## Trying to find math inside everything else

### How to Lie with Statistics – Stations

I base my statistics unit on the book How to Lie with Statistics, by Darrell Huff, because I think it contains a lot of really important information that everyone should know to live their lives and to stop themselves being taken advantage of. (Which is one of the majors benefits of learning math, as it’s so easy for people who know math to swindle people who don’t.)

The problem is, though, all that important information that I think is so critical is not that important in the minds of the NY Board of Regents. Last year I went ahead and taught the whole unit around it anyway, but I’ve learned the errors of my ways when I found that my students were lacking in, say, the ability to make a box-and-whisker plot.

To compensate, I (along with my fabulous co-teacher) did a one-hour lesson that I broke up into stations, with each station representing a different “Lying Technique” that I wanted the students to learn about. (I had already covered The Sample with the Built-in Bias and The Well-Chosen Average as a normal lesson prior, because those are still relevant topics.) Each station lasted about 10 minutes, with some time for wrap-up and transit.

First page of Station 1

I also did this to support the project I had them working on, which is the topic of another post.

Stations in pdf form.

### Egyptian Fractions

As I stated earlier, I’ve been trying hard this to integrate the other subjects more into my math lessons (and the other teachers are happy to work vice versa, because I’m on a great grade team). This process is made easier by actually having a Special Ed co-teacher for one section, and she specializes in math (and sees every subject, so can comment on all of them). So my first lesson explicitly tying history to math just went off, a lesson on Egyptian Fractions.

My goal for this lesson was really to get some fraction practice in while still learning something new, while also highlighting the “symbol that represents the multiplicative inverse,” , which I’d tie in on the next lesson about exponents (aka an exponent of -1). We worried, though, that the translation process would be too tough while dealing with fractions. That’s when we came up with this:

The Fraction Board has 60 square on it (which will be good reference for when I deal with sexagesimal Mesopotamian numbers soon), so each piece is cut to fit the amount of square that will cover that fraction of the board. To make the boards, I just made a 6×10 table in word as square-like as I could, printed on card stock. Then I cut the pieces out of the extra boards and had slave labor student volunteers color them in for me.

Each fraction have multiple pieces to represent the different ways you can fit them. (For example, 1/2 is 30 square, so I have a 3 x 10 piece and a 5 x 6 piece). But each fraction is also colored the same, because in Egyptian Fractions you can only use one of each unit fraction.

Then I would put up a slide like this on the board:

And the students would have to make that shape on their boards, with no overlapping and only using each color once. For the first one I shared a possible solution:

But I got really excited when the students could come up with multiple different solutions for each problem. And I would increase the difficulty of each one, until I would just get to a fraction with no picture:

And they still nailed it. Eventually I would move away from the boards and show the process of how to do it without the boards. We’d do some simultaneous calculation (using the greedy algorithm or more natural intuition) and checking on the board. Then we’d try with non-sexagesimal fractions. And every time we would translate our answers into hieroglyphics as well. So by the end of the lesson they could work on a worksheet where I just gave a fraction and they gave me hieroglyphics in return. (Not all of them could do this completely, but most could do some of the sheet). I think, overall, it went pretty well.

Egyptian Fraction Slides (Powerpoint)

Egyptian Fractions Slides (pdf)

(WordPress doesn’t seem like it’ll host my slides in their original Keynote form. That’s bothersome.)