big idea 1 - the derivative as a limit
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8/4/2019 Big Idea 1 - The Derivative as a Limit
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AP Calculus AB
Student Learning Target Progress
I. Big Idea: The Relationship between limits and derivatives
A. Students will understand that a derivative of a function is a limit of
secant lines
1. Calculate average rate of change
2. Write an equation of a tangent line and normal line to a curve at a point
B. Students will understand how to find a limit graphically and analytically
1. Define a limit as the function values (y-value) given certain x-values
closer and closer to some value of x.
2. Define and determine the existence of a limit
a) Determine the existence and equality of right- and left- hand limits
(1) In non-piecewise functions
(2) In piecewise functions
b) Identify when a limit does not exist
(1) Identify when RHL does not equal LHL graphically and
algebraically
(2) RHL or LHL increases or decreases infinitely graphically and
algebraically
(3) Function oscillates infinitely at that point graphically andalgebraically
3. Analyze limits graphically
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AP Calculus AB
Student Learning Target Progress
a) At a point
b) On an open or closed interval c) Over the domain of the function
C. Define and identify the derivative as the limit of the difference quotient.
1. Write and analyze a derivative of a function using the definition of a
derivative
2. Identify a limit of a difference quotient as a derivativea) As a function
b) At a point
8/4/2019 Big Idea 1 - The Derivative as a Limit
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AP Calculus AB
Student Learning Target Progress
Calculate average rate of change. 1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
Write an equation of a tangent line and normal line to a curve at a point
1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
Define a limit as the function values (y-value) given certain x-values closer and closer to some value of x. 1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
8/4/2019 Big Idea 1 - The Derivative as a Limit
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AP Calculus AB
Student Learning Target Progress
Analyze limits graphically 1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
Analyze limits algebraically 1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
Analyze limits algebraically - Infinite limits. 1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
8/4/2019 Big Idea 1 - The Derivative as a Limit
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AP Calculus AB
Student Learning Target Progress
Determine if a function is continuous in terms of limits..
1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
Determine if a function is continuous in terms of limits..
1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
Write and analyze a derivative of a function using the definition of a derivative and the alternative definition of a derivative
1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
8/4/2019 Big Idea 1 - The Derivative as a Limit
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AP Calculus AB
Student Learning Target Progress
Identify a limit of a difference quotient as a derivative. 1st Assessment 2nd Assessment 3rd Assessment
My understanding of this target: New to me I kind of get it I get it! Every time! Let me teach!
Questions I still have:
8/4/2019 Big Idea 1 - The Derivative as a Limit
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AP Calculus AB
Student Learning Target Progress
Schedule:
DayDate Learning
Targets Learning TargetBooksection Suggested practice problems:B G
3 9/12 9/13 1 Calculate average rate of change. 2.1 p.89 #2, 4
2 Write an equation of a tangent line and normal line to
a curve at a point 2.8
p. 161 4-8 (note: f’(a) is the slope of a
function at x=a)
3 Define a limit as the function values (y-value) given
certain x-values closer and closer to some value of x. 2.1p.89 #5, 8, 9
4 Define and determine the existence of a limit
2.3
p. 101 #7
p. 109 2, 44,45,46
5 Analyze limits graphically 2.2 p 100 5, 8, 13, 14
4 9/14 9/15 6 Analyze limits algebraically
2.3
p.109 #3,6,9,10,11,12, 13, 15, 16, 19,
22, 23, 26, 27, 39
p.144 #1, 3, 6, 7, 8, 15, 16, 17, 22, 24,25, 29, 31,
5 9/16 9/19 7 Analyze limits at infinity 2.6 p.99 #21-28(no calculator),
6 9/20 9/21 8 Determine if a function is continuous in terms of
limits.
2.5
p.131 #1, 3, 5, 6, 15, 16, 20, 35, 36,
39, 40, 42, 45
7 9/22 9/23 9 Write and analyze a derivative of a function using the
definition of a derivative and the alternative definition
of a derivative 2.7
p. 162 13 – 18
8 9/26 9/27 10 Identify a limit of a difference quotient as a derivative 2.7 p. 162 19 – 24
Skill Assessments:
Burgundydate
Gold date Learning Targets
9/14 9/15 1, 2, 3, 4, 59/22 9/23 1, 2, 3, 4, 5, 6, 7, 89/28 9/29 1, 2, 3, 4, 5, 6, 7, 8, 9, 10