Welcome to our Mathematics Evening

Please take a seat

First of all – 10 questions

whiteboards ready!

What is 207 minus 134?

What is 207 subtract 134?

Can you decrease 207 by 134?

What is 134 less than 207?

What is the difference between 207 and 134?

What is the remainder when 134 blocks are removed from a pile containing 207?

I have £207 and spend £134, how much do I have left?

I had 207 books and lost 134 of them, how many does this leave?

What is 207 take away 134?

From 134 how many more to make 207?

Subtraction Vocabulary

• You have just seen 10 different ways of asking the question 207-134

• There are other pieces of subtraction vocabulary as well

• The answer was 73

• You don’t always see the word subtraction when you have to subtract.

This evening we aim to…

Take an in depth look at subtraction. By…

• Showing you how the children need to develop their subtraction skills through the year groups and levels.

• Looking at the non-mental methods we teach and the order in which we teach them.

• Showing you which mental maths facts are crucial to each stage.

Why are we doing this?

• From your feedback after last year’s calculation night, more parents commented that they felt less comfortable practising subtraction with their children than addition.

• Also pupils (not just our pupils, pupils nationally) find subtraction harder than addition for any two given numbers.

How do the children’s

subtraction skills progress?

Level 1• Understand subtraction as take away.• Use practical and informal methods to subtract a

one digit number from a one digit or two digit number

8-5= 7-3= 15-6 = 23 – 8 =• Subtract a multiple of 10 from any 2 digit number 43-10= 67-10= 56-10=• Find the difference by counting up• Begin to recognise the inverse 10-4 =6 6+4 = 10• Solve simple one-step problems • Record calculations using number sentences that

include the appropriate symbols

The story of 5 teddy The story of 5 teddy bearsbears

Once there were 5 teddy bearsOnce there were 5 teddy bears

1 2 3 4 5

1 fell off the shelf …1 fell off the shelf …

… … then there were 4 then there were 4

55 -- 11 ==441 2 3 4

10 – 2 =

8

10 – 3 =

7

Finding the difference between

2 numbers

1

2

7

6

5

4

3

1

2

The difference is 5.

The red tower has 5 more blocks

What is the difference between2 and 7?

1 2 63 4 5 10987

1 2 3 4

What is the difference between4 and 10?

The difference is 6

There are 6 more yellow blocks

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 10

0

Level 1• Count backwards from any number to 20• Say the number that is one less than any number to 20• Count back in 10s• Know by heart subtraction facts for numbers up to 5• Recognise that subtraction has to be done in a particular order• Calculate by taking away objects or by counting back on number

line• Find the difference by counting on• Write number sentences using symbols• Use objects, pictures and number sentences to answer a problem• Answer subtraction calculations using known facts• Understand and use words that link to subtraction

Break for Mental Work

• You are about to participate in a Year 1 Mental and Oral Starter (this usually lasts for around ten minutes at the beginning of every maths lesson, throughout school) which will help you with the skills needed for subtraction later!

• You will need your number fans

• By Miss Chapman

Year 2

• Subtract mentally a one digit number or a multiple of 10 from any two digit number

• Use practical and informal written methods to subtract two digit numbers

• Derive and recall all addition and subtraction facts for each number to 10

• Recognise subtraction as the inverse of addition

Level 2• Count back in equal steps of 2, 5 and 10• Partition numbers to 100 beyond • Derive and recall all addition and subtraction facts for each number to at

least 10, all pairs with totals to 20 and all pairs of multiples of 10 with totals up to 100

• Subtract by partitioning 56-6• Subtract 10 from a two digit number• Subtract a multiple of 10 from a two digit number• Subtract by counting back or finding the difference by counting on• Subtract the nearest multiple of 10 and adjust• Partition the number to be subtracted 43-23• Choose how to solve a problem and explain the method• Record working out for subtraction problem• Understand the relationship between subtraction and addition. Say the

subtraction that matches an addition sentence visa versa• Explain how they know to use subtraction to solve a problem

Inverse

• Addition is the inverse of subtraction.• Answers can be checked by using the

inverse operation.• We can solve ‘missing number’

problems by using the inverse method.

25 – 19 = 6 19+6 =25 6+19 = 25

Can you turn these addition number sentences into

subtractions?•6+2=8•9+7=16•23+41=64•39+22=61

•8 – 2 = 6•16-7 = 9•64- 23 = 41•61-39=22

Can you make a different subtraction?

This method can be used to check answers.

9+4=

13

Check an answer by turning it into a subtraction

13-4=

9 or 13-9=4

Solve a missing number problem

+7=15

The children use the numbers they have been given!

+7=15

It is an addition, so start at the end and turn it into a subtraction…

15-7= 8

8

Subtract the nearest multiple of 10 and adjust

52 – 9 =

5342First subtract ten.

But that’s one too many, so now add one back.

Now you’ve subtracted 9 from 52 by subtracting ten then adding 1 back.

Subtract the nearest multiple of 10 and adjust

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0

Subtraction – Level 2Using a blank number line to solve

calculations and problems. Also known as finding the difference.

74-27=

53 – 25 =

Lets find the difference!

+5 +10 +10

10+10= 20

28

25 30 40 5350

+3

5 + 3= 8

53

Try these76 – 43

102 – 84

302 - 153

Use number line method.

Start at the lowest number.

Add on to the next multiple of ten.

Then add to the ten below the final number.

Then add on to the final number.

Remember to COUNT ON NOT BACK

Try it with decimals, it can become complicated.

SUBTRACTION – Mental Facts are Crucial

Number line method- Must know (not be able to work out but know) your

number bonds to ten

4+6=? as well as 7+?=10 and 1+?=10

Because you always add upto the next multiple of ten

- You also need to know which multiple of ten comes next.

e.g. 60 is the next multiple of ten after 54

- You need to be able to add ten and small multiples of ten.

Number Line Method

• Some pupils continue to use it into L3, 4, 5

• Can become very complicated depending how efficiently it is used (especially with decimals)

• We don’t discourage pupils from using it if they are using it properly.

2nd break for Mental Work

• This Mental and Oral Starter helps develop place value.

• By Mrs Asvadi

Level 3 Expectations

• Subtract a two digit number from another (mentally)

• Subtract a three digit number from another (written)

• Subtract an amount of money from another (written)

• To solve 1 or 2 step problems where these calculations are needed

Level 3

• Understand the value of each digit in a 3 digit number• Partition to 100 beyond simple tens and ones

e.g. 54 = 40+14 or 30+24• Know by heart subtraction facts for numbers up to 20• Subtract 2 digit numbers using an efficient method• Record the steps of subtraction method• Check answer using inverse• Use subtraction to solve problems

Expanded decomposition

As the children progress through level 3 AND have a thorough understanding of place value and partitioning, we start to teach them the more ‘standard methods’

Try these765 – 543

402 – 284

3092 - 1534

Use the expanded decomposition method.

SUBTRACTION – Mental Facts are still Crucial

Expanded Decomposition MethodMust be know the subtraction facts9-4 13-6 17-6 and others

Must be able to subtract a tens number from another (upto 200)

80-30 120-40 170-90 and others

Must be able to subtract a hundreds number from another

400-200 800-200 300-200 and others

Subtraction – compact decomposition

Efficient for all subtractions. Can get ‘messy’ if performing a calculation like 2004 - 997

Try these765 – 543

402 – 284

3092 - 1534

14.16 – 12.95 Use the compact decomposition method.

62.2 – 35.95

SUBTRACTION – Mental Facts are Crucial

Compact Decomposition MethodMust be know the subtraction facts to twenty9-4 13-6 17-6 and others

Must understand that in the example below they are really subtracting 30 from 70and not 3 from 7 (even though theyreally are subtracting 3 from 7!)

Subtraction – compact decomposition

PROs and CONs

•You never have to do a subtraction that is harder than 18-9

•You must understand your ‘place value’ for the method to have any relevance to you or real life

•You must know your number facts upto 20 – 10

(any number to twenty subtract any number

upto ten)

•Can become ‘messy’ when you have a

thousands number on the top.

• To subtract thousands numbers

• To subtract decimals to 2 decimal places

• To use subtraction as a part of wider problem solving

• To solve 1 or 2 step problems where these calculations are needed

(From L4 onwards the method must be efficient)

Level 4 Expectations

Level 5 Expectations

• To subtract one decimal from another, where the decimals do not have the same number of digits

12.1 – 8.45 31.98 – 2.345 19 – 4.8

• To solve two or more step problems with these calculations.

Which method is best?

Which method is best?

• Actually it depends on the question asked!

• Knowledge of number facts (addition and subtraction) underpins all calculations, no matter how large or involved (i.e. decimals) the numbers are.

Thank you for taking part

• We hope it has been useful

• This PowerPoint will be placed on the school website.

• Please feel free to ask any questions, to members of staff, about the calculation strategies used.