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St Swithun Wells Catholic Primary School Maths Calculations We all know the importance of being able to confidently carry out simple mathematical calculations and how often we do this throughout our day. In school we frequently hear from parents that they are struggling to help their child complete their homework because the way ‘we do things’ is so different from how they ‘did’ maths at school. In response to this we have put together a simple guide explaining the main way we teach mathematical calculations and how these build up and progress through the school. Our main emphasis is on developing children’s understanding of calculations and encouraging children to use practical equipment, visual images and mental strategies. As their understanding develops children begin to record. This guide will show you the ways children use to record.

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The progression of calculation strategies for addition, subtraction, multiplication and division. Children are introduced to the processes of calculation through practical, oral and mental activities. As they begin to understand the underlying ideas, they develop ways of recording to support their thinking and calculation methods and learn to use the appropriate signs and mathematical language. The overall aim is that by the time they leave primary school they: have a secure knowledge of number facts and a good understanding of the four operations; are able to use this knowledge and understanding to carry out calculations mentally; can use diagrams and informal jottings to help record steps and part answers; have an efficient method of calculation for each operation that they can use with confidence; use a calculator effectively, check the steps involved and decide if the numbers displayed make sense.

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When teaching addition, subtraction, multiplication or division we plan for the following; First experiences need to be practical activities with concrete equipment. Children then need to be allowed to record in their own ways through drawing pictures and making jottings. They can then move onto recording in more standard ways such as those demonstrated by the teacher. Children will need to see number lines used so they can form visual images for the number operations and eventually being able to draw own number lines to solve addition, subtraction, multiplication and division problems. Connections need to be made between different strategies.

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Strategies for addition: 1.Count on in ones – use practical apparatus 2.Count on in ones from the biggest number – fingers to nose 3.Adding tens, then ones – use structured number line and blank number line 4.Partitioning single digits: 9 (5 + 4) 5.Partitioning larger numbers 6.Compact method such as column addition.

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1.Count on in ones, using practical apparatus 2. Count on in ones from the biggest number 9 +1 1011121314 9 + 5 = 14 Strategies for Addition

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3. Adding tens, then ones. 37 + 15 Strategies for Addition +1 +10 37 +1 52 47 +1 4. Partitioning single digits +5 +4 11 + 9 (4 + 5) 11 15 20

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364 + 258 5. Partitioning larger numbers Strategies for Addition +200 364 564614 + 50 + 8 622 +30 81 111116 + 5 81 + 35

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6. Compact method such as column addition 300 + 60 + 4 200 + 50 + 8 500 + 110 + 12 30+ 7 10+ 5 40 + 12 = 52 Strategies for Addition 364 +258 622

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Strategies for subtraction 1.Counting back in ones 2.Counting back in tens, then ones. 3.Finding the difference by counting on 4.Partitioning and recombining without decomposition 5.Partitioning and recombining with decomposition

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1.Count back in ones, using practical apparatus 2 34 5 6 7 8 9 9 - 2 3 456 Counting back in ones, using a number line 1 2 7 8 9 10 1 Strategies for Subtraction

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2. Counting back in tens and then ones. 27 - 13 -10 14 1617 15 27 3. Finding the difference by counting on in tens and then ones. +10 +1 23 27 13 +1 Strategies for Subtraction

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4.Partitioning and recombining without decomposition – using a number line. - 9 - 20 - 100 57 86 186 66 5. Using an expanded column subtraction. 753 - 231 700 + 50 + 3 200 + 30 + 1 500 + 20 + 2 = 522 - Strategies for Subtraction

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6. Partitioning and recombining with decomposition. 741 - 367 700 + 40 + 1 300 + 60 + 7 301 + 70 + 4 = 374 11130 600 741 367 374 1113 6 - - Strategies for Subtraction

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Strategies for multiplication 1.Repeated addition starting with pictures, then moving on to a number line. 2.Simple arrays (what do you see?) 3.Arrays involving partitioning 4.Grid method 5.Grid method using 2 and 3 digit numbers.

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1.Repeated addition, starting with objects or pictures Repeated addition, using a number line 0 5 15 1020 + 5 Strategies for Multiplication

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2. Simple arrays (what do you see?) Strategies for Multiplication Describe what you see. 4 rows of 3 teddy bears. 5 + 5 + 5 + 5

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3. Arrays involving partitioning 2 305 Strategies for Multiplication 35 x 2

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4. Grid method 10 3 1 10 x 10 = 100 10 x 3 = 30 1 x 10 = 10 1 x 3 = 3 143 Strategies for Multiplication 11 x 13

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5. Grid method up to using 2 and 3 digit numbers x10 5 100 50 880 40 250 200 25 partitioned into 2 tens and 5 ones 18 X 25 = 450 Strategies for Multiplication

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x307 10030007003700 20 600140 740 5 150 35 185 4625 125 X 37 = 4,625

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Strategies for division 1.Doubling/halving, making sets 2.Count in multiples of 2, 5 and 10 3.Sharing and grouping 4.Using arrays to explain partitioning 5.Use inverse to link multiplication and division problems 6.Simple chunking 7.Chunking with larger numbers

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Strategies for Division half of 8 is 4 8 ÷ 2 = 4 double 4 is 8 4 x 2 = 8 1. Doubling and halving, making sets.

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Strategies for Division 2. Count in multiples of 2, 5 and 10 2 4 6 8 10 10 ÷ 2 = 5 How many 2s in 10?

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Strategies for Division 3. Sharing and grouping

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Strategies for Division 4. Using arrays to explain partitioning There are 95 parents coming to a school production. The school hall is wide enough for 17 chairs in a row. The caretaker has set out 6 rows. Are there enough chairs for all the parents? How could you calculate the answer?

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5. Using inverse operation (multiplication used to solve division) 20 x 5 = 100 100 ÷ 5 = 20 100 ÷ 20 = 5 Strategies for Division

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6.Simple chunking 198 ÷ 6 6 √ 198 60 x 10 138 60 x 10 78 60 x 10 18 18 x 3 0 Answer = 33

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Strategies for Division 7.Chunking with larger numbers In Barton zoo a week’s supply of 1256 apples is to be shared equally between 6 elephants. How many apples will each elephant get? 6 √ 1256 600 x 100 656 600 x 100 56 54 x 9 2 209 Answer is 209 remainder 2 The compact short division is: 6 √ 1 2 5 6 209 rem 2 In this example, the digits need to be carefully aligned in the appropriate columns. An advantage of a strategy based on repeated subtraction of ‘chunks’ is that the same method can be extended to work with two-digit divisors. 1 5

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