read, write, order and compare numbers up to 10,000,000 and determine the value of each digit
round any whole number to a required degree of accuracy
use negative numbers in context, and calculate intervals across 0
solve number and practical problems that involve all of the above
Pupils should be taught to:
multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
perform mental calculations, including with mixed operations and large numbers
identify common factors, common multiples and prime numbers
use their knowledge of the order of operations to carry out calculations involving the 4 operations
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
solve problems involving addition, subtraction, multiplication and division
use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
Pupils should be taught to:
use common factors to simplify fractions; use common multiples to express fractions in the same denomination
compare and order fractions, including fractions >1
add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, × = ]
divide proper fractions by whole numbers [for example, ÷ 2 = ]
associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, ]
identify the value of each digit in numbers given to 3 decimal places and multiply and divide numbers by 10, 100 and 1,000 giving answers up to 3 decimal places
multiply one-digit numbers with up to 2 decimal places by whole numbers
use written division methods in cases where the answer has up to 2 decimal places
solve problems which require answers to be rounded to specified degrees of accuracy
recall and use equivalences between simple fractions, decimals and percentages, including in different contexts
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