Category Archives: Assignments

In-Class Group Project Activity 10/8/14 – Puzzle Making

Assignments, Project

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 #5.  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: Samuel, Kenny, Rahat, Justin
Group 2: Deborah,Josiel, Sanaya, Irania
Group 3: Xiong, Abdelmajid,Sarah, Mei
Group 4: Daniela, Ryan, Yuyu, Fuzail

 

Week 7 Assignments

Assignments

Written work: none
WeBWorK – extension granted: WeBWorK #5 is now due Tuesday, 10/13, at midnight
OpenLab – OpenLab #6 due Thursday, 10/15* before class
(* the final part of the assignment, to create a Conjecture and bring it to class, is due in class on Tuesday, 10/20)

OpenLab #5: Bridges and Walking Tours

Assignments, OpenLab Assignments, , , ,

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

Assignments, ,

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

Assignments, ,

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

Assignments, OpenLab Assignments, ,

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.

OpenLab #2: Mathography

Assignments, OpenLab Assignments, ,

This assignment is due Thursday, September 10, at the end of the day

NOTE: Normally, OpenLab assignments are due on Thursday at the start of class. However, Thursday, 9/10, runs on a Monday schedule, so our class does not meet.  Instead, this assignment is due at the end of the day.

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.