575_homework_2017

Homework

05/08
  1. Read Section 6.15 in SA for discussion in class on Thursday.
  2. Exercises 6.15: 1, 2, 4.
  3. Finish your second paper. Due 05/10.
  4. Begin preparing for the final exam, which will be given in class one week from today, 03/15, 5:30-7:30 PM. (A list of study topics is on the “Additional Notes and Files” page.)
05/03
  1. Read Sections 6.13 and 6.15 in SA as preparation for Tuesday’s class discussion. You may find it useful to glance over the review of geometric series in Section 6.12, also. Send me a question by Monday evening. Due 05/07.
  2. Exercises 6.13: 1, 2, 4, 6. (There is something seriously wrong with the description of the procedure in Question 6. What is it?)
  3. Continue working on your second paper. Due 05/10.
05/01
  1. Read Sections 6.7 and 6.8 in SA as preparation for Thursday’s class discussion.
  2. Exercises 6.7: 1, 2(a)(e), 3(a); Exercises 6.8: 1, 9, 11(1)(c), 12.
  3. Work on your second paper.
04/26
  1. Read Sections 6.4 and 6.5 in SA as preparation for Tuesday’s class discussion.
  2. Exercises 6.4: 1, 2, 3(a)(c), 5, 10, 11; Exercises 6.5: 1, 3, 4, 9.
  3. Hand in Exercises 6.2: 6; Exercises 6.3: 1, 4; Exercises 6.5: 9. Due 05/03.
04/24
  1. If you have not already done so, please, please, please experiment with reflections using patty paper, and develop your conjectures on the result of composing two reflections, in time for Thursday’s class.
  2. Read Sections 6.1, 6.2, and 6.3 in SA as preparation for Thursday’s class discussion.
  3. Exercises 6.2: 1, 2, 3, 5, 6; Exercises 6.3: 1, 2, 3, 4.
  4. Start working on your second paper. Due 05/10.
04/19
  1. Experiment with composing reflections, using patty paper or otherwise. Develop conjectures on the result of composing two reflections:
    1. in parallel lines;
    2. in intersecting lines.
  2. Complete a solution of the light reflection task, and bring it to class on Tuesday.
04/17
  1. Read through the Common Core Geometry standards for Grade 8 and High School. Come to class on Thursday with questions and aha’s: anything you would like to know more about, and anything that struck you as particularly insightful. (Be ready to share at least one of each.)
  2. Now that we have indicated how to prove the SAS triangle congruence criterion using transformations, try to come up with transformation proofs of the ASA and SSS congruence criteria. We will discuss these proofs in class on Thursday. (The ASA proof is quite like the SAS one we did in class; you may find the SSS criterion harder to prove.)
  3. Send me an e-mail with your thoughts on the “Math is everywhere” video project. “Yes” or “No” would be sufficient, but I would also appreciate your thoughts on how it might best be made to work, or perhaps be made to work in future years. Due 04/18.
04/12
  1. Read sketches 14 and 15, “On Beauty Bare: Euclid’s Plane Geometry” (p. 127), and “In Perfect Shape: The Platonic Solids” (p. 133) in BG.
  2. Exercises 10.4: 1, 4, 5, 9, 10, 11, 14, 15.
  3. Read Section 10.9 in SA for discussion in class on Tuesday. Send me a question on the reading (either BG or SA) by Monday evening. Due 04/16.
  4. Hand in Exercises 10.3: 12, 13; Exercises 10.4: 8, 14. Due 04/19.
04/10
  1. (Re)-read Section 10.3, and read Section 10.4.1 for discussion in classs on Thursday.
  2. Come up with a solution to the Tricky Pool problem for discussion in class next Tuesday.
  3. Exercises 10.2: 1, 2; Exercises 10.3: 4, 7, 8, 11, 12 13, 16.
04/05
  1. Read Sections 10.1, 10.2, and 10.3 in SA for discussion in class on Tuesday. Send me a question on the reading by Monday evening. Due 04/09.
  2. Read sketch 16, “Shapes by the Numbers: Coordinate Geometry” (p. 137) in BG.
  3. Exercises 9.7: 1 (try to do this without using the vertical or horizontal line tests), 2, 3, 5, 7.
  4. Hand in Exercises 9.4: 2; Exercises 9.7: 2, 3. Due 04/12.
04/03
  1. Read Section 9.7 in SA for discussion in class on Thursday. Send me a question on the reading by Wednesday evening. Due 04/04.
  2. Exercises 9.3: 12, 14; Exercises 9.4: 2, 5.
03/29
  1. Read Section 9.4 in SA for discussion in class on Tuesday. Send me a question on the reading by Monday evening. Due 04/02.
  2. Exercises 9.3: 1, 2, 4, 5, 10.
  3. Hand in Exercises 9.2: 9, 14; Exercises 9.3: 10. Due 04/05.
03/27
  1. Read Sections 9.1, 9.2 and 9.3 in SA for discussion in class on Thursday.
  2. Exercises 9.2: 1, 2 (and represent this function in as many of the text’s 7 ways as you can), 6, 7, 9, 13, 14.
03/08
  1. Continue preparing for the midterm exam, which will be given in class one week from today, 03/15. (A list of study topics is on the “Additional Notes and Files” page.)
  2. Since we did not discuss your results last time this activity was assigned, follow the link to the Common Core standards on the “Useful Links” page, and look for standards which involve the Pythagorean Theorem, or which are connected to it in some way. Be prepared to volunteer some of your discoveries in class next Tuesday. Due 03/13.
  3. (If you have not completed them already) Exercises 4.4: 1, 6, 8.
03/06
  1. Study the proof of the Pythagorean Theorem in the “Kou-Ku and the Peacock’s Tail” file. (You can also find it as proof 9 on the Cut-the-Knot website.) Be prepared to explain the proof to a partner on Thursday.
  2. (Re-)read the Australian TIMES modules on “Area, Volume, and Surface Area”, and “Cones, Pyramids, and Spheres”, for discussion on Thursday.
  3. Begin preparing for the midterm exam, which will be given in class one week from Thursday, 03/15. (A list of study topics is on the “Additional Notes and Files” page.)
03/01
  1. Read the Australian TIMES modules on “Area, Volume, and Surface Area”, and “Cones, Pyramids, and Spheres”. (Links are on the “Useful Links” page, in the “Area and Volume” section.) Briefly skim through Section 4.4 of SA on volume. Be ready for a discussion of volumes of cylinders and cones, and a comparison of the approaches to volume taken in these different resources, on Tuesday. Send me a question on the readings by Monday evening. Due 03/05.
  2. Remember to bring a round (circular) object to class on Tuesday. (See the instructions posted on 02/27.) Due 03/06.
  3. Begin thinking about possible topics for your first paper. Hand in a 1-paragraph proposal next Thursday. Due 03/08.
  4. Exercises 4.3: 1 (Does the answer depend on the side length of the square? Why or why not?), 5, 6, 7, 8, 9, 10, 11; Exercises 4.4: 1, 6, 8.
  5. Hand in Exercises 4.2: 3; Exercises 4.3: 8, 9; Exercises 4.4: 8. Due 03/08.
02/27
  1. Read sketch 12, “A Cheerful Fact” (p. 113), and sketch 13, “A Marvelous Proof: Fermat’s Last Theorem” (p. 119) in BG.
  2. Exercises 4.2: 1, 2, 3, 4, 9, 10, 12, 16, 19, 21.
  3. Read Section 4.3 of SA for discussion on Thursday.
  4. We have not looked at the Common Core standards for at least a week now. Follow the link on the “Useful Links” page, and look for standards which involve the Pythagorean Theorem, or which are connected to it in some way. Be prepared to volunteer some of your discoveries in class next Tuesday. Due 03/06.
  5. Bring a round (circular) object to class next Tuesday. Not too small (a button would be too small), but reasonably portable (a tractor tyre would probably not work, though a detachable bicycle wheel would). Plates, aluminum cans, etc. Be creative, but make sure your object is circular. Due 03/06.
02/22
  1. Read sketch 11, “Intrigue in Renaissance Italy,” (p. 109) in BG.
  2. Read Sections 4.1 and 4.2 of SA for discussion next time.
  3. (Optional) Read Sections 3.6 and 3.7 of SA, on the solution of quadratic, cubic and quartic (4th degree) equations. There is some beautiful mathematics in these sections, but unfortunately not enough time to cover it properly in class.
  4. Hand in Section 3.4: 3, 5; Section 3.5: 2(e). Due 03/01.
02/20
  1. (Re)-read Section 3.5 of SA, for discussion in class on Thursday.
  2. Section 3.4: 1, 3, 5, 7; Section 3.5: 2(a)(d)(e), 3.
02/15
  1. Read sketches 8 (p. 97) and 17 (p. 143) in BG.
  2. Read Section 3.4 of SA, and Section 3.5 if possible, for discussion in class on Tuesday.
  3. Section 3.2: 2, 13, 14, 16, 20.
  4. Hand in Your solutions to questions 3, 5, 6, 7, and 8 on the “Euclidean Algorithm for Polynomials” exercise sheet. Due 02/22.
02/13
  1. Look through the introduction to the “Euclidean Algorithm for Polynomials” exercise sheet (on the “Additional Notes and Files” page), and see if you have questions about any of the definitions. We will try to clear these up in Thursday’s class.
  2. Read Sections 3.1 and 3.2 of SA, for discussion in class on Thursday. You do not have to send me a question on this reading, but you should feel free to do so anyway, if anything is not clear.
02/08
  1. Read the section “Algebra Comes of Age” in BG (pp. 37-43).
  2. Review again the arguments from Tuesday on the Euclidean Algorithm and greatest common divisors, and try to complete Exercise 8 from Section 2.6 (using Theorem 2.30 to prove Theorem 2.16) before next Tuesday’s class. We will use these ideas to give a second proof of the Fundamental Theorem of Arithmetic, so you will need to be familiar with them.
  3. From SA, Exercises 2.9: 1, 3, 4, 5, 9, 10, 11, 15.
  4. Read Section 2.7 of SA for discussion in class on Tuesday. Send me a question on the reading by Monday evening. Due 02/12.
  5. Hand in Exercises 2.6: 8; Exercises 2.9: 5, 9, 15. Due 02/15.
02/06
  1. Read the sections “Medieval Europe” and “The 15th and 16th Centuries” in BG (pp. 33-37).
  2. Review today’s arguments on the Euclidean Algorithm and greatest common divisors. You may need some of these facts during Thursday’s class.
  3. Read Section 2.9 of SA for discussion in class on Thursday. You do not have to send me a question on this reading, but you should feel free to do so anyway, if anything is not clear.
  4. From SA, Exercises 2.6: 1, 3, 5, 7, 8.
02/01
  1. Explore today’s warmup problem (“You have 7-minute and 11-minute egg-timers. How can you time a 15-minute egg?”) Change the numbers: what eggs can you time with these timers? What eggs can you time with other timers (for example, 6-minute and 10-minute timers)?
  2. Read the sections “Meanwhile in India” and “Arabic Mathematics” in BG (pp. 25-33).
  3. From SA, Exercises 2.4: 1, 3, 4, 6, 14; Exercises 2.5: 4, 5, 6.
  4. Read Sections 2.5 and 2.6 of SA, and be ready to discuss them in class on Tuesday. Send me a question on this reading by Monday evening. Due 02/05.
  5. Hand in Exercises 2.2: 2; Exercises 2.4: 3, 6; Exercises 2.5: 5. Due 02/08.
01/30
  1. Read the section on “Greek Mathematics” in BG (pp. 15-25).
  2. From SA, Exercises 2.2: 2, 4(a)(b), 9, 13; Exercises 2.3: 7, 8, 14, 17.
  3. Read Section 2.4 of SA, and be ready to discuss it in class on Thursday. Send me a question on this reading by Wednesday evening. Due 01/31.
01/26
  1. Read “History in the Math Classroom” and “Beginnings” (through to the top of page 15) in Math Through the Ages (BG).
  2. From SA, Exercises 1.2 (p. 5): 2, 4, 8, 13; Exercises 1.3 (p. 13): 5, 14, 25.
  3. Hand in Exercises 1.2: 8, 13; Exercises 1.3: 14, 25. Please do not hand in your first drafts: give me carefully written, viable arguments. (MP3) Due 02/01.
  4. Read Sections 2.1, 2.2 and 2.3 of SA, and be ready to discuss them in class on Tuesday. Send me a question on this reading by Monday evening. Due 01/29.
01/23
  1. Read the remaining Standards for Mathematical Practice. Make notes on anything that resonates with you, and anything that you find problematic or that you have questions about. Send me a question on the practice standards by Wednesday evening. (We will discuss the standards, and your questions, on Thursday.) Due 01/25.
  2. Answer the fifteen Discussion Questions (handed out in class), and bring 2 copies of your answers to class on Thursday. (I will collect and keep one copy, so you will need a second for future reference.) Due 01/26.
  3. Read Chapter 1 (pp. 1-13) of The Mathematics that Every Secondary School Math Teacher Needs to Know (SA) and be ready to discuss it in class on Thursday.