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Key Stage 3 - Number

Understand and use place value for decimals, measures and integers of any size

<Place value and multiplying and dividing by powers of ten>

Order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, ≠, <, >, ≤, ≥

<Putting numbers into rank order>

Use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

<Finding the HCM and LCM>

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

<Add and subtract decimals>   <Multiply decimals>   <Divide decimals>   <Finding a fraction of a number>

<Multiplication of a 3 digit by a 2 digit number>   <Division of a 3 digit by a 2 digit number>  

<Convert between improper fraction and mixed numbers>   

<Add and subtract fractions using a fractions wall>   <Add and subtract fractions>

<Add and subtract mixed numbers>   <Multiply fractions and mixed numbers>   

<Divide fractions and mixed numbers>

Use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

<Bracketand order of operations>

Recognise and use relationships between operations including inverse operations

<Checking with inverse>

Use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

Interpret and compare numbers in standard form A x 10n 1≤A<10, where n is a positive or negative integer or 0

Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and or 0.375 and )

<Change fractions into decimals>   <Change decimals into fractions>   

Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%

<Find a percentage of a number without a calculator>    <Find a percentage of a number>

<Finding on quantity as a percentage of another>

Interpret fractions and percentages as operators

<Simplify fractions>    <Change percentages into fractions>

<Convert between percentages into decimals>

Use standard units of mass, length, time, money and other measures, including with decimal quantities

Round numbers and measures to an appropriate degree of accuracy [for example, to a number of decimal places or significant figures]

<Trial and improvement>

Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b

<Approximations>

Use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Appreciate the infinite nature of the sets of integers, real and rational numbers


The National Curriculum KS3 requirements are shown below in blue text. Underneath each of these requirements work helping to address ideas involved can be viewed by clicking on the bold underlined titles.