Frogs, Fleas and Painted Cubes

Introduction to quadratic equations

In Frogs, Fleas and Painted Cubes, students build on their knowledge of linear and exponential functions to include the nonlinear polynomial relationship, which is the second-degree polynomial or the quadratic function.

  • Example of a linear function: y = 2x + 7
  • Example of an exponential function: y = 4x + 7
  • Example of a quadratic function: y = 2x2 + 3x + 4

Students will learn to recognize quadratic patterns of change in tables and graphs and they will learn to write equations to represent those patterns. They will compare and contrast quadratic patterns of change with those of linear and exponential patterns of change, which they have already studied in depth.

For an in-depth explanation of unit goals, specific questions to ask your student and examples of core concepts from the unit, go to Frogs, Fleas and Painted Cubes.

Online resources for Frogs, Fleas and Painted Cubes*

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Goals of the Unit

• Recognize the patterns of change for quadratic
• Write equations for quadratic relationships
represented in tables, graphs and problem
• Connect quadratic equations to the patterns in
tables and graphs of quadratic relationships
• Use a quadratic equation to identify the
maximum or minimum value, the x- and
y-intercepts, and other important features of
the graph of the equation
• Recognize equivalent quadratic expressions
• Use the Distributive Property to write
equivalent quadratic expressions in factored and
expanded form
• Use tables, graphs, and equations of quadratic
relationships to solve problems in a variety of
situations from geometry, science, and business
• Compare properties of quadratic, linear, and
exponential relationships

Frogs, Fleas, and Painted Cubes

Math 8 - Assessmet Investigation 2
Math 8 - Graphing Parabolas 2.5 "A closer Look at Parabolas" pp. 27-29
Math 8 - Problem 3.1 "Exploring Triangular Numbers", pp. 40-41, questions A & C
Math 8 - Problem 4.1 pp. 55-56, questions A-B

Math 8 - 4.2 A
Math 8 - ACE p65 #1-3, 6, 24
Math 8 - Assessment Inv 3
Unit review D worksheet/ study guide
Math 8 - Review
Math 8 - Assessment