Algebra I covers the study of variables, constants, expressions and equations. Upon successful completion of this course a student will understand linear equations and inequalities, relations & functions, pairs of linear equations & inequalities, exponents and polynomials, quadratic functions, data analysis and probability, exponents and radical functions, and rational functions and equations. The belief that problem solving (investigating, conjecturing, predicting, analyzing, and verifying), followed by a well reasoned presentation of results, is central to the process of learning mathematics, and that this learning happens most effectively in a cooperative, student-centered classroom. The resulting curriculum is problem-centered rather than topic-centered. There is also a continual spiraling throughout the curriculum, so topics are constantly being reinforced.
The purpose of this format is to have students continually encounter mathematics set in meaningful contexts, enabling them to draw, and then verify, their own conclusions. This pedagogy demands that students be active contributors in class each day; they are expected to ask questions, to share their results with their classmates, and to be prime movers of each day’s investigations. They are not necessarily expected to solve the exercise alone, but through collaboration with their peers, they should be able to understand it. The benefit of such participation in the students’ study of mathematics is an enhanced ability to ask effective questions, to answer fellow students’ inquiries, and to critically assess and present their own work. The goal is that the students, not the teacher or a textbook, be the source of mathematical knowledge.
Course Content (separated by subject as there is no Units)
This concept will allow students to define and operate with real numbers, which include solving equations with one variable, apply said equations, working with inequalities, and solving absolute value equations and inequalities. Student will be able to use the foundations of real numbers to solve more complex equations.
Solving and Graphing Linear Equations
Students will be able to understand and compute linear equations. In this section, students will be able to understand the idea of rate or slope, and how it affects the initial rate. Students will also be able to graph equations and apply it to real world situations. Students can take this information and find other information based on their inferences of the graph or calculation of the linear equation. Furthermore, students will be able to manipulate the equation to find other linear equations related to the original equations, relate distances by using the Pythagorean theorem, and event relate the linear equation to a circle.
In this concept, students will be introduced to the parts of polynomials including the definition of terms, coefficients, and variables how each of them relate to each other. Students will be able to identify and define a polynomial. Furthermore, students will learn different operations with polynomials including adding and subtracting, multiplying, factoring, dividing, and solving polynomials. This concept will allow them to work with later concepts such as rational expressions and quadratic expressions.
Rational expressions are no more than expressions that also have a denominator. The concept will take expression a step further and introduce simplifying and solving using various techniques. Students will be able to compute, define, and operate with rational expressions. Students will also be able to apply these basics to solving equations, manipulating expressions, and applying to real world situations.
Roots and Radicals
Students should already have a strong concept of the definition of roots. In this concept, students will go beyond memorizing, and compute and simplify them in order to work the roots and radicals in other expressions. Students will be able to understand rational exponents and radicals, and how they relate to each other. Simplifying both roots and radical expressions will allow students to work with it and use operations with radical expressions. Students will also work with equations that have roots and radicals and be able to solve, simplify, and manipulate. Students will also cover complex numbers and real world applications.
Learning to understand, simplify, and calculate with exponential functions is important for other concepts such as quadratics and rationals. Students will be able to define and use the zero and negative exponent rules, and simplify exponential expressions. Furthermore, students will need to apply exponential functions and relate them to situations such as geometric sequences, zero problems, and even quadratics.
Quadratic Equations and Inequalities
Quadratics will be the next progression beyond linear equations that the students will be introduced to. Simply, many topics including trajectory will be introduced to the usefulness of quadratics. Students will explore the basics of quadratics, which include understand quadratic graphs, the properties of A, B, and C for the standard equation, and what a zero means for a quadratic equations. Students will then be able to find the features of the quadratics by using various techniques such a solving by completing the square, factoring quadratics, and using quadratic equations. Students will also apply all of these with quadratic inequalities. Furthermore, students will need to apply their understanding to real life situations such as trajectory or sizes of rectangular plot.
System of Equations
Using system of equations shows the relationship between two or more equations, thus the importance of this concept. Students will understand the concept of system of equations and see real life situations to understand its use and purpose. Students will be able to solve two variable system of equations and use it to apply and find point of intersection or lack thereof. Furthermore, students will also apply this in system of inequalities, and see relationships between two inequalities.
Data Analysis and Probability
Students will be introduced to concepts of data analysis and probability. This will include analyzing surveys and samples, measures of central tendencies, interpretations of box and whiskers plots and other graphs, finding probability and odds, finding permutations and combinations and their probabilities, finding disjoint and overlapping events, as well as what it takes to make a good graph. Students will explore and apply this to real life situations.