Hyper-Solving Quadratic Equations
This plan uses student created HyperStudio Programs to present, review, and summarize various methods of solving quadratic equations.
A lesson plan for grades 9–12 Mathematics
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
Teachers will need knowledge of HyperStudio software.
Students will use textbooks and notes for reference material.
A planning sheet for the Hyper-Studio stacks is helpful. You can make your own and require the students to plan each card of the program 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 HyperStudio software and the HyperStudio CD
At least one zip drive and disk will be needed because the slide shows do not fit on a regular disk. The zip drive can be moved from one machine to another to save the material the students create.
A presentation system for the computer will be helpful.
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 the HyperStudio software, 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 stack.
Activities
Groups of students ( two to five) will each create a HyperStudio 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 card, an introduction, and a conclusion.
The teacher will need to circulate and give program advice and feedback on the way the cards look. Are they readable from a distance?
Students who do not finish in the alloted 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 cards at first and then go back and edit them to add buttons and actions.
Related websites
http://www.hyperstudio.com
Comments
My Algebra II students really like to have mathematical procedures put into word form. A few years ago I began storing this information in HyperStudio stacks to keep from having to recreate it and to make the presentation more interesting. It has been a popular addition to my classes. Students began asking if they could create their own programs, and have done so with good results. 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.
Powerpoint is another program which would work well for this.
Advanced HyperStudio 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)
Grades 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.
Grades 9–12 — Algebra 2
- Goal 2: Algebra - The learner will use relations and functions to solve problems.
- Objective 2.02: 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.
- Objective 2.04: Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data.
- 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.
- Objective 2.02: Use quadratic functions and inequalities to model and solve problems; justify results.
Grades 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.
- Objective 3.02: Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve problems.
- 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.
- Objective 4.02: Use quadratic functions to model and solve problems; justify results.
Grades 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.
- Objective 3.02: Use quadratic functions and inequalities to model and solve problems; justify results.
Grades 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.
- Objective 2.01: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.
Grades 9–12 — Pre-Calculus
- Goal 1: Number and Operations - The learner will describe geometric figures in the coordinate plane algebraically.
- Objective 1.02: 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.
- Objective 1.02: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.
Grades 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.
- Objective 2.01: Use quadratic equations to model and solve problems; justify results.



