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Grade Ladder – Number
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-√3in 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