Adapted from the NYS Department of Education publication, A Toolkit for Mathematics Educators: Key Idea Tasks to Enhance Success (KITES)
Using problem simulations, students will explore the pattern of snow accumulation and possible variations to develop an understanding of functional relationships. As the activities proceed through the grade levels, various methods of describing, representing, and extending patterns will be introduced.
- Pose snowfall problem as described in the Activity Sheet, Item 1. There is snow on the ground and snow begins to fall at a constant fractional rate.
- Have students write an algebraic equation to model the situation and state the appropriate domain.
- Sketch the graph of the function.
- Discuss independent and dependent variables in the context of the problem.
- Discuss the slope and y-intercept and explain what they represent in this situation.
- Have students use the equation to make predictions.
- Discuss the concept of extrapolation by having students make predictions outside the domain of the data.
- Have students sketch a graph that appropriately models a particular situation involving snowfall over a period of time with varying rates (see Activity Sheet, Item 2).
- Have students interpret graphs, both verbally and algebraically, involving snowfall over a period of time with varying rates (see Activity Sheet, Item 3).
- Pose a situation involving two linear models of snowfall in two different towns (see Activity Sheet, Item 4). Have students find the point of intersection (same snow accumulation) both graphically and algebraically through a system of equations.
- Have students use a graphing calculator to confirm their solution. (Compare data in the stat plot to the linear equation and the table.)