Clifton Upon Dunsmore Fluency Policy

Clifton upon Dunsmore C of E Primary School Fluency Skills Policy for Mathematics Mastery 2019 “The answer is only the beginning.”

Fluency and automatic recall of number facts can be ‘scary’ and intimidating for some children. This fear can become difficult to

Fluency and automatic recall of number facts can be ‘scary’ and intimidating for some children. This fear can become difficult to overcome if children begin to feel ‘not good’ or scared about automaticity of number facts. To ensure children are able to learn it is important that we develop a risk-free environment where learning is valued over performance Where the environment praises speed and ‘first to get the answer right’, it emphasises a competitive view of mathematics. Unfortunately, this has the effect of ‘hiding’ how fluency is developing in other pupils and implies that mental calculation is a performance. This can adversely affect pupils’ desire to engage. Instead, we promote a range of approaches that are more effective in engaging pupils to discuss and reason about their strategies. A risk-free classroom has an ethos that is underpinned by the following attributes: 1. Everyone has something to contribute and we all value those contributions 2. An appreciation that we each see things differently – there may be one answer, but there are a myriad of available journeys 3. This is not about guessing what is in the teacher’s head 4. There is an expectation that we have to try to communicate our ideas so that everyone else can understand them and that we are expected to try and understand the thinking of others 5. There is an expectation that we have to listen to what others say and then try to build on it - agreeing and disagreeing by offering proof. All of the following approaches can be utilised in shared, whole-class learning discussions. It is not an exhaustive list but provides a flavour of available possibilities.

To understand the numbers they are working securely with and develop number concepts alongside the procedures, the CPA approach allows pupils to demonstrate and explore learning across a range of representations. For example, when very young pupils learn about ‘3 + 2’ they need to learn that the symbols stand for the operation of addition i.e. adding 2 to 3. They also need to understand the concept of a sum. In the CPA approach, pupils would explore the calculation using concrete apparatus to identify the ‘2’, the ‘3’ and the sum 5 as well as pictorial representations of the same calculation and the abstract notation (including language) to better understand both the procedure of adding 2 to 3 and the idea of sum. Without exploration through a range of representations, we cannot expect pupils to develop a full understanding of the underpinning concepts, facts and skills that are integral to developing good mental fluency. Schools should decide on core representations. They also need to ensure that variations of these are also included so that once pupils are able to they can be supported to assimilate learning to new representations.

Practice is a key approach to developing the automaticity needed to reduce cognitive load. Pupils who have facts and skills at their fingertips are more likely to attend to the particulars of new learning than those that do not. These pupils have to work harder and are over-burdened. At Herts for Learning, we think of practice not as meaningless repetition of facts in which pupils chant without thought or as a series of isolated facts learnt at home then tested in school, but as a chance to rehearse them within exercises that develop better thinking. Practice is an opportunity to keep facts and skills ‘simmering’ and a further chance to vary the ways that they are presented. Schools should be mindful of the quality of practice rather than the quantity. Similarly, they are advised to focus upon the facts and skills that will make the greatest difference to mental fluency at each phase.

Practice is a key approach to developing the automaticity needed to reduce cognitive load. Pupils who have facts and skills at the

Secure mental fluency is dependent upon a range of underpinning core concepts that develop over the primary phase.

Reception One more, one less up to 10 Year 3 Year 4 Year 5/6 Year 1 Year 2 Number facts within 10 Number facts within 20 All addition root facts to All addition root facts to All addition root facts 20 20 to 20 Key Skills All addition root facts, Adding 1 (e.g. 7 + 1 and 1 including bridging 10 Doubles of numbers to 10 Doubles of numbers to 10 Doubles of numbers to + 7) (e.g. 7 + 7) (e.g. 7 + 7). Apply to any 10 (e.g. 7 + 7). Apply to Key Skills 2 digit number ( e.g. 37 + 3, 4 and 5 digit number Doubles and near double Doubles of numbers to 10 Near doubles (e.g. 5 + 6 37) ( e.g. 437 + 437) of numbers to 5 (e.g. 3 (e.g. 7 + 7) and 6 + 5) + 3, 4 + 5, 5 + 4) Near doubles (e.g. 5 + 6 Near doubles (e.g. 5 + Near doubles (e.g. 5 + 6 Bridging (e.g. 8 + 4 and 4 and 6 + 5) Apply to 2 6 and 6 + 5) Apply to Adding 2 (e.g. 4 + 2 and and 6 + 5) + 8) digit numbers – e.g. 14 larger numbers – e.g. 2 + 4) +15; 35 + 36 etc) 149 +150; 235 + 236 Bridging (e.g. 8 + 4 and 4 + Compensating Adding 9 etc) Number bonds to 10 8) and 19 by adding 10 or 20 Bridging (e.g. 8 + 4 and 4 (e.g. 8 + 2 and 2 + 8) and adjusting. (e.g.34 + + 8) Apply to 2 digit Bridging (e.g. 8 + 4 and Compensating adding 9 by 19 = 34 + 20 -1) numbers, e.g. 78 + 6 = 78 4 + 8) Apply to 2 digit Adding 0 to a number adding 10 and adjusting. 10 more, 10 less + 2 + 4) numbers, e.g. 78 + 6 = (e.g. 3 + 0 and 0 + 3) (e.g. 4 + 9 = 4 + 10 -1) 78 + 2 + 4) Explicit use of number Compensating Adding 9, Adding 10 to a number facts to add 1, 10, 100 to 19, 29… to 99 by adding Compensating Adding (e.g. 5 + 10 and 10 + 5) numbers up to 30. 10, 20, 30 …100 and 9, 19, 29… to 99 by adjusting. (e.g.34 + 99 = adding 10, 20, 30 …100 The ones without a 34 + 100 -1)Adding 11, 21, and adjusting. (e.g.34 + family 5 + 3, 3 + 5, 6 + 31 etc. 99 = 34 + 100 -1) 3, 3 + 6 (these pairs of facts are the only ones Chn to share fluency Chn to share fluency which don’t fit in any of strategies to add 2 digit strategies to add up to the other families, nos. 3 digit nos. though the last two can be related to counting in 3s)

Addition root facts Children need to be taught strategies to solve these facts. Most children don’t magically become fluent in these facts even in KS2, particularly for those facts which bridge 10. If they aren’t explicitly taught to solve e.g. 6 + 7 by thinking ‘double 6 and one more’ or to solve 12 – 8 by using 'find the difference' strategies, then many children will get stuck on inefficient counting based approaches. 0+0=0 0+1=1 0+2=2 0+3=3 0+4=4 0+5=5 0+6=6 0+7=7 0+8=8 0+9=9 0+10=10 1+0=1 1+1=2 1+2=3 1+3=4 1+4=5 1+5=6 1+6=7 1+7=8 1+8=9 1+9=10 1+10=11 2+0=2 2+1=3 2+2=4 2+3=5 2+4=6 2+5=7 2+6=8 2+7=9 2+8=10 2+9=11 2+10=12 3+0=3 3+1=4 3+2=5 3+3=6 3+4=7 3+5=8 3+6=9 3+7=10 3+8=11 3+9=12 3+10=13 4+0=4 4+1=5 4+2=6 4+3=7 4+4=8 4+5=9 4+6=10 4+7=11 4+8=12 4+9=13 4+10=14 5+0=5 5+1=6 5+2=7 5+3=8 5+4=9 5+5=10 5+6=11 5+7=12 5+8=13 5+9=14 5+10=15 6+0=6 6+1=7 6+2=8 6+3=9 6+4=10 6+5=11 6+6=12 6+7=13 6+8=14 6+9=15 6+10=16 7+0=7 7+1=8 7+2=9 7+3=10 7+4=11 7+5=12 7+6=13 7+7=14 7+8=15 7+9=16 7+10=17 8+0=8 8+1=9 8+2=10 8+3=11 8+4=12 8+5=13 8+6=14 8+7=15 8+8=16 8+9=17 8+10=18 9+0=9 9+1=10 9+2=11 9+3=12 9+4=13 9+5=14 9+6=15 9+7=16 9+8=17 9+9=18 9+10=19 10+0=10 10+1=11 10+2=12 10+3=13 10+4=14 10+5=15 10+6=16 10+7=17 10+8=18 10+9=19 10+10=20

Year 1 Year 2 Year 3 Year 4 Year 5/6 Subtracting 0 and 1. Recall all subtraction Recall all subtraction root Recall all subtraction Recall all subtraction Key Skills root facts root facts Subtracting 0 facts root facts Subtracting 1 Know subtraction facts Key Skills: Key Skills: Key Skills: for all numbers up to 20 Doubles – when you see 14 Doubles – when you see Doubles – when you see Subtracting from 10 – – 7, think 7 + 7 = 14 14 – 7, think 7 + 7 = 14 14 – 7, think 7 + 7 = 14 use 10 frames Key Skills: Think addition – when we Doubles – when you see see 7 – 5, think 5 + 2 = 7 Think addition – when we Think addition – when we 14 – 7, think 7 + 7 = 14 see 7 – 5, think 5 + 2 = 7 see 7 – 5, think 5 + 2 = 7 Fact families – to recall Think addition – when we ‘missing number’ – e.g. 8 – Fact families – to recall Fact families – to recall see 7 – 5, think 5 + 2 = 7 5, recall 5 + 3 = 8, 3 + 5 = ‘missing number’ – e.g. 8 – ‘missing number’ – e.g. 8 8,8 – 3 = 5, 8 – 5 = 3 5, recall 5 + 3 = 8, 3 + 5 = – 5, recall 5 + 3 = 8, 3 + Fact families – to recall 8,8 – 3 = 5, 8– 5 = 3 5 = 8,8 – 3 = 5, 8– 5 = 3 ‘missing number’ – e.g. 8 – Compensating subtracting 5, recall 5 + 3 = 8, 3 + 5 = 9 and 11 by subtracting 10 Compensating Compensate subtracting 8,8 – 3 = 5, 8 – 5 = 3 and adjusting subtracting 9 and 11 by 9, 19, 29… by subtracting 10 and subtracting 10, 20, 30 Bridging – e.g. Counting adjusting and adjusting back: 14 – 6 (14 – 4, then 10 -2) or counting Bridging – e.g. Counting Bridging – e.g. Counting forward: 6 + 4 + 4 back: 14 – 6 (14 – 4, then back: 14 – 6 (14 – 4, then 10 -2) or counting 10 -2) or counting Explicit use of number forward: 6 + 4 + 4 forward: 6 + 4 + 4 facts to subtract 1, 10, 100 to numbers up to 3 Count back in steps of 2, Count back in steps of 2, digit. 3, 4, 5, 6, 7, 8, 9, 10, 25, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50 and 100 and 1000 50 and 100 and 1000 from any given number from any given number

Subtraction root facts Note that in subtraction facts not all subtractions within 20 are strictly root facts, e.g. 17 - 5 is not considered a root fact (7 - 5 is the root fact for this). In theory, the majority of these facts are learned in Years 1 and 2. Although this is a Year 2 objective, unless we continue working on this through KS2, some children will never have these. (Year 1 facts highlighted in green) - 0 1 2 3 4 5 6 7 8 9 10 1 1-0=1 1-1=0 2 2-0=2 2-1=1 2-2=0 3 3-0=3 3-1=2 3-2=1 3-3=0 4 4-0=4 4-1=3 4-2=2 4-3=1 4-4=0 5 5-0=5 5-1=4 5-2=3 5-3=2 5-4=1 5-5=0 6 6-0=6 6-1=5 6-2=4 6-3=3 6-4=2 6-5=1 6-6=0 7 7-0=7 7-1=6 7-2=5 7-3=4 7-4=3 7-5=2 7-6=1 7-7=0 8 8-0=8 8-1=7 8-2=6 8-3=5 8-4=4 8-5=3 8-6=2 8-7=1 8-8=0 9 9-0=9 9-1=8 9-2=7 9-3=6 9-4=5 9-5=4 9-6=3 9-7=2 9-8=1 9-9=0 10 10-0=10 10-1=9 10-2=8 10-3=7 10-4=6 10-5=5 10-6=4 10-7=3 10-8=2 10-9=1 10-10=0 11 11-1=10 11-2=9 11-3=8 11-4=7 11-5=6 11-6=5 11-7=4 11-8=3 11-9=2 11-10=1 12 12-2=10 12-3=9 12-4=8 12-5=7 12-6=6 12-7=5 12-8=4 12-9=3 12-10=2 13 13-3=10 13-4=9 13-5=8 13-6=7 13-7=6 13-8=5 13-9=4 13-10=3 14 14-4=10 14-5=9 14-6=8 14-7=7 14-8=6 14-9=5 14-10=4 15 15-5=10 15-6=9 15-7=8 15-8=7 15-9=6 15-10=5 16 16-6=10 16-7=9 16-8=8 16-9=7 16-10=6 17 17-7=10 17-8=9 17-9=8 17-10=7 18 18-8=10 18-9=9 18-10=8 19 19-9=10 19-10=9 20 20-10=10

Year 1 Year 2 Year 3 Year 4 Year 5/6 Count in multiples of 2, Recall and use From Year 2 - Recall and Recall and use Revision of all times 5 and 10. multiplication and use multiplication and multiplication and tables and division division facts for the 2, division facts for the 2, division facts for 6, 7, facts up to 12x12. Recall and use all 5 and 10 multiplication 5 and 10 multiplication 8, 11 and 12 doubles to 5 + 5 and tables, including tables multiplication tables corresponding halves. recognising odd and even numbers. Recall and use multiplication and Recall and use all doubles division facts for the 3, to 10 + 10 and 4 and 9 multiplication corresponding halves. tables. Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, Recall and use multiplication and division facts for the 3, 4 and 9 multiplication tables.

Multiplication facts It is imperative the each year group take responsibility for teaching the times table facts required as their end of year expectation (see chart). Children can become overloaded is expected to learn all their facts in Year 4. If children have not grasped appropriate facts, intervention needs to occur within year group to remedy this in time for the Times Table screening. X 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 3 4 5 6 7 8 9 10 11 12 2 2 4 6 8 10 12 14 16 18 20 22 24 3 3 6 9 12 15 18 21 24 27 30 33 36 4 4 8 12 16 20 24 28 32 36 40 44 48 5 5 10 15 20 25 30 35 40 45 50 55 60 6 6 12 18 24 30 36 42 48 54 60 66 72 7 7 14 21 28 35 42 49 56 63 70 77 84 8 8 16 24 32 40 48 56 63 72 80 88 96 9 9 18 27 36 45 54 63 72 81 90 99 108 10 10 20 30 40 50 60 70 80 90 100 110 120 11 11 22 33 44 55 66 77 88 99 110 121 132 12 12 24 36 48 60 72 84 96 108 120 132 144 Year 2 (or earlier) Year 3 Year 4

I can… Example use all addition root facts to 10 See addition root facts table. e.g. 3 + 0 and 0 + 3 add 0 add 1 e.g. 7 + 1 or 1 + 7 add 2 e.g. 4 + 2 or 2 + 4 add 10 e.g. 5 + 10 and 10 + 5 Use doubles and near doubles of numbers to 5 “When a work out 4 + 5 I can just double 4 and add 1.” recall number bonds (also known as e.g. 8 + 2 and 2 + 8 ‘complements’) to 10 subtract 0 and 1 6–0=6 Subtracting numbers from 10 6–1=5 –4=6 10 – 6 = 4 count in multiples of 2, 5 and 10. “I can count in 5s: 5, 10, 15, 20, 25…” recall and use all doubles to 5 + 5 and “What is double 5?” corresponding halves “What is half of 10?” “What is double 3? “What is half of 6?”

I can… Example use all addition root facts to 20 See addition root facts table on the back of this sheet. recall all doubles of numbers to 10 add near doubles 7 + 7, 8 + 8… Apply to 2 digit numbers ( e.g. 37 + 37) bridge 10 to add numbers quickly 6 + 7 - think ‘double 6 and one more’ Apply to larger numbers – e.g. 149 +150; 235 + 236 When tackling 8 + 7 you could do 8 + 2 to make 10, and then add 5 add 9 by adding 10 then subtracting 1. 14 + 9 = 14 + 10 -1 recall all subtraction root facts See subtraction root facts on the back of this sheet. “What is the difference between 16 and 9?” use my knowledge of doubles to help with When you see: subtraction. 14 – 7, think 7 + 7 = 14 “How would you quickly calculate 12 – 6?” use addition to find the difference when numbers “I know that 6 + 6 = 12, so 12 – 6 = 6” are close together When we see 7 – 5, think 5 + 2 = 7 use fact families to find the ‘missing number’ “How would you use addition to calculate 8 – 5?” “I know that you need to add 3 to five to make 8, so the difference between 8 and 5 is 3.” I had 9 fidget spinners. I gave some to my friends, and I still have 4 left. How many did I give away? 9-?=4 I know that 4 + 5 = 9, so 5 fidget spinners were given away. recall and use multiplication and division What is half of 8? facts for the 2, 5 and 10 multiplication Is it possible to halve 3? tables halve numbers to 10

I can… Example subtract 9 by subtracting 10, and adding 1 34 - 9 = 34 - 10 +1 subtract 11, by subtracting 10, and subtracting 1. 34 - 11 = 34 - 10 - 1 use ‘bridging’ to subtract numbers quickly Counting back: 14 – 6 (14 – 4, then 10 -2) or counting forward: 6 + 4 + 4 Use number facts to subtract 1, 10, 100 to Times Table Rock stars numbers up to 3 digit. (from Y2) recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables

I can… Example Use all addition root facts to 20 See addition root facts table on the back of this sheet. recall all doubles of numbers to 10 7 + 7, 8 + 8… add near doubles Apply to 3 digit numbers ( e.g. 437 + 437) 6 + 7 - think ‘double 6 and one more’ Apply to larger numbers – e.g. 149 +150; 235 + 236 8 + 7 - could do 8 + 2 to make 10, then add 5 use ‘bridging’ to add numbers quickly Apply to 2 digit numbers, e.g. 78 + 6 “I would split 6 into 2 and 4, then add the 2 to make 80, then the 4 to make 84” add 9 by adding 10 then subtracting 1. add 11, by adding 10 then adding 1. 34 + 9 = 34 + 10 -1 Use number facts to add 1, 10, 100 to numbers 34 + 11 = 34 + 10 + 1 +10 +100 up to 3 digit. +1 34 256 recall all subtraction root facts See subtraction root facts on the back of this sheet. “What is the difference between 16 and 9?” use my knowledge of doubles to help with subtraction. When you see: 14 – 7, think 7 + 7 = 14 use addition to find the difference when numbers “How would you quickly calculate 12 – 6?” are close together “I know that 6 + 6 = 12, so 12 – 6 = 6” When we see 7 – 5, think 5 + 2 = 7 “How would you use addition to calculate 18 – 15?” “I know that 5 + 3 equals 8, so 15 + 3 must equal 18, therefore 18 – 15 =3”

I can… Example use fact families – to recall ‘missing number’ I had 9 fidget spinners. I gave some to my friends and I still have 4 left. How many did I give away? subtract 9 by subtracting 10, and adding 1 subtract 11, by subtracting 10, and subtracting 1. I know that 4 + 5 = 9, so I gave away 5 fidget spinners. use ‘bridging’ to subtract numbers quickly 34 - 9 = 34 - 10 +1 34 - 11 = 34 - 10 - 1 Counting back: 14 – 6 (14 – 4, then 10 -2) or counting forward: 6 + 4 + 4 -1 -10 -100 34 Use number facts to subtract 1, 10, 100 to 256 numbers up to 3 digit. (from Y2) recall and use multiplication and Times Table Rock Stars division facts for the 2, 5 and 10 multiplication tables Recall and use multiplication and division facts for the 3, 4 and 9 multiplication tables.

I can… Example quickly recall all addition root facts to 20 See addition root facts table on the back of this sheet. recall all doubles of numbers to 10 add near doubles 7 + 7, 8 + 8… Apply to 3 digit numbers ( e.g. 437 + 437) 6 + 7 - think ‘double 6 and one more’ Apply to larger numbers – e.g. 149 +150; 235 + 236 8 + 7 - could do 8 + 2 to make 10, then add 5 use ‘bridging’ to add numbers quickly Apply to 2 digit numbers, e.g. 78 + 6 “I would split 6 into 2 and 4, then add the 2 to make 80, then the 4 to make 84” add 9, 19, 29… by adding 10, 20, 30 … and sub- 34 + 9 = 34 + 10 -1 tracting 1. add 11, 21, 31… by adding 10, 20, 30… and adding 34 + 11 = 34 + 10 + 1 1. explain how I add large numbers in my head. “What strategies would you use to add together 99 and 136?” “I would add 99 by adding 100, then subtracting 1” quickly recall all subtraction root facts to 20 See subtraction root facts on the back of this sheet. use my knowledge of doubles to help with “What is the difference between 16 and 9?” subtraction. When you see: 14 – 7, think 7 + 7 = 14 use addition to find the difference when numbers “How would you quickly calculate 12 – 6?” are close together “I know that 6 + 6 = 12, so 12 – 6 = 6” When we see 7 – 5, think 5 + 2 = 7 “How would you use addition to calculate 18 – 15?” “I know that 5 + 3 equals 8, so 15 + 3 must equal 18, therefore 18 – 15 =3”

I can… Example use fact families – to recall ‘missing number’ I had 9 fidget spinners. I gave some to my friends and I still have 4 left. How many did I give away? subtract 9, 19, 29… by subtracting 10, 20, 30 and adding 1 I know that 4 + 5 = 9, so I gave away 5 fidget spinners. subtract 11, 21, 31… by subtract ing 10, 20, 30… 34 - 9 = 34 - 10 +1 and subtracting 1. 34 - 11 = 34 - 10 - 1 use ‘bridging’ to subtract numbers quickly Counting back: 14 – 6 (14 – 4, then 10 -2) or counting forward: 6 + 4 + 4 count back in steps of 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, Start at 35 and count back in steps of 4 50 and 100 and 1000 from any given number Start at 1000 and count back in 50s Revision of all times tables and division facts up to 12x12.

Support for parents: Expectations and ways to help children of each year group achieve fluency at home with the help of their parents. This could be shared at the beginning of the year and set as home learning or delivered in sequence with fluency learning in the classroom.

Helping your child become more fluent in maths (Year 1) I can… Examples/ideas …quickly recall all addition facts to See the addition and subtraction root facts table How quickly can you recall these 10 addition facts? (This means not having to use your 0+0=0 0+1=1 0+2=2 0+3=3 0+4=4 0+5=5 0+6=6 fingers to count up or down but to either just know the answer or know 1+0=1 1+1=2 1+2=3 1+3=4 1+4=5 1+5=6 1+6=7 a quick way of working it out.) 2+0=2 2+1=3 2+2=4 2+3=5 2+4=6 2+5=7 2+6=8 3+0=3 3+1=4 3+2=5 3+3=6 3+4=7 3+5=8 3+6=9 4+0=4 4+1=5 4+2=6 4+3=7 4+4=8 4+5=9 4+6=10 …recall all doubles of numbers to 5 2 + 2, 4 + 4… When you play board games, try doubling up whatever is on the dice. Or try doubling the square you land on. …add 0, 1, 2 or 10 to any number “What is 3 add 10?” “3 and 10 equals 13.” …recall and use multiplication and See website for games and challenges. division facts for the 2, 5 and 10 What is half of 8? Is it possible to halve 3? Try halving three apples. multiplication tables …halve numbers to 10

Helping your child become more fluent in maths (Year 2) I can… Examples/ideas …quickly recall all addition and See the addition and subtraction root facts table on 8 + 5 = 13 could be thought of as 8 + subtraction root facts to 20 the back of this sheet. 2 + 3 = 13 (This means not having to use your You can also look on the school website - curriculum/ fingers to count up or down but to maths for more ideas. either just know the answer or know a quick way of working it out.) …recall all doubles of numbers to 7 + 7, 8 + 8… When you play board games, try 10 and use this knowledge to help doubling up whatever is on the dice. with subtraction “Can this help you double larger numbers? How would Or try doubling the square you land you double 17?” on. …add 9 adding 10 and subtracting 1 “Well, double 10 is 20, and double 7 is 14. I just add 20 and 14 to make 34.” Double house numbers as you walk to “Can you double 25?” school. “How would you quickly calculate 12 – 6?” “I know that 6 + 6 = 12, so 12 – 6 = 6” “How would you add together 9 and 16?” “I would add 9 to 16 by adding 10 to 16 to make 26, and then subtracting 1 to make 25.” …recall and use multiplication and Times Table Rock Stars division facts for the 2, 5 and 10 multiplication tables …halve numbers to 10 What is half of 8? Is it possible to halve 3? Try halving three apples.

Helping your child become more fluent in maths (Year 3) I can… Examples/ideas …quickly recall all addition and See the addition and subtraction root facts table on 8 + 5 = 13 could be thought of as 8 + subtraction root facts to 20 the back of this sheet. 2 + 3 = 13 (This means not having to use your You can also look on the school website - curriculum/ fingers to count up or down but to maths for more ideas. either just know the answer or know a quick way of working it out.) …recall all doubles of numbers to 7 + 7, 8 + 8… When you play board games, try 10 and use this knowledge to help doubling up whatever is on the dice. with subtraction “Can this help you double larger numbers? How would Or try doubling the square you land you double 17?” on. “Well, double 10 is 20, and double 7 is 14. I just add 20 and 14 to make 34.” Double house numbers as you walk to “Can you double 125?” school. “How would you quickly calculate 12 – 6?” “I know that 6 + 6 = 12, so 12 – 6 = 6” …add near doubles 5 + 6 = 5 + 5 + 1 = 11 Apply to larger numbers – e.g. 49 + 50; 235 + 236 … add 9 adding 10 and subtracting 1. “How would you add together 9 and 136?” … add 19 adding 20 and subtracting 1. “I would add 99 to 136 by adding 10 to 136 to make 146, and then subtracting 1 to make 145.” … add 11 by adding 10 and adding 1. … add 21 by adding 20 and adding 1. Times Table Rock Stars …recall and use multiplication and Times Table Rock Stars division facts for the 2, 5 and 10 multiplication tables …recall and use multiplication and division facts for the 3, 4 and 9 multiplication tables.

Helping your child become more fluent in maths (Years 4-6) I can… Examples/ideas …quickly recall all addition and See the addition and subtraction root facts table on 8 + 5 = 13 could be thought of as 8 + subtraction root facts to 20 the back of this sheet. 2 + 3 = 13 (This means not having to use your You can also look on the school website - curriculum/ fingers to count up or down but to maths for more ideas. either just know the answer or know a quick way of working it out) …recall all doubles of numbers to 7 + 7, 18 + 18… When you play board games, try 20 and use this knowledge to help doubling up whatever is on the dice. with subtraction “Can this help you double larger numbers? How would Or try doubling the square you land you double 37?” on. …add near doubles “Well, double 3 is 6, so double 30 is 60. Double 7 is 14. …explain how I add large numbers I just add 60 and 14 to make 74.” Double house numbers as you walk to in my head. “How about doubling 237?” school. “How would you quickly calculate 12 – 6?” “I know that 6 + 6 = 12, so 12 – 6 = 6” 5 + 6 = 5 + 5 + 1 = 11 Apply to larger numbers – e.g. 149 + 150; 235 + 236 “How would you add together 99 and 136?” “I would add 99 to 136 by adding 100 to 136 to make 236, and then subtracting 1 to make 235.” …recall and use multiplication and Times Table Rock Stars division facts for up to 12 x 12 multiplication tables

Support for teachers: Document from Herts for Learning with progression is structured into phases. In Years 1 to 4, this is organised into individual year groups. At the beginning, there is a section entitled ‘Pre-operational Learning’. This helps ensure that the foundations are secure by the end of EYFS and in the first few weeks in Year 1 before mental fluency within numbers to 10 begins. This also supports the early identification of gaps and barriers. In each year group / phase, the progression is organised into the National Curriculum Programs of Study domains: number and place value; addition and subtraction; multiplication and division including fractions. Within these domains, key concepts (ideas), skills (which can be utilised) and strategies (methods) are exemplified within the relevant number ranges. At the end of each phase, a selection of possible examples that align with a given strategy or skill are included. For KS1 and UKS2, there are examples taken directly from the relevant end of key stage assessments (2016) and sample papers. When designing opportunities to practise or for strategy discussions, these will support teachers to explore and / or guide pupils towards a particular strategy.