Reflection: Complex Tasks The Tangent Line Problem - Day 1 of 2 - Section 3: Explore


One of the most common first approaches to this problem is that students will find the average rate of change instead of the instantaneous rate of change. As shown in this student work, students will find the rate of change from 0 to 1 second instead of exactly at 1 second.

The good thing about this is that students are thinking slope which is a huge part of this task. As a teacher, I tried to get them to notice that this was not the same as instantaneous rate of change. Some students tried to pick two points really close together to get a better estimate. Other students abandoned slope and tried other methods.

Conceptually, I wanted students to realize that the slope was not constant and that the slope at 1 second is not the same as the slope from 0 to 1 second.

  Complex Tasks: A Common First Approach
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The Tangent Line Problem - Day 1 of 2

Unit 13: Limits and Derivatives
Lesson 3 of 13

Objective: SWBAT to find the slope of the tangent line to a function.

Big Idea: Limits and slope join forces to help solve a difficult problem.

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Math, Precalculus and Calculus, Derivatives, Number Sense and Operations, Tangent Lines at Derivatives, PreCalculus, limit, derivative, tangent line, slopes, function
  46 minutes
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