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Elementary Mathematical Modeling week 1, week 2, week 3, week 4, week 5, week 6, |
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Date |
Activities |
| ANN: Please read the Introduction of the book, pages 1-10. Try the problems at the end of the Introduction Chapter, probably on pages 9-10. We will discuss them today and next time. I handed out photocopies of the book if needed. They are available from me in person. In class, I gave out the syllabus for Math 137. Students and I introduced ourselves to each other. I covered many course policies, many of which you will see on the syllabus. Please read the syllabus. I handed out the Math Resource Center handout that describes our tutoring center. A note about the book: The syllabus calls for the third edition of the book. However, the second edition is acceptable. There are very few differences as I can see. We may have minor adjustments due to the fact that some will have the second and some will have the third edition. | |
August 22 |
ANN: Please read chapter 1, pages 11-20. You will see problems on pages 12, 15, 17, and 19. As you read each chapter, stop to work the problems as they arise. Do not look at the book's solution but instead try to solve each problem with your own ideas. When you think you are done or stuck, read the book's solution. Feel free to amend your solution as you see fit after you read the book's solution. ANN: Please complete number 6 "Dangerous Maneuvers" on page 22 (page 21 if you have the third edition of the book) for next class. Everyone will write their diagram on the board next class. Be sure to make a diagram but do not worry about the specifics. Just about anything will work. In class, we discussed the problems on pages 9-10 at the end of the Introduction Chapter. Mainly, we worked to get to know one another but this gave us a nice intro to the class too. We had a great discussion. |
| ANN: Please read the handout Polya's Problem Solving Techniques. It serves as a good introduction to the class. We will discuss it next time as needed. ANN: Please return any book photocopies that are no longer needed. In class, we were randomly assigned to tables. Please stick to these seats until we choose again in a few weeks. In class, we discussed the main points of the chapter 1 reading. We then went on to discuss number 6 "Dangerous Maneuvers" on page 22 (page 21, third edition of the book). As many students drew their pictures on the board, we reveled in the breadth and variety of the class' diagrams. We spent a little time using one of the diagrams to answer the question from the book. Small groups then completed their first group assignment. Groups worked on number 1 on page 21 (page 20 in third edition of book; I handed out Grid Paper to be used sideways) and turned in one copy per group. Include a complete, labeled diagram with an explanation. You should explain how to read the diagram for the first few steps at least. For this and all group work throughout the semester, everyone should write their own copy and decide the one paper that should be turned in with everyone's names. Circle your name if your copy gets turned in so I can return it to you. All students should check the work that is turned in. For this particular problem, do not let yourself assume a pattern; it is best to draw out the worm's journey the whole way. Also, make sure your drawing is understandable once it is complete (and not just a jumbled mess). | |
August 29 |
[August 31 is the last day to drop for a full refund.] ANN: Please read chapter 2, pages 27-43. Problems are on pages 28, 32, 33, 35, 39, and 40. The problem on page 32 is the same as that on page 12 in chapter 1, but it is done using a different technique. I gave out a few photocopies of chapter 2 for those who still do not have the book. In class, I returned the graded assignment from last time. I forgot to bring (but included it here) a Grade Sheet to help you record your grades. Using it is optional; we do not have an online system to keep track of grades so I provide this instead. Please, when you get a graded group paper back, share it with the other group members. We discussed number 4 "Floor tiles" and number 5 "Stone Necklace" on pages 21-22 in small groups and as a whole class. (These problems are both on page 21 in the third edition of the book.) I handed out a piece of grid paper that we used to help draw out part of the room in number 4. This helped us see that four tiles would fit exactly in three linear feet. Small groups then explored number 2 "Ups and Downs of Shopping" on page 21. We finished with a whole class discussion. |
| No school for Labor Day | |
September 5 |
ANN: Please read chapter 2 as assigned last time if you have not. We will work on chapter 2 material both today and next class. Last class, I returned the graded assignment from the previous class but forgot this Grade Sheet to help you record your grades. I handed it out today. Using it is optional; we do not have an online system to keep track of grades so I provide this instead. Please, when you get a graded group paper back, share it with the other group members. I handed out Inductive versus Deductive Reasoning and asked students to work on it for next time. The first page has little to do but read it. It defines the difference between inductive and deductive reasoning. The second page asks you to explore a problem with palindromic numbers. Do the first half of this page; if you want to explore the bottom half you can but it is not necessary. We will discuss it next time with specific emphasis on the difference between inductive and deductive reasoning. To prepare you for this worksheet, we briefly discussed palindromes (words like mom and dad and racecar) and what it means to be divisible by 11. In class, we then discussed the chapter 2 reading and the handout Polya's Problem Solving Techniques a bit. We went on to start the worksheet, for chapter 2, The Fundamental Counting Principle and Systematic Lists. We got through number 5 together as a whole class. We will continue this next time but you do not need to do more on your own for now. |
| ANN: Exam 1 is coming up, probably sometime in the last week of September. It will cover chapters 1-3 and 5 as well as the concept of inductive and deductive reasoning. ANN: Please read chapter 3, pages 47-54 (problems on pages 49 and 52) and page 60 about group work and page 64 for the chapter conclusion. In class, we thoroughly discussed the handout Inductive versus Deductive Reasoning. We then spent some time, in small groups, working on The Fundamental Counting Principle and Systematic Lists. Work on the remainder on your own for next time. I want to spend 15-20 minutes in small groups to discuss it before it is turned in Wednesday. I will collect it individually so be sure it is complete on your own copy. | |
September 12 |
ANN: Exam 1 is set for Wednesday, Sep. 26. It will cover chapters 1-3 and 5 as well as the concepts of inductive and deductive reasoning. We worked on The Fundamental Counting Principle and Systematic Lists. Specifically, we went over numbers 8a and b as a whole class. I then gave small groups 20 minutes to finish up any work on the worksheet. Most people were not ready to turn it in so I will collect it Monday at the beginning of class. As a whole class and in small groups, we then worked on Magical Math Puzzles. We completed number 1, parts a through c, together. Students completed number 2, parts a and b, in small groups. I asked students to complete number 3, just parts a and b, for next time. Part c is a little whacky so wait on that if you want. We will continue our discussion of this worksheet next time. |
| ANN: Please read chapter 5, pages 115-125 and page 134. Problems are on pages 117 and 123. (We are skipping chapter 4 and some of chapter 5.) In class, I collected the worksheet The Fundamental Counting Principle and Systematic Lists, one paper per person. (Some of you turned it in last time.) We then worked to complete Magical Math Puzzles. It was not collected. We discussed the chapter 3 reading as a whole class. We discussed number 1 "Square roots" and number 3 "Parking lot" on page 65 for chapter 3. | |
September 19 |
ANN: Exam 1 is set for Wednesday, Sep. 26. It will cover chapters 1-3 and 5 as well as the concepts of inductive and deductive reasoning. I handed out Math 137 Exam 1 Review and told students to work it as a study guide. I also showed students where my solutions were posted under Assorted Handouts and Tutorials. You should work the problems on your own before you look at my solutions. In class, we discussed number 6 "Dartboard" on page 65 for chapter 3. We then discussed number 10 "The Three Squares" on page 67 for chapter 3. I asked students to start looking at in small groups but then we completed the problem with the help of the worksheet Exploration: Elimination of Possibilities Technique: Chapter 3, Number 10 "The Three Squares". The purpose of the worksheet was to lead us through the rather daunting problem by using the elimination of possibilities method described in chapter 3. We, as a whole class, went through pages 1-4 and small groups completed page 5 together. One paper per group was collected. We moved on to chapter 5 so I had a few ideas to discuss from the chapter 5 reading. Small groups, followed by the whole class, discussed number 1, parts a - c and f, on page 134. |
| ANN: Exam 1 is set for Wednesday, Sep. 26. It will cover chapters 1-3 and 5 as well as the concepts of inductive and deductive reasoning. I handed out extra copies of Math 137 Exam 1 Review and told students to work it as a study guide. Small groups, followed by the whole class, discussed number 4 "Rectangular dots" on page 135 for chapter 5. For number 4, think about the pictures and find a pattern in them. You can do it as a sequence like number 1 was done (last class) but it is harder. We then discussed number 7 "Last digit", page 136, as a whole class for chapter 5. Lastly, small groups completed Bunnies! An Exploration of the Fibonacci Sequence for chapter 5. It was collected, one per group. Some small groups had time to work on the Math 137 Exam 1 Review together. | |
September 26 |
ANN: Please read chapter 6, pages 145-155. Problems will be on pages 147, 151, and 153. We will use guess-and-check to solve these problems. Take care to rate your guesses as the book shows. It is very helpful. The page 151 problem is similar to one we have done before but, this time, a drawing will be unwieldy so try guess-and-check. In class, we took Exam 1. See syllabus on details for make-ups and look in your email for a message from me. |
| ANN: Please read chapter 6, pages 155-165. Problems will be on pages 155, 158, and 160. Use guess-and-check to solve these problems. Take care to rate your guesses as the book shows. It is very helpful. In class, we chose new random groups. If you missed today, you and I will place you when you return to class. We discussed the first chapter 6 reading (pages 145-155). In particular, I spoke of using Google to look up relevant formulas like area and perimeter of rectangles and the general flow of the guess-and-check method. We discussed number 1 on page 166 "Dimes and quarters" in small groups, and then as a whole class. We then started to work on Percents Notes (partial notes from my Math 112 class) to help prepare us for the upcoming problems that will use percents. We got through example 3. We will continue from there next time. | |
October 3 |
ANN: Please read chapter 7, pages 175-183. Problems will be on pages 177, 180, and 182. ANN: The last day for late work from weeks 1-8 is Monday, Oct. 15. After that point, I will not take late work from weeks 1-8 and you will be given a 0 for any missed work. In class, we finished our work on the Percents Notes (partial notes from my Math 112 class) from last time. We skipped number 5 on these notes. We worked through number 3 "Tax" on page 166 for chapter 6 in small groups and then discussed it as a whole class. We briefly discussed the chapter 6 reading from pages 155-165. Small groups completed number 2 "Markdown" and number 8 "A bunch of change" on pages 166-167. It will be collected, one per group. Not all groups were done so I told students to work on the problems individually 'til next class. I will give you 5 minutes next time to finish up as a group and decide whose paper to turn in. |
| ANN: Please read chapter 7, pages 184-190. Problems are on pages 184 and 186. They are mixture problems. Try to write down the sub-problems on which the chapter is focused. ANN: Please do page 170, number 1 "Stock Profit" to be turned in individually next time. It is similar to page 166, number 3 "Tax" that we did in class. Use a guess-and-check table and write your answer in the form of a sentence with appropriate units for full credit. In class, we spent a few minutes to wrap up any outstanding group discussions for number 2 "Markdown" and number 8 "A bunch of change" on pages 166-167 (chapter 6) from last time. It was then collected, one per group. Students who were absent last time were asked to simply do the problems on their own and turn them in Wednesday. We then discussed number 11 "Going home from college", page 167 for chapter 6, as a whole class. We spent a few minutes discussing the first chapter 7 reading (pages 175-183). Small groups, followed by the whole class, discussed number 2 "Sharing expenses" and number 1 "Coffee" on page 191, taking note to do as chapter 7 instructs and write down the sub-problems or steps needed to do the problem. | |
October 10 |
ANN: Please read chapter 8, pages 199-207. Problems are on pages 202, 203, and 206. In class, I collected page 170, number 1 "Stock Profit", one paper per person, reminding students to include a sentence with appropriate units. We continued our discussion of chapter 7 with number 4 "Six Squares" and number 8 "Car trip" on page 191. For number 4, do not change the shape of the picture. It is important. Remember to write subproblems down before you attack the problem. We spent a very brief time discussing the second chapter 7 reading on pages 184-190. Small groups completed Additional Mixture Problem. It was not collected. Students started to work on Mixture Problems: Salt Concentration: Guess-and-Check Method in small groups. It will be collected, one per group. Pages 1-5 work to understand these mixture problems. Page 6 gives us a problem to solve using the guess-and-check method of chapter 6. Students were asked to work on pages 1-4 for Monday and we will continue then as groups. |
| We continued to work on Mixture Problems: Salt Concentration: Guess-and-Check Method in small groups. Number 5 on this worksheet is a type of problem from chapter 7 but we use guess-and-check from chapter 6. It was collected, one per group. Actually, three groups were able to turn it in. The members of the other two groups will be completing it on their own and turning it in, one per person. It will still count as a group grade. Small groups then, for chapter 7, worked on number 13 "Box" on page 193. I added the requirement that you tell what the individual dimensions are as well as the total volume. In addition, know that the dimensions are all whole numbers. We discussed it as a whole class. | |
October 17 |
ANN: The average of the last exam is 72%. Well done. ANN: Please read chapter 8, pages 211-223. Problems are on pages 211, 213, 215, 217, 218, and 220. The page 217 problem will be discussed today in class. For page 213, know that 100 centimeters equals 1 meter and 3.281 feet equals 1 meter. Do not round answers until the end. The problems on pages 218 and 220 involve compound units like square feet and something called passenger-miles. In class, I collected the graded worksheet from last time individually from five students, although it will still be recorded as a group grade. Small groups then started working on Mixture Problems with Guess-and-Check. Groups had some time to work together but not finish. I will collect it, one per person, at the beginning of the class next time. We briefly discussed the first chapter 8 reading from pages 199-207. We covered the idea of unit analysis as a whole class. We, as a whole class, discussed the problem on page 207 "Gas consumption". We made one-n-oes as the book describes and used them for the problem. I handed out pink slips of paper for you to use for this purpose. Keep them a few days for other problems (including one that will be due next week) and then hand in any blank extras so I can reuse them please. In small groups, and then as a whole class, we completed the page 217 problem "Fastball". |
| ANN: Please do number 1 "Soda calories" on page 223 for chapter 8, to be handed in next time. Use one-n-oes (and turn them in) as the book describes (pages 207-216) for full credit. ANN: Please read chapter 9, pages 233-239 (problems on pages 234 and 237), read pages 243-246 (problem on page 243 and on pages 245-246, a discussion of the chapter's strategy), read page 251 (problem between waves), and read pages 254 (waves)-257 to wrap up the chapter. The problem on page 251 is a repeat of the chapter 6, page 160 problem. However, this time we are addressing it by solving an easier, related problem as chapter 9 instructs. In class, I collected Mixture Problems with Guess-and-Check from last time. Small groups then worked on number 2 "Christina's trip", parts a-f only, on page 224 for chapter 8. You can use one-n-oes if you like but they are not required. The whole class then went over the answers. We discussed the second chapter 8 reading briefly. We worked, as a whole class, on number 7 "Fireplace insert" on page 225 for chapter 8. We had ten minutes to start working on number 4 "Another Long Commute" on page 224 for chapter 8. Groups got started but we will need to finish next time. | |
October 24 |
ANN: The tentative date for Exam 2 which will cover chapters 6-10 is Monday, Nov. 5. This date is still tentative. The exam may be Wed. of that week but will not be earlier. In class, I collected number 1 "Soda calories" on page 223 for chapter 8. Remember to include the one-n-oes as described in the assignment. We finished our work on number 4 "Another Long Commute" on page 224 for chapter 8. I briefly discussed the chapter 9 reading, paying particular attention to the problem on page 234. We then started number 3 "Sum of odds" on page 258. (This problem is number 2 in the second edition of the book but number 3 in the third edition.) We got half-way through this problem, figuring that the 5,000th odd number would have to be 9,999. We will continue this one next time although I encouraged students to complete it on their own if they wanted. |
| Class cancelled due to sick day. | |
October 31 |
A researcher from the college administered a survey at the beginning of class. We finished the discussion of number 3 "Sum of odds" on page 258 from last time. (This problem is number 2 in the second edition of the book but number 3 in the third edition.) Students completed How Many Squares are in a Checkerboard? for chapter 9 and it was collected, one per group. |
| ANN: Exam 2 over chapters 6-10 is set for Wed., Nov. 14. We will not have class that Monday, Nov. 12 because it's Veteran's Day. ANN: Please read chapter 10, pages 265-268. Problems are on pages 267 and 268. However, the page 267 problem will be worked in class today. Also, please read pages 270-272 (waves). You will see a problem on page 271 that revisits the one from page 267. Finish the chapter by reading pages 279 (Applied Problem Solving heading) to page 283. These page numbers are for the second edition of the book; add 2 if you have the third edition of the book. In class, we started the discussion of chapter 10 by doing the problem on page 267 together in class. We actually got up and acted the problem out as chapter 10 instructs us. Students then had time to work on the Math 137 Exam 2 Review: Chapters 6-10 to prepare for the upcoming exam. I asked students to work on this review before next class so that the time we spend on it next time will be more productive. Remember the solutions are online under Assorted Handouts and Tutorials. | |
November 7 |
ANN: Exam 2 over chapters 6-10 is set for Wed., Nov. 14. We will not have school that Monday, Nov. 12 because it's Veteran's Day. In class, we finished up the discussion of chapter 10 by looking at number 2 "Hoop Greetings" on page 269 (page 271 in the third edition of the book) and completing a worksheet called Exploring Area and Volume with Physical Manipulatives. It was collected, one per group. Students then had time to work on the Math 137 Exam 2 Review: Chapters 6-10 to prepare for the upcoming exam. Remember the solutions are online under Assorted Handouts and Tutorials. |
| No school for Veteran's Day | |
November 14 |
ANN: Please read chapter 11, pages 295-310. Problems are on pages 299, 301, 302, and 304. These are directions for the second edition of the book. If you have the third edition, add 2 to each page number. In class, we took Exam 2. Make-ups should be taken in Haskell Testing Center through Monday of next week. See the syllabus for details. |
| ANN: Do number 15 "Write your own" on page 316 (pg 314 in second edition of book) for next time. It tells you to write your own work-backwards problem. I added the extra requirement that your problem has at least 5 steps. Provide two computer-printed copies of the problem, one with the answer and the other without so one can be turned in and the other can be solved in class. We will exchange papers and solve each others' problems next class. In class, we picked groups to work with for the remainder of the semester and then we briefly discussed the chapter 11 reading. We then spent our time working on number 3 "Cookies" on page 313 (pg 311 in second edition of book) for chapter 11 as a whole class and in small groups. We also completed number 1 "Losing streak" on page 312 (pg 310 in second edition of book) for chapter 11. | |
November 21 |
[November 26 is the last day to drop and receive a grade of W instead of D or F.] No school November 21-23 for Thanksgiving |
| Class cancelled due to sickness. Sorry. | |
November 28 |
ANN: Exam 3 will be over chapters 11 and 13. We will have it Monday, December 10. That will be the last day we meet. If school is cancelled, we will simply move the test to that Wednesday. ANN: Please read chapter 13, pages 349-358. Problems are on pages 351, 354, 356, and 357. We actually solved the first three problems back in chapter 6 (pages 147, 151, and 153.). These page numbers are for the second edition of the book; add 2 to each page number if you have the third edition of the book. We will use what we learned from the guess-and-check tables to solve the problems using algebra. In class, we completed number 5 "Used car" on page 314 (page 312 in second edition of book). Then we exchanged our work for number 15 "Write your own" on page 314. We completed another person's problem, then we had time for revisions and turned them in. |
| ANN: Exam 3 will be over chapters 11 and 13. We will have it Monday, December 10. That will be the last day we meet. If school is cancelled, we will simply move the test to that Wednesday. I handed out Math 137 Exam 3 Review: Chapters 11, 13 to help you study. Solutions are available under Assorted Handouts and Tutorials. ANN: Please read chapter 13, pages 361-363 and pages 366-371. Problems are on pages 361 (which you have seen in chapter 6, page 155), 366, and 370. We are skipping the problem on page 363. These page numbers are for the third edition of the book; subtract 2 from each page number if you have the second edition. In class, we finished the discussion of chapter 11 by doing number 9 " Shopping spree" on page 313 (page 315 in the third edition of the book). We then went on to briefly discuss the first chapter 13 reading. We completed number 2 "More coins" on page 369 (page 371 in the third edition of the book) for chapter 13. We made and solved an equation that used only one variable. We spent the remainder of our time working on the Math 137 Exam 3 Review: Chapters 11, 13. | |
December 5 |
ANN: Exam 3 will be over chapters 11 and 13. We will have it Monday, December 10. That will be the last day we meet. If school is cancelled, we will simply move the test to that Wednesday. In class, I handed out an extra page for the Math 137 Exam 3 Review: Chapters 11, 13. (Online, the review is now complete.) This page gives you two more problems which mimic some test problems. We then discussed number 6 "Fishing poles" on page 370 (number 8, page 371 in the third edition of the book). With the help of our guess-and-check table, we made two equations with two variables, and solved them. Students spent the remainder of our time working on the Math 137 Exam 3 Review: Chapters 11, 13. |
| We took Exam 3. See syllabus on details for make-ups and look in your email for a message from me. | |
December 12 |
Class cancelled to accomodate make-ups and school closures. |