June 11, 2009

This lesson introduces the concept of systems of linear equations by relying on the graphical interpretation. Students will come to understand that a system is "two or more equations plotted on the same set of axes". In subsequent lessons, this concept will be developed and nuanced to include any two equations whose variables represent the same quantities.

- Mathematics > General
- Mathematics > Algebra
- Mathematics > Equations
- Mathematics > Graphing

- Grade 6
- Grade 7
- Grade 8
- Grade 9
- Grade 10

Given a literal equation, solve for a specified variable of degree one.

Explain and illustrate how changes in one variable may result in a change in another variable.

Solve and check multi-step equations and inequalities, including distributive property, variables on both sides, and rational coefficients.

Use real-world data to express slope as a rate of change.

Graph solutions to linear inequalities.

Write linear equations given slope and y-intercept or two points.

Identify domain, range, slope, and intercepts of functions.

Develop generalizations to characterize the behaviors of graphs (linear, quadratic, and absolute value).

Classify and determine degree of a polynomial and arrange polynomials in ascending or descending order of a variable.

Apply ratios and use proportional reasoning to solve real-world algebraic problems.

Add, subtract, multiply, and divide polynomial expressions.

Analyze the relationship between x and y values, and determine whether a relation is a function.

Solve, check, and graph multi-step linear equations and inequalities in one variable, including rational coefficients in mathematical and real-world situations.

Solve and graph absolute value equations and inequalities in one variable.

Analyze the relationship between x and y values, determine whether a relation is a function, and identify domain and range.

Explain and illustrate how a change in one variable may result in a change in another variable and apply to the relationships between independent and dependent variables.

Graph and analyze linear functions.

Use algebraic and graphical methods to solve systems of linear equations and inequalities in mathematical and real-world situations.

Add, subtract, multiply, and divide polynomial expressions.

Factor polynomials by using Greatest Common Factor (GCF) and factor quadratics that have only rational roots.

Determine the solutions to quadratic equations by using graphing, tables, completing the square, the Quadratic formula, and factoring.

Justify why some polynomials are prime over the rational number system.

Graph and analyze absolute value and quadratic functions.

Write, graph, and analyze inequalities in two variables.