Mental Math

I showed my students this incredible video of Arthur Benjamin doing Mathemagic (cue up to about the 13:00 mark for the big finale). In it, he multiplies 57683 by 57683, and he does it all in his head in less than a minute. We used this as a little motivation for trying to work through some mental math problems of our own. We also analzed his strategy and how we can apply his work (though way above our level) to our own. We found that:

a) he breaks the numbers in smaller units that are easier to work with (friendly numbers)
b) he stores these numbers in his head and then adds them all together when he has worked out a couple of sums
c) he must have practiced for a long time to get this good, and therefore perseverance is an important trait in learning math

With these observations in mind, he took off and tried to develop our own mental math strategies, and recorded them in our math journal to help us remember.


Introducing Division

I am working on multiplication and the times tables with the grade 3's, it would be good if we jumped ahead and took a look at division while multiplication was fresh in our minds.  The two are related, and if students can understand division while they are learning to multiply, it will only strengthen to conceptual knowledge.  I didn't want to get to in-depth, just some basic word problems and a little investigation about the relationship between multiplication and division.

Here is the first problem I gave them:

You have 30 pieces of candy that you want to share with 7 of your friends.  How many pieces of candy will each friend get (assuming you have none)?

As a basic introduction to division, this is a pretty good question.  The question is loaded to make them think about in terms of sharing, which is a great way into defining what division actually is.  It is sharing, or re-distributing.  Tomorrow, we will look at a re-distribution question.  However, you are probably thinking to yourself, but Craig, that question is 30 divided by 7?  How can you give a question with remainder as an INTRODUCTION to division?  That is too difficult.

My response.  No.  No, it isn't.  They are numbers that are easy to work with and they understand them, and it is in a context that they get.  If you give a group of kids some candy and tell them to share it (which I actually did for his problem, gave each group a pile of 30 pieces of candy), each child will automatically become a math wizard.  The working out phase of this problem (done in small groups) literally took seconds to finish before each kid was running up to me and saying;

Mr. Craig, each person gets four pieces of candy, but there are two left over.  Can I have the extra?

Great work.  This sentence is ripe for deconstructing and perfect for a class discussion.  It includes division, multiplication, and what to do with the left-overs, aka remainders.  It also lets them develop their own way of doing division, instead of imposing a one-method-must-follow style of doing math (as I was taught when I was wee lad).  Todays lesson was three minutes of problem solving, followed by 15 minutes of talk about how we solve problems.

Tomorrow, they will get another problem, this time instead of a sharing type of question, it will be related to redistribution.  And it will also have remainders.


Japan Update #4

Well, the kids are finally coming back.  Kind of.  My students are staying in France until next year, but the younger grade is coming back this week.  It looks like I will be teaching Math to the grade 3 class, and PE and Art.  It will be good to have something to do again, even though it is not much and I will still have tons of free time.  Oh well, c'est la vie.  Hopefully starting form next week I can use this blog as a way to post ideas again, and not just updates.  Looking forward to getting back into it.

In other news, I saw a hawk catch a fish in the pond.  It was quite beautiful.