Activity 2 - Teacher Guidelines
Objective of Activity
Materials Needed:
Anticipated Student Reactions:
Questions to pose to the students:
- Students should understand that the absolute value of the parameter "a" is equal to one divided by the product of 4 and the distance from the vertex to the focus (or the distance from the vertex to the directrix).
- Students should understand that the sign of "a" (negative or positive) determines which direction the parabola will open.
Materials Needed:
- Materials needed by the student: a computer, a copy of the handout, a calculator, a pencil, access to the GeoGebra applet.
- Materials needed by the teacher: answer key to the handout, preferably a means of projecting the applet for the whole class to see (such as a Smart Board or Promethean Board).
Anticipated Student Reactions:
- The exploration portion of this task starts really starts with question 5 on the handout, and students are given the option of choosing their own vertex point. For some students, they will have trouble grasping that the vertex does not matter as it relates to the distance between the focus and directrix. Students will be looking for the "right" answer here, and giving them the freedom to choose that point can cause stress for some students.
- There is difficult jump in ideas from question 7 to question 8. The students have developed a relationship between a and p by question 8, but then are asked to consider this relationship for when a is negative. Some students will be convinced that p should be negative as well. Teachers should be ready to explain that since p is a distance, it doesn't make sense to refer to this as a negative value. Point out that the negative value doesn't affect the distance between the focus and the directrix, but only affects the shape of the graph.
Questions to pose to the students:
- These questions can be found in the handout.
- To challenge the students in their reasoning, ask them to compare their responses to another group. This will cause the students to justify their mathematical reasoning beyond "because it looks right." Guide these conversations and really push your students to use correct mathematical terms and concepts to justify their responses.