Objectives: To recognize the rate of change characteristics of linear, concave up and concave down functions.
Preliminaries/Lead-In: Before they start this activity it is a good idea to motivate why we measure how a function changes with the rate of change formula (rise/run). (Mairead does it during Activity 1.2, I do it after Activity 1.2.) Why not just measure with rise? I usually do this with two lines drawn on a graph paper - same rise, but different runs. We note rise same - I ask them if they would characterize two lines as growing at same rate? - they wouldn't say those two lines were growing at the same rate. The one that reached the rise in a shorter run is steeper, grew faster....so, rise has to be measured relative to run. Hence, the ratio. Definition listed on the first page of Activity 1.3 for data and for function. I have them go back to some 1.2 data and calculate some rates of change - we talk about it - then they are ready for Activity 1.3.
Suggested Procedures: I will probably send them away with the first 9 questions of this activity as homework. I may have a brief discussion of rate of change first. Then the beginning of next day I will come back and talk to them about what they got for those questions. I will make sure to emphasize the connection between the graph, the rate of change pattern and the labeling of linear, concave up and concave down. Then I will have them work on question 10 in small groups for around 10-15 minutes.
Wrap-Up/Take-Away: I will collect the whole worksheet but probably only grade the last question.
Possible Homework:
Follow this link to share with us how this activity (the original or your adapted version) worked in your classroom! Thank you for all of your feedback.
Alternative Versions:
If you make any adjustments to this activity we would appreciate you sharing your new version! Please save it as "YOURNAME Course Activity ....." and attach it below. Thank you!