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Mathematics 171, Winter, 2004
Geometry for Elementary School Teachers
Assignments to January 12
For Wednesday: Along with your Follow-up Report for today's class, please send us a brief note introducing yourself. I'd like to know a little of your mathematical background (especially as regards geometry), plus anything you'd like to tell me about who you are. If I were writing, for instance, I would probably tell you about my three kids (grown, but I talk about them anyway) and my Mediaeval Women's Choir — but I wouldn't feel obliged to mention either if I weren't up for it.
For Monday, January 12: In the Beckman text, read pages 2-4, do Exercises 1-5 (note that solutions are given – but do the exercises before you look!) and hand in Problems 1 – 3 on page 16.
Assignment for January 14
Do Exercises 6 - 8 on pp 11 - 15. Reallly do them. Then check your solutions by reading hers.
Do and hand in problems 4 - 7 on pp 16 - 17. The report for #7 should be at most one page.
Assignment for January 21
Note that this is a hefty assignment, since we have no class on Monday. Don't leave it until Tuesday night!
Read Section 7.2, especially the Exercises.
Do and hand in Problems 3 - 11 from pages 35 - 41
Assignment for January 26
Read all of section 7.3 , do (without turning in) the exercises, and turn in all three problems on pages 51 and 52.
Read section 7.5 up to page 63, do (without turning in) exercises 1-5, and turn in problems 1 and 3 - 5 on pages 69 and 70.
Assignment for January 28
Read sectoins 7.4 and 7.6
Turn in Problem 1 on page 57, Problem 2 on page 68 and Problems 1 - 6 on page 79 - 81.
Assignment for January 28
MATH 171 WORKSHEET AND ASSIGNMENT 1/28/04
You will be working on these in class today, discussing them from time to time and handing in whichever ones we get through. The rest are Part A of your homework. Part B is to start research on how to make a kaleidoscope. You will be making one as your Project 1. Project details will be on the web by tomorrow evening.
Today is straightedge and compass day. Don’t write on this paper, since you will be using it for homework – use however much you need to of the blank paper provided.
We will start with some warm-ups that are pretty directly from your homework, and then work our way up. Note that you must do careful drawings using your straightedge and compass – no sketches or approximations!
1) Draw two points A and B on a piece of paper. Then draw a line between them and create a perpendicular bisector of that line.
Question: if C is a point on the perpendicular bisector, what do you know about the distance between C and A and the distance between C and B? Why?
2) Draw a line segment, put a point somewhere on the segment and then draw a line through that point and perpendicular to the segment.
3) Draw a triangle and label its vertices A, B and C. Draw (carefully) the perpendicular bisector of AB, of BC and of AC.
Question: why do the perpendicular bisectors all meet at one point? Use the answer to the question in part 1.
4) If you now draw a circle with its center at the intersection of the perpendicular bisectors and passing through A, it should also pass through B and C. Check this out and be sure you see why. The circle you just drew is called the circumcircle of your triangle.
5) Elsewhere (maybe another sheet of paper) draw three points E, F and G and draw a circle that passes through all three.
6) Now draw a right triangle. Label the right angle as A and the other two as B and C. Draw the perpendicular bisectors of AB and AC. They should intersect on the hypotenuse, BC (challenge problem: why?) Call that point of intersection P. Draw the circumcircle of ABC.
7) What do you now know about the location of point P on the hypotenuse?
8) Draw another right triangle and use the information in 7 to produce a circumcircle very swiftly.
9) Draw a circle and draw in its diameter. Put a point C anywhere on the circumference. Draw a triangle with the ends of the diameter as two of its vertices and C as the third. Prove that the vertex at C is a right angle.
10) Applications: Carpenters do not carry compasses, but instead use the information from 9 in two ways. They have T-squares, but we will use cards instead
A) to sketch enough points so as to be able to make a circle. Make two dots on a piece of paper, and then use a 4 by 6 card to produce a bunch of points on the circumference of a circle
B) to find the center of a circle. Draw a circle and describe how you could find its center without folding it or using a compass.
11) Challenge problem: Draw a circle. Put a point P on the paper outside of the circle. Using information we have just been figuring out, draw a tangent to the circle which passes through the point P.
Assignment for February 4
In the text book, read 8.1 (the first section of chapter 8).
Turn in Problem 1 from page 101 and Activities 8D and 8E from the Class Activity book.
Assignment for February 9
Read 8.2 in the textbook and turn in all of the problems at the end of it.
Assignment for February 18
1) Turn in your Flatland Project (a description of the project is attached).
2) Turn in a description of two puzzles and activities you propose to do for the Math Fair. Include as many details as you reasonably can about how you propose to set up the activity. You will (I realize) be somewhat limited by the fact that I have not yet been able to tell you what level students you will be working with.
Assignment for February 23
Turn in the worksheet handed out in class.
In the textbook, read sections 8.3 and 8.4
Turn in Problem 3 from page 131
Assignment for February 25
Turn in problems 4,5,7 and 10 from pages 152 - 155
Assignment for March 1
Read Chapter 9, sections 1 and 2.
From page 181, turn in problems 1,4 and 5
Assignment for March 3
Read Section 4 of Chapter 9 (pages 192 - 204)
Turn in Problems 4, 6, 11
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