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*

• Recognize the patterns of change for quadratic relationships • Write equations for quadratic relationships represented in tables, graphs and problem situations • 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 CubesIntroduction to quadratic equationsIn

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.y= 2x+ 7y= 4x+ 7y= 2x2 + 3x+ 4Students 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 CubesOther online resourcesGoals of the Unit• Recognize the patterns of change for quadraticrelationships• Write equations for quadratic relationshipsrepresented in tables, graphs and problemsituations• Connect quadratic equations to the patterns intables and graphs of quadratic relationships• Use a quadratic equation to identify themaximum or minimum value, thex- andy-intercepts, and other important features ofthe graph of the equation• Recognize equivalent quadratic expressions• Use the Distributive Property to writeequivalent quadratic expressions in factored andexpanded form• Use tables, graphs, and equations of quadraticrelationships to solve problems in a variety ofsituations from geometry, science, and business• Compare properties of quadratic, linear, andexponential relationshipsFrogs, Fleas, and Painted CubesAssignments:Math 8- Assessmet Investigation 2Math 8- Graphing Parabolas 2.5 "A closer Look at Parabolas" pp. 27-29Math 8- Problem 3.1 "Exploring Triangular Numbers", pp. 40-41, questions A & CMath 8- Problem 4.1 pp. 55-56, questions A-BMath 8- 4.2 AMath 8- ACE p65 #1-3, 6, 24Math 8- Assessment Inv 3Unit review D worksheet/ study guide

Math 8- ReviewMath 8 - Assessment