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Lesson Plans > Mathematics > Grades 6 - 8 > Introducing the Properties of Quadratic Equations
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Kinesthetic Learner
Kinesthetic Learner
Visual Learner
Visual Learner
Auditory Learner
Auditory Learner
Technology Integration
Technology Integration

Introducing the Properties of Quadratic Equations

Understand the properties of quadratic equation

 

Grade Level: 6-8

Concept: Understand the properties of quadratic equation

Estimated Duration: 40 minutes
 
Objectives
Students will be able to:
  • relate linear equations to quadratic equations
  • identify the properties of a quadratic equation
  • draw a quadratic equation
  • understand how the coefficients a, b, and c affect the shape of a parabola
Materials
White board
Grid paper
Handout of four graphs of quadratic equations
Playdough
 
Differentiation Strategies
These strategies are used to meet the varied needs of all learners:
  • for various grade levelsVarying academic levels: uses mixed-ability groups to allow students to learn from one another, uses small- and whole-group discussions to ensure all students participate
  • for visual learnersVisual learners: incorporates graphs of quadratic equations and the labeling of the quadratic equation
  • for auditory learnersAuditory learners: uses guided questioning and discussions to identify the properties of quadratic equations
  • for kinesthetic learnersKinesthetic learners: engages students in modeling quadratic equations
Key Vocabulary
 

Coefficient
Domain
Maximum point
Minimum point
Quadratic equation
Rang
Root
Vertex
y-intercept 

 

 

Procedures

Warm Up
  • for visual learners Have students graph a linear equation, such as y = x +3.
  • Ask the students what happens when you multiply two linear equations. What would a graph of that equation look like?
  • Have them turn to a partner and take two minutes to multiply two linear equations (with coefficient a = 1)
  • for visual learners Write the product on the board, and tell the student this is a quadratic equation, a second degree polynomial, whose shape is a parabola.
Direct Instruction
  • for visual learners Illustrate a quadratic equation on the board.
  • for visual learners Write and define the terms vertex, intercepts, domain, range, and minimum and maximum point. Label each of these on the quadratic equation on the board.
  • Distribute a handout with quadratic equations showing different parabolas (one with coefficient a less than zero and one with coefficient a greater than 0).
  • Have students label the vertex and the intercepts on quadratic equations.
  • for auditory learners Explain that the parabola opens upward when the coefficient a is greater than zero and downward when the coefficient a is less than zero.
  • Ask students to explain what happens when the coefficient a is equal to zero.
  • for visual learners for auditory learners Explain and illustrate on the board how the larger the coefficient a, the more closed the graph of a quadratic function appears, and the smaller, the more open.
 
Practice
  • for various grade levels Create mixed-ability pairs.
  • Write four quadratic equations on the board with different values for the coefficient a, such that two are positive and two are negative.
  • for kinesthetic learners Using modeling clay, ask students to create a model of each of the quadratic equations.
Assessment
  • Have students illustrate the four equations in their math journals based on the models their groups made.
  • for kinesthetic learners Have students label the vertex and intercepts.
  • Explain to students how the significance of coefficients b and c: that c is the point where the parabola crosses the y access and b is the declivity at that point.
Closure
  • Extension: If your class has access to the Internet, divide students into teams and ask them to research (1) the history of quadratic equations; (2) how quadratic equations are used today; (3) the origins of the terms used to describe quadratic equations.
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