backwards in 399 add i.e. half of numbers with the expectation → appropriate 400 and then 5.6, double that as children’s knowledge of decimals and subtract 1. 3.4. place value is secured, they percentages. Sums and become ready to approach a differences formal compact method. of decimals, i.e. 6.5 + 2.7 Stage 6: Continue to Bridging Ensure all Columnar addition (formal written Pupils to be encouraged to consider practice through children are method): mental strategies first. previous decimals, i.e. confident The concept of exchange is Formal columnar: skills. 0.8 + 0.35 = recalling introduced through continued 25 forwards 0.8 + 0.2 + facts to 20 use of practical equipment +47 and 0.15 using and deriving (manipulatives). backwards in empty number facts using Teachers model: simple lines. place value. have two tens and five “I fractions, Partitioning Make links ones, which need adding to 25 decimals and using near between four tens and seven ones.” +47 percentages. doubles, i.e. decimals, add five ones to seven “I 2 2.5 + 2.6 = 5 + fractions and ones, which gives me twelve 1 0.1 percentages. ones.” Reorder exchange ten of my twelve “I decimals, i.e. ones for a ten counter.” 25 4.7 + 5.6 0.7 add my three tens and four – “I +47 4.7 tens to make seven tens.” …as… – 2 0.7 + 5.6 = 4 + I have seven tens “Altogether, 5.6. and two ones.” 1 Teachers similarly advance to model the addition of two 3-digit numbers, e.g. 25 +47
backwards in appropriate decimals and percentages. 399 → add 400 and then subtract 1. i.e. half of 5.6, double 3.4. Sums and differences of decimals, i.e. 6.5 + 2.7 numbers with the expectation that as children’s knowledge of place value is secured, they become ready to approach a formal compact method. Stage 6: Continue to practice previous skills. forwards and backwards in simple fractions, decimals and percentages. Bridging through decimals, i.e. 0.8 + 0.35 = 0.8 + 0.2 + 0.15 using empty number lines. Partitioning using near doubles, i.e. 2.5 + 2.6 = 5 + 0.1 Reorder decimals, i.e. 4.7 + 5.6 – 0.7 …as… 4.7 – 0.7 + 5.6 = 4 + 5.6. Ensure all children are confident recalling facts to 20 and deriving facts using place value. Make links between decimals, fractions and percentages. Columnar addition (formal written method): The concept of exchange is introduced through continued use of practical equipment (manipulatives). Teachers model: “I have two tens and five ones, which need adding to four tens and seven ones.” “I add five ones to seven ones, which gives me twelve ones.” “I exchange ten of my twelve ones for a ten counter.” “I add my three tens and four tens to make seven tens.” “Altogether, I have seven tens and two ones.” Teachers similarly advance to model the addition of two 3-digit numbers, e.g. Pupils to be encouraged to consider mental strategies first. Formal columnar: 25 +47 25 +47 2 1 25 +47 2 1 25 +47
draft_calculation_policy_-_updated_october_2015.docx