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

Computer Graphing Calculator Explorations

Use the built in graphing calculator feature on the Macintosh computer to explore some "parent" functions and their translations, combinations, and composites.

A lesson plan for grades 9–12 Mathematics

By Charlotte Lewis

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Learning outcomes

Students should learn the basic shapes of a variety of commom functions. They should be able to translate these functions from altered equations and know the placement of the new function.

Teacher planning

Time required for lesson

3 hours

Materials/resources

Students will each need a copy of the worksheet listing the “parent” functions and the translations.

Technology resources

Each student should have the use of a Macintosh computer with built in graphing calculator.

Pre-activities

Students need to have some basic algebra skills.

Activities

The teacher will introduce the students to the graphing calculator on the computer with a mini lesson lasting about ten minutes. Then the students will follow the directions on the worksheet. They will graph a basic “parent” function on the computer, sketch its graph, and then graph and sketch various other functions in the same family. Family functions look like f(x+n), f(x-n), f(x)+n, f(x)-n, nf(x), f(-x), and /f(x)/. The students are to be looking for patterns in the families of functions. Then they are to explore some of their own combinations and compositions of these functions. They will choose one of the graphs of these hybrid functions to represent their approach to learning mathematics. The student is to put this graph on a poster with the name of the function and a description of why he chose this particular graph. Then the student will choose a one minute piece of music to go with the function and present the poster and the music to the class.

Assessment

Assessment will be facilitated by looking at the student sketches of the functions and by presentation of the poster, music, and description of the “personal” function.

Supplemental information

The graphing calculator is found under the apple on the top menu bar of the computer. It is very easy to teach yourself to use.

Comments

One of the things I have noticed in teaching all levels of high school math is that students don’t learn the shapes of the graphs of basic functions, and they certainly don’t know how to move them about on the coordinate plane. Consequently, they are unable to sketch graphs without the use of the graphing calculator. This affects many areas of mathematics including learning trigonometry and Calculus. I especially like using the calculator on the computer because it allows the students to “animate” two dimensional curvers using functions of x and n by rapidly changing n with a slide bar or key touches. I like this as an introductory activity for one of the more advanced courses. Having students explore various composite functions and choose one whose graph reflects their own mathematical style causes them to reflect more that they might normally. Putting this personal graph on poster-board and choosing music to help explain their thoughts gives an added dimension to the usual
left brained activities they
have come to expect in mathematics.

North Carolina Curriculum Alignment

Mathematics (2004)

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 2.08: Use equations and inequalities with absolute value 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 2.10: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties

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.
  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.01: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify steps used.
    • 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.

Grades 9–12 — Integrated Mathematics 3

  • Goal 3: Algebra - The learner will use relations and functions to solve problems.
    • Objective 3.01: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.
    • 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 3.04: Use equations and inequalities with absolute value 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.

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.

Grades 9–12 — Technical Mathematics 2

  • Goal 2: Algebra - The learner will use relations and functions to solve problems.
    • 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 2.04: Use systems of equations and inequalities to model and solve problems using tables, graphs, matrix operations, and algebraic properties; justify results.