Mathematics overview: Stage 7
Unit  Hours  Mastery indicators  Essential knowledge 
Numbers and the number system  9  * Use positive integer powers and associated real roots * Apply the four operations with decimal numbers * Write a quantity as a fraction or percentage of another * Use multiplicative reasoning to interpret percentage change * Add, subtract, multiply and divide with fractions and mixed numbers * Check calculations using approximation, estimation or inverse operations * Simplify and manipulate expressions by collecting like terms * Simplify and manipulate expressions by multiplying a single term over a bracket * Substitute numbers into formulae ...view middle of the document...
g. 53 is read as ‘5 to the power of 3’ and means ‘3 lots of 5 multiplied together’Radical notation: e.g. √49 is generally read as ‘the square root of 49’ and means ‘the positive square root of 49’; 3√8 means ‘the cube root of 8’  Pupils need to know how to use a scientific calculator to work out powers and roots.Note that while the square root symbol (√) refers to the positive square root of a number, every positive number has a negative square root too.NCETM: Departmental workshop: Index NumbersNCETM: GlossaryCommon approachesThe following definition of a prime number should be used in order to minimise confusion about 1: A prime number is a number with exactly two factors.Every classroom has a set of number classification posters on the wall 
Reasoning opportunities and probing questions  Suggested activities  Possible misconceptions 
* When using Eratosthenes sieve to identify prime numbers, why is there no need to go further than the multiples of 7? If this method was extended to test prime numbers up to 200, how far would you need to go? Convince me. * Kenny says ’20 is a square number because 102 = 20’. Explain why Kenny is wrong. Kenny is partially correct. How could he change his statement so that it is fully correct? * Always / Sometimes / Never: the lowest common multiple of two numbers is found by multiplying the two numbers together  KM: Exploring primes activities: Factors of square numbers; Mersenne primes; LCM sequence; n² and (n + 1)²; n² and n² + n; n² + 1; n! + 1; n! – 1; x2 + x +41KM: Use the method of Eratosthenes' sieve to identify prime numbers, but on a grid 6 across by 17 down instead. What do you notice?KM: Square number puzzleKM: History and Culture: Goldbach’s ConjecturesNRICH: Factors and multiplesNRICH: Powers and rootsLearning reviewwww.diagnosticquestions.com  * Many pupils believe that 1 is a prime number – a misconception which can arise if the definition is taken as ‘a number which is divisible by itself and 1’ * A common misconception is to believe that 53 = 5 × 3 = 15 * See pedagogical note about the square root symbol too 
Counting and comparing  4 hours 
Key concepts  The Big Picture: Number and Place Value progression map 
* order positive and negative integers, decimals and fractions * use the symbols =, ≠, <, >, ≤, ≥ 

Possible learning intentions  Possible success criteria 
* Compare numbers * Order numbers  * Place a set of negative numbers in order * Place a set of mixed positive and negative numbers in order * Identify a common denominator that can be used to order a set of fractions * Order fractions where the denominators are not multiples of each other * Order a set of numbers including a mixture of fractions, decimals and negative numbers * Use inequality symbols to compare numbers * Make correct use of the symbols = and ≠ 
Prerequisites  Mathematical language  Pedagogical notes 
* Understand that...