8 Calculate the upper and lower bounds of 2-D 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 vice-versa Add and subtract in standard form Multiply and divide numbers in standard form Use percentages in real-life 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 real-life 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 three-digit by two-digit whole numbers Multiply decimals with one or two places by single-digit 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