Math 200: Mathematics Concepts for Teachers, Fall 2012

Reading and Homework Assignments

Week 3

HOMEWORK #3: Due Tuesday, September 18th:

Reading Assignment:

Read:        

Read pages 1-12 of the textbook in preparation for class.

 

Reading Questions:

1.  What is the idea of place value?

2.  Remind yourself: What are whole numbers, cardinal numbers, ordinal numbers, and integers.

3.  What is a set model?  A measurement model?

4.  What are numerals?

5.  What does it mean to say that we have a decimal numeration system?

6.  What is place value?

7.  How is the Hindu-Arabic numeration system different from the Egyptian numeration system (the decimal numeration system we use).

8.  Write some advantages and disadvantages of the Hindu-Arabic numeration system.

9.  How would you explain what 234 represents?

10.                        What does it mean to compose and decompose a ten?

11.                        Write questions and comments you have on the reading for today.

 

Homework Assignment:

·        1. (a) Answer the following question in two different ways (using the two main conjectures the class developed today).

How can you tell by looking at a fraction if the number represented by the fraction has a terminating decimal representation?

(b) Fully explain why these conjectures are true.

·        2. Write a list of characteristics you think are necessary in a good mathematical explanation.

HOMEWORK #4: Due Thursday, September 20th (to be turned in Tuesday, September 25th)

 

Homework Assignment:

This assignment asks you to study the textbook to gain insight into how mathematics is developed.  You will start doing that with the Singapore textbooks in this homework assignment.

·     Homework set 1 (p. 6 of Elementary Mathematics for Teachers): Problems #1-8

·     Homework set 2 (p. 13 of Elementary Mathematics for Teachers): Problems #1-6

o   For question #6:  If you would like to get the idea of a base 5 place value numeration system, arrange a large pile of objects similarly to what we did in class on 9/15.  Start with a pile of objects and separate them into groups of five, then bundle five groups of five together, etc.  You may use paper clips, if you’d like, as we did in class, or toothpicks—you can make groups of 5 toothpicks and rubber-band them together, put 5 groups of 5 toothpicks into a ziploc snack bag, etc.  You can also think about the denominations in terms of pennies, nickels and quarters, etc.

 

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