1 Mathematics Written Calculations Policy Addition Reception Children are introduced to the + sign and write their additions like this: = 5 Year 1 Children continue to write their additions like this: = 5 They also learn to write 5 = Children move onto adding three small numbers. Year 2 Children begin to use empty number lines starting with the larger number and counting on = More able children will move onto partitioning, splitting the tens and units = ( ) + (7 + 5) = = 52 Year 3 Children continue to use empty number lines with increasingly large numbers = Children use the partitioning method = ( ) + (7 + 5) = = 52 More able children will then move onto expanded methods of addition adding the most significant digits first (60+ 80) (7+5)
2 Year 4 Children will continue to use jottings where appropriate. They will use expanded methods with increasingly larg e numbers. Adding the most significant digits first More able children may investigate using the least significant figures first. Year 5 Children will use the expanded method of colum n addition, using the least significant digits first. Least significant Leading onto carrying when appropriate H T U Some children may continue to use the expanded methods with increasingly large numbers. Most will use the carrying method. More able children will move onto adding 3 numbers and numbers with decimals. Year 6 Most children will use the carrying method moving onto using decim als They will add decimals with different numbers of places and different numbers of digits.
3 Subtraction Reception Children are introduced to the sign and write their subtractions like this: 5 3 = 2. Year 1 Continue as in Reception. Year 2 Children begin to use empty number lines to support mental calculations. First they will use the number line to count back = Year Children move onto the empty number line method to count on from the smaller number to the larger number using increasingly large numbers = = Year 4 Children continue to use number lines to count up from the smaller number to the larger number = = They will use expanded decomposition with increasingly large numbers: = = = = They will move onto compact decomposition when appropriate
4 Year 5 Children will use compact decomposition with increasingly large numbers Expand to include zero values. If ready, move onto decimals. Year 6 Children will use the compact decomposition method moving onto decimals and questions where zero values exist in the larger number
5 Year 2 Multiplication Children will develop their understanding of multiplicatio n and use jotting to support calculation. Repeated addition 2 x 4 = = 8 or 2 lots of 4 or 2 x 4 or 4 x 2 Arrays 2 x 4 = 8 4 x 2 = 8 Year 3 Year 4 Continue to use repeated addition. Continue to use arrays. More able children start to use partitioning to multiply. 15 x 3 = (10 x 3) + (5 x 3) = = 45 Some children will continue to use partitioning to multiply. Most children will move onto the grid method of multiplication. They will approximate first 8 x 23 is approximately 20 x 10 = 200 e.g. 23 x 8 X = = 184 Extending to HTU x U examples e.g.153 x 4 X = = 612 Partitioning will continue to be used with all children (as year 3). More able children will then use partitioning to lead to a short multiplication method. (TU x U) Least significant 2 3 x ( 3x8) (20x8) 1 8 4
6 Year 5 The grid method will continue to be used for all children, extending to the following:- TU x TU and HTU x TU e.g. 328 x 16 X = More able children extend onto decimal Numbers (to 1 or 2 decimal places) e.g x 5 Some children may choose not to compact this method or partially compact it e.g. instead of 4800, some children may still prefer to write the 3000 & 1800 separately. X = Most children will then use partitioning to lead to a short multiplication method. (TU x U and HTU x U) 2 3 x ( 3x8) (20x8) leading to 2 3 x Year 6 Children continue to use the grid method as Year 5. Most children move onto the short mult iplication method (TU x TU and HTU x TU) 7 2 x When ready, children will use short multiplication for calculations such as 2435 x 6 and x 5. (Mostly in the context of money problems).
7 Year 2 Di vision Children will develop their understanding of division and use jottings to support calculation. Sharing equally 6 sweets are shared between 2 people. How many do they each get? Year 3 Children continue to work on grouping and sharing. Children will move onto using a number line for repeated subtraction = Children also move onto inverses. e.g. If 8 4 = 2, so 2 x 4 = 8 and 8 2 = 4 must also be correct. Children use repeated subtraction and inverse multiplication to work out problems such as: A baker bakes 24 buns. She puts 6 buns in every box. How many can she fill? Children are introduced to remainders. e.g = 4 r1 Year 4 Children will use repeated subtraction i.e. The 'chunking' method (10 X 5) (4 x 5) = 14 remainder 2 2 Extending to HTU U e.g
8 Year 5 Children will use the standard written method. They will look for opportunities to reduce workings. e.g. Instead of subtracting 10 x 6 three times, children will subtract 30 x is approximately = 40. Year (30 X 6) (2 x 6) 4 = 32 r4 Children will continue with the chunking method from Year 5. Children with understanding may start to use short division (when dividing by number up to 9 only). e.g. 3 2 r At this point, children will be shown how to record remainders as decimals and fractions. DECIM ALS FRACTIONS = = Children will move onto numbers including decimals (to 1 and 2 decimal places) More able children will use the standard chunking method extended to long division when dividing by 2 digits is approximately = (20 X 36) (5 x 36) (2 x 36) 0 = 27
9 Multiplication Chart - Up To 12 x 12 Highlight each number once the fact is known! X Suggested Practical Activities Card games. Most card games require collecting totals, matching or remembering numbers that have gone before. They are excellent practice for mental arithmetic. Dice games. Some of these can be found on the MathsSphere site - they usually involve counting or working out probabilities. Board games. Again, these are excellent, the buying of ite ms or giving of money often helps with underst anding larger amounts - up to millions! Strategy games. There are plenty of 2-player games of strategy, which involve logical thinking and working out a winning strategy - all good maths!
10 The advantage of the ideas above over more recent computer games is that they involve discussion - you can talk through strategies and why they work. Rules can always be adapted if they become a little stale - perhaps trying to lose all your money as quickly as possible rather than winning as much as possible!! Here are some suggested websites that you might find useful. uk.ixl.com