Tag: factorisation

(In keeping with our culturally sensitive ways, the title should be read with a thick Mexican accent.)

We’re working on a non-WitCHlike Crash post, but no way will that be done tonight. Luckily, frequent commenter Glen has flagged some easily postable nonsense, and we can keep the Crash ball rolling.

This A-Crash consists of a Content-Elaboration combo for Year 6 Number:

CONTENT

identify and describe the properties of prime and composite numbers and use to solve problems and simplify calculations

ELABORATIONS

understanding that a prime number has two unique factors of one and itself and hence 1 is not a prime number

testing numbers by using division to distinguish between prime and composite numbers, recording the results on a number chart to identify any patterns

representing composite numbers as a product of their factors including prime factors when necessary and using this form to simplify calculations involving multiplication such as  as which can be rearranged to simplify calculation to

using spread sheets to list all of the numbers that have up to three factors using combinations of only the first three prime numbers, recognise any emerging patterns, making conjectures and experimenting with other combinations

understanding that if a number is divisible by a composite number then it is also divisible by the prime factors of that number, for example, 216 is divisible by 8 because the number represented by the last three digits is divisible by 8, and hence 216 is also divisible by 2 and 4, using this to generate algorithms to explore

 

UPDATE (25/05/21)

Thanks, everyone, so far. We’re going nuts with work, so a quick WitCHlike update while the window is open.

0) How can ACARA be so, so, so appallingly bad with their grammar and punctuation? We honestly don’t get it. Is the content descriptor accidentally missing a pronoun, and a comma, and a preposition, or do they genuinely like how it reads?

1) Yes, the free-floating and otherwise irritating “hence”, the fact that “prime” is undefined is appalling. So is using “1” and “one” in the same sentence to refer to the same thing. So is “two unique factors of one and itself and …”.

2) Possibly John’s guess on the second elaboration is correct. What would be focussed and useful is to take a 12 x 12 table of numbers and cross off the multiples (and circle 1). So, you get the kids to do the sieve of Eratosthenes thing, and emphasise the multiples as composites. You know, a clearly expressed investigation, with clear purposes.

3) This is Year 6, and so we’re not so concerned about “Fundamental theorem of arithmetic” not being mentioned here, although of course both existence and uniqueness of the prime factorisation should have been spelled out, even if only as something to “explore”. It’s way too important to be included as just a “by the way” part of a multiplication trick. As a side point, in regard to our previous Crash post, it is notable when and how “Fundamental theorem” first appears.

4) 15 x 16? Really?

5) We’re guessing the spread sheeet activity was intended to mean using each prime at most once. Given these people can’t write, however, it’s only a guess. But if so, that would be a reasonable exercise, IF you ditched the spread sheeet, and IF you repeated the exercise a few times with varying selections of primes. None of which will happen.

6) It is unbelievably stupid to introduce prime stuff in combination with divisibility tricks. The former is, well, fundamental, and the latter is a base ten game.

7) “The number represented by the last three digits”. Of what? Who talks this way? Who talks this way and expects to be understood?

8) What are the other digits of 216?

9) Even if there were other digits, a number ending in 216 is a really stupid choice to demonstrate divisibility by 8. These things matter.