Math 200: Mathematics Concepts for Teachers, Fall 2012

Reading and Homework Assignments

Week 2

HOMEWORK #1: Due Tuesday, September 11th:

Reading Assignment:

Read:         * Some suggestions for reading a math textbook: http://home.sandiego.edu/~pmyers/textbook.html

* Guidelines for Homework Assignments: http://home.sandiego.edu/~pmyers/math200/homeworkguide.htm

* Course Syllabus: http://home.sandiego.edu/~pmyers/math200/syllabus.htm

* Textbook Preface, pp. iii-v and About the Textbook, pp.vii-x.

 

Reading Questions:

·     Write questions and comments you have on the readings for today (suggestions for reading a textbook, guidelines for homework assignments, course syllabus, Textbook Preface and About the Textbook).

 

Homework Assignment:

·     Please write a "mathematical biography:" Tell me those experiences (positive and negative) from previous math courses that have had an influence on your present confidence in doing mathematics, your liking of mathematics, and your attitudes toward or beliefs about mathematics. Include some goals you have for your mathematical growth: What would you like to accomplish this year?  What are some mathematical abilities you would like to have?  What are your expectations for this course?

·     Look at the handout “Fractional and decimal representations of various rational numbers.” Explore the question: When looking at a fractional representation of a rational number, how can we tell if its decimal representation will be repeating, terminating or neither? 

 

Write a list of conjectures (write down as many as you can—at least 5) in your exploration to answer the question.  If you can find a counterexample to your conjecture, say so and write it down.  For example,

Conjecture 1: If a fraction has an even denominator, then its decimal representation terminates. 

This conjecture is not true as we can see with the counterexample 1/6.  1/6 has an even denominator (6) and it does not have a terminating

decimal representation.

Conjecture 2: If a fraction has an odd denominator, then its decimal representation is periodic. 

This conjecture is not true as we can see with the counterexample 1/5.  1/5 has an odd denominator (5) and it has a terminating decimal representation.

 

Send me the list of conjectures via email (one per person) by Sunday evening.  Be as precise as possible when you write your conjectures.  If you find a counterexample, write it down using a complete sentence (as above).

HOMEWORK #2: Due Thursday, September 13th:

Reading Assignment:

Read: 

The list of conjectures that our class generated about the decimal representation of fractions.

Investigate online:

1)    What is a theorem?

2)    What is a conjecture?

3)    Why is 0.9999…=1?

 

Reading Questions:

For each of the following instructions, select one conjecture (or pair of conjectures) from the list and do the following:

a)     Write the conjecture as written on the list.

b)    Re-write the conjecture (if necessary) so that it is precise and uses correct terminology.

 

Find (for each do a) and b) above):

1. Your favorite conjecture.  Explain why it is your favorite.

2. A conjecture that you are sure is false.  Use a sentence to present a counterexample.

3. A pair of conjectures that are written differently but say the same thing. 

Do you think the conjectures are true?  If you do, explain why.  Otherwise write a sentence to present a counterexample.

4. A conjecture that has a counterexample that does not work.

5. A conjecture that you are sure is true.  Explain why it is true.

6. Two conjectures that are opposite of each other in some way.  Explain why they are opposites.

7. The conjecture that you feel gets us closest to answering the question, when looking at a fraction, how can you tell if it has a decimal representation that is terminating?

8. A conjecture that is not on the list that gets us closer to answering the question in 6.

Do you think the conjecture is true?  If you do, explain why.  Otherwise write a sentence to present a counterexample.

PLEASE SEND ME THESE VIA EMAIL BY WEDNESDAY AT 10:00pm.

 

Homework Assignment:

Explain what you learned in class about writing conjectures.

Explain what you learned in class about numbers and their representations.

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Comments: pmyers@sandiego.edu