Exam 3 Review notes

Hi everyone,

Two comments on the Exam 3 Review sheet:

  1. ¬†In class, I proposed a strategy for solving problem #2, which was to¬†break into cases based on the remainder when n was divided by 4. ¬†While I believe this strategy will work, it is simpler to simply look at the cases “n is odd” and “n is even”. ¬†Despite my comments in class, this method really will work (can anyone explain why?)
  2. It looks like the answer¬†for problem #7 in the answer key was all wrong – I’m not sure what happened. ¬†In any case, I’ve updated it, so it should now be correct.

Both of these corrections were due to a diligent student who will remain nameless (but, in fact, it was Irania – nice work!).

Let me know if you find anything else,

Prof. Reitz

Semester Project – Group Presentations: Description and Grading Criteria

The last significant group assignment for your semester project is a group presentation (there will be one more individual assignment, a reflection on the process). ¬†I’ll put the details here, followed by an outline of the grading criteria (the presentation is worth 20 points total).

Semester Project – Group Presentation

This is your chance to share your group’s work with the rest of the class.  Each group will give a 5-8 minute presentation, including the following items:

  • State your conjecture (this should be written down, either on a slide or on the board). ¬†Give an explanation, and an example to demonstrate your conjecture.
  • If you were able to prove your conjecture, give a proof. ¬†If not, describe briefly some of the ideas you had and strategies you tried while trying to prove it.
  • Give the class at least one puzzle to work on on their own – a challenge!
  • Give the audience a chance to ask questions (either during the presentation, or after).

Keep in mind the following:

  • You¬†must include some kind of slides (you may also put work on the board): ¬†PowerPoint, Google Slides, Prezi.com, LaTeX Beamer, or other.
  • You may decide as a group how to divide up the work, but each group member must present something to class.
  • Be aware that you will be asked at a later time to describe your own specific contributions as well as those of each group member.
  • Presentations will be given at the beginning of class on Tuesday, 12/1 and Thursday, 12/3. ¬†Your group must sign up for a presentation time before leaving class on 11/19.

 

Grading Criteria (20 points total)

_____ points (4 possible).  Basics.  Stay within time limits (5-8 minutes). All group members participate.

_____ points (6 possible).  Conjecture.  Conjecture is written down.  Explanation and example are provided.

_____ points (7 possible).  Proof of conjecture or proof process description.

_____ points (3 possible).  Challenge the class.  At least one puzzle is given for the class to work on on their own.

 

____ points TOTAL (20 possible)

 

Videos Irania Vazquez

Part 1 : Doodling in Math Class: DRAGONS   In the video, she talks about the lines repetition of zig zags and can for different structures and if in 90 degrees can outline the folds of a piece of paper folded in half multiple times.

Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3]  In this video, Vi Hart talks about spirals in nature and how they are related to the Fibonacci series. Her conjecture is that the number of spirals on plants are elements of the Fibonacci series.

What was up with Pythagoras? In this video, Vi Hart talks about how Pythagoras came up with the Pythagorean Theorem and was contradicted by a man who stated his thought off all numbers being rational was false and applied it with his discovery of the Pythagorean theorem.

Part 2: I felt really excited throughout watching several of these videos although Vi Hart does talk pretty fast and was pretty intrigued by the video of “What was up with Pythagoras?”. I was a little confused by the part where they started saying that everything was even but was odd and watched it again and realized that they were contradicting their statements. One of the things I learned from the video was that Pythagoras disliked beans with a passion and found this a little funny and silly. I really liked how she incorporated¬†drawings and examples to¬†show the ideas and concepts.¬†I found her¬†drawings cute and adorable and really help the audience visualize the idea. One of the questions that I have after watching the video would be if Pythagoras was in denial about the existence of irrational numbers,¬†¬†are there concepts today that people don’t set out into the public because they have the¬† same problem as Pythagoras. There are probably many concepts we still don’t fully understand but we should always be open to new ideas.

Part 3: This video shows the origin of the Pythagorean theorem and shows how it was derived. The Pythagorean theorem is most definitely math and students should be shown how the Pythagorean theorem was conjured instead of just given the formula. As Vi Hart said, there were no formulas or variables back then and yet they were able to make this marvelous concept from connecting different concepts. This video is related to the reading from Lockhart’s Lament. It shows the concepts of origination and how they came to be from basic concepts. There were parts in the video were I paused it and was able to see how she worked out a proof by contradiction on how the square root of 2 is not rational. It is always nice to glimpse at something and realize you understand what they are doing. I really enjoyed watching these videos.

Fuzail’s videos

1)

b. Rhapsody on the Proof of Pi = 4:  https://www.youtube.com/watch?v=D2xYjiL8yyE

proves that pi= 4.

b. Dialogue for 2:  https://www.youtube.com/watch?v=dBVoIUASFS0

This video showed that there are lots of number you can add and the result will be 2. You can say 1+2=2, ¬†¬Ĺ+¬Ĺ+¬Ĺ+¬Ĺ=2 etc. Also 2 is so friendly and easy number.

c. How I Feel About Logarithms:  https://www.youtube.com/watch?v=N-7tcTIrersThis video

This video shows different way to add, devices and multiply numbers. Which is easier to understand and logical.

2)

When I watches the first video, I was lost. I did not understand the proof even though she drow nice. I felt like she was rushing while she was explaining. If she would have take more time to explain the problem then I would understand it. I learned that the students’ understanding is based on the way a teacher teach. My question is, why does a pi relates with a circle?

3)

From my knowledge, this video did not shows a good method of teaching. As I said in last paragraph, it was fast and not clear which makes me confused to understand how does pi=4. It was a poor math teaching video. From this video we can see that if a teacher take time, ask question and explain clearly then the students will more like to understand the concepts.

Part 1

Part 2
I would like to talk about the Fibonacci video. I really enjoyed watching this. She explains how and why the sequence has the numbers they do. It is a series of numbers in which each number ( Fibonacci number ) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc.Using spirals were a great way to show the sequence and how it is incorporated in nature.
Part 3
The reason I enjoyed this so much was because my calc 2 professor while teaching this topic started to explain how nature revolved around the Fibonacci sequence. She then also said something that made me start thinking which was the reason you cant find four leaf clovers is because four is not one of the numbers in the Fibonacci sequence as you can see 1,1,2,3,5,8 the number four is missing.

Openlab # 8

A. “Math Improv: Fruit by the Foot”

This video is about how we can play tick with strip paper or fruit snack.

B. “Pi Is (still) Wrong.”

In this video, the author cooked pies to show Pi is not Pie and Pie is not Pi.

C. “Hexaflexagons”

This is also a video which talks about how to play with paper by folding it into different shapes.

I would like to focus on the video C. I did enjoy watching this because it is very interesting to see how math is being used in real life. I like this video because it reminds me how I used to play games with paper by folding it into different shapes. I felt excited about this video as I never thought different colors will make the “hexafexagon” so special. It will be fun and meaningful if we could teach little kids to play with this idea. Also, since it is about shapes, which makes it connected to math in some sense.

I think it will be a good idea if we could apply some of Ms. Vihart ‘s thoughts into teaching. This helps teachers make students engaged in some class activities. It also helps students learn the relevant materials better by doing something interesting to them. I agree it is Math as we know Math is everywhere. We could not limit Math at the work we do in class, for instance, written assignments. In Lockhart’s Lament, he talked about how Math is a form of artistic work along with its elegance. Similarly, in Vihart’s videos, she uses different tricks and games to show Math in a fun and easy way. As a result, besides classwork, it is encouraging that students should watch some videos like these to enrich mathematical minds. The same to teachers who should also learn how to deliver these ideas and knowledge to their students.