Back in mid June before I went to my workshop I sent out 2 sets of e-mail for summer math work - one to my rising precalculus students, and one to my rising geometry students. I'm still working out how I'll grade these or assess these, since this was a last minute decision, and basically given out via e-mail without any warning to the students to watch for e-mail (long story).
I'm not sure of the fairness in holding them accountable for this work since some may not even get it. What I'm leaning towards is for THIS SUMMER (as opposed to next because I'm sure this will now be a given) is to either give them extra points on the homework portion of their semester grade, or to create an extra quiz grade and assess it that way, and for the students that did not do it, they do not get the quiz opportunity.
Here's my precalculus e-mail:
You can finally breathe a sigh of relief, your summer math work has arrived. You're going to be learning a ton of cool things in precalculus next year, and there are a few things I want you to refresh your memory on: function notation, right triangle trigonometry, and special right triangles.
You're welcome to do these things in any order and at any time over the summer, but I highly recommend spreading the wealth out and not cramming it into one or two sessions. I also recommend maybe ALSO looking at the information and doing the practice once every few weeks, so it has time to soak in and get trapped in your brain cells.
Here are some suggested sites for each of the three topics. Note that they may not be the best for how you learn, so you're welcome to Google search on any of the purple topics on your own. You know if you're successful if you can complete all of the "goals" with great accuracy. By mid July, I will send you some online quizzes for each of these topics. Your job is to take the quizzes and score 80% or better. You can take various versions of the quiz as many times as you like.
Please send me e-mail once you've received this e-mail, and you can e-mail me any time during the summer.
function notation video:
1. be able to evaluate functions presented in function notation for numerical inputs (i.e. find g(7) if g(x) = 5x^3 - 9x + 1)
2. be able to evaluate functions presented in function notation for any expression input (i.e. find h(x^2+1) if h(x) = 4x - 3x^2)
3. be able to find the input that satisfies the output (i.e. find x such that f(x) = 10 if f(x) = 2x^3 - 6)
sine cosine tangent:
1. given any right triangle and a designated acute angle in that triangle, you can set up equations for sine, cosine, and tangent
2. you can pronounce "sin" accurately
3. on any right triangle with angle information given and one side length given, you can use trig to find the remaining 2 side lengths
4. on any right triangle with side lengths given, you can find the remaining angles of the triangle
special right triangles:
1. you can recognize 30-60-90 triangles and 45-45-90 triangles
2. you can quickly place the ratios of sides around either
3. you can find all exact side lengths of a special right triangle given any side
For geometry I decided to make it two-fold: actual math practice, and a project.
Here's the e-mail:
Here is your summer geometry work with instructions included in the document. I'd recommend downloading the attachment instead of just viewing so that the formatting doesn't go all crazy on you. Have fun, and look for another e-mail from me some time in July (as mentioned in the attachment).
Please send me e-mail if you have any questions.
Big Hugs and Big Math,
(here's part of the attachment):
Hello Future Geometry Kidlets,
There are 2 parts to your summer math work (you’re welcome).
Choose one of the following projects to complete. These are due the first day of class, and we’ll share out. I will do the project also and share my results.
1. Go to this link: http://www.district87.org/staff/powelln/Geometry/Projects/GoldenRatio/GRProject.htm
2. Click on various parts to see what’s what.
3. If you didn’t already, click on the “learn about pantographs” link under the “CONSTRUCTIONS” part of that page (http://www.ies.co.jp/math/java/geo/panta/panta.html). Play around with the applet on the bottom.
4. Make your own real life pantograph. Figure out how much larger you make your drawing (give me a ratio and explain how you found it). You can be creative with the objects you use. You don’t have to spend a ton (any?) money. Extra points if you can do this for free.
1. Go to this link: http://www.district87.org/staff/powelln/stringart/index.html
2. Click on the various links to explore “string art”.
3. Explore this YouTube video: (http://www.youtube.com/watch?v=gPn8obkZyPI) and possibly others shown on that page.
4. Create your own string art. Again, you can be creative with the objects you use. You don’t have to spend a ton (any?) money. Extra points if you can do this for free.
1. Go to this link: http://www.district87.org/staff/powelln/Geometry/Projects/OrigamiMobiles/OrigamiMobiles2007.htm
2. Click on the various links to explore “origami mobiles”.
3. Create your own origami mobile. You must have at least 6 different origami pieces. Your mobile must balance.
4. Again, be creative with the objects you use. You don’t have to buy origami paper. Extra points if you can do this for free with objects found around the house.
Complete the following problems. You must show all your work. I will send an answer key soon for you to check your work. I will also send a few online quizzes some time in July to make sure you understand the concepts. You can take the quizzes as many times as you want, but you must ultimately score at least an 80%.
Now the chickens come home to roost, or the fat hits the frying pan, or whatever.... I'm off to make the quiz assessments on proprofs.com. And I will also do all 3 projects for fun and to see what the various cool math aspects are.