We should also be aware that if we multiply by a number less than 1, this would correspond to a scaling that reduces the size of the quantity. For example, scaling 3 by a factor of 0.5 would reduce it to 1.5, corresponding to 3 X 0.5 = 1.5. Grouping involving remainders Children move onto calculations involving remainders. 13 ÷ 4 = 3 r1 Or using a bead string see above. Commutativity Children learn that 3 x 5 has the same total as 5 x 3. Children learn that division is not commutative and link this to subtraction. This can also be shown on the number line. 3 x 5 = 15 5 x 3 = 15 Arrays Children learn to model a multiplication calculation using Children learn to model a division calculation using an array. an array. This model supports their understanding of This model supports their understanding of the development and the development of the grid in a of partitioning and the stop method’ in a written commutativity ‘bus written method. It also supports the finding of factors of a method. This model also connects division to finding fractions number. of discrete quantities. Inverse operations Trios can be used to model the 4 related multiplication This can also be supported using arrays: e.g. 3 X ? = 12 and division facts. Children learn to state the 4 related or 2 x ? = 24 or ? x 10 = 80 facts. 3 x 4 = 12 4 x 3 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 Children use symbols to represent unknown numbers and complete equations using inverse operations. They use this strategy to calculate the missing numbers in calculations. x 5 = 20 3 x = 18 O x = 32 ∆ 24 ÷ 2 = 15 ÷ O = 3 ÷ 10 = 8 ∆ Visual representations will be used to help children to understand and articulate what they are doing when multiplying and dividing using written methods. Arrays leading into the grid method Partitioning for division Children continue to use arrays and partitioning, where The array is also a flexible model for division of larger numbers appropriate, to prepare them for the grid method of 56 ÷ 8 = 7 multiplication. Arrays can be represented as ‘grids’ in a shorthand version
We should also be aware that if we multiply by a number less than 1, this would correspond to a scaling that reduces the size of the quantity. For example, scaling 3 by a factor of 0.5 would reduce it to 1.5, corresponding to 3 X 0.5 = 1.5. Grouping involving remainders Children move onto calculations involving remainders. 13 ÷ 4 = 3 r1 Or using a bead string see above. Commutativity Children learn that 3 x 5 has the same total as 5 x 3. This can also be shown on the number line. 3 x 5 = 15 5 x 3 = 15 Children learn that division is not commutative and link this to subtraction. Arrays Children learn to model a multiplication calculation using an array. This model supports their understanding of commutativity and the development of the grid in a written method. It also supports the finding of factors of a number. Children learn to model a division calculation using an array. This model supports their understanding of the development of partitioning and the ‘bus stop method’ in a written method. This model also connects division to finding fractions of discrete quantities. Inverse operations Trios can be used to model the 4 related multiplication and division facts. Children learn to state the 4 related facts. 3 x 4 = 12 4 x 3 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3 Children use symbols to represent unknown numbers and complete equations using inverse operations. They use this strategy to calculate the missing numbers in calculations. x 5 = 20 3 x ∆ = 18 O x = 32 24 ÷ 2 = 15 ÷ O = 3 ∆ ÷ 10 = 8 This can also be supported using arrays: e.g. 3 X ? = 12 or 2 x ? = 24 or ? x 10 = 80 Visual representations will be used to help children to understand and articulate what they are doing when multiplying and dividing using written methods. Arrays leading into the grid method Children continue to use arrays and partitioning, where appropriate, to prepare them for the grid method of multiplication. Arrays can be represented as ‘grids’ in a shorthand version Partitioning for division The array is also a flexible model for division of larger numbers 56 ÷ 8 = 7