# Algebra Course Outline

**COURSE DESCRIPTION:**

Enriched Algebra I is a full-year, college preparatory
course . The course stresses equations,

radicals, polynomials, graphing, probability and statistics, functions,
factoring, and basic

trigonometric concepts.

**MISSION RELATED GOALS:**

This class will provide the student with a variety of
opportunities to demonstrate academic

excellence and intellectual curiosity by communicating effectively, solving
complex problems ,

and working with others toward a common goal.

**STUDENT EXPECTATIONS FOR LEARNING ADDRESSED:**

Students will be afforded opportunities to apply
mathematical concepts to real-world

applications. A variety of teaching methods will be used to foster an
environment that promotes

self-confidence and respect for others throughout the school and global
community.

**GENERAL PERFORMANCE OBJECTIVES:**

Students will be able to:

1. Solve first degree equations and inequalities with one variable, including

proportions, absolute value equations, literal equations , and compound

inequalities.

2. Model situations with algebraic equations.

3. Create and interpret a variety of graphs.

4. Understand and use the concept of function.

5. Graph and write linear equations using points, slope or intercepts.

6. Solve and graph systems of equations and inequalities.

7. Apply the rules of exponents using any integral exponents.8. Add, subtract,
multiply and divide polynomials.

9. Perform operations using radicals .

10. Solve quadratic equations by factoring, completing the square and applying
the

quadratic formula .

11. Understand, interpret and solve basic problems involving probability and

statistics.

12. Add, subtract, multiple and divide rational expressions.

13. Understand the meaning of the 3 basic trigonometric ratios and compute their

values.

**MASSACHUSETTS FRAMEWORK STRANDS:**

• Number Sense and Operations

• Patterns, Relations, and Algebra

• Geometry

• Measurement

• Data Analysis, Statistics, and Probability

**CURRICULUM FRAMEWORK LEARNING STANDARDS:**

I. Identify and use the properties of operations on real
numbers, including the associative,

commutative, and distributive properties. (10.N.1)

II. Simplify numerical expressions, including those involving positive integer
exponents or

the absolute value and apply such simplifications in the solution of problems.
(10.N.2)

III. Find the approximate value for solutions to problems involving square roots
and cube

roots without the use of a calculator. (10.N.3)

IV. Describe, analyze, and generalize a wide variety of patterns. (10.P.1)

V. Demonstrate an understanding of the relationship between various
representations of a

line. Determine a line’s slope and x- and y- intercepts from its graph or from a
linear

equation that represents the line. Find a linear equation describing a line from
a graph or

a geometric description of the line, e.g., by using the “point-slope” or “slope
y-intercept”

formulas. Explain the significance of a positive, negative, zero, or undefined
slope.

(10.P.2)

VI. Add, subtract, and multiply polynomials. Divide polynomials by monomials.
(10.P.3)

VII. Demonstrate facility in symbolic manipulation of polynomial and rational
expressions by

rearranging and collecting terms; factoring; identifying and canceling common
factors in

rational expressions; and applying the properties of positive integer exponents.
(10.P.4)

VIII. Find solutions to quadratic equations with real roots by factoring,
completing the square

or using quadratic formula. (10.P.5)

IX. Solve equations and inequalities including those involving absolute value of
linear

expressions and apply to the solution of problems. (10.P.6)

X. Solve everyday problems that can be modeled using linear, quadratic or
exponential

functions. (10.P.7)

XI. Solve everyday problems that can be modeled using systems of linear
equations or

inequalities. (10.P.8)

XII. Solve simple triangle problems using the triangle-angle sum theorem and/or
the

Pythagorean theorem. (10.G.5)

XIII. Using rectangular coordinates, calculate midpoints of segments, slopes of
lines and

segments, and distances between two points and apply the results to solutions of

problems. (10.G.7)

XIV. Find linear equations that represent lines, either perpendicular or
parallel to a given line

and through a given point. (10.G.8)

XV. Approximate a line of best-fit (i.e. trend line) given a set of data.
(10.D.2)

**UNITS AND THEMES:**

I. Tools for Algebra; Solving
Equations (55 days) |
10.N.1, 10.N.2, 10.P.6 |

II. Solving Systems of Equations
and Inequalities (14 days) |
10.P.2, 10.P.6, 10.P.8 |

10.P.7, 10.D.1 | |

III. Introduction to Functions and
Graphs (10 days) |
10.P.2, 10.P.7 |

IV. Graphing and Writing Linear
Equations (15 days) |
10.P.1, 10.P.2,10.N.4, |

10.G.8, 10.D.2 | |

V. Solving Systems of Linear
Equations and Inequalities(14 days) |
10.P.2, 10.P.6, 10.P.8 |

VI. Exponents (15 days) |
10.P.1, 10.P.4, 10.P.7 |

VII. Polynomials (16 days) |
10.P.3, 10.P.4 |

VIII. Quadratics (10 days) |
10.P.1, 10.P.5 |

IX. Radicals (13 days) |
10.N.3 |

X. Rational Expressions (10 days) |
10.P.3 |

XI. Review, Mid-term, finals (8
days) |

**COURSE OUTLINE:**

I. Tools for Algebra (25 days) (Chapter 1
& 2) |
10.N.1, 10.N.2, 10.P.6 10.P.7, 10.D.1, 10.P.1 |

A. Definitions of variables, terms,
equations, expressions, and real numbers. B. Order of operations/substitution. C. Operations with signed numbers D. Distributive property. E. Properties of addition and multiplication (commutative and associative) F. Scatter Plots / Measure of Central Tendency G. Probability |

II. Solving Equations (30 days) (Chapter
3) |
10.P.6, 10.P.7 |

A. Solving first degree equations. B. Modeling situations with algebraic expressions and/or equations C. Literal equations D. Working with geometric formulas E. Ratios & Proportions, similar figures F. Percent of Change G. Square Roots H. Pythagorean Theorem |

III. Solving Inequalities (14 days)
(Chapter 4) |
10.P.6 |

A. Solving inequalities using
addition, subtraction, multiplication and division. B. Compound Inequalities C. Absolute Value Equations |

IV. Introduction to Functions and Graphs
(10 days) (Chapter 5) |
10.P.2, 10.P.7 |

A. Various graphs and their usage B. Functions C. Writing function rules D. Direct variation/ Inverse variation E. Describing Number Patterns |

V. Graphing and Writing Linear Equations
(15 days) (Chapter 6) |
10.P.1, 10.P.2,10.N.4, 10.G.8, 10.D.2 |

A. Slope B. Graphing lines C. Equation of a line D. Parallel and perpendicular lines E. Line of Best Fit/Correlation F. Graphing absolute value equations |

VI. Solving Systems of Linear Equations and
Inequalities (14 days) (Chapter 7) |
10.P.2, 10.P.6, 10.P.8 |

A. Graphing B. Substitution C. Addition/Elimination D. Applications of Systems of Linear Equations E. Linear Inequalities F. Systems of inequalities |

**VII. Exponents (15 days)** (Chapter 8)

A. Properties of exponents

B. Scientific notation

C. Geometric sequences

D. Exploring exponential functions

I. Exponential Growth and Decay

VIII. Polynomials (16 days) (Chapter 9) |
10.P.3, 10.P.4 |

A. Addition and subtraction B. Multiplying and factoring C. Multiplying patterns D. Factoring trinomials |

IX. Quadratics (10 days) (Chapter 10) |
10.P.1, 10.P.5 |

A. Finding and estimating square roots B. Solving equations of the form ax^2 +bx + c = 0 C. Quadratic formula D. Completing the square E. Comparison of methods |

X. Radicals (13 days) (Chapter 11) |
10.N.3 |

A. Simplifying and approximating radicals B. Operations with radicals C. Radical Equations |

XI. Rational Expressions (10 days)
(Chapter 12) |
10.P.3 |

A. Simplifying B. Multiplying and Dividing C. Adding and Subtracting D. Solving rational equations |

**XII. Review, Mid-term, Finals (**8 days)

**SUGGESTED INSTRUCTIONAL STRATEGIES**

1. Lecture

2. Written Exercises

3. Group Work

4. Projects

5. Use of Manipulatives

6. Use of a Variety of Questioning Techniques

7. Board work

8. Calculator Activities

9. Games (Math Jeopardy, etc.)

10. Student Presentations

11. A variety of assessment tools (partner quizzes, etc.)

**SUGGESTED INTEGRATED ACTIVITIES:**

1. Students will role a pair of numbered cubes and
graphically organize their results. They

will then determine the experimental probabilities and compare this to
theoretical

probability.

2. Students will use Geosketchpad to explore systems of linear functions.

3. Stations/ Differentiated Instruction

4. Interactive games

**USE OF TOOLS/TECHNOLOGY**

1. Projector with Smartboard Technology

2. Use and overhead projector with transparencies

3. View video selections

4. Computer Lab/Portable Computer Lab

5. Interactive Games

6. Smartboard

**ASSESSMENT TECHNIQUES**

1. Students will take free-response performance tests

2. Students will participate in classroom discussions and demonstrate problem

solving on the chalkboard or lap boards

3. Students will work in cooperative situations and report their results

4. Students will prepare integrated projects

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