This activity brings out a visual, conceptual understanding of many function vocabulary words. You need to wrap up the lesson with a very explicit discussion of important vocabulary. Use the graphs from the competition to discuss how each of the vocabulary was present, for example, the initial amount was the distance the walker was from the motion detector at the very beginning (time 0 seconds). Have students add these conceptual definitions to their unit organizer as you hold a whole group discussion.
Big Ideas to Discuss:
1. What it means to be a function? Conceptually understand that one output for every input is the definition of a function, which is why some of the graphs were impossible. The motion detector can only detect one person at a time so even if two are in front of the CBR it will only show one person therefore the graphs are impossible to create.
2. Characteristics of linear and non -linear graphs such as constant rate of change in an increasing or decreasing direction. Changes in speed cause curves such as quadratic graphs, as do changes in direction. Piece-wise functions behave as several different linear functions pieced together so it looks linear in pieces.
3. Domain and Range: Domain is the independent quantity graphed on the x-axis (time is independent and moved forward with out student control). Range is the dependent quantity graphed on the y-axis (the walking directions dictated how the students moved so the movement depended on the directions)
4. Rate of change and initial amount in regards to walking direction and where to start, how fast to walk, increasing or decreasing distance.
Continue the voting for a winning graph and make sure you have a great prize for the winning team who wrote the directions and the team that followed the directions to walk.
Wrap up the lesson by putting the graph on the board and asking students to answer the following questions as an exit slip.
1. What type of graph is represented (linear, quadratic, piece-wise, exponential)
2. Write a story to describe how Woody and Bullseye could have been riding at the time the graph was made.