When: TR 2:30p-3:45p
Where: B321 Van Vleck Hall
Lecturer:Professor Joel Robbin
Office:313 Van Vleck Hall
Telephone: 3-4698
Email: robbin@math.wisc.edu
Office hours: TR 11:00-12:00 a.m.  W 10:00-12:00 a.m.
Text Books: Elementary Geometry for Teachers,
by Parker & Baldridge.
Singapore Math 3b, 5b, 6b.
New Elementary Mathematics Syllabus D.


An important theme in this course is that math problems can usually be solved in many ways and that a teacher must be comfortable with all possible ways of doing a problem so that s/he can deal with novel approaches and unexpected questions.

My plan for the course (subject to midcourse corrections) is to divide it into nine parts (one for each chapter in the texbook EGT) and end the semester with each student doing a presentation in class. For each chapter we will begin with a quick overview and then work on the problems in groups with each group presenting some solutions to the entire class. Prepare for each class by studying the appropriate sections in the text and working on the problems. The problems will then be handed in for grading and in the class period after they are returned, there will be a quiz on the chapter. At the end of the semester each student will be assigned a topic. The student will prepare an age appropriate lesson on the topic and present it to the class. (The class will play the role of elementary school students.)

Two Amusing Math Problems

Here are two amusing math problems that I encountered in the last three days.
  1. I received the following email concerning my 50th High School Class Reunion:
    A chart (that won't reproduce on my computer) shows that 41% of Senn High students today were born outside the U.S.; North America 258; Asia 145; Africa 118; Europe 34; and South America 13.
    Assuming that none of today's Senn High students were born in Australia, Antarctica, on islands, or on the high seas, how many students attend Senn today?

  2. While at the football game my friend said to me, "One team has exactly twice as many points as the other." I said, "Reversing the order of the digits of one score gives the other." Were both of us right?

Addition and Subtraction

In class the "join and count method" for adding two positive integers a and b: Take two disjoint sets A and B having a and b elements respectively and join them together of form a new set. The new set then has a+b elements. We also discussed the "mark and translate" method for adding two positive real numbers a and b on a number line: Using a yardstick draw a line and mark zero and a on the line. Then translate the yard stick so that zero and a align and mark b. The distance from the the last mark to the original zero is a+b. Consider the following:
  1. What is a good way of explaining why the two methods give the same answer? Hint: Make appropriate sets A and B.
  2. What is the analog of the "join and count method" for subtraction?
  3. What is the analog of the "mark and translate" for subtraction?
  4. How would you apply these methods to angles?

Is a picture a proof?

You can cut up a triangle and rearrange the pieces to make one of larger area!

The area of a circle.

Here is a circle of radious 10 drawn on graph paper.
  1. How many squares are strictly inside the circle?
  2. How many squares intersect the inside of the circle?
  3. How many squares intersect the (boundary of) the circle?

Some Standards.


Here are the assigned problems for each chapter.
  1. Chapter 1. Learning to measure. Due: Thursday Sep 13, 2007.
    1. Section 1.1 Measurement Problems. #1-2, #4-10.
    2. Section 1.2 Measuring Length. #3-4, #6-7, #9-12.
    3. Section 1.3 Measuring Weight and Capacity. #1-12.
    4. Section 1.4 Measuring Angles. #1-10.
  2. Chapter 2. Geometric Figures. Due: Thursday Sep 27, 2007.
    1. Section 2.1 Fundamentals. #1-7.
    2. Section 2.2 Triangles. #1-6.
    3. Section 2.3 Quadrilaterals. #1-3,6,7,10,11.
    4. Section 2.4 Constructions. #1-11.
  3. Chapter 3. Finding Unknown Angles. Due: Thursday Oct 4, 2007.
    1. Section 3.1 Unknown Angle problems. #1-6.
    2. Section 3.2 Using Parallel Lines. #1-5.
    3. Section 3.3 Angles of a Polygon. #2-5.
  4. Chapter 4. Deductive Geometry. Due: Tuesday Oct 16, 2007.
    1. Section 4.1 Unknown Angle Proofs. #1-12.
    2. Section 4.2 Congruent Triangles. #1-7, 10.
    3. Section 4.3 Applying Congruences. #1,3,6, 11.
    4. Section 4.4 Quadrilaterals. #1-3, 5.
    5. Section 4.5 Transformations and Tessalations. #1-8.
  5. Chapter 5. Area. Due: Tuesday Oct 23, 2007.
    1. Section 5.1 Units. # 2,4,8.
    2. Section 5.2 Rectangles. # 1,2,3,5,19,12.
    3. Section 5.3 Triangles, Parallelograms, Trapezoids. # 1,2,3,4,5,9.
  6. Chapter 6. Pythogorean Theorem. Due: Tuesday Nov 6, 2007. Quiz on chapters 5 and 6 on Thursday Nov 15.
    1. Section 6.1 Introduction. # 1-12.
    2. Section 6.2 Square Roots. # 1,2,7-9,12,14,15.
    3. Section 6.3 Special Triangles. # 1-6, 10, 16, 17.
  7. Chapter 7. Similarity. Due: Tuesday Nov 20, 2007. Quiz: Nov 29.
    1. Section 7.1 Introduction.# 1,8,9-13.
    2. Section 7.2 Similar Triangles.# 1-6, 7.
    3. Section 7.3 Coordinates and Slope.# 2, 7,9,10,12,16,17.
    4. Section 7.4 Trigonometry.# 1-3.
  8. Chapter 8. Circles etc. Due: Tuesday Nov 27, 2007. Quiz Dec 6.
    1. Section 8.1 Conversion and Rescaling. # 6-9.
    2. Section 8.2 Circles and Pi.# 3-7.
    3. Section 8.3 Sectors.# 3,6,9.
  9. Chapter 9. Volume and Surface Area. Due: Thursday Dec 6, 2007. Quiz Dec 13.
    1. Section 9.1 Introduction. # 1-3, 8.
    2. Section 9.2 Metric Volume. # 1-6, 8.
    3. Section 9.3 Prisms and Cylinders. # 3-8.
    4. Section 9.4 Pyramids and Cones. # 1,2,5.
    5. Section 9.5 Spheres. # 1,2,4,5.


Here is an assignment on definitions and tessellations due on Tuesday November 27.