TheMatheMagician.uk | Number Steps 1 ↠ 12 Scaffolding ↠ Mastery

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Below there are 206 Number Topics

Number is probably the most important area in GCSE Maths

This area underpins almost every other topic that you are going to study!

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  Step 01  

Number
Key Stage 2 - GCSE Basics
 

PLAYLIST

  • Round positive whole numbers to the nearest 10, 100 or 1000
  • Add, subtract multiply and divide integers - positive and negative
  • Use standard column procedures to add and subtract whole numbers
  • Know by heart multiplication facts up to 10 × 10
  • Use halving
  • Use doubling
  • Partition to multiply mentally TU × U
  • Find a difference by counting up through the next multiple of 10
  • Add three or more multiples of 10
  • Recognise multiples up to 10 × 10
  • Apply simple tests of divisibility (2, 9, 10, 5)
  • Know square numbers, 10 × 10, 1 × 1 to 5 × 5
  • Order positive and negative integers
  • Use diagrams to compare two or more simple fractions
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  Step 02  

Number
Key Stage 2 - GCSE Basics
 

PLAYLIST

  • Apply four operations in correct order to integers and proper fractions
  • Extend written methods to HTU × U
  • Understand addition and subtraction as they apply to whole numbers and decimals
  • Multiply and divide integers by 10 and 100, and explain the effect
  • Understand that halving is the reverse of doubling
  • Apply simple tests of divisibility (3, 6, 4, 25)
  • Know square numbers 6 × 6 to 9 × 9
  • Put digits in the correct place in a calculation
  • Know what each digit represents in numbers with up to two decimal places
  • Be able to use > or < correctly between two positive decimals. Decimals should be to 4 or 5 significant figures
  • Be able to order positive decimals with the largest on the left. Decimals should be to 4 or 5 significant figures
  • Be able to order positive decimals as a list with the smallest on the left. Decimals should be to 4 or 5 significant figures
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  Step 03  

Number
Key Stage 2 - GCSE Basics
 

PLAYLIST

  • Round decimals to the nearest whole number
  • Multiply and divide decimals by 10, 100, 1000, and explain the effect
  • Multiply by 0
  • Understand multiplication as it applies to whole numbers and decimals
  • Understand division as it applies to whole numbers and decimals
  • Extend written methods to HTU ÷ U
  • Use standard column procedures to add and subtract decimals with up to two places
  • Extend written methods to TU × TU
  • Know and use the order of operations
  • Quickly derive associated division facts
  • Check a result by working it backwards
  • Round numbers to decimal places
  • Recognise and use multiples and factors (divisors) and use simple tests of divisibility
  • Identify numbers with exactly 2 factors (primes)
  • Understand the difference between factor, multiple and prime numbers
  • Find all the factor pairs for any whole number without any support
  • Able to determine factors and multiples of numbers by listing
  • Understand the vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples.
  • Recognise that every number can be written as a product of two factors
  • Convert terminating decimals to fractions, e.g. 0.23 = 23/100
  • Recall known facts including fraction to decimal conversions
  • Extend mental methods of calculation to include percentages
  • Calculate simple percentages
  • Recognise the first few triangular numbers
  • Know square numbers beyond 10 × 10
  • Find roots of square numbers upto 100 (i.e. roots upto 10)
  • Compare decimals in different contexts
  • Understand and use decimal notation and place value
  • Approximate before carrying out an addition or subtraction
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  Step 04  

Number
Key Stage 3 - Pre GCSE
 

PLAYLIST

  • Round numbers to significant figures
  • Use symbols =, ≠, <, >, ≤, ≥
  • Multiply three-digit by two-digit whole numbers
  • Divide three-digit by two-digit whole numbers
  • Divide three-digit by two-digit whole numbers
  • Extend written methods to U.t × U
  • Multiply decimals with one or two places by single-digit whole numbers
  • Begin to add and subtract simple fractions and those with simple common denominators
  • Add and subtract positive integers from negative integers
  • Multiply and divide negative integers by a positive number
  • Add and subtract integers - positive and negative numbers
  • Multiply and divide negative integers by a negative number
  • Be able to subtract integers and decimal with up to two decimal places
  • Be able to add and subtract integers and decimal with varying numbers of decimal places
  • Be able to add and subtract more than two integers or decimals with up to two decimal places, but with varying numbers of significant figures and using a mixture of operation within the calculation
  • Use the order of operations with brackets, including in more complex calculations
  • Use inverse operations
  • Simplify fractions by cancelling all common factors
  • Be able to work with calculations where numbers are squared within a bracket
  • Know that the contents of brackets are evaluated first
  • Use conventional notation for priority of operations, including brackets and powers
  • Add and subtract decimals - positive and negative
  • Find common factors and primes
  • Recognise and use common factor, highest common factor and lowest common multiple
  • Find the prime factor decomposition of a number less than 100
  • Find the HCF or LCM of two numbers
  • Know the prime factorisation of numbers up to 30. They must give their answers as powers
  • Recognise two digit prime numbers
  • Calculate simple fractions of quantities and measurements (whole-number answers)
  • Extend the percentage calculation strategies with jottings to find any percentage, e.g. 17.5% by finding 10%, 5% and 2.5%, and adding
  • Use index notation for squares and cubes and for positive integer powers of 10 (e.g. write 27 as 3³ and 1000 as 10³)
  • Be able to order negative decimals with the smallest on the left. Decimals should be to 2 or 3 significant figures
  • Be able to order negative decimals with the largest on the left. Decimals should be to 2 or 3 significant figures
  • Be able to use > or < correctly between two negative decimals. Decimals should be to 2 or 3 significant figures
  • Order fractions, decimals and percentages
  • Make estimates and approximations of calculations - use a range of ways to find an approximate answer
  • Check a result by considering if it is of the right order of magnitude
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  Step 05  

Number
Key Stage 3 - Pre GCSE
 

PLAYLIST

  • Divide decimals with one or two places by single-digit whole numbers
  • Add and subtract simple fractions with denominators of any size
  • Multiply a fraction by an integer
  • Be able to multiply any number by 0.1 and 0.01
  • Be able to divide any number by 0.1 and 0.01
  • Understand the effect of multiplying by any integer power of 10
  • Understand the effect of dividing by any integer power of 10
  • Add and subtract negative integers from positive and negative numbers
  • Use mental strategies for multiplication - doubling and halving strategies
  • Use mental strategies for multiplication - partitioning two 2 digit numbers where one number includes a decimal (both numbers have two significant figures)
  • Use mental strategies for multiplication of decimals - doubling and halving strategies
  • Have strategies for calculating fractions and decimals of a given number
  • Add and subtract up to 3 fractions mixing both addition and subtraction into the calculation, with denominators less than or equal to 12 and using the LCM denominator in the calculation - the answer can be a mixed number
  • Add mixed number fractions without common denominators, where the fraction parts add up to more than 1
  • Multiply an integer by a fraction
  • Be able to work with calculations where the brackets are squared or square rooted
  • Be able to estimate answers to calculations involving 2 or more operations and BODMAS
  • Apply systematic listing strategies
  • Multipy and divide decimals - positive and negative
  • Find lowest common multiple by listing
  • Recognise rules relating to odd and even numbers
  • Understand the vocabulary of highest common factor, lowest common multiple
  • Use division to convert a fraction to a decimal
  • Convert a terminating decimal to a fraction and simplify the fraction
  • Work interchangeably with terminating decimals and their corresponding fractions ( such as 3.5 and 7/2 or 0.375 or 3/8)
  • Learn fractional equivalents to key recurring decimals e.g. 0.333333..., 0.66666666..., 0.11111... and by extension 0.222222...
  • Know the denominators of simple fractions that produce recurring decimals, and those that do not
  • Interpret percentage as the operator 'so many hundredths of'
  • Calculate fractions of quantities and measurements (fraction answers)
  • Give the positive and negative square root of a square number
  • Know all the squares of numbers less than 16 and be able to know the square root given the square number
  • Use index notation for small integer powers, e.g. 24 = 3 × 2³
  • Find and interpret roots of non square numbers using square root key
  • Extend mental calculations to squares and square roots
  • Extend mental calculations to cubes and cube roots
  • Be able to estimate square roots of non square numbers less than 100
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  Step 06  

Number
Key Stage 3 - Pre GCSE
 

PLAYLIST

  • Identify upper and lower bounds for rounding of discrete and continuous data
  • Identify the upper and lower bounds of a measurement
  • Recognise that measurements given to the nearest whole unit may be inaccurate by up to one half in either direction. Use error intervals.
  • Understand that each of the headings in the place value system, to the right of the tens column, can be written as a power of ten
  • Write numbers as a decimal number of millions or thousands, e.g. 23 600 000 as 23.6 million
  • Use knowledge of place value to calculate the product or division of two decimals where one or both are less than 1 and at least one has two digits other than zero.
  • Divide integers and decimals, including by decimals such as 0.6 and 0.06 (divisions related to 0.t × 0.t or 0.t × 0.0h, 0.0h × 0.t and 0.0h × 0.0h)
  • Use standard column procedures to add and subtract integers and decimals of any size, including a mixture of large and small numbers with different numbers of decimal places
  • Multiply and divide by decimals, dividing by transforming to division by an integer
  • Divide an integer by a fraction
  • Be able to simplify expressions containing powers to complete the calculation
  • Understand which part of an expression is raised to a power by knowing the difference between 3 × (7 + 8)² and 3² × (7 + 8) and (3 × (7 + 8))²
  • Recognise and use relationships between operations, including inverse operations
  • Calculate average speed, distance, time - in mph as well as metric measures
  • Convert between metric speed measures
  • Understand the effect of multiplying or dividing any number between 0 and 1
  • Multiply and divide simple fractions (proper and improper) - positive and negative
  • Add and subtract fractions (proper and improper) -positive and negative
  • Use halving and doubling strategies on fractions to find decimal equivalents of other fractions, e.g. 1/4 = 0.25 so 1/8 is half of 0.25 etc. Original fact is given
  • Convert a fraction to a decimal to make a calculation easier
  • Be able to find square roots by factorising, e.g. square root of 324 is square root of 4 × 81 which is 18. 324 = 4 × 81 should be given
  • Be able to find cube roots by factorising, e.g. cube root of 216 is cube root of 8 × 27 which is 6. 216 = 8 × 27 should be given to them
  • Mentally be able to calculate the squares of numbers less than 16 multiplied by a multiple of ten, e.g. 0.2, 300, 0.400
  • Combine laws of arithmetic for brackets with mental calculations of squares, e.g. (23 − 13 + 4 − 8)²
  • Combine laws of arithmetic for brackets with mental calculations of cubes, e.g. (23 − 13 + 4 − 8)³
  • Combine laws of arithmetic for brackets with mental calculations of square roots, e.g. √(45 + 36)
  • Combine laws of arithmetic for brackets with mental calculations of cube roots, e.g. ³√(89 + 36)
  • Be able to use mental strategies to solve word problems set in context using square roots and cube roots mentally
  • Establish index laws for positive powers where the answer is a positive power
  • Extend the patterns by using the index law for division established for positive power answers, to show that any number to the power of zero is 1
  • Use an extended range of calculator functions, including +, -, x, , x², √x, memory, xy, x1/y, brackets
  • Order fractions by converting them to decimals or otherwise
  • Use one calculation to find the answer to another
  • Express a multiplicative relationship between two quantities as a ratio or a fraction
  • Use numbers of any size rounded to 1 significant figure to make standardized estimates for calculations with one step
  • Know there are different ways of finding an approximate answer
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  Step 07  

Number
KS4 - Foundation GCSE
 

PLAYLIST

  • Understand that each of the headings in the place value system, to the left of the units column, can be written as a power of ten
  • Multiply both sides of an inequality by a negative number
  • To understand the difference between squaring a negative number and subtracting a squared number within a more complex calculation
  • Find the reciprocal of simple numbers/fractions mentally, e.g. 10 and 1/10, 1/3 and 3 etc.
  • Understand the order in which to calculate expressions that contain powers and brackets in both the numerator and denominator of a fraction
  • Know that a number multiplied by its reciprocal is 1
  • Know that the reciprocal of a reciprocal is the original number
  • Use conventional notation for priority of operations, including roots and reciprocals
  • Understand and use compound measures: density; pressure; speed
  • Round numbers and measures to an appropriate degree of accuracy (dp or sig fig)
  • Find HCF and LCM using Prime Factors
  • Use prime factorisation to represent a number as a product of its primes using index notation
  • Recognise that prime factor decomposition of a positive integer is unique
  • Add and subtract fractions (mixed) - positive and negative
  • Use the square, cube and power keys on a calculator
  • Use the index laws to include negative power answers and understand that these answers are smaller than 1
  • Use the laws of indices to multiply and divide numbers written in index notation
  • Convert between currencies
  • Estimate answers to calculations by rounding numbers to 1 sig fig
  • Check reasonableness of answers
  • Estimate answers to one-step or two-step calculations
  • Write numbers greater than 10 in standard index form
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  Step 08  

Number
KS4 - Foundation GCSE
 

PLAYLIST

  • Multiply and divide simple fractions (mixed) - positive and negative
  • Calculate with roots (surds - exact values)
  • Write numbers less than 10 in standard index form
  • Order numbers written in standard index form
  • Convert between large and small numbers into standard form and vice-versa
  • Add and subtract in standard form
  • Multiply and divide numbers in standard form
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  Step 09  

Number
KS4 - Foundation GCSE
 

PLAYLIST

  • Use inequality notation to specify simple error intervals due to truncation or rounding
  • Estimate powers and roots of any given positive number
  • Recall that n⁰ = 1 and n⁻¹ = 1/n for positive integers n as well as n½ = √n and n⅓ = ³√n for any positive number n (Note: n½ is n to the power ½ and n⅓ is n to the power ⅓)
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  Step 10  

Number
Key Stage 4 - Higher GCSE
 

PLAYLIST

  • Use the product rule for counting (i.e. if there are m ways of doing one task and for each of these, there are n ways of doing another task, then the total number of ways the two tasks can be done is m × n ways)
  • 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
  • Understand that the inverse operation of raising a positive number to a power n is raising the result of this operation to the power 1/n
  • Simplify surd expressions involving squares ( e.g. √12 =√ (4 × 3) = 2 √3)
  • Use fractions, surds and pi in exact calculations, without a calculator
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  Step 11  

Number
Key Stage 4 - Higher GCSE
 

PLAYLIST

  • 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
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  Step 12  

Number
Key Stage 4 - Higher GCSE
 

PLAYLIST

  • Topic does not reach Step 12

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