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# Formative Assessment: Limits and Derivatives

Lesson 6 of 13

## Objective: SWBAT show understanding of limits and derivatives.

*50 minutes*

#### Partner Quiz

*25 min*

I start class today by giving a partner quiz that assesses student understanding of limits and derivatives. I believe that partner quizzes are great opportunities to** incorporate mathematical discourse into your classroom**. Every group will have at least one question where there is disagreement; it is awesome to walk around and hear your students giving reasons and justifications to support their claims. It is also an opportunity to critique the reasoning of their partner if they disagree (**MP3**).

**One grouping strategy** is to order the students from highest to lowest grade in the class.In a class of 30 students, for example, I would go through and match up #1 with #16, #2 with #17, #3 with #18, etc. This way each pair is grouped in a similar way and there is the same differential between each pair. I find that this grouping really encourages conversations because there is never a huge gap between ability levels.

I give my students about 25-30 minutes to work on this quiz. Each student gets their own quiz but I tell them that I will only grade one and each person will get the same grade. I don't specify which one I will grade so I say that they should have the same work and answers on each page. **This holds each member responsible.**

In the video below I discuss one question from the quiz that I particularly like because it is a great formative assessment to see if students understand derivatives.

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#### Summarize

*25 min*

For the remainder of the class, students will work on this homework assignment that provides a good summary of our work with derivatives. They are still fairly new to students so I wanted to provide a time to take a breather and put everything together. On the worksheet, students are asked to **use the limit method and shortcuts to find derivatives**. There are also problems where students have to work with tangent lines and interpret results.

#### Resources

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: The Limit of a Function
- LESSON 2: Techniques for Finding Limits
- LESSON 3: The Tangent Line Problem - Day 1 of 2
- LESSON 4: The Tangent Line Problem - Day 2 of 2
- LESSON 5: The Power Rule
- LESSON 6: Formative Assessment: Limits and Derivatives
- LESSON 7: Derivatives and Graphs
- LESSON 8: The Second Derivative
- LESSON 9: Maximizing Volume - Revisited
- LESSON 10: The Rock Problem
- LESSON 11: Unit Review: Limits and Derivatives
- LESSON 12: Unit Review Game: The Row Game
- LESSON 13: Unit Assessment: Limits and Derivatives