Thomas recently turned 6 and is clearly ready for more conceptional learning. He has learned so much with very little formalised instruction. I have helped him learn all the letter sounds and he can read simple books with some help. Like Lady, he will most likely be able to read very well when he is 8 or perhaps earlier. He has a good understanding of arithmetic, although until a few weeks ago, he'd never answered a written maths question. He has, however, spend ages counting the coins (and a few notes) in his Tardis money bank, he has played loads of board games, some card games, many hours worth of computer games. He has played with Lego and wooden bricks, Geomag and measuring cups. We have baked and weighed and measured as part of real life. He has been able to double and half quantities in his head, he has been taught how to add 2 small numbers by putting the larger number "in his head" then counting on the next number on his fingers. So when I wrote out a page of addition and subtraction sums, I just had to tell him what the plus and minus symbols represent, and he easily completed the questions correctly. Right away I was able to present him with more difficult sums.
We often have discussions about numbers. For a long time he asked about the biggest number and asked how long it would take you to count to it, then was fascinated by the idea of infinity. He asks about astronomical distances so I have to look them up and explain concepts like light years to him. He asked his Dad how long it would take to walk around the sun, so we looked up the numbers and showed him how to divide the distance by the speed to get the time taken, (approx. 1 million hours or approx 114 years, assuming you survive).
Gordon has talked to them about Graham's number and the Planck length as examples of the largest and smallest numbers used in science. More usefully, we've mentioned how amazing it is that any number can be expressed using just 10 digits, (and why we use 10) but how they can also be written in other ways, like the Roman numeral system. Thomas has also been introduced to negative numbers and fractions.
He asks how old I was when he was born, or what age he'll be when Lady is 18, and although I used to just tell him and explain how I worked it, now I get him to figure it out. He understands money, so it's a great tool in explaining concepts like place value. (He says he wants to be rich when he grows up, perhaps he will!) Looking at a catalogue recently, he remarked on how expensive the hot-tubs are (he and Lady covet these items; dream on, my children!). He said, "it's ten thousand, four hundred and ninety nine pounds, that's nearly fifteen thousand pounds!"
He asked me on Wednesday how long before we went to his gymnastics class, and I said 1 hour and 15 minutes. He responded, "OK, 75 minutes." He asked what time that would be so I told him, 3.15. He said, "when both hands are at the 3."
Yup, you've got it!
He was helping me put the shopping away yesterday and he saw the box of eggs, and said, "You bought 10 eggs." I asked him to count them, so he did, and acknowledged that there were actually 12 eggs. He started looking at them, grouping them with his hands, and told me that there were 2 groups of 6, then 4 groups of 3. I showed him the other multiples. It took about a minute, and he learned because he was noticing the patterns in the quantities for himself, and I was just there to help explain and confirm what he discovered.
It's good to reflect sometimes, on how they're doing and to see the methods of learning we've adopted, working so well.