Today was the first day of a week long workshop put on by a local chapter of math teacher circles. What a fun day! We spent the morning working on problems and talking about problem solving. An amazing group of high school students from Los Angeles presented a workshop this afternoon about their work in The Algebra Project and the Young People Project.

This was a big take away for me from the morning session. Any guesses on what it is?

A spatial multiplication table?

ReplyDeleteNice! Your prize is in the mail.

ReplyDeleteAvery, I was there! I will look forward to meeting you tomorrow evening, at the banquet. I loved the 3-color games we did with the Young People's Project folks.

ReplyDelete(What do you look like? Will you email me? suevanhattum on hotmail)

I'm doing the Thursday afternoon workshop.

Oh! Pretty! What was the take away from it? Do younger kids find it easier to grasp? Or just that it was new to you? I've never seen it before!

ReplyDeleteThanks! I'm glad you enjoyed the multiplication table.

ReplyDeleteAmong other things, I hope the takeaways include: Using area as a model makes multiplication easier to understand. It also makes the distributive property visual. It can give us an easy way of summing all the numbers in the multiplication table. For *some* younger kids, it turns a big pile of numbers into something with real visual meaning to them.

http://www.msri.org/specials/festival/activities/MultiplicationTable.pdf and especially http://www.msri.org/specials/festival/activities/MultiplicationPascal.pdf have some more nice multiplication table facts.

The first link there has a nice question: you can use the multiplication table, as Avery pointed out to me on Monday, to prove that (1+2+...+n)^2 = 1^3 + 2^3 + ... + n^3. The question is, for what lists of numbers other than 1 through n is this true? (I think I know a way of generating tons of lists for which this is true, but I don't know a way of proving that this way generates every possible list).

The second link has a nice relationship between the multiplication table and pascal's triangle, specifically the sums of the / diagonals of the multiplication table and the tetrahedral numbers.

Just found your blog via Sue's blog. Loving it! Are there math circle meetings in the south bay/peninsula area? I'm a sci teacher in San Jose, but it sounds really interesting.

ReplyDelete@ Sue: Nice meeting you last night!

ReplyDelete@ Sam: Josh did a great job of summing up many of the ways this representation can be powerful. I have to say that the basic reminder that multiplication can be modeled with rectangular areas is really nice. I wonder if other models for multiplication (such as stretching the number line) could somehow be represented in a "times tables?"

@Josh: Thanks for replying to Sam (ie doing all the work).

@Jason: Thanks for stopping by. As for meetings in the south bay, check out:

http://www.mathteacherscircle.org/circle/

http://math.stanford.edu/circle/

Avery,

ReplyDeleteFor peninsula/south bay math circles, you can add to your list: http://www.sanjosemathcircle.org .

And maybe http://funmathclub.com .

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