chunking for subtraction -...

chunking for subtraction (2)

When you use chunking for subtraction, be carefulwhen negative numbers are involved.

Use chunking to subtract 35 from 72.

72 – 35

40 –3

37What do you do when there are 3 digits? It’s easy!

206 – 138

100 –30 –2

70 68

Start with the 10s.

70 – 30 is 40.

I have to do 2minus 5. When I do that I am 3

short which is –3.

Finish off bysubtracting3 from 40.

100 – 30is 70.

0 – 30 isshort 30.

Combine 70and –2 forthe answer.

6 – 8 isshort 2.

200 – 100is 100.

Natural Maths Strategies © 2007 Blake Education

open number line for subtraction

You can show 72 – 48 on an opennumber line in three ways.

Start at 48 andwork up to 72.

48 50 70 72

+ 2 + 20 + 2

48 50 70 72

– 2 – 20 – 2

24 30 70 72

– 6 – 40 – 2

The difference is2 + 20 + 2 = 24.

Start at 72 andwork back to 48. The difference is

2 + 20 + 2 = 24.

Start at 72 and work back 48 to the answer.

The answer is 24.


chunking for subtraction (1)

When you break subtraction into chunks, it is easy tosubtract the parts and put them back together.

Use chunking to subtract 24 from 57.

57 – 24

30 3

33What do you do when there are 3 digits? It’s easy!

369 – 237

100 30 2

132

Start with the 10s.50 – 20 is 30.

Next, subtract4 from 7.

Finish off byadding 30

and 3.

Start with the 100s. 300 – 200 is 100.

Then subtractthe 10s and

the 1sseparately.

Finish off byadding 100,30 and 2.


ZigZagfor subtractionYou can show the strategies you used

for a subtraction with a zigzag.

What different ways can you show 75 - 38?

75

35

37

- 40

+ 2

fn

co

75

40

37

- 35

- 3rf

I’ll subtract 35 to get to a

friendly number, then I’ll just have 3 to subtract.

I’ll round 38 up to 40 and then adjust.

I’ll subtract 30, then I’ll split 8 into 5 and 3.

75

45

40

– 30

– 5

fn

btt

37

- 3rffn


rounding

Here are somemore examples.

Adding with friendly numbers is easy.That is why it is a good strategy to round up or down to the nearest 10.

32 3077 80

20 21 22 23 24 25 26 27 28 29 30

50 51 52 53 54 55 56 57 58 59 60

2 is less than5, so rounddown to 30.

Look at the 1s anddecide how to round.

7 is more than 5,so round up to 80.

When the number ends in a 5, round up to the friendly number above.

20 24

50 53

26 30

55 60


EstimatingYou often need to know roughly how much the answer should be.

Estimating is a quick way of finding out.

53 + 26 + 72 + 19 + 22 = ?First, round these

numbers to the nearestfriendly number

53 + 26 + 72 + 19 + 22 = ?

50 + 30 + 70 + 20 + 20 = ?

50 + 100 + 40 = ?The estimate

is 190.The actual answer is 192,so the estimate was close.

Rounding and estimating also work well with money amounts.

Round these to the nearest 50 cents before adding. You’ll never be far out!

$3.65 + $1.25 + $7.40 = ?

rf d


CompensatingWhen you see that a number is

near to a friendly number, you canadd by compensating.

50 + 17 = 67

50 + 17 + 1 = 68

51 + 17 = ?

Now compensate by adding

the missing 1.

51 rounds to 50, a friendly

number, so add 50 instead.

Compensating works really well for subtraction too!

72 - 29 = ?

72 - 30 = 42

72 – 30 + 1 = 43

This time,compensate by adding the extra 1.

29 rounds to 30, a friendly number, so subtract 30

instead.


Secret code

Now you know so many strategies,you can use the secret code toshow how you work things out.

I like to use number splitting

to turn an addition into a rainbow fact.

36 + 77

100 13

113

ndrf

fn

s —count on co —double d —turnaround ta —rainbow fact nd —near double nd —friendly number fn —bridge through 10 —number splitting —compensating

co

d

ta

rf

nd

fn

btt

ns

cmp

I like to round to a friendly number and I always remember

to compensate.


Chunking and multiplication

To multiply 54 by 6, split the 54 into 50 + 4:

You can use chunking for multiplication – just remember to multiply the 10s and the 1s separately.

54 × 650 × 6= 300

4 × 6= 24

+

324

To multiply 36 by 7, split the 36 into 30 + 6:

36 × 7

= 210 = 42+

252

Add the two parts of the

multiplication.

You only need to show the answers for the two parts of the

multiplication.

Then add the parts

for the final answer.


Chunking and division

Sometimes, a division problem can be mademuch easier by chunking (or number splitting).

To divide 36 by 4, first chunk the number 36 into two parts that are familiar:

The number to be divided can be chunked in different ways:

36 ÷ 420 + 16

9

Chunk the 36 into two

parts that you know how to divide by 4.

5 + 4÷÷

Add the results ofthe two divisions

to get your answer.

72 ÷ 660 + 12

How would thisdivision becompleted?


Bridge through 10Sometimes it helps to split a number to turn

an addition into a bridge through 10.

9 + 1 is 10. And 3 more is 13.

80 + 20 is 100.

And 40more is 140.

Split 4 into1 + 3.

Split 60 into20 + 40.

Use ‘bridge through 10’ to add 9 and 4.

9 1310+1 +3

FinishStart

80 140

100+20 +40

Use ‘bridge through 100’ to add 80 and 60.Start Finish

Natural Maths Strategies© 2007 Blake Education

Bridge back through 10Sometimes it helps to split a number to makea subtraction into a bridge back through 10.

Use ‘bridge back through 10’ tosubtract 4 from 13.

Use ‘bridge back through 100’ tosubtract 60 from 140.

13 – 3 is 10.10 – 1 is 9.

9 1310-1 -3

14080

100-20 -40

100 - 20 is 80.

140 - 40is 100.

Split 4 into3 and 1.

Split 60 into40 and 20.

Finish Start

Finish Start


To add 30 and 70, think of rainbow facts.

30 + 70

0 10 20 30 40 50 60 70 80 90 100

100

100

100

100

100

If you know yourrainbow facts to 10,you can use themwith the friendly

numbers.

Rainbow facts100100

Rainbow factsRainbow factsRainbow factsRainbow facts

To add a list of numbers, start by looking for rainbow pairs.

2 8 + 6 5 + 8 3 + 4 7


landmark numbers

Use landmark numbers to add 26 and 76.

Landmark numbers can be used with larger numbers too . . .

Landmark numbers make adding much easier. All you need to know is that:

25 + 25 = 5025 + 50 = 75

25 + 75 = 10050 + 50 = 100

25 + 25 + 25 + 25 = 100

The two nearest

landmark numbers are 25 and 75.

We know that 25 + 75 is 100.So 26 +

76 is 102.

25 75

2575

50100

250 750

5001000


Number splittingSplitting a number into two parts can make addition much easier!

To add 26 + 37, you could split 37 into 2 parts to find the partner that makes 26 into a friendly number.

Remember: Split one number to make the other number into a friendly number.

26 + 37 = ?

26 + 4 + 33 = ?

30 + 33 = 63

Or you could find the partner thatmakes 37 into a friendly number.

26 + 37 = ?

23 + 3 + 37 = ?

23 + 40 = 63

3 + 7is a

rainbow fact.

Split the 6into 3 and 3.

6 + 4is a

rainbow fact.

Split the 7into 4 and 3.

rf

rf

ns

ns


chunking for addition

When you break an addition into chunks, it is easyto add the parts and then put them back together again.

Use chunking for addition to add 46 and 35.

46 + 35

70 11

81There are other ways of chunking 46 + 35.

46 + 35

76

81This one has one less step – it saves brain space!

Start with the 10s.40 + 30 is 70. Next, add

5 and 6.

Finish off by adding

70 and 11.

It’s easy to add46 to the friendly

number, 30.46 + 30 is 76.

Split 35 into30 + 5.

76 + 5is 81.


open number line for addition

You can show 36 + 43 on an opennumber line as two jumps.

The open number line is also a great way to show different addition strategies.What strategies were used for these

different ways of finding 27 + 53 + 29?

Start thenumber line

at 36.

Then split 43 into 40 + 3

and add the40 first.

I could userainbow facts . . .

. . . and friendly numbers, or I could change the order.

36 76 79

+ 40 + 3

53 60 80 100 109

+ 7 + 20 + 20 + 9

40 90 100 109

+ 50 + 7 + 3 + 9


I’ll do a turnaroundand then add on a

friendly number. ThenI’ll use a rainbow fact.

I’ll add on a friendly

number first. 36

86

94

+ 50

+ 8

fn

nd

30

80

94

+ 50

+ 14

fn

fn

58

88

90

+ 30

+ 2

fn

rf

94

I know that 6 + 8 = 14 so I can add that onto a friendly

number.

+ 4fn

ZigZagfor addition

You can show the strategies you used for an addition with a zigzag.

What different ways can you show 36 + 58?


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