Tag: openlab

OpenLab #7: Advice for the Future

Assignment (due Thursday, December 12).  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?

Week 8 Assignments

Written work, Due Tuesday, October 22, in class:
Chapter 4 p.100: 4, 5, 10, 11
Odd problems are worth 4 points, even problems worth 8 points.
WeBWorK – none
OpenLab – Recall: OpenLab #5 due at the beginning of class on Thursday, 10/24.  NOTE: Please complete the writing portion on the OpenLab, but bring your Conjecture to class on 10/24 (do not post your Conjecture to the OpenLab

 

Week 6 Assignments

NOTE: Next week Tuesday 10/8 there are no classes at City Tech.

Written work – None.
WeBWorK – Assignment #5, due Thursday, October 10th, at midnight.
OpenLab – OpenLab #4, due Thursday, October 10th, before class.

OpenLab #4: Bridges and Walking Tours

The assignment below is due BEFORE CLASS on Thursday, October 10th (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 10/10 (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 the example above.

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!

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!

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.  For each of the four graphs below (G1 – G4), decide whether it is possible to create a walking tour crossing each bridge exactly once.  Post your solutions here (TO POST A SOLUTION, JUST LIST THE POINTS OF YOUR WALKING TOUR IN ORDER).  If it is not possible to create a create a solution, say so!Euler Paths G1-G4

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/67467551
Here is a solution: (start at A) – A, B, D, A, E, B, C, E

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/67467556

 

Week 5 Assignments

Week 5 Assignments

NOTE 1: Exam #1 will take place on Thursday,  9/26 (first half of class).
NOTE 2: Next week Tuesday 10/1 there are no classes at City Tech.
NOTE 3: The following week Tuesday 10/8 there are no classes at City Tech.

Written work – none
WeBWorK – Assignment #4, due Thursday, October 3rd, at midnight. You are encouraged to start working on Assignment #5, which will be due one week later.
OpenLab – OpenLab #4: Bridges and Walking Tours due AT START OF CLASS on Thursday, 10/10.

 

Week 4 Assignments

Week 4 Assignments

UPDATE: WeBWorK Assignment #4 will be due next week, Thursday 10/3.

Written work – none
WeBWorK – Assignment #3 and Assignment #4, due Tuesday, September 24th, at midnight.
OpenLab – none

STUDY – for your first exam, taking place on Thursday, September 26th, during the first hour of class.  A review sheet will be posted at least 1 week prior to the exam.

Week 3 Assignments

Week 3 Assignments

Written work – Sec 1.8 p.29: 3, 5, 6, 8, due Tuesday, 9/17 (in class)
WeBWorK – Start on WeBWorK 3, (it will not be due until Tuesday, 9/24 at midnight).
OpenLab – OpenLab #3, due Thursday, 9/19 (at start of class).

 

OpenLab #2: Mathography

This assignment is due Thursday, September 12, at the start of class.

Assignment.  Choose ONE of the following two topics.  Write a reply to this post, responding to the topic.  Begin by telling us which topic you chose. (1-2 paragraphs).

Topics.

  1. Sometimes people can recognize a time when their opinion of math dramatically changed either for the better or the worse. If such a time happened to you, tell us about it.
  2. Choose an experience you had in which you suddenly understood a math concept (it could be any kind of math, from elementary school up through college).  Describe what happened.  Do you think you could explain it to others in a way that they could have the same flash of understanding?

Extra Credit.  For extra credit, write a response to one of your classmates’ comments.  Do you feel the same, or different?  Did you learn anything?  Did you get any ideas about teaching, or about learning?

Why are we doing this, anyway?  We are following two ideas that have come up already in class — things that may not seem related to learning math, but research shows that engaging in these activities can dramatically increase the amount that you learn, and change the way you learn it.  The first is writing – something not typically associated with mathematics.  When you express your ideas in words, it forces you to think them through very carefully, detail by detail.  A great way to check and see if you really understand something is to try to explain it to someone else, either out loud or in writing.  Example: if you know how to add fractions, try teaching it someone who doesn’t know how.  The second is called metacognition, or “thinking about thinking.”  This happens when you think about what was going on in your head while you were working on a problem or trying to learn a new idea.  What train of thought did you follow?  Where did you get stuck, and what did you do next?  What were you feeling at the time? and so on.  Combining writing and metacognition can be a tremendously powerful tool in identifying the ways we learn best and the ways we make mistakes, and learning to improve.  However, like any skill, it takes practice.  That’s why we’re getting started by writing a little about our past experiences with mathematics.