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K–12 teaching and learning · from the UNC School of Education

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Learning outcomes

Students will review five methods of solving quadratic equations, think about them in an organized manner, and identify when to use each method most efficiently. They will also work in groups, plan the steps of the project, and help each other with skills and techniques.

Teacher planning

Time required for lesson

3+ hours

Materials/resources

  • Students will use textbooks and notes for reference material.
  • A planning sheet for the slides is helpful. You can make your own and require the students to plan each slide of the slideshow in as much or as little detail as you want. I would at least require them to write out the text they plan to include.

Technology resources

Computers with PowerPoint

Pre-activities

I planned this as a review of solving quadratic equations, so students need to have worked through the unit first. They should be informed that this project is coming up so they can plan for it as they learn each method of solving. If you appoint the groups and give them planning sheets at the beginning of the unit, you will save time at the end.

Students need some knowledge of using PowerPoint, but I have found that they can be taught this on the spot in a few minutes and continue to learn while they are working on the slideshow.

Activities

  1. Groups of students (two to five) will each create a PowerPoint slide show on how to solve quadratic equations using five methods: graphing, factoring, completing the square, the quadratic formula, and properties of equality. The slides should include a written description of the steps for each method, guidelines on how to choose the most efficient method for different types of quadratic equations, hints for other students, and any memory devices or other tricks they may know or invent. In order to make the show interesting they should also include music, color, and graphics. Readability of the slides is a prime consideration. They also need a title slide, an introduction, and a conclusion.
  2. The teacher will need to circulate and give program advice and feedback on the way the presentations look. Are they readable from a distance?
  3. Students who do not finish in the allotted class time need firm deadlines on presenting the final product. As much preliminary work as possible should be done in the planning stages.

Assessment

The evaluation will be in two parts. The completed slide shows are to be shared with the class and can be evaluated for completeness, accuracy, and interest. The students will also have a written test on the unit.

Supplemental information

Students tend to spend too much time on the graphics and sounds in the beginning. Encourage them to create basic slides at first and then go back and add to graphics and sound if desired.

Comments

My students really like to have mathematical procedures put into word form. I think the planning and execution of this project will help them remember the steps better and give them a better overview of the unit. They do tend to only look at the trees and not the forest. Working in groups will help the weaker students along as well.

Advanced PowerPoint students may wish to include their own photographs, art work, or music - making the project more appealing to multiple intelligences and different learning styles.

North Carolina curriculum alignment

Mathematics (2004)

Grade 9–12 — Algebra 1

  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.02: Graph, factor, and evaluate quadratic functions to solve problems.

Grade 9–12 — Integrated Mathematics 2

  • Goal 3: Data Analysis and Probability - The learner will collect, organize, and interpret data to solve problems.
    • Objective 3.02: Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve problems.
      • Interpret the constants, coefficients, and bases in the context of the data.
      • Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.
  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.02: Use quadratic functions to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.

Grade 9–12 — Integrated Mathematics 3

  • Goal 3: Algebra - The learner will use relations and functions to solve problems.
    • Objective 3.02: Use quadratic functions and inequalities to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.

Grade 9–12 — Integrated Mathematics 4

  • Goal 2: Geometry and Measurement - The learner will describe geometric figures in the coordinate plane algebraically.
    • Objective 2.01: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.

Grade 9–12 — Technical Mathematics 2

  • Goal 2: Algebra - The learner will use relations and functions to solve problems.
    • Objective 2.01: Use quadratic equations to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.
    • Objective 2.03: Create, interpret, and analyze best-fit models of linear, exponential, and quadratic functions to solve problems.
      • Interpret the constants, coefficients, and bases in the context of the data.
      • Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

  • Common Core State Standards
    • Mathematics (2010)
      • High School: Algebra

        • Reasoning with Equations & Inequalities
          • ALG.REI.4Solve quadratic equations in one variable. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form. Solve...
      • High School: Functions

        • Interpreting Functions
          • FUN.IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ Graph linear and quadratic functions and show intercepts, maxima, and minima. Graph square root,...
          • FUN.IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and...