(a) Understand key terms such as perfect square, integer, positive integer, non-negative integers.
(b) Prime factorise a number and use to find the LCM, HCF of two numbers. Understand when numbers are 'coprime'.
(c) Know the divisibility laws from 3 to 11 and be able to break down into multiple divisibility rules for larger numbers. Use these rules to mentally prime factorise numbers rapidly and have a sense if a number is prime. (d) Find factors of a number using its prime factorisation (e.g. is 20 a factor of 24 x 3 x 53?) and determine the number of factors of a number.
Extension: (i) Reason about divisibility on each side of an equation and of terms, and find integer solutions to linear equations (i.e. linear Diophantine equations).
(ii) Further uses of prime factorisations: (1) Squares and cubes (2) Trailing zeroes.
A series of posters on teaching methods I don't like, including details of the original method, my pedagogical complaints, and my preferred method.