# 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.

**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 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.

**ALGEBRA I (H)**

Course Frequency: Full-year 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

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.

**Core Topics/Questions/Concepts/Skills**

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

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

**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 |
10.N.01 |

7] apply the distributive property
to algebraic expressions and use the distributive property to solve real-life 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 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 |
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 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 |
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 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
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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