Graphs can be used to solve
equations and show a variable's behavior clearly. The most important
aspect of this work is to discuss what makes sensible graphs and
why. Failure to do this may make students good at performing the
conversions from data to graph, but they will not understand why.
Students use paper for notes, pencils
Teacher and students think a number and apply a function to it. Students then supply the second variable as the answer. For example "I am thinking of a number. Let's call it x. If I double it and add 4 the answer is y. This is the equation for 2x+4=y."
Once they understand that every time they use this equation the same thing happens, students will be able to construct a table on paper.
Using Graphing Calculator and Microsoft Excel, students construct a formula that will represent 2x+4=y. Cell B2 contains the formula =SUM(2*a2+4).
Students derive other values
for y which only a graph makes possible.
X | Y |
4 |
12 Formula (2*a2+4) |
8 | 20 |
16 | 36 |
32 | 68 |
64 | 132 |
128 | 260 |
1. Use more complex formulas
2. Find real-life applications for these equations and graphs
3. Students present each other with actual numbers and derive formulas
4. Plot data with different
graphs to determine which make most meaningful way to display
info and why