Algebra 1

Algebra I is an introductory course for ninth grade students to transition them from middle school to high school mathematics. Pathfinder Tech follows the Model Algebra 1 Traditional Pathway from the Massachusetts Mathematics Curriculum Frameworks. This course is a graduation requirement for all students which emphasizes that Algebra 1 focus on the following 4 areas:

(1)  deepen and extend understanding of linear and exponential relationships;

(2)  contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions;

(3)  extend the laws of exponents to square and cube roots;

(4)  apply linear models to data that exhibit a linear trend.

(Click here to read more about the Massachusetts Mathematics Curriculum Frameworks.)

Learning Targets Students will be able to...

• Solve one-step equations in one variable using addition or subtraction.

• Solve one-step equations in one variable using multiplication or division.

• Solve two-step equations in one variable.

• Solve multi-step equations in one variable.

• Solve equations in one variable that contain variable terms on both sides.

• Solve equations in one variable that contain absolute-value expressions.

Learning Targets Students will be able to...

• Identify solutions of inequalities in one variable.

• Write and graph solutions of inequalities in one variable.

• Solve one-step inequalities in one variable using addition or subtraction.

• Solve one-step inequalities in one variable using multiplication or division.

• Solve multi-step inequalities in one-variable.

• Solve inequalities in one variable that contain variable terms on both sides.

• Solve compound inequalities in one variable.

• Graph solution sets of compound inequalities in one variable.

• Solve inequalities in one variable that contain absolute-value expressions.

Learning Targets Students will be able to...

• Identify functions from various representations (graphs, tables, mappings).

• Identify key features of a relation, such as domain and range.

• Use function notation to evaluate a function. (graphs)

• Use function notation to evaluate a function. (equations)

• Graph functions given a limited domain.

• Graph functions given a domain of all real numbers.

• Recognize and extend arithmetic sequences.

• Recognize and extend geometric sequences. 

• Use explicit formulas to find a given term in an arithmetic sequence.

• Use explicit formulas to find a given term in a geometric sequence.

Learning Targets Students will be able to...

• Identify x- and y-intercepts from graphs and from equations in standard form.

• Graph lines using equations in standard form.

• Find slope using a graph.

• Calculate slope using the slope formula. 

• Graph lines using equations in slope-intercept form.

• Write linear equations in slope-intercept form.

• Identify parallel and perpendicular lines from their equations.

• Write equations to describe lines parallel and perpendicular to a given line.

Learning Targets Students will be able to...

• Evaluate expressions containing zero and integer exponents.

• Simplify expressions containing zero and integer exponents.

• Use multiplication properties of exponents to evaluate and simplify expressions.

• Use division properties of exponents to evaluate and simplify expressions.

• Classify polynomials and write in standard form.

• Add and subtract polynomials.

• Multiply polynomials.

Learning Targets Students will be able to...

• Factor polynomials using the greatest common factor.

• Factor quadratic trinomials of the form x^2 + bx + c.

• Solve quadratic equations by factoring.

• Identify characteristic of a quadratic functions from a graph or equation.

• Graph a quadratic function in standard form.

Learning Targets Students will be able to...

• Identify solutions of systems of linear equations in two variables.

• Solve systems of linear equations in two variables by graphing.

• Solve systems of linear equations in two variables by substitution.

• Solve systems of linear equations in two variables by elimination.

• Compare and choose an appropriate method for solving systems of linear equation.

• Solve special systems of linear equations in two variables.

• Classify systems of linear equations and determine the number of solutions.

• Graph and solve linear inequalities in two variables.

• Graph and solve systems of linear inequalities in two variables.