Tuesday, December 14, 2004

A more productive day :)

Well I told myself today that we really had to DO something! So this morning we did Maths as usual - definitely something not even worth attempting in the afternoon! Joel was on a revision exercise and it glared at me those concepts he has fully grasped and those he has not. He gets number order, forwards and backwards, position and place (eg 1st, 4th, etc...), greater and lesser, the fact that addition and subtraction are opposites (1 + 3 = 4 & 4 - 1 = 3) - but only just, some number 'facts' he has off pat, including most of the '10 bonds' eventually, he gets the idea of making 10 first, but seems to really be struggling with the HOW still! Over the weekend I managed to buy a little desk-top sized blackboard for next to nothing in The Works. So today we did giant sized calculations on it! He had to do the sum 6 + 7. Initially he wrote the answer 11 :( SO... we got out the blackboard. He wrote the sum out. Then we chatted;

Me -"what do you have to do first?"
J - "make 10."
Me - "OK. Which number are we going to make into 10?"
J - "the 7."
M - "good! How many more do we need?"
J- " 3." (so far so good)
M - "Where do we get the 3 from?"
J - "the 7." (sigh!!)
M - "no"
J- "no, no the 6." (no, no really meaning whoops, must be the other one then!)
M - "OK then. Fly in 3 - that's how many we need remember - from the 6."
Joel draws a nice big arrow, representing an aeroplane flying 3 (people) over from the 6 to the 7 and writes a 3 next to the 7. [we have used frogs on lily pads before, people on aeroplanes was a new idea today!!]
M - "OK good, so now how many are left where there were 6?"
J - looking blankly "6."
M - feeling slightly irritated "no there were only 6 to start with and 3 just flew over to the 7, so how can there be 6 left still?"
J - "oh, oh, oh,....4"
M - "try again..."
J - this time actually saying "6 take away 3... 3."
M - "Great! So now we have 3 people over here (writing and circling a 3, whilst crossing through the 6) and how many over here (pointing to the 7 & 3)?"
J - "7."
M - Now with a little MORE irritation in her voice at the fact that he simply does not seem to be looking at the board, or is he really not SEEING what HE has actually worked out!? "No Joel, the 7 people isn't 7 anymore because 3 more people flew over. How many people are there now?"
J - (looking to his left) "6!"
M - (RRRRRRRRRRRRRRRRRRRRRRR!!!) "NO!! You have 7 & 3, how can you have 6!!"
J - "oh, oh, oh....10!!"
M - "hooray!! (I cross through the 7 & 3 and write 10 - BIG). SO, what do we do now? Look at the sum, what KIND of sum is it?"
J - "a plus."
M - "which means we have to..."
J - "add."
M - "OK. Go on then."
J - " 3 add 10...13!" (that bit was easy!!)

On to the next one 8 + 8! By the time we had done three more like this I think he had just a little more idea of what to do, but who knows!!

Splitting numbers I THOUGHT he understood until today, when he wrote that 16 consists of 16 & 6!! He was given the initial 16 and the part 16, he just had to fill in the 0!!

So after all that was over we 'played' with coloured rods and blobs on blackboards for a while, writing numbers in the colours that the rods represent & colour mixing to represent added together bonds (eg orange + pink = a mucky browny colour (12)!

Then we drew some circles and shuffled about some single cubes (one rods) to represent part and whole numbers moving along subtraction and addition lines.

This was relatively fun and he SEEMED to SEE what we were doing, I just don't know if he will be able to translate it all back into actual numbers come tomorrow. BIG SIGH!! He has another revision exercise to do tomorrow, so I'll keep you posted how it goes - if you're not too bored of reading all this that is!!

Anyway, this afternoon I decided we needed to do something a little less brain numbing! So we learnt all about the various 'Disasters of London', as Jacob entitled it. We read about the Plague, The Great Fire, The use and misuse of The Thames and how London spread out (and why) over the last 1000 yrs. The boys did seem genuinely interested and liked all the pictures and quiz questions in the book. Joel had apparently been reading it on the quiet!! Afterwards, as an English task, I got Jacob to write a short paragraph about what he had learned today. I got him to make himself a spider plan first and then to order and write whatever he wanted. I was SO pleased with what he wrote. He had obviously taken in loads. :)

Jacob's writing piece (click if you can't see it well)

While Jake did that Joel did a little bit of his "Write about Me" and produced this;

Joel's Lion

Writing about a lion (click to see bigger)


Jan said...

Aargh! at the maths conversation. That just sounds so familiar! Love the written work though. Your boys have lovely writing.

Caroline said...

Thanks Jan. Jacob can actually write much neater when he sets his mind to it, but that was not the aim of this exercise. I really just wanted him to get his ideas down quick before they were gone!! And Joel's writing has really blossomed this term. He started joining quite spontaneously and I'm very impressed with his writing too - and tell him so frequently, so that he himself is becoming quite careful about making it lovely now ;)

And I'm glad I'm not the only to have these round and round conversations with my children :)

merry said...

No. I'm sorry - there HAVE to be easier ways to do adding up than that! I sat in awe/horror at the "modern" way of adding up the other day- must take blooming hours!

You have the patience of a saint to be even trying it!

Caroline said...

Well Merry, truth is, there are easier ways - in the short term, BUT Singapore maths teaches those AS WELL. SO, basically it teaches 'counting on' for upto +3, but after that children loose track of how many they've added on and start making mistakes. It teaches use of number squares and number ladders/lines. You can teach 'put the big number in your head and then add on with your fingers' (eg 12 + 9 : put twelve in your head and then add on your fingers until you are holding up nine fingers. What is the answer). This of course only works until you run out of fingers!! This is the method used in OUR schools. But I am using the SINGAPORE way!! This is not actually a 'modern method' so much as a different one!
The advantage with the 'make 10' stratergy is that it works ad-infinitum. When you think about it is actually the way a lot of us actually add-up naturally. If I am asked 25 to 37, I will Say in my head "3 is to 40 add 22, is 62. Basically 'making 10' is the basis of rounding up and adding on. Although it seems complicated at this point it actually really works to help the child with mental arithmetic later on. It also teaches the child early, that whatever you do do one side of the sum you have to balance out on the other (the main principle of algebra).
I can already see the product of the slog with Jacob. He is quicker with some mental maths than I am, because he has all sorts of stratergies at his finger-tips and can find the most appropriate one for the task pretty well. Wheras I probably only have maybe 2 ways of doing things in my head and then I resort to paper, which is not always to hand!!
A lengthy reply - hope it's worth the read!! But you'll be pleased to know that Yesterday he really seemed to have got the addition of pat - the aeroplanes seeem to have worked (big sigh of relief)!!