Algebra 1 Summer Classes: Curriculum Overview

Overview of Algebra 1

Although the high school algebra curriculum may vary slightly from school to school and teacher to teacher, the major concepts will be the same. Most teachers assume that when students enter algebra, they already know how to solve simple 1- and 2-step equations and work with radicals and exponents. Competently performing number operations with fractions, decimals and negative numbers is also a prerequisite. If your child struggles with these skills, it would be a good idea to review them.

Linear Equations

Linear equations represent continuously increasing relationships between two variables. In other words, for every unit change in the variable x, the value of y will increase or decrease by a given amount.

For example, if you're buying cans of soup that cost $2.00 each, the relationship between the total number of cans you buy and the total cost could be represented using the linear equation y = 2x. In this equation, y represents the total cost, and x represents the number of cans purchased. Since each one costs $2.00, the total cost will always be equal to 2 multiplied by the number of cans.

If you graph this relationship, the graph will be a straight line starting at 0 and passing through the points (1,2), (3,6) and so on. The location of this line on the graph tells you the total cost of any number of soup cans.

In beginning algebra, the class might be given word problems, and the students will be asked to write and graph an equation to solve them. Other problems will be more abstract. Instead of a real-word problem, students are given a graph and asked to write the corresponding equation, or vice versa.

Systems of Equations

Once your child has mastered linear equations, he or she will learn to solve and graph systems of equations. A 'system' usually contains two equations for lines that may or may not intersect at some point. Students learn different ways to solve systems of equations by determining which variable values satisfy both equations and thus represent the point of intersection. They'll also learn that some systems have equations that don't intersect, so they have no solution.

Polynomials

Your child will also spend lots of time in beginning algebra working with polynomials, like 4x^3 + 2x - 5 and x^2 - x + 4. Complex polynomials represent relationships that are not linear. Instead, the lines representing polynomial equations may meander up and down as they progress from left to right across the graph. Your child's algebra teacher may or may not ask the class to actually graph complex polynomials, but the students will most likely learn the initial steps of the process. They'll begin by factoring the polynomial, and then they'll find its zeroes.