Course: Williamsburg Collegiate 8th Grade Math and Algebra

Curriculum

1. 11 lessons 1 Unit Language and Tools of Algebra
    
   • Lessons
   • Translating Expressions and Powers - Select Appropriate Operations

     SWBAT translate verbal and algebraic expressions.

      
   • Order of Operations and Evaluating Algebraic Expressions

     SWBAT evaluate algebraic expressions by substituting and using the correct order of operations.

      
   • Translating Inequalities

     SWBAT translate verbal expressions into inequalities.

      
   • Properties of Identity and Equality

     SWBAT identify and apply the properties of identity and equality.

      
   • Distributive Property and Combine Like Terms - Identity (-x)(-y)=xy

     SWBAT to apply the distributive property and combine like terms to simplify expressions.

      
   • Commutative and Associative Property

     SWBAT use the commutative and associative property to simplify expressions.

      
   • Logical Reasoning and Counterexamples

     SWBAT apply logical reasoning to construct valid arguments and identify counterexamples.

      
   • Square Roots and Comparing Real Numbers

     SWBAT evaluate square roots of perfect and nonperfect squares.
     SWBAT compare real numbers, including square roots.

      
   • Classifying and Graphing Numbers

     SWBAT classify numbers into sets and graph numbers on a number line.

      
   • Interpret and Create Graphs - Linear Equations (graphs)

     SWBAT to create and interpret graphs on coordinate grids.

      
   • Identify and Describe Functions

     SWBAT identify and describe functions, including domain and range.

      
2. 8 lessons 2 Unit Angle Relationships and Geometric Transformations

   UNIT 2 - Geometry: Students will love this unit because it is so visual. Students will have a chance to explore using mathematical tools to construct geometric figures. Then students will explore special angles and angle relationships. Finally students will get to investigate the different ways we can transform a figure on a coordinate plane.
   

    
   • Lessons
   • 2-1 Translating Figures

     SWBAT translate a figure in a coordinate plane.

      
   • 2-2 Dilating Figures - Dilations

     SWBAT dilate a figure on a coordinate plane using a scale factor (greater than 1 and less than 1).

      
   • 2-3 Reflecting Figures - Reflections

     SWBAT reflect a figure over the x or y axis.

      
   • 2-4 Rotations and Identifying Transformations

     SWBAT rotate a figure 90 degrees or 180 degrees, clockwise or counterclockwise.

      
   • 2-5 Properties of Transformations, Algebraic Rules

     SWBAT identify the properties preserved and not preserved in a given transformation;
     SWBAT write algebraic rules for geometric transformations

      
   • 2-7 Special Angle Relationships - Complementary, Supplementary, and Congruent

     SWBAT identify special angle relationships and find missing angle measurements

      
   • 2-8 Angle Relationships - Parallel Lines with a Transversal

     SWBAT identify angle relationships when given two parallel lines intersected by a transversal

      
   • 2-9 Writing with Angle Relationships

     SWBAT write excellent explanations to problems involving angle relationships.

      
3. 12 lessons 3 Solving Equations

   This unit is mostly about solving algebraic equations for x, but it also has a few other lessons that are somewhat different - including lessons on unit conversions and percents.

    
   • Lessons
   • 3-1 Translate and Solve Equations - Solve Linear Equalities and Inequalities

     SWBAT translate and solve one and two-step equations.

      
   • 3-2 Solving Multi-Step Equations - Solve Linear Equalities and Inequalities

     SWBAT solve multi-step equations using a variety of methods (combine like terms, distributive property, etc. - variable on one side only).

      
   • 3-3 Solve Equations with Variables on Both Sides - Solve Linear Equalities and Inequalities

     SWBAT solve equations with variables on both sides.

      
   • 3-4 Solve Equations with Angle Relationships - Solve Linear Equalities and Inequalities

     SWBAT write and solve equations using angle relationships.

      
   • 3-5 Solve Equations with Angle Relationships - Parallel Lines and Transversal - Solve Linear Equalities and Inequalities

     SWBAT write and solve equations for angle relationships when given parallel lines and a transversal.

      
   • 3-6 Unit Price and Map Scales - Solve Linear Equalities and Inequalities

     SWBAT solve problems involving unit price and map scales.

      
   • 3-7 Convert Measurements and Currency

     SWBAT convert measurements and currency using dimensional analysis.

      
   • 3-9 Percent Change, Tax, and Discount

     SWBAT calculate percent change, price after tax, and sale price.

      
   • 3-11 Percent Commission, Tip, and Simple Interest

     SWBAT to solve percent application problems, including commission, tip/gratuity, and simple interest.

      
   • 3-12 Estimating Percent Applications

     SWBAT estimate percents in application problems.

      
   • 3-13 Solving Formulas - Solve Linear Equalities and Inequalities - Identity (-x)(-x)=xy, Identity (-x)(-y)=xy

     SWBAT solve formulas for a given variable.

      
   • 3-15 Solving Equations Review - Solve Linear Equalities and Inequalities

     SWBAT review solving multi-step equations.

      
4. 6 lessons 4 Functions and Patterns

   This unit starts into linear relationships, but also includes some connected math investigations and other lessons to introduce the ideas of functions and patterns.

    
   • Lessons
   • 4-2 Representing Relationships in Multiple Ways

     SWBAT to represent a relationships using ordered pairs, mapping, tables, and coordinate grids.

      
   • 4-3 Identify Functions and Function Notation

     SWBAT identify functions and non-functions and use function notation.

      
   • 4-4 Linear Equations and Graphs - Linear Equations (rates of change) - Linear Equations (graphs)

     SWBAT identify linear equations and graph them using tables and x and y intercepts.

      
   • 4-6 Arithmetic Sequences

     SWBAT identify and describe arithmetic sequences and write an equation for the nth term.

      
   • 4-7 Proportional Relationships, Direct Variation - Slope of a Line - Linear Equations (proportional relationships) - Linear Equations (rates of change)

     SWBAT write equations for proportional and nonproportional linear relationships

      
   • 4-8 Graphing Calculator Investigation

     SWBAT use graphing calculators to explore the graphs of relations.

      
5. 12 lessons 5 Analyzing Linear Functions

   This unit is all about linear relationships and functions.

    
   • Lessons
   • 5-1 Solutions to Linear Functions

     SWBAT identify and describe solutions to linear functions.

      
   • 5-2 Finding Slope - Slope of a Line - Linear Equations (rates of change)

     SWBAT find the slope from an equation, a graph, or two points.

      
   • 5-3 Slope and Direct Variation - Slope of a Line - Linear Equations (proportional relationships)

     SWBAT apply the concept of slope in direct variation equations.

      
   • 5-4 Slope-Intercept Form - Slope of a Line

     SWBAT write equations in slope-intercept form.

      
   • 5-5 Graphing Calculator Investigation - Linear Equations (graphs)

     SWBAT investigate linear functions using graphing calculators.

      
   • 5-6 Writing Equations for Tables - Slope of a Line

     SWBAT write slope-intercept equations from a table of values.

      
   • 5-7 Write Equations Given Point and Slope, or Two Points

     SWBAT write linear equations given a point and the slope or given two points.

      
   • 5-8 Point-Slope Form

     SWBAT write linear equations in point-slope form.

      
   • 5-9 Scatterplots and Lines of Fit

     SWBAT create and describe scatterplots and draw lines of best fit.

      
   • 5-10 Equivalent Equations

     SWBAT identify equivalent equations in different linear forms.

      
   • 5-11 Parallel and Perpendicular Lines - Linear Equations (graphs)

     SWBAT identify and describe parallel and perpendicular lines.

      
   • 5-12 Linear Review

     SWBAT review linear relationships.

      
6. 8 lessons 6 Systems of Equations

   Students will learn to solve systems of equations using graphing, substitution, and elimination. They will also learn when to use each strategy, and how to apply these strategies to a variety of problems.

    
   • Lessons
   • 6-1 Solve Systems by Graphing - Linear Equations (rates of change) - Linear Equations (graphs)

     SWBAT solve systems of equations by graphing.

      
   • 6-2 Graphing Calculator Lab and Applications - Linear Equations (graphs)

     SWBAT solve systems of equations using a graphing calculator.

      
   • 6-3 Solving Systems by Substitution

     SWBAT solve systems of equations by substitution.

      
   • 6-4 Solve Systems by Substituting, Day Two

     SWBAT solve systems of equations using substitution method.

      
   • 6-5 Solve Systems by Elimination

     SWBAT solve systems of equations using the elimination method.

      
   • 6-8 Solve Systems by Elimination, with Multiplication

     SWBAT solve systems using elimination method, including multiplying one or both equations.

      
   • 6-9 Solve Systems, Choose the Best Method

     SWBAT choose the best method to solve a system of equations.

      
   • 6-10 Solve Systems, Review and Applications - Linear Equations (rates of change)

     SWBAT apply systems of equations to solve a variety of word problems

      
7. 11 lessons 7 Inequalities

   This unit involves solving and graphing linear inequalities, and systems of inequalities.

    
   • Lessons
   • 7-1 Solving Inequalities - Solve Linear Equalities and Inequalities

     SWBAT solve inequalities using addition or subtraction.

      
   • 7-2 Solving Inequalities - Solve Linear Equalities and Inequalities

     SWBAT solve inequalities with multiplication and division.

      
   • 7-3 Solving Multi-Step Inequalities - Solve Linear Equalities and Inequalities

     SWBAT solve multi-step inequalities.

      
   • 7-4 Compound Inequalities - Solve Linear Equalities and Inequalities
      
   • 7-5 Percents Workshop

     SWBAT review percent applications.

      
   • 7-6 Absolute Value Inequalities - Solve Linear Equalities and Inequalities

     SWBAT graph and solve absolute value inequalities.

      
   • 7-7 Solving Absolute Value Inequalities - Solve Linear Equalities and Inequalities

     SWBAT solve absolute value inequalities.

      
   • 7-8 Graphing Linear Inequalities - Solve Linear Equalities and Inequalities

     SWBAT graph linear inequalities.

      
   • 7-9 Graphing Inequalities with Two Variables - Solve Linear Equalities and Inequalities

     SWBAT graph inequalities with two variables.

      
   • 7-10 Graphing Systems of Inequalities - Solve Linear Equalities and Inequalities

     SWBAT graph systems of inequalities.

      
   • 7-11 Inequalities Stations Review - Solve Linear Equalities and Inequalities

     SWBAT review inequalities.

      
8. 10 lessons 8 Polynomials

   In this unit, students learn to identify and describe polynomials. Then we move on to a variety of operations using polynomials.

    
   • Lessons
   • 8-1 Multiplying Monomials

     SWBAT multiply monomials, using laws of exponents.

      
   • 8-2 Dividing Monomials

     SWBAT divide monomials.

      
   • 8-3 Identify and Describe Polynomials

     SWBAT Identify and Describe Polynomials

      
   • 8-4 Add and Subtract Polynomials

     SWBAT add and subtract polynomials.

      
   • 8-5 Polynomials Review Day and Jeopardy

     SWBAT review polynomials and negative exponents.

      
   • 8-6 Multiply Monomials and Polynomials

     SWBAT multiply monomials and polynomials.

      
   • 8-7 Divide Polynomials by a Monomial

     SWBAT divide a polynomial by a monomial.

      
   • 8-8 Multiply Polynomials

     SWBAT multiply polynomials.

      
   • 8-9 Special Products

     SWBAT identify special products using FOIL method.

      
   • 8-10 Operations with Scientific Notation (Select Appropriate Operations)

     SWBAT apply operations to scientific notation.

      
9. 6 lessons 9 Factoring

   Students learn to factor using the GCF and factor trinomials.

    
   • Lessons
   • 9-1 Factor Monomials

     SWBAT factor monomials.

      
   • 9-2 Factor Binomials

     SWBAT factor binomials using the GCF.

      
   • 9-2.5 Factor Binomials

     SWBAT factor binomials using GCF and grouping.

      
   • 9-3 Factor Trinomials

     SWBAT factor trinomials.

      
   • 9-4 Factor Trinomials

     SWBAT factor trinomials.

      
   • 9-6 Factoring Perfect Squares and Differences

     SWBAT factor perfect squares and differences.

      
10. 12 lessons 10 Quadratics
     
    • Lessons
    • 10-1 Graphing Calculator Lab - Quadratics

      SWBAT explore graphs of quadratic functions using graphing calculators.

       
    • 10-2 Graphing Quadratic Functions

      SWBAT graph quadratic functions using a table of values.

       
    • 10-3 Solving Quadratic Equations by Graphing

      SWBAT solve quadratic equations by graphing (finding the roots).

       
    • 10-4 Completing the Square

      SWBAT solve quadratic equations by completing the square.

       
    • 10-5 Quadratic Formula

      SWBAT use the quadratic formula.

       
    • 10-6 Review Quadratics

      SWBAT review quadratic functions.

       
    • 10-7 Quadratic Formula and the Discriminant

      SWBAT determine the number of solutions of a quadratic function using the discriminant of the quadratic formula.

       
    • 10-8 Exponential Functions

      SWBAT identify and describe exponential functions.

       
    • 10-9 Exponential Functions Investigation

      SWBAT investigate exponential functions.

       
    • 10-10 Graphing Exponential Functions

      SWBAT graph exponential functions.

       
    • 10-11 Exponential Growth and Decay

      SWBAT solve problems involving exponential growth and decay.

       
    • 10-12 Quadratics Review

      SWBAT review the quadratic functions unit.

       
11. 8 lessons 13 Statistics and Probability
     
    • Lessons
    • 13-1 Sampling and Bias

      SWBAT evaluate different sampling methods and explain the concept of bias.

       
    • 13-2 Counting Outcomes - Tree Diagrams and Fundamental Counting Principle - Probability (combinations)

      SWBAT count outcomes using tree diagrams and the fundamental counting principle.

       
    • 13-3 Combinations and Permutations - Probability (combinations) - Probability (dependent and independent events)

      SWBAT identify and apply combinations and permutations.

       
    • 13-4 Compound Probability - Probability (dependent and independent events)

      SWBAT find compound probabilities for dependent and independent events.

       
    • 13-5 Theoretical and Experimental Probability - probability (predictions)

      SWBAT identify theoretical and experimental probability using probability simulations.

       
    • 13-6 Classify and Organize Data, Day 1

      SWBAT classify and organize data.

       
    • 13-7 Classify and Organize Data, Day 2 - Data and Central Tendency

      SWBAT classify and organize data.

       
    • 13-8 Box and Whisker Plots

      SWBAT construct box and whisker plots.