Algebra II (Frothingham)

Course Description

Connecting math to the real world is a meaningful way for students to apply their logic and accuracy skills. Using various mathematical equations to model real life situations students will explore these relationships and use them to problem solve and predict future conditions and to evaluate and critique the world around them. This course will work at normal pace and introduce more sophisticated topics originally addressed in Algebra I and Geometry courses.  Topics covered include:  Linear models, non-Linear models such as exponential, quadratic models and inverse models, absolute value, logarithmic functions and probability.

Schedule of Major Topics

Semester 1:

Review of Number Sense:

Working with other number bases (dozens/binary), converting to/from decimal to/from duodecimal/binary including exploring how to represent “decimal point” place values (e.g. what does 0.01 represent in another base).

Radicals

Proving the Pythagorean Theorem and understanding what is a radical.

Quadratic Functions:

Recognizing a quadratic function from its graph, its equation, and patterns in the second differences in a table of values, finding the zeroes of a quadratic, finding the vertex, factoring, completing the square, converting to/from vertex form and standard form, making a quadratic model from three points or the vertex and one other point.

Project:  Solving for the position(s) of a potato launcher to successfully land on a target given some angles/distances.

Semester 2:

Exponential Functions:

Learning the laws of exponents and how to apply them to operations and understanding the relationship between exponential verses radical notation.  Learning how to create exponential growth and decay equations to model real world phenomena.

Project:  Presentation to fully describe a student chosen real world exponential growth/decay situation.

Logarithmic Functions:

Learning the laws of logarithms and how to apply them to operations. Solving for variables within logarithmic/exponential equations.

Linear Functions:

Solving systems of equations by:  Graphing,  Setting equations equal to each other (one kind of substitution),  General substitution,  Elimination

Turning constraints into algebraic equations and inequalities

Graphing single-variable inequalities on a number line

Graphing inequalities and systems of inequalities on a coordinate plane

Algebraically manipulating inequalities

Recognizing the feasible region in a system of inequalities

Identifying corner points of the feasible region (graphically and algebraically), and interpret their meaning in the context of a problem

Use systems of inequalities to optimize

        Project:         Optimizing a bakery business working with several linear constraints.

Probability:

Being able to determine the probability of one or more series of events in real world situations such as working with cards, dice, coins or other situations

Being able to calculate experimental probability with real data.

Using Simulations to find experimental probability

Project:  Organizing and conducting a systematic investigation that includes empirical observations and theoretical analyses