H E L E N   K E L L E R  M I D D L E  S C H O O L

One can never consent to creep when one feels an impulse to soar...Helen A. Keller

MATH:

Grade 8


Math Algebra


COURSE DESCRIPTION - MATH

The eighth grade mathematics curriculum is comprehensive and allows the student to get a taste of a variety of topics that will be encountered in greater depth at the high school.  The program of study gives students a broad mathematical background by focusing on inquiry-based, experiential activities.  The curriculum lays the foundation for the formal study of algebra, geometry, probability and statistics, and trigonometry at the high school. Basic skills are reviewed at the beginning of each school year in preparation for the Connecticut Mastery Test, given in September. The remainder of the year is divided into seven instructional units:

Integers
  • Integers and Absolute Value
  • Comparing and Ordering Integers
  • Adding Integers
  • Adding Integers (more than two at a time)
  • Subtracting Integers
  • Matrices
  • Multiplying Integers
  • Dividing Integers
  • Solving Equations Involving Integers
Statistics – Graphing
  • Bar Graphs and Histograms
  • Histograms Using a Graphing Calculator
  • Circle Graphs
  • Line Graphs
  • Line Graphs Using a Graphing Calculator
  • Interpreting Graphs
  • Measures of Central Tendency (Mean, Median and Mode)
  • Measures of Central Tendency Using a Graphing Calculator
  • Measures of Variation (Range, Quartiles, Interquartile Range, Outliers)
  • Box and Whisker Plots
  • Box and Whisker Plots Using the Graphing Calculator

 Statistics – Probability

  • Probability of Simple Events
  • Counting Outcomes
  • Tree Diagrams
  • Fundamental Counting Principle
  • Permutations
  • Combinations
  • Factorial
  • Permutations and Combinations Using a Calculator
  • Probability of Compound Events
  • Using Sampling to Predict

  Fractions, Decimals & Percents

  • Divisibility Patterns

  • Prime Factorization

  • Greatest Common Factor

  • Rational Numbers

  • Decimals as Rational Numbers

  • Writing a Decimal as an Equivalent Fraction

  • Least Common Multiple

  •  Comparing & Ordering Rational Numbers

  •  Adding & Subtracting Like Fractions

  • Adding & Subtracting Unlike Fractions

  • Multiplying Fractions

  • Dividing Fractions

  • Solving Equations Involving Fractions

Ratio & Proportions

  • Ratios and Rates

  • Unit Ratios and Unit Price

  • Solving Proportions

  • Using Proportions to Solve Applications

  • Percent of Change

  • Similar Triangles

  • Similar Polygons

  • Indirect Measurement

  • Trig Ratios (Sine, Cosine, Tangent)

  • Using Trig Ratios to Solve Applications

  • Pythagorean Theorem

  • Problem Solving Using Pythagorean Theorem

  • Scale Drawings and Models

Algebra  

  • Solving Two-Step Equations

  • Solving Equations with Parentheses

  • Solving Equations with Variables on Both Sides

  •  Functions

  • Cartesian Coordinate System

  • Equations with Two Variables

  • Using Tables to Graph Linear Functions

  • The Meaning of Slope

  • The Geometry of Slope

  • Slope-Intercept Form of a Line

  • Scatterplots

  • Line of Best Fit

  • Graphing Systems of Equations

  • Graphing Quadratic Functions

Geometry

Classifying Triangles

  • Pythagorean Theorem

  • Problem Solving Using Pythagorean Theorem

  • Congruent Triangles

  • Congruent Triangles

  •  Similar Triangles

  • Classifying Quadrilaterals
    Area and Perimeter of Polygons

  • Volume and Surface Area of Solids

  • Interior and Exterior Angles of Regular Polygons

  • Properties of Circles

  • Parallel and Perpendicular Lines

  • Complementary and Supplementary Angles

  • Properties of Angles

KEY TEXT

Middle School Math: Course 3, McDougal Littel



COURSE DESCRIPTION - Algebra

Algebra begins the formal study of abstract mathematics and requires the higher-level thinking skills of analysis, synthesis and application.  It is the first pre-calculus experience, which involves higher-order equation solving techniques and increasingly difficult applications.  Students must be firmly rooted in their numerical and basic equation-solving skills. The program proceeds at a pace suitable for the outstanding student, and it requires daily homework and regular nightly review.  The course needs to include those topics covered in a Barlow honors-level algebra class.  There is a midterm exam given in January and a final exam given in June, which broadly assess the level of competency of each student.

The year is split into units as follows:

The Rules of Algebra

  • Solving Equations

  • Properties of Equality

  • The Substitution Property

  • The Distributive Property

  • Applications of Equation Solving

Signed Numbers

  • Comparing Numbers on the Number Line

  • Addition of Real Numbers

  • Subtraction of Real Numbers

  • Multiplication of Real Numbers

  • Division of Real Numbers

  • Special Relationships

  • Line Graphs, Bar Graphs and Histograms

Working with Equations

  • Equations with Variables on Both Sides

  • Special Equations

  • The Distributive Property in Equations

  • Rate Problems

  • Equations with Absolute Value or Squared Quantities

 Working with Inequalities

  • Solving Inequalities

  • Using Inequalities

  • Compound Inequalities

  • Circle Graphs and Pictographs

 Graphing

  • Tables, Graphs and Equations

  • Slope-Intercept Form of an Equation

  • The Geometry of Slope

  • Other Forms of Linear Equations

  • Non-linear Graphing

  • Scattergrams

 Formulas and Functions

  • Working with Formulas

  • Special Formulas of Geometry

  • Using the Quadratic Formula

  • Literal Equations

  • Functions and Relations

  • Function Notation and Graphing

  • Mean, Mode and Median

 Systems of Equations

  • Solving Systems of Equations by Graphing

  • More About Linear Systems

  • Solving Systems by Substitution

  • The Multiplication-Addition Algorithm

  • Solving Systems of Inequalities by Graphing

 Exponents and Radicals

  • Large Numbers

  • Multiplication Properties of Exponents

  • Division Properties of Exponents

  • Negative and Zero Exponents

  • Simplifying Radicals

  • Rationalizing

  • Radical Equations

  • Other Roots and Fractional Exponents

 Polynomials

  • Anatomy of a Polynomial

  • Addition and Subtraction of Polynomials

  • Multiplication of Polynomials

  • Special Multiplication

  • Factoring

  • Factoring Trinomials

  • Factoring Special Polynomials

 Proportion and Rational Equations

  • Ratio and Proportion

  • Applications of Proportion

  • Simplifying Rational Expressions

  • Multiplication and Division of Rational Expressions

  • Solving Rational Equations

  • Addition and Subtraction of Rational Expressions

 KEY TEXT

Algebra 1: An Integrated Approach, McDougal Littell


 


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