Download Lesson Plan - Calculus and Vectors

Subject: Calculus and Vectors
Grade Level:
12
Topic: Chapter 5 - Derivatives of Exponential and
Trigonometric Functions
Teacher: Kathryn Navarro and Nadine
Long
Date:
Time (min): 70 min
Learning Goals
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Students will be able to work with other students to come up with a single answer
Students will be able to communicate their understanding through words
Students will be able to solve problems which require optimization of angles
1. Ministry Expectations
Strand: Derivatives and their Applications
Specific Expectation(s):
2.5 solve problems arising from real-world applications by applying a mathematical model and the
concepts and procedures associated with the derivative to determine mathematical results, and interpret
and communicate the results
2. Pre-Assessment
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Calculate angles and side lengths of triangles using trigonometry
Derivatives of trig functions
Derivatives of inverse of trig functions
Optimization problems requires the derivative of a function to be set equal to zero and then
solved for x
3. Required Resources
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Calculus and Vectors Nelson Textbook
String (15 pieces of string cut to 15 m each)
Side walk chalk
5 mini sticks
5 tennis balls
Chart paper
Markers
4. The Main Lesson
a) Agenda
1. Bell work – Derivatives of tan functions
2. Minds On – Optimizing Angles (Outdoor activity)
3. Group Work for Optimizing Angles
4. Sharing Solutions
b) Bell Work Questions
Find the derivatives of the following:
1. y = tan(3x)
2. y = tan(x2) – tan2(x)
3. y = 2tn(x) – tan(2x)
Total time: 5 min
c) Introduction – Minds On
Total Time: 20 min
Get classes attention: Grade 12’s eyes on me.
Ask class: What trigonometric functions have we learned to take the derivatives of? (answer: sin, cos, and tan)
Yesterday we learned how to use sin, tan and cos to determine lengths of triangle sides and angles. We have also
done some optimization problems, particularly with exponential functions. Today we’re going to take it a little
farther and do optimization with trigonometric functions. Present the following problem:
The distance between the goal posts in hockey is 1.8 m. If Sidney Crosby is on the goal line, 0.91 m outside one of
the goal posts, how far should he go out (perpendicular to the goal line) to maximize the angle at which he can
shoot at the goal.
1.8 m
0.91 m
Hint: Maximize the angle , in the following diagram.
 Draw the following diagram on the board
x

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hand out popsicle sticks to each student and tell them to get into groups based on shapes (5 groups of 4)
Tell students that we will first try this out outside. One person from each group must come up to get a
meter stick, a mini stick, a ball, string and a piece of chalk. Also, one person should be the recorder and
should bring a notebook and pencil to jot down ideas.
o Three students can act as the posts and the 3 m point, and each hold onto the string. The fourth
person is Sidney Crosby and holds the end of all three strings. They can then move further away to
visualize the angles.
Ask students to line up at the door and take them outside
Come back in to class when time is up.
c) Teaching Plan – Action
Get the classes attention – Grade 12s, eyes on me.
Total Time: 30
 Ask students to sit with their groups
 Have one student return materials get a piece of chart paper and marker
 Ask students to come up with a solution together (one per group) and write it on the chart paper
 They must be clear and explain their steps and reasoning for what they are doing
 After they have figured it out, ask what other factors may contribute to the success of Sidney Crosby
scoring
d) Consolidation & Assessment
Total Time: 15
Get the classes attention – 5,4,3,2,1
 Ask the students to tape their chart paper on the board
 Ask each group to come up and explain their solution and thought process
o If anyone made a mistake, ask students what the misconception was or how they could fix it
5. Optional Home Activity
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The test is in two days
Give students questions they could do for practice if the need it
Pg. 263 #2, 6, 10, 12 and 17