Grade Descriptors - Number
Integers, Decimals, Powers, Indices and Surds

Read, write and order integers up to and including 4 digit numbers

Order, add and substract positive and negative integers within context

Round whole numbers to the nearest 1000

Use the symbols < and >

Be able to use mental methods to find remainders after division

Be able to use mental methods to add and subtract integers

Use written methods to multiply and divide upto three-digit numbers by a single-digit
number
Grade 1

Multiply and divide whole numbers by powers of 10
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Be aware of using the orders of operation

Understand and use inverse operations

Identify square numbers up to 102

By inspection, recognise odd and even numbers

Know the definition of a prime number and be able to list the first 10 prime numbers

Know the definition of multiples and be able to recognise multiples

Identify factors of 2-digit numbers
Fractions and Decimals

Use vocabulary associated with fractions such as numerator and denominator

Recognise simple fractions when illustrated on a shape

Write fractions to describe shaded parts of a shape or diagram

Use diagrams to find equivalent fractions

Use diagrams to compare fractions

Convert simple fractions into decimals (such as tengths and hundredths)

Recognise when fractions are equivalent

Be able to recognise descriptions of fractions and write down the corresponding fractions
(eg. write down the fraction "three quarters")
Grade 2

Find equivalent fractions through simplification

Find equivalent decimals

Calculate simple fractions of quantities

Be able to use written methods to add and subtract decimals with common denominators

Be able to convert simple metric units into imperial units
Integers, Decimals, Powers, Indices and Surds
Grade Descriptors - Number

Understand positive and negative numbers as positions on a number line

Be able to order, add and subtract positive and negative integers within context

Round whole numbers to the nearest 10, 100 or 1000

Round decimal numbers to one decimal place or nearest whole number

Multiply and divide 3-digit numbers by 2-digit integers

Be aware of and use the order of operators including simple brackets

Use inverse operations in the context of integers

Multiply any integer or decimal by powers of 10

Understand use decimal notation and place value

Identify square numbers up to 122

Identify square roots up to 122

Be able to proficiently use a calculator to find square roots

Be able to calculate and identify highest commfon factors and lowest common multiples in
simple scenarios
Fractions and Decimals

Multiply and divide decimals with up to two places by single-digit whole numbers

Understand the concepts of place value

Add and subtract simple fractions (up to those where there is an obvious calculation to
make the denominators the same)

Express one number as a fraction of another, including having to give their answer in it's
simplest form

Multiply fractions by integers

Convert between metric units (eg. grams to kilograms)
Integers, Decimals, Powers, Indices and Surds

Be able to round to 2 decimal places when required

Round positive numbers to the power of 10 and decimals to the nearest integer

Add and subtract integers of any size using simple written notation

Use and apply the order of operations to more complex situations (including the use of
multiple brackets)
Grade 3

Multiply and divide integers and decimals by 0.1 and 0.01

Be able to use positive and negative square roots, cube and cube roots

Use index notation for small positive integer powers

Be able to find prime factors of a number (prime factor decomposition)
Fractions and Decimals
Grade Descriptors - Number

Be able to add and subtract any decimal numbers (including those with differing amounts
of decimal places)

Be able to recognise and convert between mixed numbers and improper fractions

Comfortably multiply integers by fractions (including those where they must convert from
a mixed number prior)

Be able to use a calculate the enter fractions and use it to carry out simple calculations
involving fractions

Use written division methods to convert a fraction to a decimal

Recognise recurring decimals can be illustrated as fractions (not required to be able to
convert from recurring decimals to fractions at this point)

Order fractions in ascending and descending order, including those which have different
denominators

Order decimals in ascending and descending order, including those which have a differing
number of decimal places

Use inequality signs to show comparisons between two fractions, two decimals, and one
fraction and one decimal

Convert a fraction to a decimal to make calculations easier

Convert recurring decimals to fractions

Be aware that rounding during intermediate calculations can significantly affect the
accuracy of an answer

Know that division is multiplicative inverse
Integers, Decimals, Powers, Indices and Surds

Use and understand the order of operations including powers

Use rounding to provide estimates to an answer

Use rounding to give solutions to an appropriate degree of accuracy, even if not
specifically requested
Grade 4

Be able to round decimals to any given accuracy

Recognise equivalences between 0.1, 1/10 and 10-1

Recall from memory the cubes of 1,2,3,4,5 and 10.

Use index notation for integer powers

Know and use the simple index laws for multiplication and division of positive integer
powers

Recognise the index law when numbers are raised to the power of zero

As well as being able to prime factors of a number, be able to write answers using index
notation

Be able to find the lowest common multiple (LCM) and highest common factor (HCF) using
Grade Descriptors - Number
Venn Diagrams and Prime Factors

Convert any numbers in standard form

Convert out of standard form

Add, subtract, multiply and divide numbers that are written in standard form

Be able to enter and use a calculator when working with standard form
Fractions and Decimals

Be able to divide by decimals by converting to division by an integer (eg. 6 ÷ 0.2 is the
equivalent to 60 ÷ 2)

Add and subtract any mixed fractions

Divide mixed numbers by whole numbers

Multiply mixed number fractions

Understand the term reciprocal and be able to find reciprocals of any integer, decimal or
fraction

Know that any (non-zero) number multiplied by it's reciprocal with give an answer of 1

Multiply mixed number fractions

Apply the concepts of pie charts and knowing that each sector on a pie chart is equivalent
to a fraction of an amount

Divide a fraction by a fraction

Be able to convert simple recurring fractions into decimals using the division method
(such as 1/3 or 3/7)
Integers, Decimals, Powers, Indices and Surds

Use index notation including the use of negative powers

Be able to estimate the answer to square roots and cube roots (for example, the square
root of 70 must lie between 8 and 9)
Grade 5

Be confident simplifying fractional and negative powers by referring to relevant index laws

Find the LCM and HCF of a number when given the prime factorisation of each number
Fractions and Decimals

Be able to write down the upper and lower bounds of a number to a given degree of
accuracy.

Use upper and lower bounds in calculations

Comfortably be able to round to given decimal places or significant figures, including
applying bounds

Grade 6
Estimate answers to one and two step calculations with the use of rounding numbers
Integers, Decimals, Powers, Indices and Surds
Grade Descriptors - Number

Recall index factors such as n0, fractional powers (integers to the power of a half and a
third)

Understand the definition of a surd

Be able to work with surd notation and be able to simplify surds into their simplest form

Decompose surds into their simplest form, for example √12 = 2√3

Be able to multiply simple surds, for example √16 × √4 = 8
Fractions and Decimals

Convert a fraction to a recurring decimal

Convert a recurring decimal to a fraction
Integers, Decimals, Powers, Indices and Surds

Solve complex problems using index laws

Without the use of a calculator, find the value of problems involving positive, fractional
and negative indices
Grade 7

Rationalise simple fractions with a surd in the denominator (eg. 3 / √3)
Fractions and Decimals

Be able to write the denominator in terms of its prime factors, figure out if a fraction can
be converted to a recurring or absolute decimal.

Use upper and lower bounds in calculations such as area, perimeter and within fractions
where the a combination of bounds may be required
Integers, Decimals, Powers, Indices and Surds
Grade 8-9

Understand the definition of a rational and irrational number

Use rational and irrational numbers in context

Use surds in complex calculations, including
o
Simplifying large surds
o
Rationalise more complex denominators eg. 1/(2 + √3)