Focus Question – How do you recognize a non-linear equation in a graph, table, or equation?
This is a relatively new topic for students. Students should have knowledge of what a linear functions look like so because of this they should be able to contrast to discover, they will have a clue in recognizing nonlinear functions. This should be easily true for graphs, but less easy for tables and equations.
Students will work on the packet linked below in their groups. The packets guide students to discover that if the lines are not straight then they are nonlinear (obviously). They then go down the path to discover that if they try to find rate’s of change for the values in the table then they will vary or not be constant. This should show them how to recognize if a table of values is linear or nonlinear.
After students attempt the problems to to discover the above, I will circulate around the room and check in with each group to make sure this understanding is cemented.
Finally students will complete #4-10 for homework. Which allows them to think through if the equations are linear or nonlinear without graphing or making a table.
Have students in groups write down the equations that they thought were linear and which were nonlinear. Have students discuss and find common characteristics that allowed them to discover if they were linear or not.
Use Desmos.com for students to test out their “characteristics” from above. Graph similar equations to see if they are also linear/nonlinear.
Discuss the discoveries as a class and make a list of things to look for in an equation that guarantees it will be nonlinear.
Have students do a few problems from the book p. 330-1 to check for understanding.
Spend the rest of time reviewing for the Functions Test.