Algebra Homework Question

[ruggief]

Year 9 son has an algebra test tomorrow and is happy with most apart from questions on magic numbers. I have never come across these?
Question is solve the following equations using magic numbers a+b and a times b
apologies I can't figure out the algebraic x on my keyboard so have substituted k instead

2ksquared + 10k +5
2ksquared + 10k + 10 =0

Many thanks if anyone can shed a light on these for us

[fiction-factory]

Yes, that's pretty much what iw as trying to say at 23:15 last night, jim.
I admire your patience on this.
I agree that some year 9s in top set could do the ones where the numbers can be done by inspection/trial and error, but I feel the majority of year 9s wouldn't even be able to multiply double brackets or factorise quadratics, and most would get confused when negative terms or solutions are involved.
I wonder whether this was some sort of extension task for maybe maths club/G&T group.

[ruggief]

Thank you all especially Jim360 and Fiction Factory.

No it wasn't an extension task. The whole year group sit the same test annually with Distinctions on offer for the top perfomers. He is in set 2 maths so is one of those who will take GCSE in Year 10 not Year 11. It just seemed such an odd concept which I couldn't grasp, neither could my daughter who is year 11 (GCSE this Summer). He talked about factoring and knew that in this 'Magic numbers' process you multiply two of the numbers together and add two together ignoring the x's and x squares then solve the resulting equations a+b=c and a times b =c. I solved it my way as did my daughter (using same method) and we all three of us got the same answer. Even though his seemed very long winded with lots of extra steps. I will mention this thread to his to teacher at the parents conference and with your permission will print off your calculations to show?
He said the test went very well was easy should get the result later today.

[jim360]

As you can imagine I was too busy typing and scratching my head trying to make sure I'd understood and properly explained the "magic number" method and just overlooked your answer, FF. Sorry! I of course agree with everything you've said. In the end I think the "magic number" approach isn't dreadfully hard as long as it's made clear *why* it works, which apparently it wasn't given the example that was marked as "correct" despite being wrong.

Glad to be of help, ruggie :) If you do print things off (as far as I'm concerned everything I write is instantly available for whoever to use as they wish) then can I suggest either hiding the disparaging remarks about the teacher, or at least making it clear that they were being written by someone who was at the time rather tired and slightly hacked-off?

[Peter Pedant]

Many many thanks Jim
for the time you have spent doing this

( you cd have been redesigning the universe or something)

I think it is inevitable that with that amount of work someone is gonna say - "foo dat a lot of stuff hieroglyphs I fink!"

I thought the idea might be to generate number pairs
BUT - that means you exclude imaginaries and less than whole number answers
which er may not be an advantage
we were shielded from complex numbers for a very long time in case it corroded our developing brains ....

thanks anyway Jim

[jourdain2]

My thanks, too, Jim. Like f-f, I can't envisage many of the year 9s I've taught - and still meet in school - coping with the problem, but you know maths teaching better than I.

[jim360]

It might depend on the school in question -- also bear in mind that I tend to teach 1st-year university students and it's been a while since I was in a high school.

[ruggief]

Thank you so much. I will of course be in selective in the posts I show. Proud mummy results came back today with a 98% for joint third in the year. Top chap got 100%. Whole year sat the test apart from the Academic Scholars in Set 1.

[jim360]

Glad to hear of the good news. Well done that lad!

[fiction-factory]

No-one has mentioned the 'completing the square' method yet!

[jim360]

Be careful what you wish for :P