Year 8 algebra homework

[Emochild]

Help?

[CadleCrap]

The negative " flips" the fraction' then raise each number to power 3

(8/5)^3 gets rid of the negative

Then 83/53

[iemma321q]

The negative means you take the reciprocal of the fraction i.e. The denominator becomes the numerator and vice versa.
You then need to cube both values.

So the answer would be 512/125

[Emochild]

Thanks

She's got several wrong examples in her book (because she couldn't do it in class) and no text book so we are doing this blind

[noblegiraffe]

Yeah, she's getting it wrong because this stuff is really hard. I was doing it with my Y12s as part of AS level this week. It's old GCSE A*/A grade.

[Emochild]

So not really appropriate for yr 8 set 2 in a non-selective school then?

[MsMermaid]

I'm about to do it with my top set year 9. It'll be the first time they've seen it. It is hard.

My year 12s still get some of it wrong.

[mineofuselessinformation]

Does she have a mymaths login? She can access the online lessons if she has - use the search bar for negative powers / negative indices.

[noblegiraffe]

I certainly wouldn't attempt to teach it to Y8 set 2, so if she's struggling I'd try to tell her not to worry too much and maybe write a note to the teacher rather than spending lots of time looking up resources.

[mathsy]

That is definitely a tricky topic even for year 12's. I teach in a pretty decent secondary school and I might cover that topic as a challenge for top set year 9 if I was feeling adventurous

[Emochild]

Noble, she was moved down from set 1 at the start of the year, her confidence is shot

Doesn't matter what I say -in her mind she's rubbish at maths

Also not the sort of school where notes saying homework was too hard are acceptable

[CrotchetQuaverMinim]

That's hard for Year 8.

They need to, for a start, have a really good grasp of fractions, especially division, and also knows that the line in the middle of the fraction also means division, which I find a lot of pupils can be shaky on. If she's not sure she's understood the lesson, then I'd double check that she knows, for example, that 1 over (5/8) means 1 divided by 5/8, and that she knows how to divide fractions by multiplying by the reciprocal. Similarly, can she divide 1/5 by 1/8 to get 8/5.

Then I'd want to make sure she has basics like knowing that something like 5/5 = 1 (again, sounds simple, but a surprising number of children don't see it as obvious!). And making sure that she can cancel when she has something like (8x18)/(3x2) - understanding the principle of being able to divide any of the top numbers by any of the bottom numbers, to simplify the problem without having to work out the multiplication. So realising that (5x5x5x5)/(5x5) would leave 5x5, etc.

Then they need to be very clear on what powers are - how to square and cube things, and that it's different that multiplying by 2 or 3 (another common mistake), and also that something to the power of 0 is equal to 1. That leads them to understanding the power rules - things like when you are multiplying numbers (of the same base) to a given power, you add the powers (i.e., 62 x 65 = 6^7 , because it means (6x6)x(6x6x6x6x6), which if you take the brackets out because it's all multiplication, is the same as 6x6x6x6x6x6x6).

And the same thing when you subtract, so 58/52 = 56, because it's (5x5x5x5x5x5x5x5)/(5x5), and you can cancel two of the 5s on the bottom with two of them on the top, which leaves 56 on top. That explains why you can just subtracting the powers, rather than having to write that out each time.

But if the top has a smaller power than the bottom, say 52/5*6, then it means (5x5)/(5x5x5x5x5x5), and if you cancel two of the 5s from the top with two of them on the bottom (making them both equal to one), you are left with 1/(5x5x5x5), or 1/54. And yet you can see that if you simply subtract the powers, you would get 5-4 (i.e., a negative power). Therefore 5-4 must be the same as 1/54.

Finally, you also have to know enough about multiplying fractions, to realise that if you want to put a fraction to a power, it doesn't matter if you think of it as, say (3/4)2 or 32/4^2, because when you multiply fractions, you are multiplying both the numerators and denominators, so both parts will end up to the appropriate power.

ONLY THEN would I want someone to attempt a question like this!

Yes, it's possible to just teach children rules about these - I see a lot of pupils who have been taught rules only: if the powers are divided you subtract and if is a negative number, you write 1 and then put the original number underneath, or you take the fraction and just write it upside down, and voila, correct answer. They have no real idea why, they don't really understand fractions/powers securely to begin with, and it's all just rote memory - which they then forget quite easily! They can often get the questions right in the homework because they just copy what they've done previously, but it's meaningless.

Sorry, this has been very long, but I hope it helps explain what sort of things she should have been learning before a question like this is given, and that can help you judge if it's suitable for the set or not. If they do know all the previous steps that I mentioned, then great, they are obviously teaching intensively, but thoroughly, and I know one local school that does really push maths in the lower years but seems to do it fairly well. I've also seen other schools, especially with lower sets, just try to teach rules with no understanding, to try and get them onto complicated work too early.

[troutsprout]

Crotchet can you come and live in my house please ?
OP .. I clicked on that pic and felt a wave of panic on your behalf

[noblegiraffe]

No wonder her confidence in maths is shot if that is what she is being presented with, without at least being told 'this stuff is really hard, if you get it that's great but if not don't worry as it will come around again later'.

By 'note to the teacher' I meant one saying 'DD tried her best but really struggled with this' to get her out of trouble for not doing the homework, not 'Mumsnet says this is a stupid thing to be teaching Y8 set 2'

[JustRichmal]

I agree with Crotchet, there are a lot of steps to this sum which she needs to be secure in.; the most difficult of which I think is the idea of a negative power. If you google Khan Academy negative exponents and also negative exponent intuition there are a couple of videos which should help. (in America powers are called exponents)

Doesn't matter what I say -in her mind she's rubbish at maths

This, more than anything, I think is the problem. It is the anxiety of not being able to do maths that stops otherwise good students. However, the easiest way to learn maths is not to worry about understanding it first off. If you just walk away from it the subconscious works on it for you and when you come back it has become easier. If you can get her to approach it with an attitude of not mattering whether or not she understands it this time, it will become a lot easier for her to take in new ideas.

[user1475598697]

Some parents with a bit of a maths background (definitely not for children) find this website helpful.

www.quickmath.com/

Given your problem it produced 12 lines of explanation which is a bit excessive but did demonstrate most of the manipulations on the way to the solution.