What We Will Be Studying...
We will start the year off slowly and pick up the pace as we go along and get more familiar with the way our class functions. Before we get into the specific knowledge and skills we will be working on, I want to throw out a few "big idea" questions or "essential questions" that will be guiding us through the course.
- How can we make sense of problems?
- How do we take something unfamiliar and use what we know to familiarize it?
- How can we prove our thinking with reason? And compare our reasonings with others?
- How are we able to recognize patterns? Make use of them?
This is just a sneak peak into the big questions we will look at. I have come up with some but I want us to come up with some more together! Together we will discover more about to uses and practicalities of math.
Our course topics:
The Real Number System
- Categorizing numbers
- Understanding differences between groups
- Placing numbers in groups with reason
- Are there numbers that don't fit into the the real number system?
Expressions
- Simplifying expressions
- Using context to quantify expressions
- Understand difference between expressions and equations
- Factoring quadratics- finding the zeros
- Completing the square
- Exponent properties and exponential expressions
Polynomials and Rational Expressions
- Properties
- Operations with polynomials
- Factors and zeros of polynomials
- Rewriting rational expressions
Creating Equations and Inequalities
- Use context to form an equation
- Represent relationships in equations with multiple variables
- Graphing equations
- Discovering and understanding the constraints of an equation or inequality
- Representing constraints graphically
- Rearrange formulas to solve for a specific variable
Reasoning with Equations and Inequalities
- Explain the reasoning of the process of solving an equation
- Solve radical equations and explain extraneous solutions
- Solve equations and inequalities in one variable
- Solving quadratics and the quadratic formula and writing solutions in a+bi form
- Solving a system of equations suing substitution and graphically
- Finding the intersection of a system of equations and what that represents in the given context
- Solving equations and inequalities graphincally