Assignments for MATH 2008

Fall 2009

Date assigned	Assignment
Tues, Aug 18	Carefully read the syllabus. Explore the linked pages. I encourage you to sign up for membership in the Georgia Council of Teachers of Mathematics (GCTM) at http://www.gctm.org/. Membership is free if you have not taught professionally; the cost is $20 otherwise. Due Thursday, August 20 by 2:00 PM: Mathography due through Vista. Read Section 1.1. Work the following problem for Thursday. Come prepared to share how you thought about the problem. A Clinking Glasses Problem At a party, someone proposes a toast.  Each of the 20 people in the room wants, to “clink” glasses with everyone else.  How many “clinks” will there be?  (There is exactly one “clink” for each pair of people.) The Pigs and Chickens problem is given below. We discussed several solution strategies in class. There are 4 strategies for solving the problem on pages 7-10 of your textbook. You should read these and be sure they make sense to you. Pigs and Chickens A farmer has a daughter who needs more practice in mathematics.  One morning the farmer looks out in the barnyard and sees a number of pigs and chickens.  The farmer says to his daughter, “I count 24 heads and 80 feet.  How many pigs and how many chickens are out there?”
Thurs, Aug 20	We convinced ourselves that if there are 20 people at the party, we can divide the product of 20 and 19 by 2. We were also convinced that if there are 5 people at the party, dividing the product of 5 and 4 by 2 yields the correct number of clinks. We also knew that if there were 500 people, the sum of the counting numbers 499 and smaller would yield the correct number of clinks; that is, 499 + 498 + 497 + 496 + 495 + . . . + 4 + 3 + 2 + 1 yields the correct number of clinks. However, it is too tedious and timeconsuming to add these numbers so the question is: If I find the product of 500 and 499 and divide this product by 2, will the answer give me the sum of those 499 counting numbers that I am convinced gives me the correct number of clinks? This method worked for 20 people and 5 people but does it always work? So, you are to figure out if there is a mathematical reason for me to find the number of clinks by doing ( 500 * 499)/2 . I suggest that you revisit 20 people and 5 people and see if you can make sense of why (20 * 19)/2 and (5*4)/2 worked, respectively. In other words, what does 20 * 19 really mean? Why would I multiply those numbers for 20 people? Then, why does it make sense to divide by 2? Reconsider the problem we acted out in class to make sense of it. Also for Tuesday: Read pages 10 - 17 and work these problems on pages 26 - 27: problem 1 (try to use a strategy other than guess and check and other than algebra) problems 10, 14, 22, 27, 31.
Tue, Aug 25	Investigate 2 ancient numeration systems: Go to http://www.nevada.edu/~matovina/ancient_systems.htm to investigate the Egyptian numeration system. (The Babylonian numberation system is also at this site but you are not required to investigate it.) Go to http://www.factmonster.com/ipka/A0769547.html to determine how to read and write Roman numerals. You should understand the rules for expressing a number in Roman numerals. For ex: Can you write MIM? What about IIII?
Thurs, Aug 27	Cut out the squares and strips on the blue paper. Put in an envelope and bring to class. See what additional patterns you can find in Pascal's Triangle--(handout given in class).
Tues, Sept 1	Each of you was assigned a number in class. You are to shade in all multiples of your number on the copy of Pascal's triangle given to you in class. Shade so that you can still read the number beneath the shading. Work problems 12 and 15 on page 55. Be able to explain your thinking.
Thurs, Sept 3	Complete handout on Alphabetia.
Thurs, Sept 10	Addition and subtraction problems in Alphabetia. Also, 2 problems in Vista to submit by Sat evening.
Tues, Sept 15	These are the responses to Alphabetian homework shared in class. Test on Thursday. Here is the information on problem solving we discussed in class--I had promised you copies of these slides.
Thurs, Sept 17	Problem 9 part e on page 55 was to determine if the following argument is valid or invalid: If I were rich, I would buy a cabin. I am not rich. Therefore, I have not bought a cabin. Notice that the if‐then statement tells you what I will do provided I am rich. Nothing is said about what I will do if I am not rich. You may only conclude that if I am rich, you can expect me to buy a cabin. Thus, I may still buy a cabin even though I am not rich. Remember, I only told you what I would do if I am rich.  So…this argument is invalid since you can make no conclusions about what I will do if I am not rich. I may buy a cabin or I may not! Homework for Tuesday: Pages 54-55/3, 6, 7, 8, 9 (as you work problem 9, think logically).
Tues, Sept 29	Work problem 14 on page 120.
Thurs, Oct 1	Quiz Tues, Oct 6 over representing base 10 numbers in multiple ways including word names and expanded notation. Be sure you know how to regroup, for example, a representation of 3 hundreds + 2 tens + 4 ones as 2 hundreds + 9 tens + 34 ones and can explain how the regrouping is done. Know the correct spelling for word names of numbers. Homework: Complete the subtraction problem assigned in class. Then read carefully pages 131-143 (stop at estimation). As you read, pay close attention to the properties of addition--do you understand their meaning? Also note the alternative algorithms such as the "partial sums" strategy on page 138 and the lattice algorithm on page 142 and be sure you understand why they work. Do you also understand why the common algorithm or traditional algorithm for addition works--can you make sense of it (see pages 139-141)? Work these problems for homework: Page 150 / 4,5,6,7,8,16,19, 20 In class today we justified why 2 raised to the zero power is 1; we also showed why 3 raised to the zero power is 1 and why 10 raised to the zero power is 1. Examine the powers of 0; that is, consider the 4th power of 0, the third power of 0, etc. Based on your observations, what conjecture can you make about 0 raised to the 0 power?
Tues, Oct 6	Read pages 154- 166. Beginning on page 166 work problems/ 8, 10,11,12,18,20,21,26, 30 Read section 2.1, pages 61-76 on sets.
Thurs, Oct 8	MONDAY, OCTOBER 12 IS MIDTERM. IF YOU PLAN TO WITHDRAW FROM THE CLASS, YOU SHOULD DO SO NO LATER THAN MONDAY. We will have a test Thursday, Oct 15 over our numeration system. Here is a Concept Sheet for the test. HOMEWORK: Consider the number 3.46. As a minimal collection, it is represented as 3 ones + 4 tenths + 6 hundredths. Represent 3.46 in 4 additional ways by determining different values of ones, tenths, hundredths, and thousandths that will have a value of 3.46. Be sure you can offer a mathematical explanation as to why 0.3 and 0.30 are equivalent. Can you offer a mathematical explanation to determine which of these numbers is bigger: 0.27 or 0.24. When I was taught to add and subtract decimal numbers, I was told to "line up the decimal points." WHY? What is the mathematical justification for doing this? Give a mathematical reason for the steps you take in subtracting 1.8 from 5.
Tues, Oct 13	Homework to do for next Tuesday: Page 76/ 8, 13, 18 (parts a & b only), 19, 22, 23 Solve the Walt Disney World problem found at http://www.chaselink.com/tune/. The solution is given so you can check your work after solving. Solve these Venn Diagram problems found at http://www.glencoe.com/sec/math/prealg/mathnet/pr01/pdf/1302a.pdf
Tues, Oct 20	Page 76 / 1, 2, 3, 5, 6, 12
Thurs, Oct 22	What kinds of numbers belong to the following sets of numbers? real numbers; whole numbers; counting or natural numbers; integers; rational numbers; irrational numbers
Tues, Oct 27	We will have a quiz Thursday over sets--including Venn Diagrams and sets of numbers. You should understand the concepts of subset, intersection of sets, union of sets, etc. Here are the items we used in class today: Sets of Numbers Unit 1 of Grade 2 in the Georgia Performance Standards Frameworks The activity on Venn Diagrams from Shodor can be found at http://www.shodor.org/interactivate/activities/VennDiagrams/?version=1.6.0_12&browser=MSIE&vendor=Sun_Microsystems_Inc.&flash=10.0.22
Thurs, Oct 29	Here is the Multiplication and Division--Grouping and Partitioning handout. Then write word problems appropriate for the elementary classroom according to these directions: a) Write a "groups of" multiplication problem for 16 x 18. Use candy and bags in your problem. b) Write a division problem that can be solved with repeated subtraction for 12 divided by 3. Use children and cookies in your problem. c) Write a division problem that can be solved with fair sharing for 12 divided by 3. Use children and cookies in your problem. Read pages 168-175 and pages 189-192. Do problems 4, 20, and 21 on pages 186-187. Do problems 48, 49, 54, 56.
Tues, Nov 3	The homework for Thursday follows. This homework includes some of the problems in the previous homework but additional problems from pages 186-187 have also been included. I've also given the pages for the problems 48, 49, 54, & 56. Read pages 168-175 and pages 189-192. Do problems 4, 13, 14, 17, 19,20, 21 on pages 186-187. On pages 209-210 do problems 48, 49, 54, 56. Complete the handout given in class--the one where you modeled with pictures or manipulatives to find the answers.
Thurs, Nov 12	Division homework Also for HW: Use an area model to find the product of 25 and 46--that is, draw a rectangle with dimensions of 25 and 46. Show how the area model is related to the partial products method of multiplying (20 + 5) by (40 + 6).
Tues, Nov 17	Read pages 215-229---be sure you understand the divisibility tests. On pages 229-230, do problems 2,3, 7, 8, 10, 12, 14, 15, 16 Test 3 Concept Sheet--test Tuesday.
Tues, Dec 1	Work the problems with fractions given to you in class. Final exam concept sheet The final exam is Thurs, Dec 10, 10:00-12:00.