Welcome to our Mathematics Evening Please take a seat

First of all – 10 questions whiteboards ready! Don’t worry it isn’t too hard

What is 134 less than 207? What is 207 minus 134? What is 207 subtract 134? What is the difference between 207 and 134? Can you decrease 207 by 134?

From 134 how many more to make 207? What is 207 take away 134? What is the remainder when 134 blocks are removed from a pile containing 207? I had 207 books and lost 134 of them, how many does this leave? I have £207 and spend £134, how much do I have left?

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.

Take an in depth look at subtraction. By… 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. What do we mean by written? Rough translation L1 = Y1 L2 = Y2 L3 = Y4 L4 = Y6 (nationally and we understand that all pupils are different)

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. Questionnaire Past SATs analysis

How do the children’s subtraction skills progress? Look at subtraction through the levels, how we teach it and how can you support it.

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 bears 1 2 3 4 5 Once there were 5 teddy bears

1 fell off the shelf … … then there were 4

5 - 1 4 = 1 2 3 4

10 – 2 = 8

10 – 3 = 7

Finding the difference between 2 numbers

7 6 5 4 3 2 2 1 1 What is the difference between 2 and 7? The difference is 5. The red tower has 5 more blocks 3 2 2 1 1 16

What is the difference between 4 and 10? 2 3 4 5 6 7 8 9 10 1 2 3 4 What is the difference between 4 and 10? The difference is 6 There are 6 more yellow blocks 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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 1

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 13-9= 4 or

Solve a missing number problem +7=15

The children use the numbers they have been given! 8 +7=15 15-7= 8 It is an addition, so start at the end and turn it into a subtraction…

Subtract the nearest multiple of 10 and adjust 52 – 9 =

Subtract the nearest multiple of 10 and adjust 4 5 2 3 But that’s one too many, so now add one back. First subtract ten. Now you’ve subtracted 9 from 52 by subtracting ten then adding 1 back.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Subtraction – Level 2 Using a blank number line to solve calculations and problems. Also known as finding the difference. 74-27= Why count on and upwards? You could break up the +40 jump into jumps of ten until you become confident with the adding a multiple of ten.

Lets find the difference! 53 – 25 = 28 +10 +3 +5 +10 25 30 40 50 53 53 10+10= 20 5 + 3= 8

Try these 76 – 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. When using HTU you may wish to add on hundreds at some point

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. Small multiples of ten upto 70 You need to be able to work out the complements to ten quite quickly (2-3 seconds) or you lose your train of thought.

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. We don’t mind them using it into L345 if they use it correctly Miss out some steps it is quite good Use every step for 321.94 – 112.67 and it has 10 calculations including one where you have to add 9 numbers There are some shortcuts but these are unique to each question so difficult to be taught.

2nd break for Mental Work This Mental and Oral Starter helps develop place value. By Mrs Asvadi Place value is needed for written column subtraction the 2 in 627 is not really a 2 but a 20

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 Need to be able to partition numbers (in their head and on paper) Need to know subtraction facts At this stage subtraction becomes subtraction rather than adding on Problems may have a subtraction and an addition or otherwise for second part

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’ What is partitioning? All three things are key to understanding the method

Try these 765 – 543 402 – 284 3092 - 1534 Use the expanded decomposition method. It does work for decimals as well

SUBTRACTION – Mental Facts are still Crucial Expanded Decomposition Method Must be know the subtraction facts 9-4 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 these 765 – 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 Method Must be know the subtraction facts to twenty 9-4 13-6 17-6 and others Must understand that in the example below they are really subtracting 30 from 70 and not 3 from 7 (even though they really 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. Need to know less facts but understand more.

(From L4 onwards the method must be efficient) Level 4 Expectations 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) Need to have an understanding of decimals place value Efficient (not putting 1034 dots and rubbing out 876 for 1034 – 876)

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. Eg 45.1 – 2.89

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. Although pupils have to have a deep understanding of maths to pick the right method based on the question/number type. We have had some pupils in the past that have done this. One reliable method AND KNOWLEDGE OF KEY NUMBER FACTS SHOULD SEE THEM ABLE TO ANSWER ANY QUESTION

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.