## Last Math Lessons

On the first day of school, I promised all my students that I'd do my best to make math relevant and challenging. I also promised to never waste their time, therefore they could expect to do math every day in my class, including the last day of class.

I did not promise them that math would be fun because doing math is always fun to me. I am not ashamed to share here that I gave out math puzzles at my kids' birthday parties when they were younger (I actually shared this bit on Twitter), also at a baby shower that I gave, and... get ready for this... at my own wedding. Straight up.

(I know I wasted my kids' time when I gave them three benchmark tests during the year and spent days reviewing for the state test.)

Math 6

I called this lesson How Many Regions? (Adapted from AIMS)

I gave each student a piece of 4-by-4-inch paper and a handful of 6-inch long thin strips of construction paper. Each strip placed on the square paper would represent a "cut."

Question: What is the maximum number of regions that you can divide the square into using n number of "cuts"?

We did the first two cuts together as a class, and each student kept track of the data in their journal.

Because the goal was to get the maximum number of regions from the cuts, the kids learned quickly that the cuts needed to intersect. For example, two non-intersecting cuts created only 3 regions. A kid yelled out, "Parallel cuts!" Gotta forgive kids who blurt out academic language!

This class has been working with a pattern worksheet almost every Monday in my class, so they know to look for a recursive rule and try to find the equation for the nth term. Recursively, they saw the pattern, so it didn't take long for them to figure out that for any n (cuts), the maximum number of regions is the sum of n and the number of regions from the previous n.

With 30 seconds left of class, I told them my gift to them was to try and figure out the equation. Matt asked, "Can I email you then over the summer?"

Algebra 1

Our 8th graders' last day of classes was yesterday (Wednesday). They'll show up this evening for their promotional ceremony, dressed to the hilt, the girls in their 7-inch heels.

I needed a quick one-period lesson, so I had them make 2012 Clocks. This is a common assignment: using all 4 digits in "2012" and each digit only once, they had to create expressions that would equal to the hours of 1 through 12 on a clock.

They were engaged and busy because if they didn't use class time wisely, then they'd have to sacrifice their hair-and-make-up time today to get it in to the mean teacher who didn't-even-give-us-the-last-class-to-sign-yearbooks-and-hug-each-other.

Geometry

I've seen different versions of this problem; the first time I worked on it was when it involved 3,000 bananas and 1 camel traveling 1,000 miles. I know there's a perfectly good strategy called "solve a simpler problem," but we could also start with a simpler one!

I gave my kids Desert Crossing, also from AIMS:

You live in a desert oasis and grow miniature watermelons that are worth a great deal of money, if you can get them to the market 15 kilometers away across the desert. Your harvest this year is 45 melons, but you have no way to get them to the market, except to carry them across the desert. You have a backpack that holds up to 15 melons, the maximum number that you can carry at a time. To walk across the desert, you need a certain amount of fluid and nourishment that is supplied by the melons you carry. For each kilometer you walk (in either direction), one melon must be eaten.

Your challenge is to find a way to get as many melons as possible to market.

(From Desert Crossing, Just for the Fun of It!, AIMS Education Foundation)

As I type this, Slater does not know that I will be awarding him the Math Excellence Award at the Promotional Ceremony this evening.

Here is Slater's work that shows one way to get the correct answer of 8 watermelons.

I did this a few weeks ago and forgot all about it; so here's a little blurb on it.

Each student quickly constructed these two prisms from two same size papers. (Dan Meyer folded them into
cylinders.)

Question: Pretend the two prisms have bottoms on them, which one holds more popcorn? Take a look... Okay, grab the one you think holds more, or grab both if you think they're both equal.

And this was how they grabbed:

Then they measured and calculated the volume.

My favorite student comment: The tallness didn't make up for the fatness.

Estimating volume is a funny thing.

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###### Comments

• June 14, 2012 2:38 PM Sue VanHattum wrote:
Your Math 6 project is one I've done with math circles. I called it the Magic Pancake problem. I did an online math circle once using it. I didn't like how it worked. I like to do these things for real in person. But my write-up is here.
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1. June 15, 2012 7:36 PM fawnnguyen wrote:
I appreciated your listing the pros and cons of doing the activity online. It'd be too hard for me (from watching the first 10 minutes of it) for the same reasons you'd stated. In class I was able to get everyone's attention with this question: "Ryan used 5 cuts to make 16 regions which we believe is the maximum number based on the recursive rule. But some of you have fewer, like 14 or 15 regions. So, what did Ryan do differently with his cuts?" The sharing that I saw among the kids following this question made me wish the class could go on for another 3 hours!

I downloaded Elluminate to watch your webinar -- my first time -- and it was cool, with voting features and all. Sure, the real deal is desired, but I like doing math in my pajamas too! Thank you, Sue.

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• June 14, 2012 7:25 PM Matt wrote:
Fawn, there is no shame in subjecting your wedding guests to a bit of mathematics. I did it too! http://www.mathgoespop.com/2011/09/wedding-mathematics-part-3.html
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1. June 15, 2012 8:01 PM fawnnguyen wrote:
Holy cow, Matt, I'm speechless. But I did leave you a comment over at your post.

I'm not worthy. Andrew (@mr_stadel) and Sadie (@wahedahbug) both quickly conceded the geek title to me upon learning that I subjected children to math problems at parties. But you, sir, you are Obi-Wan Kenobi. Oh, you do know who that is, right? See, no wonder you're behind in the watching movies department, you've been moonlighting as the mathewedding planner. It's all love from me, Matt.

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1. June 16, 2012 7:38 AM Matt wrote:
Thanks! I can't take much credit for the centerpieces - I was just in charge of the math inserts. Some of the tables had math books, but some of the unluckier ones didn't - every table had a book or two, though. Nothing makes for a fun wedding like having a literate guest list.
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• June 15, 2012 3:22 AM Nathan Kraft wrote:
"The tallness did not make up for the fatness."
Unfortunately, this is my problem.
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1. June 15, 2012 7:01 PM fawnnguyen wrote:
That's because you're always attached to your tuba, Nathan. And it's a good thing!
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• August 26, 2013 9:32 AM Jeff Bacholzky wrote:
I am wondering if you can send me a clearer image of Slater's solution to the watermelon problem. I am a math teacher and the best I could come up with was 6 melons at the end. I can't quite make out Slater's solution with the image shown.
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1. August 26, 2013 7:35 PM fawnnguyen wrote:
Hi Jeff. I don't have Slater's original to recapture his work, but I'm attaching the whole problem here. Enjoy!
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