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.
Back to Reading and
Homework Assignments Back to Math 200
Comments:
pmyers@sandiego.edu