1 Numbers and the number system
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1.1 Integers
1.1.AIntegers
understand and use integers (positive, negative and zero)
1.1.BPlace value
understand place value
1.1.CDirected numbers in practical situations
use directed numbers in practical situations e.g. temperatures
1.1.DOrder integers
order integers
1.1.EThe four rules of addition, subtraction, multiplication
use the four rules of addition, subtraction, multiplication and division
1.1.FBrackets and the hierarchy of operations
use brackets and the hierarchy of operations
1.1.GOdd, even, primes, factors and multiples
use the terms ‘odd’, ‘even’, ’prime numbers’, ‘factors’ and ‘multiples’
1.1.HPrime factors, common factors and common multiples
identify prime factors, common factors and common multiples
1.2 Fractions
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)
1.2.BMixed numbers and vulgar fractions
understand and use mixed numbers and vulgar fractions
1.2.CCommon denominators
identify common denominators
1.2.DOrdering fractions and fractions of quantities
order fractions and calculate a given fraction of a given quantity
1.2.EExpress a given number as a fraction of another number
express a given number as a fraction of another number
1.2.FAdding and subtracting fractions
use common denominators to add and subtract fractions and mixed numbers
1.2.GFractions, decimals and percentages
convert a fraction to a decimal or a percentage
1.2.HUnit fractions as multiplicative inverses
understand and use unit fractions as multiplicative inverses
1.2.IMultiplying and dividing fractions
multiply and divide fractions and mixed numbers
1.3 Decimals
1.3.ADecimal notation
use decimal notation
1.3.BPlace value
understand place value
1.3.COrder decimals
order decimals
1.3.DConverting terminating decimals
convert a decimal to a fraction or a percentage Terminating decimals only
1.3.ETerminating decimals as fractions
recognise that a terminating decimal is a fraction
1.4 Powers and roots
1.4.ASquare numbers and cube numbers
identify square numbers and cube numbers
1.4.BSquares, square roots, cubes and cube roots
calculate squares, square roots, cubes and cube roots
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
1.4.DPrime factor decomposition
express integers as a product of powers of prime factors
1.4.EHighest common factors (HCF) and lowest common
find highest common factors (HCF) and lowest common multiples (LCM)
1.5 Set language and notation
1.5.AThe definition of a set
understand the definition of a set
1.5.BSet notation
use the set notation ∪, ∩, ∈ and ∉, with E for the universal set and ∅ for the empty set
1.5.CUniversal and empty sets
understand the concept of the universal set and the empty set and the symbols for these sets
1.5.DComplements of sets
understand and use the complement of a set, using the notation A'
1.5.EVenn diagrams to represent sets
use Venn diagrams to represent sets
1.6 Percentages
1.6.AMeaning of percentage
Understand that a percentage is a number of parts per 100.
1.6.BExpress a given number as a percentage of another number
express a given number as a percentage of another number
1.6.CExpress a percentage as a fraction and as a decimal
express a percentage as a fraction and as a decimal
1.6.DPercentages as operators
understand the multiplicative nature of percentages as operators
1.6.ESimple percentage problems
solve simple percentage problems, including percentage increase and decrease
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
1.6.GCompound interest and depreciation
use compound interest and depreciation
1.7 Ratio and proportion
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
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
1.7.CThe process of proportionality to evaluate unknown
use the process of proportionality to evaluate unknown quantities
1.7.DMissing quantities in direct proportion
Calculate an unknown quantity when quantities vary in direct proportion, including completing a value table.
1.7.EWord problems about ratio and proportion
solve word problems about ratio and proportion Including maps and scale diagrams
1.8 Degree of accuracy
1.8.ARound integers to a given power of 10
round integers to a given power of 10
1.8.BRounding to significant figures or decimal places
round to a given number of significant figures or decimal places
1.8.CUpper and lower bounds
identify upper and lower bounds where values are given to a degree of accuracy
1.8.DEstimating numerical calculations
Use estimation, including rounding values to one significant figure, to evaluate numerical approximations.
1.9 Standard form
1.9.A
calculate with and interpret numbers in the form a × 10ⁿ, where n is an integer and 1 ≤ a < 10
1.10 Applying number
1.10.AApplying number in everyday life
use and apply number in everyday personal, domestic or community life
1.10.BCalculations with metric units
Carry out calculations using metric units of mass, length, area, volume and capacity.
1.10.CTime, money and currency calculations
Carry out calculations with time and money, including currency conversion.
1.11 Electronic calculators
1.11.A
Use a scientific electronic calculator to determine numerical results.