These are a couple of exceptionally bright 10 year olds who came to a two hour session for enrichment not because they are having trouble.... If you would like more info about Math Tutoring on Maui go here.

They start the class with a simple whole brain warm up exercise where they have to build the addends for 7 thru 10. They have to use both hands simultaneously and they race me. I also have a tray. Right now they cannot beat me but soon the students will surpass the master...

Here is a shot of them using the blocks. They are racing to see who can get the problem st done first. We did the basic one step percentage problems, there are 3 kinds:

20% of 60 =?

24 is 60% of what number?

What % of 70 is 21?

We did a bunch of problems for each kind, then we did a mash up where all three kinds were in the problem set. It's always more fun with two or more students because we can race and get more problems done in less time.

Just for fun I taught them how to convert base ten to binary but forgot to snap a picture or two then we moved on to percentages. Here you see the problems and sketch of the solutions plus a matrix for the second problem so they can arrange their thoughts. They were using the blocks to figure these out at first then moved on to drawing them.

We spent a lot of time on binary conversion and percentages and they begged me to do algebra. That's not an exaggeration. So for the last 40 min or so we did some factoring. Started off easy and worked our way up. Here the student is doing a fast sketch and the writing the symbols...

What you don't see is the time we spent modeling these problems with the blocks. The base ten blocks are like training wheels, and these two wanted them to come off as soon as possible. Here we went directly to symbols no sketches no blocks...

You can tell how confident they are by asking "do you want an easy one or a hard one?" By the end of it they were saying, "give us some hard ones!!" Of course there are no hard ones when you understand what you are doing. (BTW x

^{2}-18x - 81 cannot be factored, but x

^{2}- 81 can. Look for a lesson on the difference of two squares soon.) They have fun and get a sense of satisfaction because they know much older kids who have a hard time with these...I will remind you that these are 10 year old boys.

This is a bad shot but shows economy of symbol. We don't need to write (x-9) twice. We talked about square numbers and what that meant. Soon they will be evaluating these for various values of x. Ie f(x)=5 or 10 or 2 etc...and they will see the result is always square. When it was over they thanked me profusely. One of them who was coming for the first time admitted that he thought it was going to suck but instead he had a good time and couldn't wait for the next session.

Neither can I.

Crewton Ramone Does Algebra With 4 and 5 Year Olds.

More at Crewton Ramone's House of Math.

I showed my father this technique for factoring polynomials (he was an algebra professor). He had difficulty applying it to problems with negative values. How do you 'make a rectangle' with negative values?

ReplyDeleteThanks! I have been desperately trying to find a good set of base-10 blocks like you show in your videos, but having a rough time with it.

Sean you put the blocks on top to show cutting away...I don't generally go into negative expressions for free on the net...lol...hero zero...it is simple and elegant for showing negative values...and factoring the difference of two squares for example but can also easily show (x+3)(x-4) use your imagination and play with it. This called directed discovery...sort of...for real directed discovery we both need blocks and I'd need to be there...check out my FB page I'm putting together a free webinar, may cover that briefly because the question keeps coming up...

ReplyDeleteEbay has a great set but I see it only has 6 hours to go on the auction and by the time you see this will probably be over...feel sorry for the person selling it the bid is 99 cents and it's a lot of stuff...constantly check ebay for blocks. Mortensen Math Direct has them tell them I sent you, you will find that they are not cheap...Math U See also sells them but they don't come with the trays...

ReplyDeleteOk got to my Facebook Page there is a photo that shows how to do negatives...

ReplyDeletehttp://tinyurl.com/2eujmbk