1. Factors, multiples, primes and powers
[ N2.1 Core Plenary]
Investigate the truth of one or more of these claims. Don’t forget to support any conclusions you reach.
Preamble
Five number investigations based on factors, powers and prime numbers. Depending on the time available, including homework perhaps, children may be able to attempt most of these. However it is important that time is available for them to present their findings to the whole class – this may kindle some useful discussion. Depending on conditions it might be worthwhile to consider proof and counter-example in an informal manner.
Possible content
Using prior knowledge of primes, factors and powers in an investigative context.
Resources
None.
Solution/Notes
All prime numbers apart from 2 and 5 end in 1, 3, 7 or 9. Even numbers are divisible by 2, and numbers ending in 5 or 0 are divisible by 5, leaving just 1, 3, 7 or 9.
For a number between zero and one, cube roots are larger than square roots.
Taking 1 from a multiple of 6 does produce some prime numbers, but not always, e.g. 36 – 1 = 35.
Having its final digit “sticking” on itself for whole number powers is not unique to 6, it is also true for powers of 5 (and also, one could make the case, for 1!).
Whole numbers are not always the sum of two primes – for example: 27, 35, 51, etc.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010