Any maths teachers around?

[Verycold]

Please can you give me your thoughts on this hw questions:

Can every cube of a number be written as the difference of two square numbers?

How many different ways can you make a sum that is equal to 20?

Are they for the same group? The cubes being difference of two squares is something I'd give to a set 1/2. The sum to twenty is something is give to a low ability set.

What year would you say?

Well the cubes one either top sets in. Ks3 or middle sets in ks4.

The sum to twenty, assuming the use of sum to mean add. Middle/ bottom sets ks3 and bottom sets ks4.

Although of course all schools (and children) are different.

Am I massively missing something here? Sums to twenty is something my year 1 did last year.

(not a maths teacher, just a parent, tiptoes out of thread before I get caught in the wrong place)

I agree that sums to twenty is easy. However, very low ability children will still find this a challenge even in year 11.

The sum to 20 thing is about a systematic way to describe how many solutions there are

Should a year 7 be able to do
It?

.

Sum to 20 I think most children over the age of 7 could do? I am a maths teacher!
Investigating cube numbers is a top set year 9/10 kind of question!

If it's find every sum to 20 in a systematic way, then both of the questions are fairly challenging, and I wouldn't expect a year 7 to do them, unless in a high flying top set and with a lot of prep for it in class

If your year 7 had this as a hw, with no preparation, what would you do?

Because I'm at a loss!

For the cube number question, I would get your dc to write down the 1st 20 square numbers and find some differences and see if any are cube numbers (also list some cube numbers). To answer the question, they just need to find a cube number that can't be found and why.

For the sum to 20, it can be as easy or complicated as they want to make it. The question does not state how many numbers need to make up the sum, so theoretically you could have 1+1+1+1+.....+1=20.

Actually as a maths teacher, I thinks it's an interesting investigation to teach finding results systematically. I would start with
19+1
18+2
18+1+1
17+3
17+2+1
17+1+1+1 etc

Hope that helps.

Crumble, I thought of starting that way, but just showing the examples doesn't answer the questions, and I don't know how to get there!?

If the 1st question just needs a yes or no answer with a bit of proof then it's easy to disprove. 1 cubed is 1. There are no 2 square numbers which have a difference of 1.

Are they meant to prove the cube number thing?

But in order to answer the question your dc has to do the examples. They will notice patterns and be able to extrapolate an answer to the question.

If I had set this without an explanation (which is improbable) I would be wanting to see how they tackled it, not just whether they got the "right" answer.

You need to let your dc tackle this with a small amount of guidance, don't try doing it for them.

If you include 0 as a square number then it is I suppose (can't remember if 0 counts as a square number or not though)

I think so Miranda! If you google it you can findvery long proofs, not sure what an 11 year old can do with that!

But I agree if nothing sake has been said about it then it's how your DC approaches it that is the important thing

She is just baffled by it, I'm not sure how much I should insist on her persevering!

I am now trying to prove it myself (not sure my jet lagged brain is quite up to it )

No they won't need to do a degree level mathematical proof. All the teacher is looking for is a counter example which disproves the hypothesis that all cube numbers can be made using the diff of two squares, with a year 7 explanation.

Ok... Will try and tackle it again tomorrow...