Math 200: Mathematics Concepts for Teachers, Fall 2012

Reading and Homework Assignments

Week 4


HOMEWORK #4: Due Tuesday, September 25th:

Reading Assignment:

Read: 

* Read section 1.3 (pages 14-18) of the textbook in preparation for class.

Reading Questions:

1.  What is addition?

2.  Describe some useful models used for addition.

3.  What are some properties of addition?  Give examples.

4.  How many addition facts does a child need to memorize.  Explain.

5.  What is an equation? What does the equal sign mean?

6.  Give several examples of incorrect uses of the equal sign and explain why they are incorrect.

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

         

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.

(a)  Convert 431 base five and 1012 base five to decimal numbers.

(b)  Convert 91 and 456 to base five numerals.

(c)   Find the sum of 341 base five and 214 base five without converting to decimal numerals.  Think of adding different sized bundles separately and re-bundling as appropriate.

 

·        In class we came in with the following conjectures:

a)     If a number can be written as a fraction with a denominator of the form 2x 5y, where x and y are whole numbers, then the number has a terminating decimal representation.

Another way of writing this conjecture is:

If a number can be written as a fraction with a denominator whose prime factorization has only 2’s and 5’s, then the number has a terminating decimal representation.

b)    If a fraction has a denominator which is a factor of a power of 10, then the number represented by the fraction has a terminating decimal representation.

1. Cid says that these conjectures are true because ½=0.5, ¼=0.25, 1/10=0.10, and those numbers etc.  Is Cid correct?  Explain.

2. Prove completely that these conjectures are true.


Due Thursday, September 27th before class:

 

1)    Experiment with your iPads.  If the programs are not loaded onto your iPad (try to find iMovie, for example), go to the help desk and have them load the apps for you.

2)    Read the instructions for pen pal letters carefully.  Let me know via email if you have any more questions.

3)    Email to pmyers@sandiego.edu your introductory pen pal letters.

4)    Go to the Blackboard class page and share/answer something on the iPad Thoughts, Surprises and Discoveries Forum.

 

Reading Assignment:

Read: 

* Re-read section 1.3 (pages 14-18) of the textbook in preparation for class.


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Comments: pmyers@sandiego.edu