Here is another session with a bright ten year old. She has a favorite game already which is what's under the cup but we did a lot more than that... This post can be found on Emma's page with some full motion vids of previous sessions.
First we built towers with addends for ten, then we built towers of 3's and 5's and 4's and so on and then we laid them down and counted how many...and popped a bit of pop corn, which is when I remembered to get a camera out.
Math is fun with a bit of food...organic air popped pop corn with real butter and real coconut oil and a bit of pink salt and brewers yeast...healthy and good for her brain. Later we slacked our thirst with "vitamin c juice" (emergen-c)...
All we are doing is counting and comparing.
Fours, fives, threes, nines, eights...we compare them to 36 which is 3 tens and a six on top...count how many fours makes 36, note that 9 fours and 4 nines is the same...see that 5's don't make it into 36 evenly...you get 35 and one left over and that's 7 fives. We just talk about numbers count them and eat popcorn. This is math.
She points out a few things. I point out a lot of things, sometimes I point out something erroneous and see if she agrees...like two fours is the same as 9.
"No," she says. "Three 3's are the same as nine not two fours..." We laugh and joke around and count. She can see two 2's are the same as a 4 and "two twos" is fun to say. This is math.
Multiplication, addition, division: it's just counting.
They don't all have to go "the right way" some are sideways some are upside down (we didn't talk about negatives at all), and it made it easier to count the twos especially because you don't lose your place bacause they don't all look the same. We HEARD some very distinct patterns when counting by 5's and discovered some easy rules that she made up when counting by 2's...and she could see 6 is three twos and two threes, and six 6's are indeed the same as 36. We ate popcorn and slurped some vitamin c juice. This is math.
Then we cleaned up a little and made squares. I cannot tell you how important it is to build squares especially after working with teen agers in geometry, trig and pre-calc. So many problems could be avoided if they had some experience with squares. Here we learned about the square root symbol and what it means...make a square and count one side.
That little hook thingy on the side says count the one side. Note the beautiful blend of blocks and symbols to bring the point home...we put all the squares under the square root sign and counted one side...we also spent some time counting the whole square which for a ten year old takes a little work...especially the seven square. But counting the side was super easy peezy chicken squeezy. This is math. Why does it have to be hard?
This along with using both hands uses both sides of the brain. "This" meaning blending blocks and symbols, the blocks very much right brain, that square root symbol decoded by the left brain if there are such things. I prefer whole brain and one side doing a bit more work than the other although we can see now with science and machines the exact areas that "light up" when certain tasks are presented to it. I am very interested in nuero feedback and will be perusing that angle a little more in the coming months because I just don't have enough to do already.
Note she uses both hands often times while building blocks. This is important for whole brain learning too...engage all the senses, including smell and taste. The popcorn adds a favorable relationship to math...simple. Pavlov can explain it to you if you don't already get it. Encourage your students to use BOTH hands at the same time if at all possible.
Not shown was a fun game of what's under the cup as a reward for doing a lot of math and being good. The reward for doing math is of course more math...at Crewton Ramone's house of math this only makes sense.
One thing I want you to take note of is counting forward not backward. Lets say we have 13 and there is a 7 showing which means there is 6 under the cup. You train the child to compare the 7 with the ten and see it needs 3 more...plus the 3: means it must be 6 under the cup for some students I may even put two threes...they don't take seven and subtract it from 13...
Count forward not backward. Subtle but important tip
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I forgot to mention this kid is supposed to be ADHD or ADD or something. We played math and only math for over an hour.