Home
 About
 PreCalculus
Date 
Entry Task 
Activity 
Assignments
and Homework 

1/27 
Complete the following
tasks in order:

Introduction to
polynomial functions. (Case study of Taylor Polynomials) Work on Lesson 3.1 (pp. 179181) JR: Why must the sum, difference, and product of polynomials always be a polynomial? 
pp.182183 #4, 7 Uses of Polynomials: Phases of the Moon (USNO) Pixar and Points Today's Goal: Student's will understand at least one example of polynomial use and will add, subtract and multiply polynomials together. 
1/28 (Block) 

Building understanding of
Polynomials and their roots: Building Polynomials Worksheet Discussion Zeros and Real Roots for higher order polynomials. JR: Provide an outline for finding polynomials which pass through particular points on the xaxis. 
Complete the following
activity to extend today's ideas about linear functions to
higher order polynomials. Cubic
Polynomial Worksheet Today's Goal: Students will learn about roots (aka "zeros") of a polynomial function. Students will learn the minimum number of points to determine a unique polynomial. 
1/30  Obtain a grading rubric located on your
table, read through each level and description. Grading Rubric 
Reflection of Final Assessment. Use the THIS
document as a guide. Note: To communicate this reflection, you may type, hand write, video tape, audio record, PowerPoint present or use other mediums. You must answer all questions to receive full credit. JR: Why is it important to reflect on assessments? 
Complete today's activity. Print your
document to turn in on Monday. 
2/2 
Pass forward "Building
Polynomial Worksheet" and your Assessment Reflection. What is The Quadratic Formula? When is it most appropriate to use? Bonus: Use the general quadratic function to derive the quadratic equation by completing the square. 
Explore the solution to a
cubic function. The Cubic Formula. Fit a curve to points and determine roots given a function. Factoring and finding roots (i.e. Zeros) JR: Compare and contrast curve modeling and curve fitting. 
Create cubic polynomials
that have the following solutions without using the
regression function on your calculator. An alternate
option may be guess and check. Show all steps of the
process and prove (by hand) the given solutions are
correct.a) (2, 0), (1, 0), (3, 0)Be prepared to show the graphs (of the polynomials) in class when your homework is checked. Today's Goal: Students will use points on the xaxis and points not on the xaxis to find a polynomial that fits the data. 
2/3 
Find a polynomial which passes through
(0,0), (0, 4), (0, 3). How might you find the polynomial if you were given points not on a particular axis? 
Motivating Question: What happens when we
only know other points? Lesson 3.2 (pp. 185  189) Expanding polynomials. JR: In your own words, detail the important information you need to remember in order to use points to create a polynomial. 
Recreate the polynomials from Feb. 2nd
using techniques learned in lesson 3.2. Be prepared to
show the matrices (and their inverses) used to calculate
the polynomials. Expand each polynomial. Compare with homework from 1/30 to ensure you have similar solutions. Today's Goal: Students will learn how to find at least one function to fit points not on the xaxis. 
2/4 (Block) 
Get ready for the quiz! Move to a
seat where you have ample room, obtain all the materials
you need before class starts, seat at most two at the
square "cafe tables" and place the paper "blinders"
between each pair of people. 
Quiz 3.1 (write an expanded polynomial that
has specified real roots and verify that points lie on a
polynomial). You may not use a calculator or notes for
this quiz. After Quiz: Using graphing calculator to find intersections, and zeros. Continue Exploring how to fit curves. JR: Compare and contrast the meaning of the zero of an equation, the roots of an equation and the solutions to an equation. 
Pg. 190 191: #1, 3, 5 Today's Goal: Continue exploring how to find polynomials which pass through points and assess student understanding of roots. 
2/6 
If
$f(x)\; =\; x^2+2x3$ and $g(x)\; =\; 2x+1$, determine algebraically the values of x where f(x) = g(x). Graph f(x) and g(x) and use the "intersect" function on your calculator to confirm your algebraic solution. 
Polynomial
Playtime Activity Use THESE notes as a guide if needed. JR: A toy ball is picked up from a tall shelf and tossed across a large gymnasium. Recall that a parametric function can model the vertical height of the ball after an elapsed time. Suppose the height equation (in units of feet) is modeled by h(t) where t is the number of seconds after the ball has been tossed. $$h(t)=16t^2+37t$$ $h(t)\; =\; 16t^2+37t$Some values of t do not make sense in the context of this problem. What interval(s) of t does this equation make sense? Which interval(s) of t does the equation not make sense? 
Read Activity 3.3 (Pg. 196203). About end
behavior of polynomial functions. Be prepared to show your notes, which must include:

2/9 
Let f(x) 2x^{3} + 2x^{2 }
6x

End
Behavior of a Polynomial JR: Calculate the polynomial that passes through the points (1, 49), (0, 15), (1, 1), (2, 5). Using only the equation generated, predict the end behavior of the function. 
Complete today's activity Pg. 206: # 1, 7, 11 (Sketch all graphs into your homework notebook). Today's Goal: Students will practice fitting polynomials to points, learn about end behaviors of polynomials and scale a polynomial to fit points. 
Optional Practice
Activity 
The activity on the left is optional, but
provides good practice for using the quadratic formula to
find the roots. 
Use The Quadratic Formula to obtain the
roots of the polynomial in the ET (from 2/9). Write
the polynomial in factored form. Working with your table partner

Optional activity to provide extra
practice. Falling from the Plane Activity Summative Question: What are the repercussions of multiplying a polynomial by a scalar? 
2/10 
Find the roots of the following polynomial: $y=x^2+4x+5$ Simplify your results as much as possible. 
Mathematical Duals: Video
Read the story on pg. 210. The history of Integers, Rational and Irrational Numbers. Complex numbers introduction. Distinguish between imaginary numbers. Khan's Version of today's lesson. JR: Expand (i.e. "FOIL") [x  (2 + i)] [x  (2  i)] 
Watch this Khan (Video) Correctly answer at least 5 problems. You must write down the problem, your solution and the correct answer. (Note: You may need to complete many more than the required number to get at least 5 correct). HOMEWORK PROBLEMS HERE Today's Goal: Students will learn how mathematical challenges advanced the common understanding of mathematics. Additionally students will be able to use algebra with complex numbers and reduce their function to standard form $a+bi$ where a and b are real numbers.$$ 
2/11 (Block) 
Get ready for the quiz! Move to a
seat where you have ample room, obtain all the materials
you need before class starts, seat at most two at the
square "cafe tables" and place the paper "blinders"
between each pair of people. 
Quiz 3.2 (Fit a curve to points, determine
the degree of the function created, identify the roots of
the function). Note: No materials (including batteries)
will be issued or loaned during class time. When finished with the quiz: Find the roots of $f(x)\; =\; x^2+4$. Establish the Fundamental Theorem of Algebra. Pg 216 #3, work though this problem as a class. JR: Sketch the polynomial y = x^{5}  5x^{4} + 20x^{2}  5x + 25 and determine the roots. How many roots belong to this function? Estimate the xvalue for the roots that are real (if any exist). How would you find the complex roots? 
Pg 216217 #1, 3, 4 Today's Goal: Students will understand the utility of the Fundamental Theorem of Algebra (FTA). Additionally, students will show that the FTA is true for quadratic polynomials. 
2/13 
Use the Fundamental Theorem of Algebra to
describe the roots of the function y = x^{2}
 6x + 13. 
Plotting complex numbers in rectangular and
polar coordinates. Complex Plane Overview JR: Explain why the rectangular and polar forms of a complex number represent the same number. 
Pg. 219 #7, 10 You know complex numbers can be represented in both rectangular and polar forms. The complex number can be represented both in polar and rectangular form.
Explain why = 8 using both polar coordinates and
algebra. Today's Goal: Students will represent complex numbers on the complex number plane using rectangular and polar coordinates. 
2/18 (Block) 
A point in polar coordinates can express a
number in the complex plane. What complex number is
expressed by the point (1, 45°)? 
Practice using the complex plane and
calculating distances. Complex Hexagonal Jigsaw Puzzle For those interested: A paper about complex number and springs JR: Describe the relationship between the product of 3 + 2i with it's complex conjugate and the graphical representation of these numbers. 
Complete the following steps for each
equation below:
1) y = 4x^{2}  16x + 19 
2/20 
Get ready for the quiz! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people.  Quiz 3.3 (Complex Numbers: Determine real
and complex roots, plot a complex number on the complex
plane, use the Fundamental Theorem of Algebra to rewrite a
polynomial into factored form). You may use a singe 3 x 5
note card and your calculator. Note: No materials
(including batteries) will be issued or loaned during
class time. JR: Graph y = (x^{4}  13x^{2} + 36) ÷ (x^{2}  2x) in the standard window of your calculator. Explain the appearance of the function and why you believe it behaves this way. 
None Assigned :) Consider reviewing content from Quiz 3.1 and Quiz 3.2. Today's Goal: Assess students knowledge of complex numbers. 
2/23 
Use long division to calculate 384 ÷ 7 as a mixed fraction. Show all of your work to explain your process.  Long division with polynomial functions. JR: Explain how long division and polynomial long division are similar. Provide an example of each or detail the process. 
Pg 233 #8 (Use the long division method
only) Also, compute the following quotients using polynomial division.
Today's Goal: Students will calculate P_{1}(x)/P_{2}(x) using polynomial long division. Students will also use the Remainder Theorem to express the remainder of a polynomial division. 
2/24 (Block) 
For the function f(x) = (x + 2) ÷ (x  1),
describe as many of the following features as possible. DO
NOT GRAPH!

"Be Rational!" (Station Learning Activity)
See THESE
notes to clarify information from stations.

This homework is due on 3/2. Note: Some problems may cover concepts NOT at your station. During class, we will continue the activity. All problems should be solvable by the due date. Pg. 229233 # 1, 2, 3, 4a, 7 Lesson Goals: Students will learn about basic asymptotic behavior that results from polynomial division including domain and range of asymptotic functions. Additionally, students will recognize a polynomial which results in a curve with a hole. 
2/25 (SAT Day) 
Visit THIS
website from the creators of the SAT. Explore the links to learn about how the SAT is being redesigned. 
Sample
SAT Questions (Math,
Reading, Writing, Essay) Sample SBA Assessment (Math and English/Language Arts) JR: What will you do to prepare for upcoming standardized tests? 
(Optional) SAT Prep and sample test on Khan
Academy. Last day to complete extra credit. Today's Goal: Students will learn about the new SAT and the SBA assessments, how they assess knowledge and practice some problems. 
2/27 
For the function g(x) = (x + 2)(x  3) ÷ (x
 1), describe as many of the following features as
possible. DO NOT GRAPH!

Continue "Be Rational!" (Station Learning
Activity) JR: Complete the JR for each associated station you visited today. Build a rational polynomial that:

See homework column from 2/24. Due 3/2. Lesson Goals: Students will learn about basic asymptotic behavior that results from polynomial division including domain and range of asymptotic functions. Additionally, students will recognize a polynomial which results in a curve with a hole. 
3/2 
Complete the task or answer the question
for each station:

Debrief/Overview of polynomial division and
asymptotic functions. Practice building rational
functions. See THESE notes to review concepts on rational polynomial functions. For more practice with identifying attribute of rational functions, use THIS link. JR: Without a calculator, build a function that

Chapter 3
Review Problems Collaborate on THIS Google Doc. Do not delete others' work. (Optional: For additional practice problems see book review starting on pg. 242) 
3/3 
Create a rational function that has an xintercept at x = 1 and x = 5, a vertical asymptote at x = 0.5 and x = 2, horizontal asymptote at y = 2 and passes through the point (0, 10).  Inclass review: Questions from homework,
activities, and quizzes will be answered. Bring your
papers and ask questions! JR: Which concept(s) are you least confident? What specific steps will you take to become more confident in this/these skills? 
Continue Chapter
3 Review Problems to prepare for Test 3.1 and 3.2 Test review with Mr. G  3:30pm4:30pm. Collaborate on THIS Google Doc. Do not delete others' work. 
3/4 (Block) 
Get ready for the exam! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Put yourself in a positive mental state.  Test 3.1. You may use YOUR calculator and a 3 x 5 note card* (writing on both sides is permitted). Measurement devices (e.g. ruler and protractor) are also allowed. Note: no materials (including batteries) will be issued or loaned during class time. Expect questions on:
*Note cards may not be mechanically reproduced (no
photo copies, word processing, etc.). JR: Describe your own progress towards learning
about polynomial functions. What is needed next to
improve your understanding? 
Continue studying for Test 3.2, send questions to Mr. G. 
3/6 
Get ready for the exam! Move to a seat where you have ample room, obtain all the materials you need before class starts, seat at most two at the square "cafe tables" and place the paper "blinders" between each pair of people. Put yourself in a positive mental state.  Test 3.2 You may use YOUR calculator and a
3 x 5 note card* (writing on both sides is
permitted). Measurement devices (e.g. ruler and
protractor) are also allowed. Note: no materials
(including batteries) will be issued or loaned during
class time. Expect questions on:

None :) Today is the last day to turn in homework for credit. Test Corrections: Wednesday 3/11 (AM/PM) 
3/9 
Which of these functions has a vertical asymptote? Explain how you know. 
Slant Asymptotes From Station 2 of the station activity, sketch a graph of each of the functions in the fifth column on page 3. JR: Describe all of the possible end behaviors of a function. Consider trigonometric, rational functions, polynomial functions, exponential functions, square root function, etc. 
Bring Pressure
vs. Altitude graph (from 8 September). If you cannot
locate this graph, recreate this for class. (Recommended) Review exponent rules from Algebra. Test Corrections: Wednesday 3/11 (AM/PM) 