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# Course Syllabus for Math 935

**REQUIRED MATERIALS:** notebook, writing utensil,
scientific calculator, agenda book,

graph paper

**COURSE DESCRIPTION:**

Students in this Mathematics course are provided with small group instruction
which addresses

the concepts and factual information in a manner consistent with his/her
identified special needs.

This full-year course is designed for students who need extra time and practice
on algebraic

skills. Algebra is presented with real-world applications to make mathematics
relevant. This will

be accomplished through the use of more manipulatives, activities, and an
exploratory approach

to learning.

**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. Identify and describe a wide variety of patterns

2. Represent and describe mathematical relationships using variables

3. Analyze functional relationships

4. Describe and represent relationships with models, tables, graphs and rules

5. Use computations, estimations and proportions to solve problems

6. One and Two step solutions to equations and inequalities with one and two
variables

7. Graph linear relationships

8. Identify, simplify, and factor polynomial expressions

9. Develop techniques and problem solving strategies to use in a variety of
situations

10. Apply measures of central tendency to interpret data

11. Use simulations to estimate probabilities and determine the likelihood of
outcomes using

theoretical probabilities

**MASSACHUSETTS FRAMEWORK STRANDS:
**• Number Sense

• 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. Use estimation to judge the reasonableness of results of computations and of solutions to

problems involving real numbers (10.N.4)

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

VI. 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)

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

VIII. 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)

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

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

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

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

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

functions. (10.P.7)

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

inequalities. (10.P.8)

XIII. Identify figures using properties of sides, angles and diagonals. Identify the types of

symmetry. (10.G.1)

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

Pythagorean theorem. (10.G.5)

XV. 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)

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

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

XVII. Calculate perimeter, circumference and area of common geometric figures. (10.M.1)

XVIII. Select, create, and interpret an appropriate graphical representation (e.g., scatterplot,

table, stem-and-leaf plots, box-and-whisker plots, circle graph, line graph, and line plot)

for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to

communicate information about the data. Use these notions to compare different sets of

data.(10.D.1)

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

XX. Describe and explain how the relative sizes of a sample and the population affect the

validity of predictions from a set of data. (10.D.3)

**UNITS AND THEMES:**

I. Integers and Variables | 10.N.1, 10.N.2, 10.P.6, 10.P.7, 10.D.1 |

II. Rational Numbers | 10.N.1, 10.N.2, 10.D.1 |

III. Algebraic Expressions, Equations and Inequalities | 10.P.3, 10.P.4, 10.P.6, 10.P.7 |

IV. Linear Functions | 10.P.1, 10.P.2, 10.P.7, 10.G.8, 10.D.2 |

V. Systems of Equations and Inequalities | 10.P.2, 10.P.6, 10.P.8 |

VI. Families of Functions | 10.P.2, 10.P.7 |

VII. Introductory Statistics | 10.P.1, 10.P.6, 10.D.1, 10.D.2, 10.D.3 |

VIII. Exponents | 10.P.1, 10.P.4, 10.P.7 |

IX. Polynomials | 10.P.3, 10.P.4, 10.P.5 |

X. Square Roots and Radicals | 10.N.3 |

XI. Introduction to Basic Geometric Concepts | 10.M.1 |

XII. Review MCAS, Midterm, Final Exam |

**COURSE OUTLINE:**

I. Integers and Variables |
10.N.1, 10.N.2, 10.P.6, 10.P.7, 10.D.1 |

A. Order of Operations

B. Operations with integers

C. Using variables and equations

D. Solving problems using tables and equations

II. Rational Numbers |
10.N.1, 10.N.2, 10.D.1 |

A. Operations with fractions

B. Using ratios, proportions and percents

C. Experimental and theoretical probabilities

III. Algebraic Expressions, Equations and
Inequalities |
10.P.3, 10.P.4, 10.P.6, 10.P.7 |

A. Adding and subtracting expressions

B. Solving literal equations

C. One step equations with addition and subtraction

D. Simplifying polynomials by combining like terms

E. Solving inequalities with addition and subtraction

F. Multiplying and dividing expressions

G. One step equations using multiplication and division

H. Solving problems involving percent

I. Solving multi step equations

J. Algebraic and geometric applications

K. Absolute value equations and basic inequalities

IV. Linear Functions |
10.P.1, 10.P.2, 10.P.7, 10.G.8, 10.D.2 |

A. The coordinate plane

B. Graphing linear functions using various methods

C. Direct variations

D. Vertical and horizontal lines

E. Parallel and perpendicular lines

F. Graphing linear inequalities

V. Systems of Equations and Inequalities |
10.P.2, 10.P.6, 10.P.8 |

A. Graphing and identifying intersection point

B. Solving by substitution

C. Solving by elimination

D. Graphing systems of inequalities

VI. Families of Functions |
10.P.2, 10.P.7 |

A. Identity and graph linear functions

B. Identity and graph absolute value functions

C. Identity and graph quadratic functions

VII. Introductory Statistics |
10.P.1, 10.P.6, 10.D.1, 10.D.2, 10.D.3 |

A. Measures of central tendency

B. Interpreting and drawing graphs

C. Circle graphs

D. Scatter plots and line of best fit

E. Stem and Leaf Plots and Box Whisker Plots

VIII. Exponents |
10.P.1, 10.P.4, 10.P.7 |

A. Properties of exponents

B. Multiplying and dividing monomials

C. Scientific notation

IX. Polynomials |
10.P.3, 10.P.4, 10.P.5 |

A. Adding and subtracting polynomials

B. Using the distributive property and foil

C. Factoring out greatest common factor

D. Factoring difference of two squares

E. Factoring trinomials in the form x^{2} + bx + c

F. Solving quadratic equations in the form x^{2} + bx + c = 0 by factoring and use
of the

quadratic formula

X. Square Roots and Radicals |
10.N.3 |

A. Estimating square roots

B. Simplifying square roots

C. Pythagorean Theorem

D. Simplifying radicals

E. Operations with radicals

XI. Introduction to Basic Geometric Concepts |
10.M.1 |

A. Basic geometry terminology

B. Perimeter and area of basic polygons

XII. Review MCAS, Midterm, Final Exam |

**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.)

12. As specified by Individualized Educational Plan

**SUGGESTED INTEGRATED ACTIVITIES:
**1. Scatter Plots

2. Surveys

3. Dice activities for probability

4. Study stock market for percentage of change

5. Using graph paper to determine the maximum area given a fixed perimeter

6. Create 3-dimensional boxes to maximize volume

7. Use food labels to study proportions

8. Study various linear relationships and create the function rule

**USE OF TOOLS/TECHNOLOGY:**

1. Use of scientific and graphing calculators

2. Overhead projector and transparencies

**ASSESSMENT TECHNIQUES:**

1. Students will take free-response performance tests

2. Students will answer questions orally

3. Students will do written presentations at the board

4. Students will work in cooperative groups and report their results

5. Students will participate in classroom discussions

6. Students will prepare integrated projects

7. Homework evaluation