## Geometry – Day 57 – Tessellation Project Cont’d & Area I

Why We’re Here:

1. We’ll make our own tessellations from a hexagonal base.
2. We’ll review the methods for finding area of rectangles, parallelograms, and triangles.

Materials:

1. Scissors
2. Index cards, pre-printed with a square and a hexagon.
3. Tesselations Project sheet

The Breakdown

1. Opener + Review (15 minutes)
2. Demonstrate Hexagon Tessellation (15 minutes)
3. Crafty Scissors Project Work Time! (35 minutes)
4. Clean Up (5 minutes)
5. Break (5 minutes)
6. Show and Tell (1.5 minutes)
7. Area Notes (20 minutes)
8. Area Classwork (20 minutes)

Attachments

Slide Deck

1. 54% (Times Newspapers)
2. You can also use hexagons to make tessellations.
3. Show how to make the cuts.
4. Do you see it? Do you?!
5. And do you know what’s special about The Angry Wolf?
6. He’s got friends.
7. Do you see the hexagons?
8. Introduce the second part of the project.
9. We’re bypassing any investigations here. This was a standard in, I dunno, sixth grade? So we’re just going to review.
10. Show them how to build a rectangle from the pieces.
11. Show them how to double the triangle to make a rectangle.
12. See revisions.

Notes & Revisions:

1. Should definitely have cracked some harder examples on slide 13, heavier on the Algebra. Next time give the area and work backwards to find base or height.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. #### e

February 22, 2007 - 9:29 am -

Do you do proofs in your geometry? In slide 6, for example, they could have proved that the area of any triangle is bh/2. The picture is there, they’d just need to put the words to it, use some triangle congruence and alternate interior angle thm. It would have been a nice exercise, I think.

2. #### e

February 22, 2007 - 6:25 pm -

Oops. There are 5 slides with number 6 on them. The one where you write the area of a triangle; 11. in the notes.

3. #### dan

February 22, 2007 - 6:32 pm -

Oh sure, yeah, okay. Y’know, the bulleted lists are not having fun inside some RSS readers. Firefox is fine, but, who knows.

Anyway, I took the opportunity to take them through an extremely informal proof of the conjecture, basically just a derivation of the formula. But I don’t think my easily-frustrated, fidgety, hedonistic high school students would’ve called an official foray back into proofs “nice.” Not by any definition of the word.

I hope that’s the difference between higher education and high school, but telling my kids, “Now let’s try a proof,” would’ve been a showstopper, I’m positive. Which is kind of a bummer.

4. #### e

February 23, 2007 - 7:51 am -

So, are you saying that there are absolutely no proofs in your curriculum? Not even proofs with triangle congruence and such? What else do you do in the geometry class? Now I have to see the textbook :) As for “…would’ve been a showstopper”, my attitude is that students don’t necessarily know what’s good for them :)

5. #### dan

February 23, 2007 - 5:23 pm -

Oh, no, we’ve got a unit on proofs. It’s a monster failing that I couldn’t make them enjoy proofs as much as I did when I was them.

But for me to be moving through area, building momentum there, only to break pace for a quick proof. Nah. There’s too much negative association there I don’t want to bleed all over this new topic. Maybe at the end of the area unit and, even then, only for a homework assignment.