Algebra and Beyond

Essential Question: How do we use math to model real life situations?

Unit 1: Exploring Functions
• Review conceptual understanding of topics related to linear relationships.
• Review the skills required to graph a line, to calculate the intersections of two lines, and to calculate x and y intercepts.
• Become familiar with function notation and investigate functions with a graphing calculator.
• Become familiar with domain and range of a function.
• Become familiar with multiple representation of a linear relationship to model real life situations.
• Become familiar with function machines.

Unit 2: Sequences
• Become familiar with various sequences, including arithmetic and geometric sequences
• Become familiar with writing equations and graphs of arithmetic and geometric sequences.
• Become familiar with generators and common differences of sequences.
• Become familiar with discrete and continuous sets of data.
• Become familiar with multiple representations of sequences to model real life situations.
Major Assignments:

Unit 3: Exponential Functions
• Become familiar with exponential function as an extension of geometric sequences
• Be able to identify exponential relationships, including decay and growth, and be able to write an equation to describe the relationship.
• Become familiar with the concept of multipliers.
• Become familiar with negative and fractional exponents.
• Become familiar with rules of exponents.
• Become familiar with the relationship between roots and fractional exponents.
• Be able to solve for unknown base or power without using logarithms.

Unit 4: Exploring Parabolas
• Become familiar ways of calculating the vertex of a parabola by “completing the square” or averaging the intercepts
• Be able to shift the vertex of y= x2 left, right, up and down
• Be able to sketch the graph of a parabola from its equation.
• Be able to write an equation based on the location of the vertex on the coordinate plane.
• Become familiar with vertex for y = a(x – h)2 + k
• Understanding the concept of compression and stretch of a parabola and be able to calculate the compression/stretch of a real life parabola.
• Be able to write an equation for the path of a parabola if the vertex and another point is given.

Unit 5: Parent Graph
• Become familiar with an extended set of parent graphs, including cubic, exponential, hyperbola, and absolute value.
• Become familiar with some non-functions graphs and equations, including sleeping parabolas and circles.
• Be able to sketch the graphs of the above functions and non-functions from their equations.
• Be able to write equations for the graphs of functions and non-functions.
• Become familiar with the concepts of locators
• Become familiar with various orientations of locators of parents graphs, including left, right, up and down.
• Learn to use asymptotes as locators for graphs of exponential and hyperbolas.

Unit 6: Systems of Linear Inequalities
• Be able to graph linear inequalities
• Be able to find the solution of a system of inequalities
• Be able to apply feasible region to real life situations
• Understand the concepts of feasible regions as it is applied to possible productions to maximize profits.

Unit 7: Introduction to Statistics
• Review the basic measure of central tendencies, including mode, median, mean, and outliers of data sets.
• Become familiar with standard deviation and it application to real life situations.
• Become familiar with z-scores and raw scores and their applications to real life situations.
• Become familiar with a normal curve.
• Construct histograms for various kinds of data sets.
• Become familiar with Student’s T-Test and apply it to real data form biology exit project.

Readings: 
College Preparatory Mathematics: Volume One and Two
Interactive Mathematics Program: The Pit and The Pendulum
Media Used: 
Graphing Calculators TI84
Calculator-Based Rangers (motion detectors)
Geometer's Sketchpad
Excel
Significant Assignments: 

A test at the end of every unit

Significant Activities or Projects: 

Unit 1 Pencil Sharpening Lab

Unit 2 The Bouncing Ball Exhibition: Part I and II

Unit 3 Fast Cars Struggle Problem and The Student Loan Problem

Unit 4 Parabolic Path Exhibition (take video of yourself throwing a ball and find the equation to model the path of the ball's flight)

Unit 5 Artistic design using the Sketchpad and parent graphs

The Mathematics of Corporate Responsibility Exhibition (use inequalities represent a corporation's profits and discuss equity issues connected to the math)

The Pendulum Exhibition (determine which variables, when changed, affect the period of a pendulum)

Sample PBATs: 
The Bouncing Ball Exhibition
Changing the Period of a Pendulum
Additional PBATs grow out of the problem-solving activities detailed above