Electronic Graphing

Make These Designs

by Henri Picciotto

"Make These Designs" is an activity I have used in Algebra classes, over many years. It can be done with just about any electronic grapher. Its purpose is to reinforce students' understanding of the connection between the graph of a linear function, and the parameters m and b in the formula y=mx+b.

Originally, I used a graphing program I had written in the Logo language for this activity. Then I used the TI-82, then the TI-83/84, then the TI-89 calculator. Now I use GeoGebra or Desmos.

To get this many lines onto the screen may require using some of the special features of the calculator or software. On the TI-83/84, calculators, one can graph ten functions. To get more, students can use bracketed lists of parameters, and in fact, that approach is far more convenient even on the TI-89. In GeoGebra, one can use the Sequences command to save time. (See the respective documentation, or e-mail me for more information.)

Extensions

Basic Trig: The "starburst" design (the first one) can be brought back after students know a little trig, with the additional constraint that the lines are 15 degrees apart. (See also other lessons that connect slope and basic trigonometry.)

Algebra 2: Make These Parabolas (See also Parabolas and Quadratics, which provides preparation for this.)

Precalculus: Find These Polynomials.
If you create a "Find These Rational Functions" worksheet in this style, send it to me. I'll post it here and credit you.

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Related pages on this site:
Electronic Graphing
The Geometry of Linear Graphs
More algebra
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