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# Is John Guilty

Lesson 1 of 13

## Objective: SWBAT determine the angular and linear speed of a moving object

## Big Idea: By analyzing data from an accident students will determine whether a driver was speeding when he wrecked his vehicle.

#### Teacher Notes

*1 min*

Today's activity lends itself to putting names of local students and school personnel as the major players. I developed this activity after reading the article "Creative Writing in Trigonometry" by Julia Barnes in the Mathematics Teacher 92(6).

Students do not need to have angular and linear velocity formulas (i.e linear velocity =arc length /time, angular speed = central angle /time, or linear speed= radius time angular velocity). Student can problem solve by finding the circumference of the wheel then multiplying by the revolutions then convert the units. The formulas will be developed later by using this activity as a reference.

Reference:

Barnes, Julia. "Creative Writing in Trigonometry." *Mathematics Teacher *92.6 (1999): 498).

Learning Targets for this unit include solving basic trigonometric equations.

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#### Bell work

*5 min*

As we start this unit I have students determine the answer to the bell work. The tasks remind students of concepts that will be used in today's activity. After giving students time to work, I will ask several to share their results on the board. As I invite them to the board I will ask them to write out circle and circle area formulas that they remembered and used in the task.

My students occasionally mix up circumference and area, but for a concept like this I do not need to offer corrections because I've encouraged my students to assist each other (**MP3**, **MP6**). I may remind students to use appropriate units, however. Some have not yet learned the importance of using them consistently.

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#### Is John Guilty

*35 min*

Once the bell work is complete, I give students the John and the Home Video activity. I have my students work in pairs to determine the results from the video and police officer. Students then discuss the information in the prompt to see if that information will make a difference. As I walk around the room I ask students questions such as:

- Does the weather make a difference?
- What about the trash on the floor?
- How can the police officer determine the distance the truck traveled?
- What other information could be used to help determine which person is correct?

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#### Closure

*5 min*

As class ends I bring the class back to make sure the students understand the assignment. Students are given the scoring guide that gives them an idea on what the structure of the paper will look like. Most students have not written an argument using the mathematics as the evidence for the argument. This activity requires students to make sense of a problem (MP1), Construct a viable argument (MP3), Reason quantitatively (MP2) and attend to precision (MP6) along with other mathematical practices. Here are some rough drafts from previous years.

I give students one week to complete the writing. I will then review the papers, make suggestions and give students a final due date for the paper.

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- UNIT 1: Introduction to Learning Mathematics
- UNIT 2: Functions and Piecewise Functions
- UNIT 3: Exponential and Logarithmic functions
- UNIT 4: Matrices
- UNIT 5: Conics
- UNIT 6: Solving Problems Involving Triangles
- UNIT 7: Trigonometry as a Real-Valued Functions
- UNIT 8: Graphing Trigonometric Functions
- UNIT 9: Trigonometric Identities
- UNIT 10: Solving Equations
- UNIT 11: Vectors and Complex Numbers
- UNIT 12: Parametric and Polar graphs and equations

- LESSON 1: Is John Guilty
- LESSON 2: Radian Measure Day 1 of 2
- LESSON 3: Radian measure Day 2 of 2
- LESSON 4: Coterminal and Reference Angles
- LESSON 5: Sine and Cosine Day 1 of 2
- LESSON 6: Sine and Cosine Day 2 of 2
- LESSON 7: Developing the Unit Circle
- LESSON 8: Evaluating Trigonometric Functions
- LESSON 9: Finding the angle when given the function value
- LESSON 10: How do you find the Inverse of a Trigonometric Functions
- LESSON 11: Using Inverses to Evaluate
- LESSON 12: Review of Trigonometric Functions as Real Valued Functions
- LESSON 13: Assessment of Trigonometric Functions as Real Valued Functions