My next unit in geometry is on transformations. I'm going to lay out all my options and then organize them via blog post, just for fun.
As a geometry team at school we got together and decided these were the important ideas:
- translate
- rotate about the origin multiples of 90 degrees
- reflect over a variety of horizontal and vertical lines, not just the axes
- wait to dilate until we get to similarity, for now rigid transformations only
- use the phrase rigid transformations
- use the prime notation P -> P'
- incorporate language about congruence, including corresponding parts
- one of our textbooks emphasizes coordinate rules, we will not emphasize them, in fact we will encourage students to physically rotate the paper rather than memorize a rule
Last year I had kids draw block letters on the coordinate plane and then perform two transformations in different orders (first translate then reflect vs. first reflect then translate) and compare. The worksheet is not getting along with scribd or I'd share.
This year I think I will have students do one example of each type (translate, rotate, reflect) individually or in pairs and then take notes on the basic definitions as a whole class activity (most kids are familiar with the terms but I have a crew of English Language Learners, definitions are important). From there we will break into stations.
- transformation mini golf (the game link isn't working at the moment, I hope it's back soon!)
- draw your own image and then transform it all three ways
- basic practice problems
- more advanced practice problems (last year's sheet? MCAS problems?)
- something with transparencies, because we have them and they're cool
And that's my outline. We are going to spend about a week on this. What have you done in the past? I know other people have different mini golf options - I think I have some links saved at school but I am currently at home.
Your unit looks very much like the one we did earlier this semester. The only difference I'm seeing is that we included rotational and point symmetry. This was new for us this year, so it is good to see someone else planning a unit as we did. Thanks for sharing and helping me to see where we made some good decisions. We also decided to wait for dilation until similarity, it seemed like one more thing to confuse students at this point when we weren't going to use it specifically right away.
ReplyDeleteTeresa Ryan
Curious about this question - How sophisticated do the algebraic manipulations become here? My Geom teachers have shied away from much in the way of transformational/coordinate geometry. I tend to think that this is an interesting vein to mine. I'd love to 'hear' how this turns out.
ReplyDeleteTeresa- do you mean symmetry within a given figure? That should be included in here too.
ReplyDeleteMrDardy- which question? We don't generalize anything algebraically, the only thing that gets generalized at all is a thought experiment on which transformations are commutative.
I can't talk up Swish enough. It's an amazing game that teaches kids to think in rotation, reflection and translation, putting the whole thing in their minds.
ReplyDeleteEven better, it does so without them thinking they are doing math!!
I used the internet wayback machine to try to find that minigolf link. It looks like the site in the UK that originally hosted it is down (hopefully not forever, but maybe) so here's the wayback link: http://web.archive.org/web/20121206130826/http://www.mathsonline.co.uk/nonmembers/gamesroom/transform/golftrans.html
ReplyDeleteThanks Justin and Max! I'll check those both out.
ReplyDelete