

then gives us the answer to our original problem.

65 – 22

–2 –263 – 20 = 43

a

b

c

d

e

f

g

h

i

j

4

5 Solve these problems using the bump strategy. Show your working out:

a

c Janae collected toy pigs and by the end of

b Megan saved $194 in 1 year. Her sister Jeda

d

Mental strategies – bump strategy

The bump strategy is when the number closest to ten

to start the

process. The other number must adjust to compensate.

BUMP

MENTAL STRATEGIES FOR MULTIPLICATION

SERIES TOPIC


Multiplication and Division

Mental multiplication strategies – doubling strategy

1

3

2

a = 30 × 2 + 6 × 2 = 60 + 12 = 72

b

c d

Complete these

4

11

15

Double

21

25

3241

12

50

Double

DOUBLES

SERIES TOPIC



a

10 × =

2 × =

+ =

b

10 × =

2 × =

+ =

1

Mental multiplication strategies – split strategy

10 × 5 = 50 2 × 5 = 10

50 + 10 = 60

SPLIT

SERIES TOPIC



Mental multiplication strategies – doubling strategy

1

In this last table choose a 2-digit

by 8 and double it

a 12 × 4 =

24

48

b 15 × 4 =

c 18 × 4 = d 22 × 4 =

e 16 × 8 = f 35 × 8 =

g × 8 =

once

twice

10 × 4 = 40

20

40

11 × 8 = 88

22

44

88

48

SERIES TOPIC



Use the split strategy to answer these:

Mental multiplication strategies – split strategy

26 × 4 20 × 4 + 6 × 4

80 + 24 = 104

1

a 34 × 3 30 × 3 + 4 × 3

90 + =

b 45 × 5 × + ×

+ =

c 52 × 4 × + ×

+ =

SERIES TOPIC



Mental multiplication strategies – compensation strategy

3 × 10 = 30 3

3 × 20 = 60 3

1

2

a

5 × 30 = – 5

b

3 × 20 = – 3

c

2 × 40 = – 2

a 3 × 2 =

3 × 20 =

c

b 5 × 3 =

5 × 30 =

d 4 × 4 =

4 × 40 =

COMPENSATION

SERIES TOPIC

7F 1Multiplication and DivisionCopyright © 3P Learning

Mental multiplication strategies – compensation strategy

a

b

c

d

e ________ × ________ – ________ =

1

2

a

b

c

d

e 7 × 62 =

20 3 3 57

40 3 3 123

6 × 62 = 372

strategy with numbers such as

SERIES TOPIC



a 18 × 3

× =

b 14 × 4

× =

Mental multiplication strategies – doubling and halving

16 × 3

8 × 6 = 48

1

DOUBLING AND HALVING

SERIES TOPIC

3F 1Multiplication and DivisionCopyright © 3P Learning

a

c

b

d

Ten Thousands Thousands Tens Units4

44

4

Mental multiplication strategies – multiply by 10s, 100s and 1 000s

a

d

g

b

e

h

c

f

i

1

2

3

T Th Th T U1 7

T Th Th T U4 3

T Th Th T U T Th Th T U

MULTIPLYING BY 10, 100, 1000

MENTAL STRATEGIES FOR DIVISION

SERIES TOPIC



1

a

b

c

Division – sharing and groupingFAIR SHARES/EQUAL GROUPS

SERIES TOPIC

27D 4Copyright © 3P Learning


a

c

groups are there if there

b

d

2

3

Division – sharing and grouping

LINKING WITH MULTIPLICATION

SERIES TOPIC



a × =

÷ =

b × =

÷ =

c × =

÷ =

2

6 × 4 = 24

24 ÷ 4 = 6

Division – linking multiplication and division facts

a × 4 = 12

12 ÷ 4 =

c × 4 = 16

16 ÷ 4 =

b × 5 = 30

30 ÷ 5 =

1

SERIES TOPIC

11FMultiplication and DivisionCopyright © 3P Learning

2

a b c

Mental division strategies – use multiplication facts

a _______

b _______ × 11 = 121

c _______

d _______

e _______

f _______

g _______

1

a

c

e

g

i

b

d

f

h

j

2

3

7263

36

36 16

4432

24

36 24

42

6

8

Doing maths without knowing

facts is hard.

makes your life much easier. It’s worth persevering

SERIES TOPIC



Mental division strategies – halving strategy

1

2

a

c

b

d

IN

80

140

20

IN

8

12

4

4

6

2

IN

42

90

60

IN

100

36

60

IN

24

36

IN

18

50

100

HALVING

SERIES TOPIC



Complete the


3

4

16

8

8

4

4

4

4

a b

14

30

569082

2042÷ 2

36

12

6020084

884452

÷ 4

a 80 ÷ 4 =

c 64 ÷ 4 =

e 244 ÷ 4 =

b 48 ÷ 4 =

d 120 ÷ 4 =

f 88 ÷ 4 =

SPLIT

SERIES TOPIC



Mental division strategies – split strategy

1

2

3

125 ÷ 5

100 25 ÷ 5 ÷ 5 20 + 5 = 25

a 115 ÷ 5

÷ 5 ÷ 5

+ =

b 135 ÷ 5

÷ 5 ÷ 5

+ =

a 64 ÷ 4

÷ 4 ÷ 4

+ =

b 116 ÷ 4

÷ 4 ÷ 4

+ =

a 330 ÷ 3

÷ 3 ÷ 3

+ =

b 612 ÷ 3

÷ 3 ÷ 3

+ =

SERIES TOPIC

F12 Multiplication and DivisionCopyright © 3P Learning

2

Mental division strategies – use multiplication facts

a

b

c

4

5

6

a 6 × 7 = 42

d

b

e

c

f 11 × 21 = 231

SERIES TOPIC

G12Copyright © 3P Learning

Multiplication and Division2

Mental division strategies – dividing by multiples of ten

80 ÷ 10 = 8

80 ÷ 100 = 0.8

80 ÷ 1 000 = 0.08

480 ÷ 40

480 ÷ 10 ÷ 4 OR 480 ÷ 4 ÷ 10

a =

b =

c =

d = =

e = =

1

2

3

a

d

g

b

e

h

c

i

a

d

b

e

c

ten. Look at 225 ÷ 5.

SERIES TOPIC

13FMultiplication and DivisionCopyright © 3P Learning

2

Ten Thousands Thousands Tens Units4

44

4

Mental division strategies – divide by 10s, 100s and 1 000s

a

b

c

d

e

f

1

2

a

c

b

d

T Th Th T U4

T Th Th T U4 3

T Th Th T U T Th Th T U

32

DIVIDING BY 10, 100, 1000

SERIES TOPIC

F14 Multiplication and DivisionCopyright © 3P Learning

2

halve halvehalve


1

2

a

b

c

d

e

3for you.

a =

b 24 =

c =

d =

e 72 =

f 32 =

a 32 16

36

b 24

72

144

c

856 7

5

SERIES TOPIC

G10Copyright © 3P Learning

Multiplication and Division2

a

c

b

d

These problems have been worked out already but there are 2 wrong answers. Tick the ones that have

216 ÷ 18 = 12

Mental division strategies – using factors

5

4

Check each line

make notes as you go.

a

=

=

=

c

=

=

=

b

=

=

=

d

=

=

=

USING FACTORS

TESTS OF DIVISIBILITY

SERIES TOPIC

11GCopyright © 3P Learning

Multiplication and Division 2

a

d

b

e

c

Test these rules. Circle the numbers that match the stated rule.

2

4

5

10

100

8

3

9

Mental division strategies – rules of divisibility

Divisible by 2432

Divisible by 5 Divisible by 43 432

Divisible by 10 Divisible by 3 Divisible by 1004

1

2

a

c

e

g

b

d

h

Documents

MENTAL COMPUTATION STRATEGIES - St Hilda's School€¦ · d Z i µ u P Ç ] o } µ ( µ o Á Z v ] v P ] u o X > } } l Z } Á Á } Z ] Á ] Z ï ô X ò = î X ò W 1 First we jump