Illustration of how to use Dienes equipment to ensure children have an understanding of place value when using columnar addition. Stage 5: Count Use apparatus Continue to Expanded vertical method, leading to Informal columnar: forwards and and practice columnar addition: Adding the tens first: backwards in knowledge of previous Teachers model a column steps of value to stage and method that records and explains powers of 10 add decimals, make links partial mental methods. Adding the ones first: for any given i.e. 3.8 + 2.5 = between remains an emphasis on the number up to 5 + 1.3 known facts language of calculation, e.g. one million. Reorder and addition plus seventy equals ‘Forty Continue to increasingly pairs for and ten.’… add ‘Seven count complex fractions, six equals thirteen.’ …before forwards and calculations, percentages recombining numbers. Teachers backwards in i.e. 1.7 + 2.8 + and also model the language of: simple 0.3 = 1.7 + 0.3 decimals tens add seven tens total ‘Four fractions. + 2.8 Doubles and eleven tens or 110.’ Count forward Compensating halves of Teachers similarly advance to and i.e. 405 + decimals, the addition of two 3-digit – 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
Illustration of how to use Dienes equipment to ensure children have an understanding of place value when using columnar addition. Stage 5: Count forwards and backwards in steps of powers of 10 for any given number up to one million. Continue to count forwards and backwards in simple fractions. Count forward and backwards in appropriate decimals and percentages. Use apparatus and knowledge of value to add decimals, i.e. 3.8 + 2.5 = 5 + 1.3 Reorder increasingly complex calculations, i.e. 1.7 + 2.8 + 0.3 = 1.7 + 0.3 + 2.8 Compensating – i.e. 405 + 399 → add 400 and then subtract 1. Continue to practice previous stage and make links between known facts and addition pairs for fractions, percentages and decimals Doubles and halves of decimals, i.e. half of 5.6, double 3.4. Sums and differences of decimals, i.e. 6.5 + 2.7 Expanded vertical method, leading to columnar addition: Teachers model a column method that records and explains partial mental methods. remains an emphasis on the language of calculation, e.g. ‘Forty plus seventy equals and ten.’… ‘Seven add six equals thirteen.’ …before recombining numbers. Teachers also model the language of: ‘Four tens add seven tens total eleven tens or 110.’ Teachers similarly advance to the addition of two 3-digit numbers with the expectation that as children’s knowledge of place value is secured, they become ready to approach a formal compact method. Informal columnar: Adding the tens first: Adding the ones first: