Below is a link to a folder with the unit plan as well as each lesson plan:
https://drive.google.com/drive/folders/1a7b8uVXJj0466ErJnWDj8KFVF_lATDb2?usp=sharing
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The game/trick that I want to share is one that I learned from my dad. The trick involves creating a series of flash cards each representin...
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I feel very fortunate to be able to easily recall my favorite math teachers and struggle to bring to mind a least favourite. In reflecting o...
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My solution using conventional algebra: My solution without symbolic algebra: If 2 people eat one dish of rice, 3 people eat one dish of br...
Thanks Jacob! Here are some suggestions and proposed revisions to refine your unit plan:
ReplyDeleteGood rationale for this unit.
Your project is an interesting one, but I think that students will need quite a bit more guidance in (a) seeing the relationship between prime factorization and art, and (b) finding their own unique artistic forms for expressing relationships of prime factorization. I'd like to see how you will clarify the project topic and help students get involved enough that they can represent prime factorization as art. Perhaps it would be helpful to have each group choose a different artistic medium? (for example, a drawing, sculpture, origami installation, poem, instrumental music composition, dance, performance art, video, ...?) You might need to work through an example with the class for starters. They have probably never done this kind of math project before, and what you don't want is for kids to search the internet for someone else's math art project, in desperation!
You will also need to put together a fairly detailed rubric or marking scheme indicating your expectations for the project, especially since it is the main summative assessment of the unit. Do you think you might need to augment it with one other form of summative assessment -- for example, a brief interview with each student about what they learned and what still puzzles them about the unit, or something similar? I leave that to your judgement...
I am a bit worried about having students hand in correct solutions to all the comprehension quizzes at the very end of the unit. Again, I think this might lead some people to desperate measures like copying from others in the class if they feel they can't get everything ready at once. Is there a way kids could do this a bit at a time, so that you can see how they are doing and connect with each student who might need support before the unit is over?
In your second lesson, I suspect that 15 minutes is probably not enough to truly engage with the locker problem. Do you want students to work on it themselves, or do you want to (more or less) use it as a demonstration that you do? Similarly with the scales problem -- these take people a good deal longer than you've scheduled if they are really engaging with them on their own. (I love these puzzles, and wouldn't want to rush people through them without them having enough time to engage, get stuck, get unstuck, etc.)
For your second lesson, if you can fit it in, there's a great activity that Amanda Fritzlan led with our 442 class last year (when we had a lot more meeting time!), experimenting with/ proving Euclid 7.1 with subtracting different lengths of string! (Book VII. Proposition I:
When two unequal numbers are set out, and the less is continually subtracted in turn from the greater, if the number which is left never measures the one before it until a unit is left, then the original numbers are relatively prime.) You might want to ask Amanda about the details of this cool activity.
I strongly suspect that formulating arguments about whether 1 is an odd number will take more than 5 minutes as well! And as Matt suggests, you may need to scaffold the idea of making a mathematical argument, as many students will never have encountered this before. I suggest that you might want to have kids work in groups of three first, so that the boldest or most vocal students don't dominate the conversation and leave the others silent and passive.
I am very interested in your ideas about gesturing prime factorization and about the vertex-labelling game! But you haven't given any explanation of these in your lesson plan. Please clarify and exemplify for me (and your SA)!
ReplyDeleteIn lesson 3: what is it you expect students to notice about cycles? (Please clarify!) And once again, how does the gesturing of LCMs work? (Is this related to Sarah Chase's Number Theory dance ideas?)
Remember that students will have encountered LCMs in earlier grades as they learned to work with fractions, so make sure that your lesson helps them recollect what they already know and then build on it.
I like Matt's suggestion about using prime factorization to create their own secret code! It would take a bit of research to find a simple yet effective secret code activity that uses primes -- or perhaps it could be an error-correcting check digit activity, if primes are involved there? The idea of showing a short video is nice too.
Generally, I think you might be assuming that Grade 10 students will be able to solve problems and puzzles as fast as you do. They will not -- or if one or two moves that fast, the rest will not! Make sure to give kids enough time to really engage. If you rush them, most will just disengage and give up. Pace yourself, and be ready to teach fewer things, more in depth -- or to tell a bit so then give lots of time for participation.