#### Skills

- Creativity
- Critical Thinking
- Project Based Learning

### External References

Roller coasting through Functions

To determine the time it takes for a roller coaster to reach the bottom of its tallest drop. Students conclude by creating their own roller coasters.

Example of students final product 1

A student´s roller coaster model having scale in consideration.

### Learning Objectives

- Evaluate functions using the order of operations.
- Describe and represent functions using tables, graphs and rules.
- Compare and relate representations of the same relation.
- Model and solve contextualized problems using various representations, such as graphs, tables, and equations.
- Make sense of problems and persevere in solving them.
- Model with mathematics.

### Guiding Ideas

This lesson is the finishing point of the activity started by NCTM Illuminations (see External References).

As students complete the tables regarding the values for time and height, substituting the values in the "roller coaster" function, they will see at what points the roller coaster is as it drops from its highest point.

### Student Activities

1. Students evaluate the given functions by substituting the time variable to see how long each rollercoaster takes from its highest point until zero.

2. Students choose their own value for s, in the function h = s - 16t^2, where s represents the highest point, create a data table and graph the function.

3. Students model their own roller coasters in Minecraft, by approximation, representing the drop and being creative about the rest of the roller coaster.

### Performance Expectations

As quadratic functions were not part of the curriculum, the study of these functions involved only simple substitution into formula and determining its zeros, by approximation. Students were expected to build their representations of the given function by choosing their own s in the formula h = s - 16t^2, where s represents the highest point.

One of the constrains was setting a proper scale for each minecraft block in order to correctly model the highest point.

#### Skills

- Creativity
- Critical Thinking
- Project Based Learning

### External References

Roller coasting through Functions

To determine the time it takes for a roller coaster to reach the bottom of its tallest drop. Students conclude by creating their own roller coasters.

Example of students final product 1

A student´s roller coaster model having scale in consideration.