Here are a few shots from a recent tutoring session. The child built a big tower. To the casual observer this looks like a kid spent some time building and playing with blocks what I didn't capture was all the computation that went along with it. There was also quite a bit of measurement that went intp placing the foundations so everything would line up correctly. Usually the ten block was used as a measuring stick.
There was quite a bit of multiplication and counting. For example, as the level that contained the fours (the level with the yellow blocks) was built he had to skip count by fours and answer questions like how many is eight fours....?
The tower on top with the blue blocks contains 18 fives...we practiced skip counting by two's and then counted by fives. We skip counted by two's because each level contains two fives, then we counted by fives then he figured out that he could easily count each level because tow fives is ten and counting by tens is easy. He still isn't 100% confident repeating the pattern 2, 4, 6, 8, 10...but that doesn't stop us from counting by nines or sixes or eights...he knows how many 2 sixes are due to the work with addends...and three sixes but then he uses "wanna be a ten" to figure out the rest.
18 + 6....hmmm...8 takes the two out of the six, four left 24, four needs 6, 30...etc...after a while he will know what 6 x 6 is without having to count it...he gets lots of addition and multiplication practice and has motivation because I don't always let him keep building until he answers the questions...the faster he answers the faster he get to keep playing. Most of the time the questions are easy but sometimes he has to stop and think and once in a while he has to get out a marker to keep track...for questions like "how many blocks did you use so far?" Or "how many units would you need to build this or that part?" In kid speak: "how many green ones would it take if you had to use green ones instead of fours (or whatever)?"
Some of the computation was done on the white board but most of it was done in his head.
This student has just turned seven years old. He knows his addends pretty well, and we are practicing multiplication. This tower was fun to build, he did all manner of multiplication and addition as well as measuring and simple counting.
It is paradoxical that many educators and parents still differentiate between a time for learning and a time for play without seeing the vital connection between them. -Leo Buscaglia, author (1924-1998)
After we had built the tower we practiced a little more math, here we are doing subtraction. Looks like this kid is a genius; no borrowing, and note how he is going from left to right. That's because he knows how to employ addends to solve this simple subtraction problems.
Then, and only because he asked nicely, we did some algebra, by far his favorite subject. He has some work to do with regard to making the symbols neatly but certainly he is well ahead of most 7 year olds when it comes to understanding math concepts. "I'm not even going to get out the blocks!" he exclaims. "I'm just going to draw it, okay." Because drawing on the white board is still very fun for a 7 year old.
And before you know it the hour is gone and all we did was play around with blocks.