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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, selfconfidence
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.
Guiding Principles
• All students can learn mathematics.
• Mathematical ideas should be explored in ways that stimulate curiosity, create
enjoyment of mathematics, and develop depth of
understanding.
• 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 highquality 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.
ALGEBRA I (H)
Course Frequency: Fullyear course, five times per week
Credits Offered: Five
Prerequisites : Yearly grade of A in Grade 7 Level AE or permission of Building
Leader for Mathematics
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
firstyear 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.
Core Topics/Questions/Concepts/Skills
Solve reallife 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 nonlinear equations in one variable
Applying algebra to modeling
Operations on polynomials
Graphing linear and nonlinear functions
Set theory
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
CourseEnd Learning Objectives
Learning objective  Corresponding state standards, where applicable 
1] use tables and graphs to organize reallife data  8.D.02 
2] use rates, ratios, and percents to solve reallife 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 
10.N.01 
7] apply the distributive property
to algebraic expressions and use the distributive property to solve reallife problems 
10.N.01 
8] use the properties of exponents
to evaluate and solve exponential expressions 
10.N.01 
9] use scientific notation to solve real life problems  10.N.01 
10] simplify and evaluate numerical
and algebraic expressions with and without exponents 
10.N.02 
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 
10.P.05 
20] solve and graph absolute value
equations and inequalities on a number line and coordinate plane 
10.P.06 
21] graph horizontal and vertical equations  10.P.07 
22] graph linear equations and inequalities using slope and yintercepts  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 reallife problems 
10.P.07 
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 reallife 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 inputoutput table  10.P.07 
32] solve systems of equations and
inequalities in two variables using graphing, substitution or linear combination 
10.P.08 
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 
Assessment
Students are generally assessed by inclass 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 longterm 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
linear and polynomial functions 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.
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