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Chapter 8: Analytic Geometry

Date
Entry Task
Activity & Journal Reflection
Homework
5/13
Given a triangle with the following vertices: A(0, 0), B(6, 0), and C(3, 4), list five points in (x, y) form that are equidistant from points A and B.  Explain your process.
Analytic Geometry and Loci: Activity 8.1 Pg. 469.

JR: Explain how to prove a set of points given from their coordinates will form a parallelogram.
Pg 476 # 1, 2, 3, 8. Pg 482 #3

Test Corrections Tuesday PM (5/19) and Wednesday AM (5/20)

Today's Goal: Students will understand the meaning of a locus of points and use analytic geometry formulas to compute slope, perpendicular lines, parallel lines, distance between two points, midpoint and equation of a line.
5/18
Determine the center and radius of a circle whose equation is (x - 4)2 + (y + 2)2 = 16 and graph the equation.
What does the mean triangle say to the circle?
You're pointless!

Pointed Circles Activity

JR: Does the point (7, -1) lie on the circle (x - 3)2 + (y + 4)2 = 25?
Describe a procedure to verify that a specified point A is a member of the locus of points that is r units from the point C.
Pg 482# 1, 7, 10, 15.
(hint for #10: Use equations from pg. 473)

Test Corrections Tomorrow PM (5/19) and Wednesday AM (5/20).

Today's Goal: Students will develop the equation for a circle of radius r whose center is located at (h, k). Additionally, students will recognize the equation of a circle.
5/19
List as many different graph views you can make by manipulating the Conic Section Explorer
Cutting the Conic Activity

Here are some helpful ideas to consider while exploring in the conic section activity.

Debrief Conic Sections

JR: What do you think will result from the locus of points that is equidistant from a single point F and a line l. Use today's activity to consider some of the possible options.
Read page 489-490
Complete Activity Part 1 only on page 491.

Handout 8.1 (for the activity above)

Test Corrections Today from 3:30-4:30pm and Tomorrow AM
.

Today's Goal: Students will become familiar with a conic section and shapes that can be made from sections of a cone. Introductions will be made to parabolic functions as locus of points.
5/20
(6 period)
Use the next 10 minutes to complete the following tasks:
  1. Use your book to define the terms, vertexfocus and directrix.
  2. Draw a sketch of a parabola that includes a directrix, axis of symmetry, vertex and focus.
  3. Explain the significance of each.
Debrief Last Night's Homework

(Guided) Use GeoGebra to complete question #1 on pg. 498.

Find an equation of the parabola with a vertex at (3, 1) and a focus at (3, 5).

JR: Write an equation for the parabola with vertex (5, -2) and directrix y = -5.
Complete all three tasks:
  • Pg. 499 # 2
  • Pg. 503-504 #8 (copy the graphs!)
  • Pg. 505 #11.
This is the GeoGebra Construction from today's class.

Test Corrections Today AM

Today's Goal: Students will solidify their understanding of parabolic functions as 
5/22
Sketch a graph of the following:
NotCircleSum
Modeling with Ellipses. Activity 8.4 Pg 509.

JR:  Write the standard form of an equation of an ellipse and explain the components. How is equation similar/different to the equation of a circle?
Pg. 516 #1, 3 and Pg. 517 #6.

Today's Goal: Students will become familiarized with an ellipse as a conic section, including the creation of an ellipse and the formula for creating this shape. 
5/26 For each, categorize as a circle, ellipse or parabola and define the center(s), foci, vertices, and directrix if they apply.
  • Ircle
  • Llips
  • Abola 
Mini-Presentation Jigsaw Activity.
  • Each person is assigned to a group and must contribute equally. If you are absent on Tuesday, begin working independently on the Task for group 4.
  • Each group is assigned an application problem.
  • Today you will have work time on the application problem as a group.
  • Friday, your group will present your solution to the class.
  • Your group will turn in a single, nicely written copy of your solution for a 10 point quiz grade. Ensure all group members names are on the written solution. This will be graded using the standard testing rubric, provided students are contributing fairly, all students will receive identical grades.
  • If you use resources outside of your group, you must cite additional assistance using APA format. Please ask Dr. Edge or Mr. G. if you have additional questions.
  • Presentations will be informal, but will count for 5 class participation points, if you have an unexcused absence on May 29, you will earn a zero. Excused absences will need to make arrangements no later than your first day returning to class.
  • See Homework Section for activity details.

JR: What are your responsibilities in your group? Specifically, describe what you are going to do to contribute to this project outside of class?

Project Information
Tasks listed by Group Number:
  1. Finding the Diameter of a Plate.
  2. Tunnel and Truck.
  3. Two Little Round Boxes.
  4. Ellipse.
Provided students are contributing fairly, each group member will receive identical grades. If a group member is:
  • Making extraordinary contributions
  • Not contributing.
  • Taking-over group responsibilities.

Please inform Mr. G as soon as possible, this may positively or adversely affect a single group members grade.


5/27 & 5/28
Smarter Balance Assessments (ELA and Math)
If you are in class, use the time to either prepare for your Friday presentation or begin studying for the Final Exam.

Consider contributing to the
Collaborative Study Guide
Continue editing presentation for Group Presentations.
5/29
Read the following guidelines and prepare for presentations:

Presenting Group: 5 points today will be from your contributions as a presenter. Be attentive, ready to answer student/teacher questions.

Audience: 5 points today will be from your engagement as an audience member. You are expected to take notes and ask questions.
Group Presentations. Each group will present for 8 minutes or less (including set-up time).

See ET for group presentation Guidelines, you are responsible for the information presented.

JR:  Reflect on your group member's performance in your group using THIS GOOGLE FORM.
(If you did not complete the task assigned May 26: Begin working on Task 5 - Hanging Around, this a completed paper outlined on 5/26 is due for you on Monday, June 1.)

Begin Studying for Final Exam.

Recommendations:
  • Rewrite the correct solution to old quizzes and tests.
  • Attempt additional practice problems for chapter 2, 3, 8, 9 and Sequences (Chapter 11 from Stewart Pre-Calculus).
  • Form a study group
Final Study Session Monday and Tuesday from 3:30pm - 4:30pm.


Final Exam and Preparation
Date
Entry Task
Activity & Journal Reflection Homework
6/1
Find a polynomial which passes through (0,0), (0, -14), (0, 12). Write in both Factored form and Expanded form.
Final Exam Prep - Quarter 3: Reviewing Polynomial Models, Logarithmic and Exponential Models

JR:  Review the list of topics for next week’s Semester Final. Write down a list (at least two specific questions for tomorrow’s Q+A Session).
Continue studying for Final Exam. Prepare questions for class.

Collaborative Study Guide

Final Study Session Today and Tomorrow from 3:30pm - 4:30pm.
6/2
Write a recursive and explicit formula for the following sequence B: {1, 6, 11, 16, ...}.

Use the explicit formula to write the partial sum of the first 20 terms using Sigma Notation.
Final Exam Prep Quarter 4: Reviewing Sequences, Series, Combinations and Probability, and  Analytic Geometry

JR: Explain how "curve matching" is fundamentally different from "modeling data."
Continue studying for Final Exams

Collaborative Study Guide

Final Study Session Today from 3:30pm - 4:30pm.
6/3
Get ready for the Exam! 
  • Move to a seat where you have ample room,
  • Obtain all the materials you need before class starts. No materials will be loaned during class!
  • Seat at most two at the square "cafe tables"
  • Place the paper "blinders" between each pair of people. Put yourself in a positive mental state.
Final Exam 2.1. You may use two 3 x 5 note cards (writing on both sides is permitted), and measurement devices (e.g. ruler and protractor). Calculators will not be allowed.

Expect questions that require you to:
  • Write an expanded polynomial that has specified real roots and verify that points lie on a polynomial.
  • Verify roots of a polynomial are solutions.
  • Determine the roots of a given polynomial.
  • Create a rational polynomial with specified intercepts and asymptotes.
  • Create a system of equations and a matrix that will solve for the coefficients of a polynomial given several specified points.
  • Write an exponential function that models a situation given two data points. Answer question using your function.
  • Solve for unknown parts of logarithmic functions and exponential functions using log and exponent laws.
  • Calculate a sequence using both explicit formulas and recursive formulas.
  • Use sigma notation to find a sum of elements in a sequence.

JR:

Continue Studying for Exam 2.2

Bring your text book to class on June 8. Students who do not turn in books by June 12 may be charged to replace the book.
6/5
All School Awards Day

Bring textbook to class Monday to turn in for the year.
6/8
Get ready for the Exam! 
  • Move to a seat where you have ample room,
  • Obtain all the materials you need before class starts. No materials will be loaned during class!
  • Seat at most two at the square "cafe tables"
  • Place the paper "blinders" between each pair of people. Put yourself in a positive mental state.
Final Exam 2.2. You may use two 3 x 5 note cards (writing on both sides is permitted), and measurement devices (e.g. ruler and protractor). Calculators will not be allowed.

Expect questions that require you to:
  • Explain the similarities and differences between a combination, permutation and other situations.
  • Compute the probability of a basic probability event (such as the probability of drawing a face card in a standard 52 card deck).
  • Write a specific term (or terms) that results from the expansion of a binomial.
  • Calculate probability of a Binomial situation.
  • Determine which conic section is represented by a given equation (specifically, Circles, Parabolas, and Ellipses).
  • Given the equation of an ellipse, determine the vertices, foci and center.
  • Write the equation for a circle given a point and radius.
  • Compute the distance between two points.

JR:

Bring your text book to class on June 8. Students who do not turn in books by June 12 may be charged to replace the book.

Today's Goal: Students will learn about hyperbolas as yet another conic section.
6/9
Senior's Last Day. Calculus Preparation


6/10



6/12



6/15



6/16
(Last Day of School)