Tag Archives: openlab

OpenLab #9: Advice for the Future

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Assignment (due Thursday, December 17 – final exam day).  Imagine that you are invited to speak on the first day of MAT 2071, to give advice to entering students.  Write at least three sentences responding to at least one of the following, describing what you would tell them.

  1. What do you wish that you had been told at the start of this class, to help you succeed?
  2. Choose one topic in the course that is especially challenging. Identify it, and give advice to students trying to master that topic.
  3. What is the most important prior knowledge (not taught in the class) that you need in order to succeed?  Why is it important?

Extra Credit.  Respond to someone else’s comment.  Do you agree? disagree? Have anything to add?

OpenLab #8: Hold your breath and dive into math – Vi Hart

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Vi Hart describes herself as a “recreational mathemusician” – she has a unique approach to mathematics and its connections to the world.  In this assignment you’ll be exploring some of her videos (she has a YouTube channel here), and using them as a basis for creating a new blog post.

Assignment (Due November 5, 2015).  Create a new blog post responding to the instructions below. Creating a new blog post allows you more flexibility than simply leaving a comment. You have the ability to edit your work after you submit it, and to include photos, videos and other media. It also allows you to contribute to the public content of our course website.

You can get started by clicking the plus sign at the very top of our site (if you don’t see it, make sure you are logged in to the OpenLab). Detailed instructions on creating a new blog post can be found here (see “Writing a Post” in the middle of the page). You should create a new post including the following:

  • The title should include the word “Videos” and also your name.
  • Your post should include responses to all three parts of the assignment described below.
  • Under “Category,” select “OpenLab Assignments” (you will see this on the right side of the screen)
  • Under tags, enter “OpenLab 8”, “Vi Hart”, and any other tags you think describe the videos you watched (for example, you might choose “pi” if it’s a video about pi).  Don’t forget to click “Add” after entering your tags in the box.
  • When you’re done, click “Publish” (the blue button towards the top right on the screen).

Instructions:

Watch at least three different videos by Vi Hart from  https://www.youtube.com/user/Vihart/ .  You should:

  • choose videos at least 2 minutes in length
  • choose videos that are related to math in some way
  • choose three videos, at least two of which should not appear on her front page (older or less popular videos).  For a full list of her videos, click the “Videos” button near the top of her page – or click here.  Scroll to the bottom and click “Load more” to see older videos.

In your post, include a response to each of the following three Parts:

Part 1. Include a link to each video you watched (3 minimum), the title, and a one or two sentence description of what the video was about.

Now choose one video to focus on.  You MUST watch it 3 times. Use it as the basis for parts 2 and 3.

Part 2.  Write one paragraph discussing the contents of the video:

  • How did you feel watching it? Did you like it, or not? Were you confused? Inspired? Bored? Excited? Bewildered?  Why?
  • What is one thing you learned from the video?
  • What is one question you have after watching it?

Part 3.  Write a one-paragraph reflection discussing what the video could mean to your own math teaching.  Is it math? Is it teaching? Is it relevant to the work you will be doing in the classroom? Is there any connection to the earlier reading assignment Lockhart’s Lament?  Any other thoughts?

Extra Credit.  You can earn extra credit by responding to one of your classmates’ posts.  As always, be kind, be respectful, be honest.

Week 9 Assignments

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Written work, Due Tuesday, November 3rd, in class:
Chapter 6 p.116: 3,4,5,8,9
      **NOTE: this assignment is not due until November 3rd, HOWEVER I strongly recommend that you spend some time working on the first problem before Tuesday October 27 – this is a tricky topic and tends to give people some trouble, so early preparation will help you!
WeBWorK – none
OpenLab – OpenLab #7 due Thursday, October 29th at the start of class

Class work: There will be group & individual work completed & submitted in class on Tuesday 10/20/15, which will count towards your “Project” grade.

OpenLab #5: Bridges and Walking Tours

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The assignment below is due BEFORE CLASS on Thursday, October 8th (it is essential that you complete it before class, as we will be doing a class activity building on the assignment).

We are going to play a game creating walking tours of cities with bridges.  We begin in the city of King’s Mountain, which is built on four land masses – both shores of a river and two islands in midstream – connected by a total of seven bridges (shown in green).

EXAMPLE 1:  Can you create a walking tour of the city that crosses every bridge exactly once?  You can begin anywhere you like, and end anywhere you like, as long as you cross each bridge just once.

Background – Graph Theory

We can simplify the picture of King’s Mountain to make it easier to deal with:

The key elements of the map are the four land masses (let’s label them A, B, C, and D) and the seven bridges (p,q,r,s,t,u and v) (thanks to mathisfun.com for the images):

For the purposes of our problem, we can simply think about each land mass as a point (A, B, C, and D), and the bridges as lines connecting the points (p,q,r,s,t,u and v) – like this:

We call this kind of picture a graph – the points are called vertices and the the lines are called edges.  Our goal of finding “a walking tour that crosses each bridge once” is now matter of tracing out all the edges without lifting our pencil (and without repeating any edge).

Assignment, Due Thursday 10/8 (beginning of class)

Warm up (This Warm Up is just for practice – you do NOT need to submit your answers – see below for the three-part Assignment to be submitted).  The following examples build on EXAMPLE 1 above.

WARM-UP EXAMPLE 2: If you are given the freedom to build one new bridge in King’s Mountain (“make one new edge in the graph”), can you do it in such a way the walking tour becomes possible?  Do it!

WARM-UP EXAMPLE 3: If you are given the freedom to destroy one bridge (“erase one edge”), can you do it in such a way that the walking tour becomes possible? Do it!

WARM-UP EXAMPLE 4: Construct walking tours for each of the following graphs (or decide if it is impossible).


Assignment.  Your assignment has 4 parts.

PART 1.  Leave a comment responding to EXAMPLE 4 (above), telling us for each one of the 8 graphs whether a walking tour is possible or not.  You only have to state whether it is possible or impossible for each one.

PART 2.  Challenge your friends:  Now it’s up to you to build your own graph, and challenge your classmates to construct a walking tour (or to determine if it is impossible).  It can consist of as many points as you wish, and as many bridges (edges) connecting them.  You MUST label your points “A, B, C…” etc.  When you’re finished, decide for yourself if a walking tour crossing each bridge exactly once is possible.   Remember, the most challenging puzzles are the ones where the answer is difficult to determine. Post two puzzles in the comments.  See the note  “POSTING YOUR PUZZLE ONLINE” below for instructions on how to draw and share graphs online.

PART 3.  Solve a friend’s puzzle.  Leave a response to a friend’s posted puzzle, giving a solution.  TO POST A SOLUTION, JUST LIST THE POINTS OF YOUR WALKING TOUR IN ORDER.

Example:
Here is a puzzle: http://sketchtoy.com/65962726 
Here is a solution: (start at A) – A, C, B, A, D, C

PART 4.  The third part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt.  Be sure to respond to each part:

Writing Prompt:  Did you enjoy this assignment? Why or why not?  Describe a connection between this assignment and our work in the class.  (If you don’t believe there is a connection, try to imagine why we are doing this).  Leave your response in the comments.

POSTING YOUR PUZZLE ONLINE.  I recommend the site sketchtoy.com – it allows you to draw something, then click “SAVE” and get a link to your drawing.  You can post the link in a comment, and we’ll be able to click on it and view your drawing.   Don’t worry if it’s not pretty!  For example, here is a graph that I drew (can you find a walking tour that crosses all edges?): http://sketchtoy.com/65962726

 

OpenLab #4: The MIU puzzle, continued

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This assignment is a continuation of OpenLab #3, on the MIU puzzle.  Your assignment this time is a little different.  Consider the following statement about the MIU puzzle:

Statement.  Any goal word (any word with first letter M, followed by a combination of U’s and I’s) can be obtained from the starting word MI using the rules of the MIU puzzle.

Assignment (Due Friday 9/25 – Because of the nature of this project, please do not post your answer before Wednesday 9/23). Do you think the statement above is true or false?  I would like you to think about it and see if you can convince yourself of the answer.  Try out different things!  If one idea doesn’t go anywhere, see if you can come up with a different approach.   This is an assignment about metacognition as well as puzzle-solving – pay attention to your thoughts and ideas, even (especially) the ones that don’t work out!

In the assignment below, you will be writing about your experience working on the MIU puzzle above.  Be sure to respond to EACH PART – detailed answers to part 2 and 3 below will gain the MOST credit.

  1. Write down what you think the answer is (is the statement TRUE or FALSE?).
  2. Describe in as much detail as you can the process of working on the assignment.  What did you think in the beginning? What are the different things you tried in order to solve the problem?  Describe each one, in the order that you tried them.
  3. Give a detailed list of the resources you used, and how you used each one (these could include anything – your brain, pen & paper, a computer (what applications did you use), the internet, other people, and so on).
  4. What activity or resource do you feel was most effective for you in working on the assignment (what helped you the most in understanding the assignment and figuring out an answer)?
  5. If you believe the statement is TRUE, post an example of a goal word that you encountered in your work that you think was most difficult to solve.  If you believe the statement is FALSE, post an example of a goal word that you believe is impossible to obtain by starting with the axiomatic word MI and following the rules.

Extra Credit.  Respond to one of your classmates’ submissions.

 

Week 4 Assignments

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Week 4 Assignments

HEADS UP: Next week there are no classes on Tuesday 9/22 or Wednesday 9/23.  We have class as usual on Thursday 9/24.  However, we also have class on Friday 9/25 as it is a Tuesday schedule.

Written work – none
WeBWorK – Assignment #3, due Thursday, September 24th, at midnight.
OpenLab – OpenLab #4, due Friday, September 25th (at start of class) – Because of the nature of this project, please do not post your answer before Wednesday 9/23.

OpenLab #3: The MIU puzzle

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We are going to play a game with strings of symbols.  This game was invented by a man named Douglas Hofstadter and found in his book Gödel, Escher, Bach. Here are the rules:

Suppose there are the symbols ‘M’, ‘I’, and ‘U’, which can be combined to produce strings of symbols called “words”, like MUI or MIUUU. The MIU game asks one to start with the “axiomatic” word MI and transform it using the following four rules, to obtain some “goal” word.  The rules state:

  1. You must always begin with the word MI, and attempt to reach the goal word.
  2. You may add a U to the end of any string ending in I. For example: MI to MIU, or MUUII to MUUIIU.
  3. You may double any string after the M (that is, change Mx, to Mxx, where ‘x’ represents any string of symbols). For example: MIU to MIUIU
  4. You may replace any III with a U. For example: MUIIIU to MUUU
  5. You may remove any UU. For example: MUUU to MU

WARM UP.  In each example, start with the axiomatic word MI and show, step-by-step, how to obtain the goal word (in each step, state which of the rules you used). These are just for practice (you do NOT need to submit your answers).

Example 1: Goal word MIU
Example 2: Goal word MIIU
Example 3: Goal word MIIUIIU
Example 4: Goal word MUUII
Example 5: Goal word MUUIIUIIU

Here is a sample solution to Example 2:
Our goal is to reach the word MIIU.  According to rule 1, we begin with
MI to MII (rule 3)
MII to MIIU (rule 2)

Assignment (due Thursday, 10/17): Your assignment has three parts.

PART 1.  First, create an MIU puzzle — that is, make up a goal word, and post it in the comments. Your goal word should be between 8 and 16 letters long.  Try to make it tricky to reach, requiring at least four steps to reach (but the more the better!).  See if you can find a clever use of the rules!

PART 2.  The second part of your assignment is to solve someone else’s puzzle.   Type your solution step-by-step, indicating which rule you used at each step.  Leave your comment as a response to their puzzle.  Only one solution per puzzle!

PART 3.  The third part of your assignment is to write a short paragraph (at least 3 sentences) responding to the following prompt.  Be sure to respond to each part:

Writing Prompt, MIU puzzle:  Did you enjoy this assignment? Why or why not?  Describe a connection between this assignment and our work in the class.  (If you don’t believe there is a connection, try to imagine why we are doing this).  Leave your response in the comments.