Your next Personal Progress Check has been assigned. Log into AP Classroom and complete the Unit 3 MCQ Part B PPC by Monday, November 25
On Monday, we will have our Unit 3 Test. We will spend Friday reviewing, and in preparation for that you should take a look at the review problems for Unit 3: pages 331-336, exercises 1, 3, 7, 9, 11, 15, 19, 20, 23, 29, 32, 40, 41. You’ll get answers and supplemental review tomorrow.
From pages 326-329, do exercises 6, 14, 15, 36
After swapping responses to the AP review problems, see the scoring guidelines here:
For each, read over the sample solution, then look at the scoring guidelines, scoring each section of the response as an E, P, or I. At the end, convert the E/P/I breakdown to a numerical score (out of 4). Give the scored document back to its owner.
If you missed the videos shown in class, you can watch them here and here. The notes sheet we started in class can be found here.
For homework this weekend, in addition to the PPC below, please read pages 305-313 (stop at “Experiments & Samples) and do exercises 1, 2, 3, 9, 13.
Reminder: Your next PPC (personal progress check) has been assigned: Unit 3 MCQ Part A. It will be due by the start of class on Monday, November 18. As with the previous PPC, there is a 25 minute timer. You are not required to work by the timer, and its expiration will not lock you out of the PPC. It is there only as a guide for how long I expect this PPC should take.
From pages 302-303, do exercises 15, 16, 18, 25, 30, 32
Your next PPC (personal progress check) has been assigned: Unit 3 MCQ Part A. It will be due by the start of class on Monday, November 18. As with the previous PPC, there is a 25 minute timer. You are not required to work by the timer, and its expiration will not lock you out of the PPC. It is there only as a guide for how long I expect this PPC should take.
Read pages 280-291 from the text, up to the section on “The Valid Survey”
From pages 300-301, do exercises 4, 7, 8, 12
In class today, we will be running a simulation that this random number generator page will be especially useful for.
For homework, take a look at simulation problems 31, 33, and 36 from the text (pages 278-279)
From pages 278-277, do exercises 25, 28, 29
From chapter 10, pages 277-278, do exercises 7, 12, 14, 20
We did some more work with Complex Fractions today. Work on the additional practice problems tonight; your first Homework Quiz will be in class tomorrow!
Read chapter 10 (pages 267-276) for some more examples of running simulations, then from the exercises on page 277, do 11, 13, 17. For running your simulation in question 17, you should do at least 20 trials, using the random numbers found on Appendix page A-81 in your textbook or elsewhere, or use the random number generator in your calculator (refer to pages 273/274 for instructions).
We talked some more about hypercubes in class today, including drawing some pictures and building our own models out of gumdrops (take care of them!)
If you’re interested in reading more about the 4th dimension, check out the links below. I especially recommend the short story And He Built a Crooked House.
- The Adventures of Fred, Bob, and Emily – a detailed look at how the lives of a 2D (Fred), 3D (Bob), and 4D (Emily) creature interact with each other. See especially the “World” section, where the author, Garrett Jones, imagines how wheels, water, and war would work in these universes.
- And He Built a Crooked House – a short story by “Big Three” science fiction writer Robert A. Heinlein about an eccentric architect who designs a house in the shape of an unfolded hypercube. An earthquake hits, and the house folds back up on itself to concerning results (see also this student film version of the story)
- Some Notes on the Fourth Dimension – some animations and movies showing the geometry of the fourth dimension, including some of those featured in the Flatland dvd bonus features.
Your homework: You were given a sheet of graph paper at the end of class. This is what you should do with it:
- Fold it in half lengthwise (“hot dog” style).
- Unfold and put a dot on the left edge of your crease.
- Flip a coin (or use some other random procedure). If the coin lands heads, draw a diagonal that goes over and up one square. If the coin lands tails, draw a diagonal that goes over and down one square.
- Continue with this pattern, creating a zig-zag across your paper, until you reach the other side. Bring that in tomorrow.
We’ve moved on to the next phase of the rational expressions unit: Complex Fractions. Don’t be intimidated by their name! These are expressions that involve “nested fractions,” meaning the numerator and denominator of the expression are both fractions (or a sum/difference of fractions) themselves.
Remember the basic process for simplifying these beastly expressions:
- Combine fractions in the numerator (finding a lowest common denominator and so on) so you have one single rational expression
- Combine fractions in the denominator (LCD, etc.)
- Keep the top fraction, flip the bottom fraction, and change the operation to multiplication (KFC)
Reminder: For Thursday, work on multiple choice question 1-15 from the Unit 2 practice exam, found on pages 264-266 of your textbook. We’ll start things off on Thursday with a brief discussion of these answers. Note: Unlike other assignments from your textbook, this assignment is required and will be checked for completeness.
In addition, you received a playing card today and corresponding instructions about producing 200 coin flips. If the card was black, I’m asking you to actually flip a coin 200 times and record the results. If the card was red, I’m asking you to make up the result of 200 coin flips (not simulate them, totally make them up). Bring in those results tomorrow as well and I will attempt to sort your results based on how they were derived (either legitimate flips or made up ones).
You had you Unit 2 test in class today, and you’ll do the test redo in groups tomorrow.
For Thursday, work on the Unit 2 practice exam, found on pages 264-266 of your textbook, specifically the multiple choice questions 1-15. We’ll start things off on Thursday with a brief discussion of these answers.
Note: Unlike other assignments from your textbook, this assignment is required and will be checked for completeness.
Report your findings for our final box-counting project here.
After talking so much these past few weeks about fractional dimension—dimension values that fill in the gaps between 1, 2, and 3 dimensions, we turn our perspective in the other direction on the number line: towards the 4th dimension. It stands to reason that the trends we’ve observed could be extended past the 3rd dimension, but considering fractals, or even Euclidean shapes, is immensely challenging for us as 3-dimensional creatures.
What helps is to consider the perspective by analogy: we can better understand the fourth dimension by putting ourselves in the mindset of a 2-dimensional creature considering the third dimension. Fortunately, this is territory that has been well-covered.
In 1884, British teacher and theologian Edwin Abbott Abbott published Flatland: A Romance of Many Dimensions. It is told from the perspective of A. Square, a denizen of the titular 2-dimensional world, and starts off explaining aspects of their universe in great detail. The second part describes his first encounter with the 3-dimensional Spaceland, and the changes to his world-view as a result.
Abbott wrote the book partly as an exercise in geometry, but also partly as a satire on the regimented Victorian-era social hierarchy. As a result, there are some rather uncomfortable characterizations of women as lower-class citizens, among other shocking commentary.
You can read the full book here (I have paper copies if you’d prefer that), but for tomorrow please at least read this excerpt.
Your first quiz of Unit 2, covering all of our work with Operations with Rational Expressions, is tomorrow, October 29.
Extra Practice Links (IXL Review)
Your Unit 2 test is tomorrow! Refer to the Unit 2 Review sheets for answers to the textbook review assignment and some additional practice problems.
If you’d like to explore the “Wandering Point” activity a bit more, and see what impact certain types of influential points have on the correlation coefficient and linear model, check out this Desmos calculator page.
We have a formal quiz on operations with rational expressions planned for Tuesday, October 29. We did some more review in class today.
Extra Practice Links (IXL Review)
We have a formal quiz on operations with rational expressions planned for Tuesday, October 29. Today in class we worked on a mastery mini-quiz.
Extra Practice Links (IXL Review)
We discussed a bit of re-expression in class today, and tonight you should read pages 232-236 and 243-246 about an overview of why we re-express and some general strategies in doing so. From pages 251-252, do 18, 19, 20, 21, 22 for a neat little story about evidence for why Pluto isn’t a planet anymore.
Your next PPC (personal progress check) has been assigned: Unit 2 MCQ Part B. It will be due by the start of class on Monday, October 28. As with the previous PPC, there is a 35 minute timer. You are not required to work by the timer, and its expiration will not lock you out of the PPC. It is there only as a guide for how long I expect this PPC should take.
Finally: Your Unit 2 test will be on Tuesday, October 29.