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1 Numbers and the number system

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  1. 1.1 Integers

    1. 1.1.AIntegers

      understand and use integers (positive, negative and zero)

    2. 1.1.BPlace value

      understand place value

    3. 1.1.CDirected numbers in practical situations

      use directed numbers in practical situations e.g. temperatures

    4. 1.1.DOrder integers

      order integers

    5. 1.1.EThe four rules of addition, subtraction, multiplication

      use the four rules of addition, subtraction, multiplication and division

    6. 1.1.FBrackets and the hierarchy of operations

      use brackets and the hierarchy of operations

    7. 1.1.GOdd, even, primes, factors and multiples

      use the terms ‘odd’, ‘even’, ’prime numbers’, ‘factors’ and ‘multiples’

    8. 1.1.HPrime factors, common factors and common multiples

      identify prime factors, common factors and common multiples

  2. 1.2 Fractions

    1. 1.2.AEquivalent fractions and simplest form

      understand and use equivalent fractions, simplifying a fraction by cancelling common factors and expressing it in its simplest form (lowest terms)

    2. 1.2.BMixed numbers and vulgar fractions

      understand and use mixed numbers and vulgar fractions

    3. 1.2.CCommon denominators

      identify common denominators

    4. 1.2.DOrdering fractions and fractions of quantities

      order fractions and calculate a given fraction of a given quantity

    5. 1.2.EExpress a given number as a fraction of another number

      express a given number as a fraction of another number

    6. 1.2.FAdding and subtracting fractions

      use common denominators to add and subtract fractions and mixed numbers

    7. 1.2.GFractions, decimals and percentages

      convert a fraction to a decimal or a percentage

    8. 1.2.HUnit fractions as multiplicative inverses

      understand and use unit fractions as multiplicative inverses

    9. 1.2.IMultiplying and dividing fractions

      multiply and divide fractions and mixed numbers

  3. 1.3 Decimals

    1. 1.3.ADecimal notation

      use decimal notation

    2. 1.3.BPlace value

      understand place value

    3. 1.3.COrder decimals

      order decimals

    4. 1.3.DConverting terminating decimals

      convert a decimal to a fraction or a percentage Terminating decimals only

    5. 1.3.ETerminating decimals as fractions

      recognise that a terminating decimal is a fraction

    6. 1.3.HARecurring decimals as fractions

      convert recurring decimals into fractions

  4. 1.4 Powers and roots

    1. 1.4.ASquare numbers and cube numbers

      identify square numbers and cube numbers

    2. 1.4.BSquares, square roots, cubes and cube roots

      calculate squares, square roots, cubes and cube roots

    3. 1.4.CIndex notation and index laws

      use index notation and index laws for multiplication and division of positive and negative integer powers including zero

    4. 1.4.DPrime factor decomposition

      express integers as a product of powers of prime factors

    5. 1.4.EHighest common factors (HCF) and lowest common

      find highest common factors (HCF) and lowest common multiples (LCM)

    6. 1.4.HAMeaning of surds

      understand the meaning of surds

    7. 1.4.HBManipulating and rationalising surds

      manipulate surds, including rationalising a denominator

    8. 1.4.HCFractional and negative indices

      use index laws to simplify and evaluate numerical expressions involving integer, fractional and negative powers

  5. 1.5 Set language and notation

    1. 1.5.AThe definition of a set

      understand the definition of a set

    2. 1.5.BSet notation

      use the set notation ∪, ∩, ∈ and ∉, with E for the universal set and ∅ for the empty set

    3. 1.5.CUniversal and empty sets

      understand the concept of the universal set and the empty set and the symbols for these sets

    4. 1.5.DComplements of sets

      understand and use the complement of a set, using the notation A'

    5. 1.5.EVenn diagrams to represent sets

      use Venn diagrams to represent sets

    6. 1.5.HAAlgebraic sets and subsets

      understand sets defined in algebraic terms, and understand and use subsets; if A is a subset of B, use A ⊂ B

    7. 1.5.HBVenn diagrams and numbers of elements

      use Venn diagrams to represent sets and the number of elements in sets

    8. 1.5.HCThe notation n(A) for the number of elements in the set

      use the notation n(A) for the number of elements in the set A

    9. 1.5.HDSets in practical situations

      use sets in practical situations

  6. 1.6 Percentages

    1. 1.6.AMeaning of percentage

      Understand that a percentage is a number of parts per 100.

    2. 1.6.BExpress a given number as a percentage of another number

      express a given number as a percentage of another number

    3. 1.6.CExpress a percentage as a fraction and as a decimal

      express a percentage as a fraction and as a decimal

    4. 1.6.DPercentages as operators

      understand the multiplicative nature of percentages as operators

    5. 1.6.ESimple percentage problems

      solve simple percentage problems, including percentage increase and decrease

    6. 1.6.FReverse percentages

      use reverse percentages In a sale, prices were reduced by 30%. The sale price of an item was £17.50 Calculate the original price of the item

    7. 1.6.GCompound interest and depreciation

      use compound interest and depreciation

    8. 1.6.HARepeated percentage change

      use repeated percentage change Calculate the total percentage increase when an increase of 30% is followed by a decrease of 20%

    9. 1.6.HBCompound interest problems

      solve compound interest problems

  7. 1.7 Ratio and proportion

    1. 1.7.ARatio notation

      use ratio notation, including reduction to its simplest form and its various links to fraction notation Express in the form 1 : n

    2. 1.7.BDivide a quantity in a given ratio or ratios Share £416

      divide a quantity in a given ratio or ratios Share £416 in the ratio 5 : 3 or 4 : 3 : 1

    3. 1.7.CThe process of proportionality to evaluate unknown

      use the process of proportionality to evaluate unknown quantities

    4. 1.7.DMissing quantities in direct proportion

      Calculate an unknown quantity when quantities vary in direct proportion, including completing a value table.

    5. 1.7.EWord problems about ratio and proportion

      solve word problems about ratio and proportion Including maps and scale diagrams

  8. 1.8 Degree of accuracy

    1. 1.8.ARound integers to a given power of 10

      round integers to a given power of 10

    2. 1.8.BRounding to significant figures or decimal places

      round to a given number of significant figures or decimal places

    3. 1.8.CUpper and lower bounds

      identify upper and lower bounds where values are given to a degree of accuracy

    4. 1.8.DEstimating numerical calculations

      Use estimation, including rounding values to one significant figure, to evaluate numerical approximations.

    5. 1.8.HAUpper- and lower-bound problems

      Solve upper- and lower-bound problems when values are given to a stated degree of accuracy.

  9. 1.9 Standard form

    1. 1.9.AStandard form

      calculate with and interpret numbers in the form a × 10ⁿ, where n is an integer and 1 ≤ a < 10

    2. 1.9.HAProblems involving standard form

      solve problems involving standard form

  10. 1.10 Applying number

    1. 1.10.AApplying number in everyday life

      use and apply number in everyday personal, domestic or community life

    2. 1.10.BCalculations with metric units

      Carry out calculations using metric units of mass, length, area, volume and capacity.

    3. 1.10.CTime, money and currency calculations

      Carry out calculations with time and money, including currency conversion.

  11. 1.11 Electronic calculators

    1. 1.11.A

      Use a scientific electronic calculator to determine numerical results.