Maths teaching ideas needed please.

[DumbledoresGirl]

Please could you help me. I need to teach a 30 minute lesson introducing square numbers to Year 5s. All I can think of is colouring in squares on squared paper. Hardly original or interesting!

I am beside myself with anxiety as this is going to be part of a job interview for my first job in 12 years. I have spent half the morning looking on the web, but I am still uninspired and rapidly panicking. Please can anyone help?

ds skipped these, remind me what one is and I'll tell you.

2x2 = 4
3x3 = 9
4x4= 16

And so on. 1,4, 9, 16, 25, 36, 49, 64 etx are square numbers.

I'm assuming year 5s are ok at maths, hmmmm. what about a game? first one to get them right wins a badge? What about find the patterns? This is quite easy, 9 time table is just 10 times take away the number that they are timsing (?? spelling!)

I have no idea of their ability. Although I will ring later when I am not in such a state of panic, and ask!

All I know is that I have to introduce square numbers. I take it they know their tables, but square numbers are new to them. I thought of building stacks of blocks to show square numbers but I can't think how to progress.

Damn it, I wish I hadn't made out I was such an innovative teacher!

(After DS piped up one day "Mummy I think they've got it wrong on this number square, how can 11 11 be so much more than 10 10?")
So I saved lots of milk bottle tops to show him how squares worked.

What has been fun is building pyramids with a 12 12 base, then 1111 or 10 *10, then gradually getting smaller. Ideally with each layer a different colour. Then looking at how the totals change.

It made me realise that we were never taught that a square number is so-called because IT IS SQAURE. And I think we need to understand this concept.
You will need a suitable resource - bricks ? or if you are near me in Surrey you could collect hundreds of plastic milk bottle tops.

You got there before me with the bricks.

Use 1 colour for 22, then add next colour for 33. Or one colour for 44 then add nother colour to make 55

You can get them working out the formula for the difference between two squared (x +1)( X-1) (I think) You would present is as "can you see a pattern in how many more bricks you need to make the next square"
There is a clear pattern, my DS (7) worked it out for himself quite happily, but he loves maths.

i would do areas first and then show that when length and breadth are the same you get a square.

then you did to do something to demonstrate that bigger number get bigger faster when you square them then smaller numbers. first divde them into groups of 2 and give each person i two counters. get them to give one counter to the other person and keep one. then put them into groups of four and get them to do the same thing- hey need more counters, do groups of 8 and even more counters. last work out the square of the number in the class which will be in the order of 900!

last think of other examples where knowing the square is useful
e.g. if you have 5 girls and 5 boys then you have 25 possible couples

Hmmm, I got out my children's old building blocks and only had enough to build up to 4x4. But I can try asking the school if I can borrow some blocks from them. They should have them

I am not sure what you mean about working out the formula. What is the (x+1) and (x-1) about?

the pattern
is (x+y) times (x-y)
so 42-22 = 62=12 = 16-4
and 62-22 = 84 =32 = 36-4

but tbh i think just gettig them to know that differences get bigger is enough

witchandchips. Thankyou for (x+y)(x-y) I've been trying to remember it for ages.
I was convinced there was a 1 in it somewhere.

Sorry, I am lost here.

DS school has little plastic cuby things that click together a bit like lego. In various colours IIRC. About 1 cm square. They might be better than bricks as smaller and lighter.

It's like this

XXXO
XXXO
XXXO
OOOO

What DS finds interesting is that there are so many more Os than Xs even though you've only gone from 33 to 44

And you can work it out as

(3-4) (3+4) = 1 7

This thread is quite frightening...DS1 is in Yr3 I am dreading his doing this as I cannot make head nor tail of it ....

Is * multiplying?

should have previewed my message first as should 2 squared and not 22 !

when you go up in steps of 1
(x-y) times (x+y) is simply x+y. the pattern is then easy to see.

3 lots of 3
versus 4 lots of 4

need to add one lot of 4 (4 extra) and give an extra one to each lot of three (3 extra) to make it 4. so 4 extra + 3 extra = 7

does this help?

Sorry Platino yes, * is "times"

Don;t worry, the teachers will probably explain it much better than we are. (Sorry DDgirl!)
Anyway, I recall learning this stuff in what would now be year 6 or 7, not year 3. We were still doing colour factors in standard 1 (shows my age)

I think colour factors are called something else now..its just neatly sized long bricks with different colours for the different numbers. So two whites make a pink etc.

okay tbh all they need to understand is (in decreasing order of importance)

1. squaring is like multipication
2. a square number makes a square
3. when you square a small number you increase it by much less then when you square a big number
4. some examples of how square numbers can be used
5. knowing the squares up to 12

DDgirl, You could teach them about the little 2 up in the air that Witchy was trying to type to indicate "squared".

Thanks. I think I understand what you were saying a bit more now. It was the lack of the little 2 that threw me!

Well, I have thought about this all day, and spoken to a couple of teachers about it. The consensus seems to be that squared numbers don't have a lot about them that needs to be learnt

I think I will get the children to investigate the difference between consecutive squared numbers (it rises by 2 each time) and maybe use that to work out some larger squared numbers (beyond 12 squared). But this will be at the end of the lesson or even possibly, a suggested extension activity.

Does anyone know if these demo lessons have to run to plan or is it OK to plan too much and say at the end "I would carry this on in the next lesson if this were for real"?