Subtract – change the numbers by adding or subtracting the Mental and semi-formal calculations for same amount multiplication and division. e.g. 22 – 17 becomes 20 – 15 = 5 72 – 27 becomes 75 – 30 = 35 Mental methods should always be used in 507 – 296 becomes 511 - 300 = 211 preference to formal algorithms. If a pupil cannot Start to use arrow notation to record thinking. ‘Instead of 53 take 19, I use mental strategies to solve a problem, they did 54 take 20’ should not be asked to record solutions using formal algorithms as this will simply take them 53 – 19 = 54 – 20 = 34 through a process rather than truly demonstrate Pupils should explore the effect of carrying out operations on an their understanding of the given task. existing equation, e.g. if they know (and write down) 20+15=35 then what is the effect of (say) doubling both sides? What happens if we add 5 to one side but not the other? What happens if we carry out different operations to both sides of the equation? Use a known fact to work out an unknown fact e.g. Can express their understanding of a particular Number bonds to 10: calculation using stories, symbols pictures and 40 + 70 40 + 60 = 100 so 40 + 70 is ten more = 110. real life situations. Near doubles: e.g. 31 + 31 is double 3 tens add 2 e.g. use a think board to record their 69 + 69 is double 7 tens take 2 away understanding of a multiplication sum and give Doubles, up to 40: valuable insight into the connections they have 139 + 139 is double 14 tens – 2 [ 280 -2] made between concrete objects, pictures and 142 + 144 is double 14 tens add 6 [ 280 + 6] diagrams and words and symbols Write number sentences using the terms ‘change’, ‘combine’ and ‘compare situations’, using diagrams and addition and subtraction number sentences. e.g. See this think board in more detail at
Mental and semi-formal calculations for multiplication and division. Mental methods should always be used in preference to formal algorithms. If a pupil cannot use mental strategies to solve a problem, they should not be asked to record solutions using formal algorithms as this will simply take them through a process rather than truly demonstrate their understanding of the given task. Subtract – change the numbers by adding or subtracting the same amount e.g. 22 – 17 becomes 20 – 15 = 5 72 – 27 becomes 75 – 30 = 35 507 – 296 becomes 511 - 300 = 211 Start to use arrow notation to record thinking. ‘Instead of 53 take 19, I did 54 take 20’ 53 – 19 = 54 – 20 = 34 Pupils should explore the effect of carrying out operations on an existing equation, e.g. if they know (and write down) 20+15=35 then what is the effect of (say) doubling both sides? What happens if we add 5 to one side but not the other? What happens if we carry out different operations to both sides of the equation? Use a known fact to work out an unknown fact e.g. Number bonds to 10: 40 + 70 40 + 60 = 100 so 40 + 70 is ten more = 110. Near doubles: e.g. 31 + 31 is double 3 tens add 2 69 + 69 is double 7 tens take 2 away Doubles, up to 40: 139 + 139 is double 14 tens – 2 [ 280 -2] 142 + 144 is double 14 tens add 6 [ 280 + 6] Can express their understanding of a particular calculation using stories, symbols pictures and real life situations. e.g. use a think board to record their understanding of a multiplication sum and give valuable insight into the connections they have made between concrete objects, pictures and diagrams and words and symbols See this think board in more detail at Write number sentences using the terms ‘change’, ‘combine’ and ‘compare situations’, using diagrams and addition and subtraction number sentences. e.g.
highland-numeracy-progression-update-2017.docx