Fall 2016 - Professor Kate Poirier

Category: Homework (Page 2 of 3)

HW #8: Due Thursday, October 13

Exercises 1-3 below are to be performed in GeoGebra. Exercises 4 and 5 are to be answered using complete sentences, including precise mathematical terminology. Email your completed homework to kpoirier@citytech.cuny.edu by 2:30pm on Thursday, October 13.

Exercises 1-3 are to be completed in GeoGebra. If you are using the desktop version of GeoGebra, attach your files to your email. If you are using the web-browser version of GeoGebra, include a link to your worksheet in the email.

Your answers for exercises 4 and 5 can be written in the body of your email, attached as a separate document, or included as text boxes in your GeoGebra file.

 

  1. Construct a triangle \bigtriangleup ABC. Construct the centroid, orthocenter, and circumcenter. Label these points G, H, and O, respectively.
  2. Put a line through two of the points constructed above. What relationship do you notice among the three points. Use the drag test to see if this relationship continues to hold. Add your conclusion as a text box in your GeoGebra worksheet.
  3. Measure the distances HG and GO. Describe the ratio $latex \frac{HG}{GO} as the triangle changes. Add this ratio as a text box in your GeoGebra worksheet.
  4. Write a clear summary of the relationships among the triangle centers that you discovered above (these relationships are the Euler Line Theorem).
  5. Does the above activity constitute a proof of the Euler Line Theorem? Why or why not?

HW #7: Article/blog post review – Due Thursday, October 6

There are lots of ways to consume information about technology in the classroom. Later in the semester, you will be reading and presenting formal research papers in the field. For this homework exercise, you’ll perform a much less formal review. Post your findings here on the OpenLab.

Instructions
  • Find an article or a blog post anywhere on the internet that discusses technology as a pedagogical tool.
  • Before you write your review, include a link to that article/post as a comment on this post to claim it as yours. Make sure none of your classmates have already chosen the same article/post.
  • Write a one- or two-paragraph summary of the article. (Write your summary so that when your classmates read it, they’ll know what the main points of the article are, and can decide whether they would like to read the article for themselves.)
  • Write a one- or two-paragraph statement expressing your opinion about the points made in the article. (You don’t have to be super precise here; you can discuss the points in the article whether you agree or disagree with them based on how they relate to your own experience.)
  • If the website where you found your article/post is not that of a well-known media organization, include one sentence about the kind of website it is. (For example, if you choose a blog post, the “About” section of the blog should tell you a bit about who the post author is.)
  • Submit your review, along with a link to your article/post as an OpenLab post. Title your post “HW #3: Review of [title of the article/post you’ve chosen].” Select the category “HW #7: Article/blog post review” before publishing your OpenLab post.
How to choose an article/blog post

You have some flexibility in terms of what you choose to review, but there are some rules you must follow:

  • Read a few different articles or blog posts before selecting one to review.
  • The article/post you choose must express an opinion about technology in the classroom, report on an academic study about technology in the classroom or discuss specific strategies for using technology as a pedagogical tool.
  • The article/post you choose should support its arguments with evidence.
  • The article/post you choose cannot simply report on a type of technology being used, or how widespread its use is. It cannot be a “how-to” guide for using a particular technology yourself.
  • The article/post you choose cannot be published by a company that is writing to promote its own product.
  • The article/post you choose should be long enough that it is insightful in some way.  Your summary/opinion should tell us why it is insightful.
  • The article/post you choose should be short enough that a fast reader could read it in under 15 minutes. (For example, you should not review a scholarly research article.)
  • If you have an article/post in mind and aren’t sure whether it is appropriate, link to it in the comments on this post and explain why you’re unsure. Leave enough time before the deadline to choose something else if I determine it’s not appropriate.
  • The article/post you choose should be written in English. If you find something that’s written in another language and that you’d really like to review, link to it in the comments on this post and explain why it appeals to you. Leave enough time before the deadline to choose something else if I determine it’s not appropriate.
Some resources

Note: some of these websites require a subscription to access articles, but will provide a selection for free to non-subscribers.

The Chronicle of Higher Education

Inside Higher Ed

New York Times Education Section

Los Angeles Times Education Setion

Washington Post Education Section

Slate

Math with Bad Drawings

dy/dan

 

 

HW #5: LaTeX scratchpad – Due Tuesday, September 27

\LaTeX (pronounced LAY-teck) is a commonly used language for typesetting math. There are many ways to use \LaTeX to create professional looking documents (most involve installing an implementation on your computer) but you can also use \LaTeX to type math right in your OpenLab posts.

Professor Reitz has some great instructions for using \LaTeX on the OpenLab here (scroll to “Typing math on the OpenLab”).

It can take some getting used to, your homework is to practice by submitting a comment on this post. Don’t worry about typing something that makes any mathematical sense, just try typing anything. Play around and make a giant mess in these comments. If something doesn’t work at first, don’t worry; just try again. (Note that your first OpenLab comment will have to be approved before it appears.)

You can mouse-over something to see what LaTeX code was. For example, mouse-over this: \frac{d}{dx} \left( \int_a^x f(t)dt \right) = F(x) to see what I entered.

If you submit something that LaTeX doesn’t understand, it will display “formula does not parse” but you can also mouse-over that to see what was submitted.

 

Other resources:

HW #4 – Due Thursday, September 22

Practice problems (do not hand in):

Venema 1.1.1, 1.1.2, Example pg 16-17, 1.2.1, 1.2.2, 1.3.1

 

Homework problems (to hand in):

  1. Perform the GeoGebra construction described in exercise 1.3.2. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Answer the question asked in the exercise by making a conjecture about the area of a triangle. Prove your conjecture.
  2. Perform the GeoGebra construction described in exercise 1.3.3. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Make a conjecture about the sum of interior angles of a triangle. Prove your conjecture.
  3. Perform a construction in Geogebra which is analogous to exericise 1.3.3, but replace the triangle with a quadrilateral. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Make a conjecture about the sum of interior angles of a quadrilateral. Prove your conjecture. (Hint: use your result from 1.3.3.)
  4. Perform a construction in Geogebra which is analogous to exericise 1.3.3, but replace the triangle with a pentagon. On paper, draw a diagram describing what you witnessed in the drag test in GeoGebra. Make a conjecture about the sum of interior angles of a pentagon. Prove your conjecture. (Hint: use your result from 1.3.3.)
  5. State and prove a conjecture about the interior angles of an n-gon, for any n. (Hint: you are generalizing the work you did in exerices 2, 3, and 4 above.)

Venema exercise 0.8.1 hint

I took a quick look at the exercises from section 0.8 today. I’m not sure I understand what the hint for 0.8.1 is getting at, so I came up with a hint of my own. Feel free to use it or ignore it.

  • Hint: try completing 0.8.2 first and then use it for 0.8.1.
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