Polynomials and Graphing

Grade Level (can be multiple): 11-12

Brief Overview of Course:
This one semester course focuses on developing students' ability to look for patterns in mathematics. Each class starts with a small logic puzzle. There are opportunities for interim assessments and final PBATs (performance-based assessment tasks) as well as quizzes, a midterm and a final examination. In addition, there are many practical applications. The following topics are covered:
- nth terms
- letter equations with restrictions
-fractional exponents
-negative exponents
-use and proof
-coordinate geometry
-slopes
-2 point equations
-midpoints
-lengths
-circles
-complete the square
-logic puzzles
-2 equations with 2 unknowns
-substitution
-elimination
-matrices
- factor
- imaginary numbers
- rationalize simple roots

Readings: 
Math Puzzles and Games by Michael Holt
Algebra and Calculus by Dennis Christy and Robert Rosenfeld
Precalculus:Functions and Graphs by Raymond A. Barnett, Michael R. Ziegler and Karl E. Byleen
Media Used: 
Calculators
Interim Assessments: 

Logic puzzle
1 6 Urban students ran a race. Each wore a different color. There were no ties.
2 Amanda lost to blue.
3 The 6-letter named runners came in consecutive order and one was green.
4 Alison lost to the runner in red but beat Iliriana.
5 Iliriana beat Mac and white but lost to Amanda.
6 The runner in white lost to Mac who lost to Amanda.
7 Heru beat Amanda by 2 places.
8 Courtney was not orange and lost to Iliriana.
9 The rider in blue lost to the rider in red but beat the rider yellow.

A Name the 6 runners in order of finish and each color each wore.
B You must prove that your solution is the only possible conclusion, in good order. Use the numbered sentences as evidence for each statement you make. If you use charts or partial charts, these must be fully explained.

Please read all of these instructions before starting.
It is known that water freezes at 32 degrees Fahrenheit (F) or 0 degrees Celsius (C) and boils at 212 degrees F or 100 degrees C. Show that the two temperature scales F and C are linear related by completing the following steps. Be sure to explain all of your procedures and show your calculations.

1) Find a linear equation that expresses F in terms of C. Neatly draw a graph of this equation. Label the axes, label the line with your equation and title your graph.
2) If a European family sets its house thermostat at 20 degrees C, what is the setting in degrees F? Find a linear equation that expresses C in terms of F. If the outside temperature in Milwaukee is 86 degrees F, what is the temperature in degrees C?
3) Explain what the slope in question 1) means in terms of converting Celsius to Fahrenheit.
4) Since we know water freezes at 32 degrees F and 0 degrees C and boils at 212 degrees F and 100 degrees C, explain why -40 C = -40 F.
Note: Show all work neatly on separate sheets.

Significant Assignments: 

The Pirates

Redbeard, Graybeard and Bluebeard were separated while being chased by the French Navy. Graybeard found himself at (-2, 13) (see the G). Bluebeard at (-12, 7), and Redbeard at (-3, -9). Redbeard took a course of Y = 2X -3 and Bluebeard took a course Y = 0X + 7 (or Y = 7) and Graybeard took a course of 7-3X = Y. When Bluebeard and Greybeard met, they continued on Graybeard's course till they met Redbeard. Then all three took course Y = X/2 till they came to Treasure Island.

1) Locate the (0, 0) center point. Put a C .
2) Locate Bluebeard's and Redbeard's starting points put a B (-12, 7) and an R (-3, -9)
3) Chart Bluebeard's course till he met Graybeard at ( , ). Use X's on the graph.
Chart Graybeard's course till he met with Redbeard at ( , ). Use O's on the graph.
Chart Redbeard's course till he met the other two at ( , ). Use +'s on the graph.
4) Chart the new course to Treasure Island and place a T at ( , ). Use *'s 0n the Graph.
Show all work on separate sheets.

Significant Activities or Projects: 

The Year Book

Here is another puzzle for you to work on. Try and use algebra this time – it is a short cut for trial and error. Use the reference sentence numbers in your setup.

1) 8 students collect $88 for Urban’s Year Book.
2) Anthony collected $2 more than Yan Mei.
3) Jesse collected twice as much as Yan Mei.
4) Levi collected the average (mean) amount.
5) Lily collected $2 more than Jesse.
6) Rachel collected the same amount as Jesse.
7) Sasha collected $1 less than Yan Mei
8) William collected as much as Sasha and Jesse together.

HOW MUCH DID EACH COLLECT?

Sample PBATs: 
Series of problem solving questions based on application of polynomials and graphing: Construction Using Circle Equation and Graphing For example: Town B is located 36 miles East and 15 miles north of town A. A local phone company wants to position a relay tower so the distance from the tower to town B is twice the distance from the tower to town A. 1) In order to find all the possible tower locations show that they must lay on a circle. Find the center and radius of this circle, and graph it. Be sure to title your graph and label both axes. Think about what your scale needs to be. 2) If the company decides to position the tower on this circle at a point directly East of Town A, how far from town A should they place the tower? Show how this location meets the criteria set out above. 3) Explain in your own words each step you did and why. Include in your explanation why you used certain formulas. 4) Write a brief analysis about why your answer makes sense. This should include a logical explanation.