Newton Burgoland Primary School Calculation Policy 2014 Introduction The following calculation policy has been devised to meet the requirements of the National Curriculum 2014, for the teaching and learning of mathematics. It is also designed to give pupils a consistent and smooth progression of learning in calculations across the school, as well providing information for parents in their support of children s work outside of school. Layout The calculation policy is organised according to year group expectations as set out in the National Curriculum 2014, however pupils will be taught according to the stage that they are currently working at, being moved onto the next stage when they are ready, or working at a lower stage until they are secure enough to move on. It is essential that children are completely secure with a stage, before moving onto the next. Information as to how you can help can be found at the end of this policy. Context It is important that any type of calculation is given a real life context or problem solving approach to help build children s understanding of the purpose of calculation, and to give them opportunity to apply their methods. In addition to the written methods explained in this policy, children will be expected to use mental maths and jottings. They will be encouraged to recognise when to use certain operations and methods, when faced with problems.
Addition Reception/Year 1 Add with numbers up to 20, using concrete objects such as counting equipment and everyday objects. Move onto numbered number lines to add, by counting on in ones. Encourage children to start with the larger number and count on. Key Vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double, most, count on, number line Year 2 Add with 2 digit numbers (two digit and tens, two digit and one digit, two digit and two digit) Use concrete apparatus and number lines to secure understanding. Use partitioning of numbers into tens and units to help with addition, moving onto written methods. Examples that do not cross the tens boundary (as above) will be used until they are secure with the method itself. After this they can move onto those that cross the tens boundary (as below). Key Vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double, most, count on, number line, sum, tens, units, partition, addition, column, tens boundary
Year 3/ Year 4 Add numbers which now include three digits, and then four digits. Include numbers of different sizes, in different orders, which require the children to organise them (line them up correctly in order to carry out column addition) using their place value knowledge. Introduce the compact column addition method, without carrying at first. 2 3 6 + 1 3 Add the units first, then tens, then hundreds. Once secure, introduce carrying using the same compact column addition method. Add units first. Carry numbers underneath the bottom line. Reinforce correct place value by reminding them the actual value is 5 hundreds add 3 hundreds, not 5 add 3, for example. Key Vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double, most, count on, number line, sum, tens, units, partition, addition, column, tens boundary, hundreds boundary, increase, vertical, carry, expanded, compact, thousands, hundreds, digits, inverse
Year 5/ Year 6 Add numbers with more than 4 digits, using the compact column addition method. Include money, measures and decimals with different numbers of decimal places. Empty decimal places can be filled with a zero to show the place value in each column. Children should be able to align numbers of any size. Key Vocabulary: add, more, plus, and, make, altogether, total, equal to, equals, double, most, count on, number line, sum, tens, units, partition, addition, column, tens boundary, hundreds boundary, increase, vertical, carry, expanded, compact, thousands, hundreds, digits, inverse, decimal places, decimal point, tenths, hundredths, thousandths
Subtraction Reception/Year 1 Subtract with numbers up to 20, using concrete objects such as counting equipment and everyday objects. Move onto numbered number lines to subtract, by counting back in ones. Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back, how many left, how much less is_? Year 2 Subtract with 2 digit numbers. (2 digit and 1 digit, and 2 digit and 2 digit) Use concrete apparatus and number lines to secure understanding. Subtract on a number line by counting back, aiming to develop mental subtraction skills. Use partitioning of numbers to help count back quicker. See below for example: (47-23) Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back, how many left, how much less is_? difference, count on, strategy, partition, tens, units
Year 3/ Year 4 Introduce partitioned column subtraction method to help understand decomposition method. Use at first where no exchanging is needed in order to help children understand the process, then moving on to compact method. 89 35 = 54 80 + 9-30 + 5 50 + 4 8 9-3 5 5 4 This method should be used with up to 4 digits numbers. Once this is secure, introduce exchanging in the same way as above, using a range of numbers, ensuring that there is always a value in a column (ie. Not using numbers such as 103) 60 70 + 2-40 + 7 20 + 5 Once children are able to do this, introduce compact column subtraction method using the same range of numbers as above. Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back, how many left, how much less is_? difference, count on, strategy, partition, tens, units, exchange, decrease, hundreds, value, digit, inverse
Year 5/ Year 6 Subtract numbers with more than 4 digits, using the compact column subtraction method. Include money, measures and decimals with different numbers of decimal places. Numbers are now more complex and can include zeros in between, where understanding is needed as to where to exchange from and to. Empty decimal places can be filled with zero to show the place value in each column. Key vocabulary: equal to, take, take away, less, minus, subtract, leaves, distance between, how many more, how many fewer / less than, most, least, count back, how many left, how much less is_? difference, count on, strategy, partition, tens, units, exchange, decrease, hundreds, value, digit, inverse, tenths, hundredths, decimal point, decimal
Multiplication Reception/Year 1 Multiply with concrete objects, arrays (making groups of) and pictorial representations. For example: How many legs will 3 teddies have? 2 + 2 + 2 = 6 There are 3 sweets in one bag. How many sweets are in 5 bags altogether? 3+3+3+3+3 = 15 Relate to repeated addition. Use groups of 2s, 5s and 10s. Key vocabulary: groups of, lots of, times, array, altogether, multiply, count Year 2 Continue to use concrete objects where needed. Use arrays and repeated addition on a number line (using at least 2s, 5s and 10s) E.g. Include numbers in any order. E.g. 3 x? = 6. Children should begin to recall multiplication facts for 2, 5 and 10 times tables through practice in counting and understanding of the operation. (They will start to look at 3,4, and 11 times tables also) Key vocabulary: groups of, lots of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times...
Year 3/ Year 4 Multiply 2 digits by a single digit number. Introduce the grid method for multiplying 2 digit by 1 digit, linking it to the layout of arrays at first. Children will need to be able to multiply multiples of 10 by a single digit, as well as recall and work out multiplication facts in the 2, 3, 4, 5, 8 and 10 times tables. (YEAR 3) Then move on to multiplying 2 and 3 digits by a single digit, using all multiplication tables up to 12 x 12, using the grid method. Encourage column addition to add accurately. 5 0 0 1 5 0-3 0 6 8 0 Children will need to be able to multiply multiples of 10 and 100 by a single digit, as well as recall all tables up to 12 x 12. (YEAR 4) Key vocabulary: groups of, lots of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times..., partition, grid method, multiple, product, tens, units, value, inverse
Year 5/ Year 6 Multiply up to 4 digits by 1 or 2 digits. Introduce column multiplication, moving on from the grid method. Show short multiplication for multiplying by a single digit. x 300 20 7 4 1200 80 28 Show long multiplication for multiplying by 2 digits. 2 Moving on towards more complex numbers. 1234 x 6 1234 x 10 Use both of these methods. Use short multiplication to multiply decimals, with up to 2 decimal places, by a single digit. Key vocabulary: groups of, lots of, times, array, altogether, multiply, count, multiplied by, repeated addition, column, row, commutative, sets of, equal groups, times as big as, once, twice, three times..., partition, grid method, multiple, product, tens, units, value, inverse, square, factor, integer, decimal, short/long multiplication, carry, tenths, hundredths, decimal.
Division Reception/Year 1 Group and share small quantities. Use objects, diagrams and pictorial representations to solve problems involving both grouping and sharing. How many groups of 4 can be made with 12 stars? = 3 Key Vocabulary: share, share equally, one each, two each, group, groups of, lots of, array Year 2 Group and share, using the and = sign. Use objects, arrays, diagrams and pictorial representations, and grouping on a number line. Children should begin to recall division facts for 2, 5 and 10 times tables. Key Vocabulary: share, share equally, one each, two each, group, groups of, lots of, array, divide, divided by, divided into, division, grouping, number line, left, left over
Year 3/ Year 4 Divide 2 digit numbers by a single digit. Introduce short division, once they are secure with grouping. Start off by not including any remainders in the answer or being carried. Link the layout to an array to help understanding. Then move onto remainders in the answer, and remainders being carried. (Focus more on understanding method rather than remainders, as children will be taught different ways of showing remainders in year 5 and 6) Recall and use division facts for the 2, 3, 4, 5, 8 and 10 multiplication tables. (YEAR 3) Move on to dividing 3 digit numbers by a single digit, using the same process as above. When the answer for the first column is zero (1 5, as in example), children could initially write a zero above to acknowledge its place, and must always carry the number (1) over to the next digit as a remainder. Recall and use division facts for all tables up to 12 x 12. (YEAR 4) Key Vocabulary: share, share equally, one each, two each, group, groups of, lots of, array, divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short division, carry, remainder, multiple, divisible by, factor
Year 5/ Year 6 Divide up to 4 digits, including remainders in all places. Pupils must now consider the meaning of the remainder and how to express it, ie. as a fraction, a decimal, or as a rounded number or value, depending upon the context of the problem. The answer to 5309 8 could be expressed as 663 and five eighths, 663 r 5, as a decimal, or rounded as appropriate to the problem involved. Once children are secure, show them how to calculate a decimal remainder, as below. Then move on to dividing at least 4 digits, by both single digit and 2 digit numbers (including decimal numbers and quantities). Different methods can be shown for dividing by 2 digit numbers, both methods of long division. Such as chunking on the left, and carry down bus shelter on the right. Both can be used as appropriate, for example, the method on the right wouldn t be as efficient for 152 32, as 32 does not go into 1 or 15 and you therefore find yourself back at the original question. Key Vocabulary: share, share equally, one each, two each, group, groups of, lots of, array, divide, divided by, divided into, division, grouping, number line, left, left over, inverse, short division, carry, remainder, multiple, divisible by, factor, quotient, prime number, prime factors, composite number (non-prime), common factor
How can parents help? Not encouraging the view that it is ok to be bad at maths. Within society, people often admit to being terrible at maths and this is seen as socially acceptable. However, admitting that you re terrible at reading doesn t have the same acceptance. It is important that children have a growth mindset, which means that they have a can do attitude that leads to perseverance and a independent desire to improve. Practise basic skills that underpin all areas of maths, such as counting, table knowledge etc. This can be done by a variety of card games, or electronic programs such as numbergym. See some links below for ideas: http://resources.woodlands-junior.kent.sch.uk/maths/ http://www.bbc.co.uk/skillswise/maths/games http://www.topmarks.co.uk/maths-games/5-7-years/counting http://www.maths-games.org/ http://www.mathschamps.co.uk/games9-11 http://www.granby.k12.ct.us/uploaded/faculty/wyzika/dice_and_ca rd_games_to_practice_math_facts.pdf Help children see the link between different areas such as subtraction and addition. Ensure that children are practising their number bonds or times tables, in which ever way they learn best. For example, repetition, writing them down, playing games etc. Using mathematical vocabulary and being overt in real life situations such as in shops, using a recipe, ordering carpet etc.