## Thursday, August 26, 2010

### Lovely Week!

I am having an amazing teaching week. :) Highlights:

• I started doing MATH origami with my Honors Geometry kids! It's fantastic!! The whole idea is that I would give them diagrammed instructions (with no words on there whatsoever), and they would have to try to figure out how to make the end product by reading the diagrams. On Day 1 of trying this (ie. today), I gave them something that I had thought would be really easy (I had tried it myself and it was relatively easy for me to figure out), and both honors classes were completely stumped (and incredibly engaged)! Yessss. This module is going to be great.

This first one was supposed to show them how to fold / cut out a regular pentagon out of a square sheet of paper. In the end, after their struggling with it for 15 - 20 minutes and having had varied levels of success / frustration, the bell rang and I announced that we'd have to re-do this particular exercise next week (ie. making pentagons again). The difference is, next time, I'll guide them through reading the diagrams step-by-step (paying careful attention to where the creases are supposed to be and which points should meet up), and we will work on precision as a class. My hopes are that their regular pentagons from next week will be precise enough to allow us to introduce some good geometric vocabulary, and to measure congruent interior angles. :) After that, I have plans for them to make a regular hexagon, followed by a tetrahedron that requires no glue!! (Even other teachers are loving the tetrahedron. I went around Open House yesterday to show off my new origami toy in between parents talking to me, and all the teachers wanted to run off with it! haha. That's how you know it's kid-ready, I guess!)

By the way, all this good stuff came from 3-D Geometric Origami, which is a super fun booklet of foldable geometric shapes (2-D and 3-D). In doing these constructions, we can introduce naturally a slew of geometric terms about faces, edges, angles, etc. I have plans to get the Honors kids stronger at independently building stuff throughout the first quarter, so that when we move on to heavy-duty compass/ruler constructions of polyhedron nets in the 2nd and 3rd quarters, they'll be kinesthetically (and emotionally) ready.

(The regular Geometry kids will benefit from the origami lessons as well, but because they will need more time getting through the regular curriculum, I'm not going to give them the serious polyhedron net construction projects later in the year. They'll still do some good compass constructions though, because I plan on doing some simple line designs with all my Geometry classes, and those require the construction of regular polygons.) :)

• In other news, all of my Geometry kids have been working on setting up algebraic equations with info embedded in geometric diagrams. They seem to be doing better this year with distinguishing the different scenarios for setting up different types of equations. I'm not sure if it's just because it's my 2nd time teaching these exact topics, or what, because I don't feel like my approach has changed drastically from last year, and the kids are having significantly less trouble. There's only been micro-changes, like this year I have emphasized the idea, "Do we have enough info to set up an equation? Do we now? Do we now??" as I put up algebraic lengths piecewise on the board. Does that really make a huge difference in their comprehension??

• Precalc has been smooth-sailing as well. This week (thus far), we did some good graph-reading, reviewed what a function is, and introduced how to identify its domain and range given a graph. I have a lovely activity for introducing functions, which I didn't come up with but I feel like has been smoothed out over the years every time I present it. Now, it's gotten down to me preparing (in advance) a series of ordered pairs representing a function, and putting them on post-its. (Input goes on one post-it, output goes on another. You stick the two post-its together, front and back.) I draw a "function magic" box on the board with an arrow going in and one coming out, and I start to reveal ordered pairs as I stick the input post-its in and return with the output value on the other side. The reason why I use post-its is simple: as I reveal the ordered pairs, I stick them onto the board in function diagrams (the ones that look like two big ovals, one for domain and one for range), and kids copy them down from the board, one ordered pair at a time. For this intro demo, I always choose some numbers with patterns, so that kids can get excited about making predictions -- and I also use a function that has shapes/symbols as inputs and where the output is consistent, ie. always 5. This way, I can show them that even when one output is shared by different inputs, the function still behaves "predictably" (ie. if it returns 5 always, that's pretty damn predictable) and is still a function. And it also shows them that functions are not limited to numeric domains and ranges.

After this, I have the kids pair up and I give each pair a set of flash cards, showing functions and non-functions in graphs, tables, diagrams, and word descriptions (ie. "a function that maps age to height"). The pairs of kids have to separate them into two piles, one for function and one for non-function. It's not fancy, but it works really well to quickly go through MANY examples and the kids are really actively engaged. In the end, we quickly go over the answers as a class.

As for teaching about domain/range of graphs, I totally stole Sam Shah's idea of domain / range meters, and the kids thought it was funny (and probably thought I was "not cool"), but it worked like a charm!! I was thrilled. Kids were beeping (umm, quietly... these kids are waaaay docile...) when they were doing their own classwork problems. heehee

I love teaching! I love the world. Off to Day 2 of Open House (this time, with freshmen parents)!! :) :)