## Reflection: Connection to Prior Knowledge The Tangent Line Problem - Day 1 of 2 - Section 3: Explore

One interesting way that students were organizing their work was with tables (as seen here). This students was finding the height as 1 second intervals throughout the path for the rock. Then they were finding the rate of change for those intervals. While not really making progress to find the instantaneous rate of change, the student was doing some really important calculus. I don't know if the students explicitly realized it but they hit on a few important concepts:

• The rate of change of the position function is the velocity function
• The derivative of the position function is the velocity function
• The velocity is not constant for the path of the rock
• Every second the velocity decreases by 32 feet per second

This student's work alone can be used later in the unit to talk about some really important concepts!

Connection to Prior Knowledge: Tables and Slope

# The Tangent Line Problem - Day 1 of 2

Unit 13: Limits and Derivatives
Lesson 3 of 13

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