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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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