V. Class 6

A. Participants engage in investigations of Equalities and Inequalities using graphing software

Participants should choose investigations that involve:

• Recognizing and applying Properties of Equality to solve equations in one variable and to understand the behavior of special case equations (e.g., absolute value, radical, factored equations equal to zero);
• Given an application problem, identifying and applying the appropriate common formula for distance, Pythagorean Theorem, Area, Circumference/perimeter, interest, and slope;
• Representing and comparing solutions of equations and inequalities (on number lines).

1. Week 6: Choose from investigations focused on Properties of Equality
   • Properties of Equality
     • Lucky Find
     • Mystery Number
     • Double Trouble
     • Triangle from a Line
   • Solve for a variable in terms of other variables
     • Multiple Solutions
     • Zero Coefficients
     • Comparing Temperatures
     • Units of Speed
     • Formulaic Properties
   • Application Problems using Common Formulas
     • Twice Reflected Over Parallel Lines (Distance)
     • Water Stop (Distance)
     • Altitude to the Hypotenuse (Pythagorean Theorem)
     • Hypatia's Triumph (Pythagorean Theorem)
     • Heron's Area (Area)
     • Minimum Perimeters (Area)
     • Biggie Size It (Area, Circumference/perimeter)
     • Changes in the Circumference (Circumference/perimeter)
     • Tangential Circles (Circumference/perimeter)
     • Tripling Perimeter (Circumference/perimeter)
     • Choosing a Loan (Interest)
     • Catching up in Savings (Interest)
     • Specific Slopes (Slope)
     • The Slope of a Curve (Slope)

    

2. Week 7: Choose from investigations focused on Equations and Inequalities in one variable
   • Inequalities
     • Solving Graphically
     • In Between
   • Special Case Equations
     • Absolute Value Functions and Transformations (Absolute Value)
     • End Behavior (Radical)
     • Reciprocal Functions (Radical)
     • Reciprocal Sums (Radical)
     • Using Roots to Generate an Equation (Factored equations equal to 0)

B. Participants add write-ups to their online portfolios
C. Revisit and revise a write-up

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Additional Resources for Weeks 6 & 7

• Dictionary Terms with Comprehension Activities
  • Absolute Value
  • Area of a Circle
  • Area of a Polygon
  • Distance
  • Inequality
  • Interest
  • Pythagorean Theorem
  • Radical
  • Slope
  • Solving an Equation
  • Variable
• External Resources
  • Solving Absolute Value Equations
  • Solving Absolute Value Inequalities

Return to the Algebra Syllabus.