# Category: Assignments(Page 2 of 3)

NOTE: As a component of OpenLab #5, each person should bring to class a conjecture or question about the Bridges and Walking Tours game.

Group Activity (30 min).  Get into your groups, arrange your chairs in a circle, and take 30 minutes to:

1. Each person should share their conjecture with the group.  For each conjecture, the group should decide if they think it is true or false (or don’t know).  The group should record their conclusion for each conjecture.

2. Choose one conjecture (or create a new one) to focus on as a group.  Your goal for the next few weeks will be to try to prove or disprove this conjecture.  Come up with several ideas about how you might prove it.

Group work due after 30 minutes:  Each group will hand in a sheet of paper with the names of the group members, the date, and the following:
– Each member’s conjecture, along with a brief description of what the group thinks – is it true or false?
– Be sure to clearly indicate which of the conjectures the group has chosen to work on – or, if you have created a new conjecture to work on as a group, include that as well.
– Two different ideas about how you might try to prove the chosen conjecture.

Reflection:  To be completed individually after group work is complete, and submitted on paper with your names and the date.  Take 5 minutes to write on the following prompt:

Briefly reflect on the process of working in a group by responding to each of these points:
1.  Describe something you learned.
2.  Describe something you contributed to the group.
3.  How did today’s work change your understanding of your assigned game?

NOTE: The homework assignment for Chapters 4 & 5 has been modified from the original calendar – it includes two additional problems (and one of the problems is now optional).

Written work, Due Tuesday, October 18th, in class:
Chapter 4 p.100: 1, 6, 7, 15, 16
Chapter 5 p.110: 1, 4, 9, 20*
Odd problems are worth 4 points, even problems worth 8 points.
* (Chapter 5 Problem 20 is optional – solutions will receive extra credit)
WeBWorK
– none
OpenLab – none

Exam #2 will take place on Tuesday, 10/25 (first half of class).

Group Activity (25 min).  Get into your groups (group assignments appear below), arrange your chairs in a circle, and take 25 minutes to:

1.  Share your responses to OpenLab #4.  Compare your answers to the given examples (do you all agree on the solutions?).  Now share your own puzzles with the group, and discuss.

2.  Create three new puzzles, as tricky as possible (try to stump Prof. Reitz!).

Group work due after 25 minutes:  Each group will hand in a sheet of paper with the names of the groups members, the date, and the three new puzzles created by the group.  You do not need to submit solutions, but you do need to be able to solve the puzzles on request.

Reflection:  To be completed individually after group work is complete, and submitted on paper with your name and the date.  Take 5 minutes to write on the following prompt:

Briefly reflect on the process of working in a group by responding to each of these points:
1.  Describe something you learned.
2.  Describe something you contributed to the group.
3.  How did today’s work change your understanding of your assigned game?

## Group Assignments

Group 1: Hanan, Ismail, Jeron
Group 2: Jose, Violanda, Kevin, Carter
Group 4: Gary,Leonardo, Armando

HEADS UP: Next week, there are no classes on Monday 10/3 or Tuesday 10/4.  Also, Thursday 10/6 will run according to a Monday schedule.  Because of this, our class will not meet next week!

HEADS UP: The week after next there are no classes on Monday 10/10, Tuesday 10/11, or Wednesday 10/12.  However, Friday 10/14 will run according to a Tuesday schedule.   This means our class will meet on back-to-back days, Thursday 10/13 and Friday 10/14.

Written work – None.
WeBWorK – Assignment #5, due Thursday, October 13th, at midnight.
OpenLab – OpenLab #5, due Friday, October 14th, before class.

The assignment below is due BEFORE CLASS on Thursday, September 29th (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 9/27 (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/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

Exam #1 will take place on Thursday, 9/22

Written work – none
WeBWorK – Assignment #4, due Tuesday, September 27th, at midnight. You are encouraged to start working on Assignment #5, which will be due one week later.
OpenLab – OpenLab #4, due Thursday, September 29th, at the start of class

Week 4 Assignments

Written work – none
WeBWorK – Assignment #3 and Assignment #4, due Tuesday, September 20th, at midnight.
OpenLab – none

STUDY – for your first exam, taking place next Thursday, 9/22, during the first hour of class.

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 word MI and transform it using the following rules, to obtain some goal word (which is given to you).  The rules state:

1. You must always begin with the word MI.
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

Example: Goal word MUI
Solution:
Step 2: MI to MII (rule 3)
Step 3: MII to MIIII (rule 3)
Step 4: MIIII to MUI (rule 4)
DONE!

Assignment (due Thursday, 9/15): 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.

Week 3 Assignments

Written work – Sec 1.8*: 3, 5, 6, 8, due Tuesday, September 13th, in class.
* GRADING: odd-numbered problems worth 3 points, even problems 5 points.
WeBWorK – Start WeBWorK 3 (due in two week, on Tues 9/20)
OpenLab – OpenLab #3, due Thursday, Sept 15th (at start of class).

NOTE: Next week Thursday 9/15 runs on a Tuesday schedule (this has no affect on us, but may affect some of your other classes).

This assignment is due Thursday, September 8, 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.

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