8 
 Calculate the upper and lower bounds of 2D measurements e.g. area
 Calculate the upper and lower bounds of other compound measurements e.g. density
 Write (3√3)² in the form a+b√3
 Rationalise a denominator

7 
 Use the product rule for counting
 Convert a recurring decimal to a fraction in simple cases
 Understand a recurring decimal to fraction proof
 Find the value of calculations using indices including fractional and negative indices
 Simplify surd expressions
 Use fractions, surds and pi in exact calculations, without a calculator

6 
 Use inequality notation to specify simple error intervals due to truncation or rounding
 Estimate powers and roots of any given positive number
 Know that n^□(64&1/2)=√n and n^□(64&1/3)=√(3&n)

5 
 Calculate with roots
 Write numbers less than 10 in standard form
 Order numbers written in standard form
 Convert large and small numbers into standard form and viceversa
 Add and subtract in standard form
 Multiply and divide numbers in standard form
 Use percentages in reallife situations: compound interest, depreciation, percentage profit and loss
 Calculate repeated proportional change
 Use calculators for reverse percentage calculations by doing an appropriate division

4 
 Find the reciprocal of simple numbers and fractions
 Use the correct order of operations for expressions with powers and brackets in both the numerator and denominator of a fraction
 Understand and use compound measures: density, pressure and speed
 Round numbers and measures to an appropriate degree of accuracy (dp or sf)
 Find HCF and LCM using Prime Factors
 Use prime factorisation to represent a number as a product of its primes using index notation
 Use the square, cube and power keys on a calculator
 Know the index law for negative powers
 Convert between currencies
 Write numbers greater than 10 in standard form
 Write lengths, areas and volumes of two shapes as ratios in simplest form
 Estimate conversions
 Use compound interest
 Represent repeated proportional change using a multiplier raised to a power
 Find the original amount in a reverse percentage problem

3 
 Identify upper and lower bounds
 Multiply or divide two decimals
 Divide an integer by a fraction
 Multiply and divide fractions and mixed numbers
 Simplify expressions containing powers
 Know the index laws for multiplication and division
 Know that any number to the power of zero is 1
 Calculate average speed, distance and time
 Convert between metric speed measures
 Understand the effect of multiplying or dividing by any number between 0 and 1
 Order fractions by converting them to decimals or otherwise
 Use one calculation to find the answer to another
 Estimate answers to simple calculations by rounding numbers to 1 significant figure
 Interpret a calculator display using standard form
 Compare ratios by changing them to the form 1 : m or m : 1
 Solve a ratio problem in context
 Write as ratio as a fraction
 Set up equations to show direct proportion and use expressions of the form y α x
 Identify direct proportion from a graph
 Use percentages in reallife situations: VAT, value of profit or loss, simple interest

2 
 Add and subtract fractions and mixed numbers with denominators of any size
 Multiply a fraction by an integer
 Be able to multiply and divide any number by 0.1 and 0.01
 Find fractions and decimals of a given number
 Apply systematic listing strategies
 Multiply and divide decimals – positive and negative
 Convert a fraction to a decimal
 Give the positive and negative square root of a square number
 Know square numbers up to 162 and know how to find roots up to √256
 Find roots of non square numbers using square root key
 Estimate square roots of non square numbers less than 100
 Know the cubes of 2, 3, 4, 5 and 10
 Compare proportions using equivalent fractions, decimals and percentages
 Use the unitary method to solve problems involving ratio and direct proportion
 Divide a quantity into more than two parts in a given ratio
 Convert one metric unit to another
 Use a ratio to find one quantity when the other is known
 Find the outcome of a given percentage increase or decrease using multipliers
 Simplify a ratio expressed in different units

1 
 Round numbers to significant figures
 Use symbols = , ≠, <, >, ≤, ≥
 Multiply and divide threedigit by twodigit whole numbers
 Multiply decimals with one or two places by singledigit whole numbers
 Add and subtract fractions with common denominators
 Add, subtract, multiply and divide with negative numbers
 Add and subtract with decimals
 Use the correct order of operations for more complex calculations
 Use inverse operations
 Simplify fractions
 Find highest common factors and lowest common multiples
 Find the prime factor decomposition of a number less than 100
 Recognise two digit prime numbers
 Calculate simple fractions of quantities
 Find any percentage of an amount (including using multipliers)
 Use index notation for squares and cubes and for positive integer powers of 10
 Order fractions, decimals, percentages and negative numbers
 Make estimates and approximations of calculations
 Divide a quantity in a given ratio
 Simplify a ratio
 Express one number as a fraction of another
 Recall equivalent fractions, decimals and percentages
 Express one given number as a percentage of another

W3 
 Round decimals to the nearest whole number
 Multiply and divide decimals by 10, 100, 1000
 Multiply by 0
 Extend written division methods to HTU ÷ U
 Use the column method to add and subtract decimals
 Be able to multiply TU × TU using a written method
 Check a result by working it backwards
 Round numbers to decimal places
 Be able to find multiples and factors
 Identify prime numbers
 Convert decimals to fractions
 Know common fraction to decimal conversions
 Calculate simple percentages
 Recognise the first few triangular numbers
 Know square numbers beyond 10 × 10
 Find roots of square numbers up to 100
 Use fraction notation to describe parts of shapes

W2 
 Understand that halving is the reverse of doubling
 Multiply and divide integers by 10 and 100
 Add and subtract with decimals
 Be able to multiply HTU × U using a written method
 Use the correct order of operations
 Know square numbers 6 × 6 to 9 × 9
 Be able to order positive decimals
 Be able to use > or < correctly between two positive decimals
 Know what each digit represents in numbers with up to two decimal places

W1 
 Round positive whole numbers to the nearest 10, 100 or 1000
 Add three or more multiples of 10
 Partition to multiply mentally TU × U
 Use doubling and halving
 Know times tables up to 10 × 10
 Add and subtract using the column method
 Add, subtract multiply and divide with small numbers including negatives
 Know square numbers, 10 × 10, and 1 × 1 to 5 × 5
 Use diagrams to compare two or more simple fractions
 Order positive and negative integers
 Convert a percentage to a number of hundredths or tenths
