InCA Assignment for 11/18

Today in class, we did a (hopefully fun!) activity introducing our next unit on Parabolas and Quadratic Equations. Your homework tonight is to reflect on two questions:

  1. Describe one thing that you learned from the Will It Hit the Hoop Desmos activity from class.
  2. What else do you think you could use a parabola to model the shape/path of?

Write your reflection on a piece of paper or record them in Socrative (room code G102KIRK)

Bring your Chromebook in tomorrow again for Part 2 of this introduction!

Fractals & Chaos Recap for 11/15

With Mr. Drix, you observed some patterns that emerge in cobweb diagrams for certain types of fixed points. For an attractor, the pattern of steps in the cobweb diagram will be drawn towards the fixed point; for a repeller they move away. Furthermore, if the fixed point is direct, the pattern of steps will look like actual steps as they move towards or away from the fixed point, trapped between the two lines defined by the function we are iterating and y = x. If the fixed point is alternating, on the other hand, the pattern will spiral around the fixed point with each step, producing a picture that most clearly gives the cobweb diagram its name.

From there, we took our first look at non-linear functions, realizing quickly that in addition to having more than one fixed point, such functions can have different types of fixed points. One could be a direct repeller, while another an alternating attractor. The cobweb diagram remains our best way to observe these differences, and we used the Geogebra-based applications found here to create them.

We looked at 4a (y = x^2) together, classifying the fixed point at 1 as a direct repeller and the fixed point at 0 as a direct attractor. We furthermore observed that -1 is a “pre-image” to the fixed point at 1, and therefore we have different behavior for different seeds. Your homework tonight is to continue and look at 4b-4f, using the cobweb diagram app linked above and the Iterated Functions Supplement to keep track of your results.

InCA Assignment for 11/15

In class today, you were given a preview of Unit 3, which will be a review of Quadratic Functions.

Complete the table using whatever methods you have available to you. Some of it you might remember from Algebra 1 or Geometry. Some you might need to look up online. If you need to go to the HW Help Room in K22, that’s fine too. You have plenty of resources available: use them!

I’ll expect this to be completed on Monday. We’ll review your answers in class.

AP Statistics Assignment for 11/15

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.

Fractals & Chaos Recap for 11/14

With Mr. Drix, you continued your work with the Iterated Functions sheet, making some observations about how we might predict the classification of fixed point we get based on the parameters of the function we are iterating (see a friend in class for the exact notes on this if you missed them!)

We also introduced a new way of visualizing the behavior of functions: the cobweb diagram. In this style of graph, we draw the function we are iterating on the same plot as the line y=x. We pick a seed and move vertically to the graph of y=f(x), then horizontally to the line y=x, resulting in the output we just got becoming the input for the next iteration. We then move vertically again to y=f(x) and horizontally again to y=x, continuing until we get a view of the behavior of the function.

Your homework tonight then is to finish question 1 (parts f and g) and to do parts a, b, and c of question 3 of the Iterated Functions sheet. Draw both the time diagram and cobweb diagram for each of these functions, and try to make some observations about how the patterns of the two representations align with each other.

AP Statistics Assignment for 11/14

Click here to review my answers to the hospital drug testing examples you did in class.

In class today, you were given two free response questions from old AP exams. Finish your responses tonight. You’ll be trading them with a partner in class tomorrow and scoring them according to the official AP scoring guidelines.

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.

Fractals & Chaos Recap for 11/13

We’ve started down the road towards understanding the mathematics of chaos by iterating linear functions. Imagine a recursively-defined sequence, where each term of the sequence is defined based on the previous value. That’s what we’re doing here: we start with a seed, then plug that seed into a formula. Each output becomes the next step’s input, and we seek to understand the long-term behavior of formulas.

We are primarily working with this classwork sheet: Iterated Functions. We’ve done parts a, b, and c for part 1, looking at the behavior of seeds both numerically and graphically, creating a plot of steps vs. value called a Time Diagram. In all three examples, we found a fixed point: a value of a seed that is constant through the formula (plugging that value in gets that same value out). Some of the fixed points were attractors, and some were repellers. We discussed how iterating the function repeatedly is a fine way to find an attracting fixed point, but obviously won’t work to find a repeller. The only option there is to solve the equation f(x) = x.

Tonight for homework, please do parts d and e of question 1, then all of question 2. You should work on identifying and classifying the fixed point (as an attractor or repeller).

InCA Assignment for 11/13

Your Unit 2 Test is tomorrow. Here are some ideas on how to prepare:

Cumulative IXL Modules

AP Statistics Assignment for 11/13 + PPC

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.

InCA Assignment for 11/12

Your Unit 2 test is on Thursday, November 14. We played a review game in class today, and tomorrow will be some time to work independently on review. We will also have a Homework Quiz tomorrow.

Today’s Links

Cumulative IXL Modules

InCA Assignment for 11/8

We did some more review with solving rational equations today, focusing especially on dealing with equations that require us to factor denominators to find a common denominator.

Today’s Links

Cumulative IXL Modules

Fractals & Chaos Recap for 11/8

We discussed some key terms that we observed in the first part of the Nova documentary (specifically: fixed point, attractor vs repeller, and strange attractor) and we modeled some of these terms in action with some magnet pendulums. At the close of the period, we also looked briefly at a Solar System simulator found here.

For tomorrow, please read the three sections mentioned on yesterday’s post from Fractals: The Patterns of Chaos

InCA Assignment for 11/7

For the last major section of the unit, we are looking at solving rational equations.

Today’s Links

Cumulative IXL Modules