Course assistant: Mauricio Duarte

Email:maduarte@math.washington.edu

Office: Padelford C-8D

Office Hours: Mondays 3:30 - 4:30 ; Fridays after class

HEADS UP!!! Don't try to do Problem 24 (the one we looked at in class today). Mauricio has proved that it can't be solved. Yes, I will certainly tell the publishers about it.


More on Project 3:

Further suggested topics: the Pythagorean Theorem and Rigid Motions -- which is an extension of what we did with symmetries. For either one a good start would be to read the relevant part of the textbook (26.1 for Pythagoras, all of 22 for Rigid Motions). After that you could either look online or in the library for other interesting stuff, or use the book in the following way: look for a set of Learning Exercises to challenge yourself with. Send me the list of your choices and I will look through and perhaps add a few, or perhaps make a few substitutions.


And to repeat what I said on Wednesday: I am not going to be counting pages. I am going to be looking for evidence that you challenged yourself and put in some heavy-duty thinking.

Assignment 1: Due Friday, January 9:

NOTE: Both of the assignments for Friday should be sent to us on e-mail. Remember to start the subject line with "171". Send them to me (warfield@math) with a cc to Mauricio (maduarte@math.washington.edu)

A) In the textbook, read the "Message to Prospective and Practicing Teachers" on pages vii - xi. Think about it, then read it again and then write a brief (1/2 to 1 page) response. If you have not taken Math 170, then the response should basically center around 1) what that you just read do you look forward to with pleasure and/or excitement and 2) what makes you feel either anxious or skeptical?
If you did take 170, you may opt instead to relate what you see there to what you did in 170 — what seems the same or different? What says the same thing as before but doesn't match what actually happened?

B) Also please send us a mathematical mini-autobiography. Basically, I am interested in how much mathematics you have had (especially how much of a geometrical nature) and how long ago you had it, and in your response to it all — i.e., how you feel about mathematics.
Please include with that your reason for taking this course. Are you planning on going into elementary education? Wondering about doing so? Just curious? Whatever! I have had excellent 171 students in all three of those categories — I'm asking because it helps me shape the course.


Assignment 2, due Wednesday, January 14

A) Make polyhedral shapes: The instructions are on p. 369 entitled "Activity 3 Fold them up (preliminary homework activity)". This may be the only homework all quarter that you can do while watching TV or chatting about the Huskies game (but don't try to do it at a Huskies game.) You will definitely need the shapes in class on Wednesday.
B) Read Section 16.1. Turn in Learning Exercises 1 – 6.
C) (optional) Check out the website mentioned in Learning Exercise 7 and see if it has anything useful to you.

ASSIGNMENT #3, Due Friday, 1/16:

Read 16.2 Do 1 – 10 and 12

Turn in #3, 5, 8, 10 and 12

Note for #8: the idea is to complete the sentence "For an n-gonal pyramid, the number of faces is ___, the number of edges is ___ and the number of vertices is ___" and a similar sentence for prisms. After completing the sentence, you need to convince us that you are right.

Note for # 12: A right rectangular prism has rectangular bases and its sides are perpendicular to its bases. I recommend using a block of non-Swiss cheese (or tofu if you are vegan) and making actual slices. Then sketch the block and mark the place where you needed to slice it to get the required polygon. (You can celebrate finishing it by eating the cheese.)

ASSIGNMENT 4, due Wednesday, January 21

Read 16.3

Do as many of the Learning Exercises as you can find time for – all involve worthwhile thinking or doing.

Turn in LE 4, 6, 7 (justify your answer) , 8, 11 [extended slightly: "Make up exercises like Learning Exercises 9 and 10 for shape A], 12, and 19

ASSIGNMENT 5: Note that we are skipping 16.4

Read 16.5 through 16.7

Hand in       16.5 # 1 (justify your answers!) and #4
            16.6 #1

Submit by e-mail one really interesting thing you find out about Platonic solids -- you can check books on geometry or math history or google Platonic solids or regular polyhedra. Submit as an e-mail message (not an attachment, please!) with subject line      

171 Platonic Solids , or
171 Regular Polyhedra


ASSIGNMENT 6, due Wednesday, Jan. 28

Read §17.1 Keep a vocabulary card or something like that, because these are all words that we will be using without redefining them.

Do as many of the LE's as you have time for.

Turn in #2 and # 9 - 12

Assignment #7 Due Friday, January 30

Read 17.2 and 17.3

Turn in 17.2 #2, 3, 4, 5
17.3 # 2 (just use the conjectures supplied by the book), 3, 6



Assignment #8, Due February 4

Read 17.4 and turn in #1 and #5
Read 18.1 and turn in #1 – 8 and 13

Assignment 9, due Friday, February 6

Read 18.3 and 19.1
      Hand in LE 19.1 #1 (why will they NOT tessellate?); 3b; 4 (do use the grid – you can!); 7 (choose 4 pentominoes and tessellate – challenge yourself with the choice); 8
     


Assignment 11, due Wednesday, February 11

Last Wednesday we computed the sizes of the interior angles for polygons having from 3 to 12 sides. We also noted that in order to be part of a tessellation, a set of polygons meeting at a vertex would have to have interior angles adding up to 360º. So your job before Wednesday is to see how many different combinations of polygons whose vertex angles add up to 360º you could find. I gave as an example three (equilateral) triangles and two squares, whose angles would add up to 3 x 60º + 2 x 90º, which is the desired 360º.

Assignment 11, due Friday, February 13

Go to http://nrich.maths.org/public/search.php?search=semiregular+tessellations

1) Click on "Tessellation Interactivity (fifth one down) and try the following 3 semi-regular tessellations.
The first should be an easy one (say 4.8.8 or 4.6.12)
The second should be any one of impossible ones. Those are 3.3.4.12; 3.4.3.12; 3.3.6.6; and 3.4.4.6 (you already saw 5.5.10)
The third should be 3.3.4.3.4, which makes a snazzy tiling, but you have to concentrate to make it work.

In each case, make a big enough piece of it to be able to print it out (black and white is fine) and put in lines indicating why you are convinced that you can tile the whole plane with your pattern.

2) Choose one of the other activities and carry it out. Tell me which one you did, either turning in some prints of it, or explaining it and how far you got. I would rather that you challenged yourself and turned in a partial solution with explanations than that you did one that you got bored with by a part of the way in.

Assignment 12, due Wednesday, Feb. 18

Read §20.1 NOTE: to get the most out of this chapter you must read it with a piece of paper in hand to cover what's below each activity. First do the activity yourself, then read on.

Turn in #4 – 6, 9, 15 and 22-25

ASSIGNMENT 13, due Friday, February 20.

Read §20.2 (again covering up solutions as you go)
Hand in all problems



ASSIGNMENT 14, due Wednesday, February 25

NOTE: I did the text book a serious injustice! There is a very clear definition of similarity on page 450.

Read §20.3 really actively: I want you to turn in some responses. You will need to use a photocopy of the isometric dot paper at the back of your book.

      Discussion 3 has some congruent pairs of figures and some similar ones. Find them.
      Activity 6: Draw figures congruent to B and F, but in a different position.
      Discussion 4: Do them all. For reference, remember that this shape is called a prism.
      Answer the “Think about”s

      Also turn in Learning Exercises #5d-I; 19, 25 and 26

NOTE: I put this on-line yesterday (Wednesday) afternoon, but it apparently got dumped out of the system, so you are getting it slightly late. If you need to finish it up over the week-end, do so (no late penalty), but do as much as you can before tomorrow to solidify what you learned in class


ASSIGNMENT 15, due Friday, Feb. 27

Read 21.1

Finish up and hand in a proof using triangle congruence that the technique given at the top of p. 481 really does produce a perpendicular bisector.

Hand in LE 1 (Support your decisions!); 3,9, 10 c&f; 15 b&c; 20 and 22


ASSIGNMENT 16, Due March 4

Read §23.1 and 2

Turn in:       From 23.1 LE 8, 9, 12, 15, 19, 20
            From 23.2 LE8, 16, 18, 19

Assignment 17, due March 6

L.E. 23.2 # 22, 23 , 27, 41

Assignment 18, due Wednesday, March 11

Read Chapter 24, all parts

Turn in LE 24.1 # 5, 9, 11, 12 g-j, 15
      LE 24.2 #8, 9, 12, 14b, 19, 21 a,b

Assignment 19, due Friday, March 13:

1) Read 24.3, and turn in Activity 3

2) Go on-line and find out something interesting about π (which you can also enter as Pi). Tell me what you found!

3) Use the tactics and results from today's class to prove that the area of a trapezoid with base lengths a and b and height h is (1/2)(a+b)h