Try our Free Online Math Solver!
Algebra I Competency
The Department's Educational Philosophy
The study of mathematics will enhance the ability of all students to problem solve and to reason . Through a strong standardized
departmental program that emphasizes problem solving, communicating, reasoning and proof, making connections, and using
representations, students will develop organizational skills, self-confidence and a positive attitude toward mathematics. Our
curriculum matches that of the Massachusetts Mathematics Curriculum Framework, and we are philosophically aligned with the
National Council of Teachers of Mathematics Standards.
• All students can learn mathematics.
• Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of
• Effective mathematics programs focus on problem solving and require teachers who have a deep knowledge of the discipline.
• Technology is an essential tool in a mathematics education, and all students should gain facility in using it where advantageous.
• All students should have a high-quality mathematics program.
• Assessment of student learning in mathematics should take many forms to inform instruction and learning.
• All students should recognize that the techniques of mathematics are reflections of its theory and structure.
• All students should gain facility in applying mathematical skills and concepts.
• All students should understand the role of inductive and deductive reasoning in mathematics and real life situations.
Background to the Curriculum
This course is now using the 2001 edition of the McDougal Littell Algebra I text: Applications Equations Graphs by Larson , Boswell,
Kanold, and Stiff. The text is supplemented with designated materials from the 1992 Dolciani Algebra I text and units on matrices
and linear programming . The entire text is covered and goes far beyond the Massachusetts State Frameworks recommendations for a
first-year Algebra course, as well as the 2000 edition of the National Council of Teachers of Mathematics. The course is, therefore,
well aligned with national and state standards. Teachers utilize other materials to enhance and deepen the curriculum content where
appropriate and make minor changes after consultation with the BDL.
Solve real-life problems using algebraic skills and concepts
Create an environment conducive to learning algebra
Stress organizational skills and the need to provide proof of all solutions
Perform operations/ simplify expressions
Solving linear and non-linear equations in one variable
Applying algebra to modeling
Operations on polynomials
Graphing linear and non-linear functions
Domain, range, and composition of functions
Topics in probability and statistics
Understanding the role of proof
Solving systems of equations and inequalities in more than one variable
Use of irrational and rational numbers in the Pythagorean Theorem
Course-End Learning Objectives
|Learning objective||Corresponding state standards, where applicable|
|1] use tables and graphs to organize real-life data||8.D.02|
|2] use rates, ratios, and percents to solve real-life problems||8.N.03|
|3] apply introductory techniques in Probability and Statistics||10.D.01|
|4] apply the Pythagorean Theorem to real life problems||10.G.05|
|5] find the distance between and midpoint between two points||10.G.07|
|6] add, subtract, multiply and
divide real numbers and solve real life
problems using real numbers
|7] apply the distributive property
to algebraic expressions and use the
distributive property to solve real-life problems
|8] use the properties of exponents
to evaluate and solve exponential
|9] use scientific notation to solve real life problems||10.N.01|
|10] simplify and evaluate numerical
and algebraic expressions with and
|11] write, use, and graph models of exponential growth and decay||10.P.01|
|12] find exact an appropriate solutions to equations involving real numbers||10.P.02|
|13] add, subtract, multiply and divide rational expressions||10.P.03|
|14] add, subtract, multiply and divide polynomials||10.P.03|
|15] rewrite and evaluate an equation in function form||10.P.04|
|16] transform radical expressions into simple radical form||10.P.04|
|17] factor polynomials and solve quadratic polynomials||10.P.05|
|18] solve quadratic equations algebraically and graphically||10.P.05|
|19] apply the quadratic formula or
complete the square to solve quadratic
equations and inequalities
|20] solve and graph absolute value
equations and inequalities on a number
line and coordinate plane
|21] graph horizontal and vertical equations||10.P.07|
|22] graph linear equations and inequalities using slope and y-intercepts||10.P.07|
|23] use standard form and slope intercept form to solve real life problems||10.P.07|
|24] identify, use, and apply the
discriminant to find the number of solutions of
a quadratic equations and real-life problems
|25] solve linear equations and inequalities using 1 or more transformations||10.P.07|
|26] solve literal equations and formulas for one of its variables||10.P.07|
|27] solve problems using a linear verbal model||10.P.07|
|28] draw a diagram to help understand real-life problems||10.P.07|
|29] solve direct and indirect variation problems (joint and comb)||10.P.07|
|30] represent real numbers on the number line||10.P.07|
|31] identify a function and represent a function with an input-output table||10.P.07|
|32] solve systems of equations and
inequalities in two variables using
graphing, substitution or linear combination
|33] apply systems of linear inequalities to real life problems||10.P.08|
|34] linear programming||10.P.08|
|35] add and subtract matrices||10.P.explor|
|36] use sine, cosine, and tangent ratios to solve real life problems||12.G.01|
|37] add, subtract, multiply and divide radical expressions||12.N.02|
|38] solve and graph rational equations and functions||12.P.08|
|39] solve radical equations||12.P.11|
Students are generally assessed by in-class tests and quizzes, which are administered regularly throughout a marking period.
Generally, two quizzes are equivalent to a test . The students’ attitude, effort, and quality of homework preparations will also impact
their term grade to a small degree. Teachers informally assess students every day by asking pivotal questions, as well as questions
involving mechanics or concepts. A standardized midyear examination and final examination are administered to all students in this
course in order to assess their long-term retention of the course material.
Technology Learning Objectives Addressed in This Course
(This section is for faculty and administrative reference; students and parents may disregard.)
|Course activity: Skills &/or topics taught||Technology standard(s) addressed through this activity|
|1] Graphing calculators to introduce graphing of
2] Graphing calculators to solve systems of linear equations
3] Graphing calculators to introduce the concept of data
analysis and best fit lines
Materials and Resources
Teachers use other texts for supplementary ideas, “Algebra with Pizzazz” puzzle sheets, and Algebra I by Dolciani for more
challenging examples. Graphing calculators are utilized throughout the course to enhance various concepts and skills.