Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium ∫ J. Sterling Morton East High School Cicero, IL AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Barbara.

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Transcript Kane and Gierut ∫ Morton East High School ∫ 2014 AP Consortium ∫ J. Sterling Morton East High School Cicero, IL AP Calculus…as easy as 3, 4, 5 ∫ ∫ ∫ Barbara.

Kane and Gierut
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Morton East High School
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2014 AP Consortium
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J. Sterling Morton East High School
Cicero, IL
AP Calculus…as easy as 3, 4, 5
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Barbara Kane
Patrick Gierut
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Collaboration &
Support
2004-2005
Everyone Takes the
AP Test
Kane and Gierut
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Vertical Teaming
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2014 AP Consortium
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Calculus at Morton
Today
AP Calculus…as easy as 3, 4, 5
Morton East High School
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2013-2014
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Morton East High School
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Apply skills
to new
situations
AP Review
Sessions
Kane and Gierut
2014 AP Consortium
AP Calculus…as easy as 3, 4, 5
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Summer
Work
Daily
Homework
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Morton East High School
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Suppose that the functions f and g and their derivatives with
respect to 𝑥 have the following values at 𝑥 = 0 and 𝑥 = 1.
If ℎ 𝑥 = 𝑓 𝑔 𝑥 , evaluate ℎ′(0).
𝒇(𝒙) 𝒈(𝒙) 𝒇′(𝒙) 𝒈′(𝒙)
0
1
1
5.6
8.2
1
3.75
–4.2
–7.9
–5.3
Kane and Gierut
x
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2014 AP Consortium
New Situation: Apply knowledge of the chain rule
using a table of values instead of functions.
AP Calculus…as easy as 3, 4, 5
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Skill: Chain Rule
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Morton East High School
2014 AP Consortium
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Kane and Gierut
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AP Calculus…as easy as 3, 4, 5
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Skill: Definite Integral, Increasing/Decreasing, Average
Value, Average Rate of Change
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Morton East High School
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2014 AP Consortium
3pm-5pm
Sat, March 22
8am-10am
Thurs, March 27
3pm-5pm
Sat, March 29
8am-10am
Thurs, April 10
3pm-5pm
Sat, April 12
8am-10am
Thurs, April 17
3pm-5pm
Wed, April 23
Sat, April 26
8am-9:30am
9:30am-11am
8am-10am
Length of Test
M/C Non-Calculator
55 min
(plus 60min discussion)
M/C Calculator
50 min
(plus 60min discussion)
FRQ Calculator
45 min
(plus 60min discussion)
FRQ Non-Calculator
45 min
(plus 60min discussion)
M/C Calculator
50 min
(plus 40min discussion)
FRQ Non-Calculator
45 min
(plus 60min discussion)
Kane and Gierut
Thurs, March 20
Type of Test
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Time
AP Calculus…as easy as 3, 4, 5
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DATE
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Time
M/C Non-Calculator
55 min
(plus 60min discussion)
M/C Calculator
50 min
(plus 60min discussion)
FRQ Calculator
45 min
(plus 60min discussion)
M/C Calculator
50 min
(plus 40min discussion)
FRQ Non-Calculator
45 min
(plus 60min discussion)
10am-12pm
Sat, March 22
12pm-2pm
10am-12pm
Sat, March 29
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12pm-2pm
Sat, April 12
12pm-2pm
8am-9:30am
Wed, April 23
9:30am-11am
10am-12pm
Sat, April 26
12pm-2pm
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2014 AP Consortium
10am-12pm
Kane and Gierut
Length of Test
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Type of Test
AP Calculus…as easy as 3, 4, 5
Morton East High School
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DATE
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
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Morton East High School
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2014 AP Consortium
Unit/Year
Schedules
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Consistent
Teaching
AP Calculus…as easy as 3, 4, 5
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Teacher
Availability
Teach
Calculus &
prepare for
AP Test
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Morton East High School
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Collegial Support: Before & After School,
Lunch/Prep Time, Weekends, Summer
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Kane and Gierut
2014 AP Consortium
AP Review Sessions: After School &
Saturdays
AP Calculus…as easy as 3, 4, 5
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Tutoring/Homework Help: Before & After
School every day
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Morton East High School
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ln 𝑥
2
−
2
1
1
− + 𝑥
2
2
𝑑𝑥
Kane and Gierut
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Volume = 1.324
Score Qualifications
0 No work or washer method never used or
used incorrectly
1 Outer radius incorrect, limits incorrect
2 Inner radius incorrect
3 Error in computation. (AP-style answer)
4 Error in notation.
5 Proper notation used throughout problem.
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2014 AP Consortium
SOLUTION: V =
3.513
1
AP Calculus…as easy as 3, 4, 5
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QUESTION: Find the volume of the solid formed by
revolving the region bounded by the graphs of
𝑦 = ln 𝑥 and 𝑥 − 2𝑦 = 1 about the x-axis.
Kane and Gierut
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Morton East High School
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2014 AP Consortium
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AP-Style Answer
Continuity
Differentiability
Derivatives
Riemann Sums
Value Theorems
Critical Points
Volume
BC Topics
AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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PreCalculus
AP Calculus
PreCalculus
Geometry
Algebra
Algebra (8th
grade)
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Geometry
Kane and Gierut
Adv Alg
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2014 AP Consortium
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Summer
Adv Alg
AP Calculus…as easy as 3, 4, 5
Morton East High School
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AP Calculus
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Morton East High School
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Geometry
Algebra
97
2012-13
82
2011-12
64
2010-11
41
2009-10
38
2008-09
49
2007-08
40
2006-07
29
2005-06
32
2004-05
25
36 BC
61 AB
Kane and Gierut
2014 AP Consortium
Summer
Adv Alg
2013-14
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PreCalculus
# Students in
Calculus
AP Calculus…as easy as 3, 4, 5
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AP Calculus
School
Year
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Morton East High School
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PreCalculus
Summer
Adv Alg
Adv Alg
Summer
Geometry
Algebra
Kane and Gierut
Algebra
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2014 AP Consortium
AP Calculus
PreCalculus
Geometry
AP Calculus…as easy as 3, 4, 5
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AP Calculus
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Morton East High School
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• Solving/Simplifying Logs/Exp
• Solving/Simplifying Polynomials
Kane and Gierut
• Calculator Usage (graphing functions,
solving equations, etc)
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2014 AP Consortium
• Rational Expressions (including factoring)
AP Calculus…as easy as 3, 4, 5
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• Unit Circle/Trig Review
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Morton East High School
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• Partial Fractions
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• Parametric Functions
• Vectors
Kane and Gierut
2014 AP Consortium
AP Calculus…as easy as 3, 4, 5
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• Polar Functions
• Limits & Continuity
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AP Calculus…as easy as 3, 4, 5
AP Calculus
Math 2/3
Math 2/3
Summer
Math 2
Math 1/2
Math 1
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PreCalculus
Kane and Gierut
PreCalculus
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2014 AP Consortium
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Morton East High School
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AP Calculus
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Avg Score:
3.427
70
Global Avg:
2.96
60
50
Score
5
3 or Higher:
75.61%
Score
4
40
Score 3
30
Score 2
Score 1
20
10
0
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2005 2006 2007 2008 2009 2010 2011 2012 2013
Years
Kane and Gierut
# of students in AP Calculus
Morton East High School
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80
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2014 AP Consortium
AP Calculus…as easy as 3, 4, 5
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90
2010
1
2011
0
2012
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2013
Kane and Gierut
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2
2014 AP Consortium
5
4
3
Morton East High School
6
AP Calculus…as easy as 3, 4, 5
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7
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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% of students
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35
30
2010
25
2011
20
2012
15
2013
Kane and Gierut
2014 AP Consortium
40
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10
5
0
Lowest 4th
Second 4th
Third 4th
Highest 4th
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Multiple-Choice
AP Calculus…as easy as 3, 4, 5
Morton East High School
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45
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35
30
2010
25
2011
20
2012
15
2013
Kane and Gierut
% of students
Morton East High School
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40
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2014 AP Consortium
Free-Response
AP Calculus…as easy as 3, 4, 5
10
5
0
Lowest 4th
Second 4th
Third 4th
Highest 4th
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45
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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Kane and Gierut
2014 AP Consortium
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Calculus
Teacher
AP Calculus…as easy as 3, 4, 5
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Morton East High School
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Student
Interest
PreCalc
Teachers
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Morton East High School
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2014 AP Consortium
Kane and Gierut
Arc Length, Parametrics, Vectors
L’Hôpital’s Rule, Improper Integrals
Sequences & Series
Convergence of Series
Taylor Series
Euler’s Method
Differential Equations, Logistic Graphs
Polar graphs
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AP Calculus…as easy as 3, 4, 5
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Attended College Board AP Summer Institute with
Ruth Dover (IMSA)
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Morton East High School
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Chapter 3
Derivatives
• Includes Vectors, Parametric
& Polar Functions
• Ends early October
Chapter 4
Applications of
Derivatives
• Ends early November
Chapter 5
Definite Integral
• Includes integration by
parts, partial fractions
• Ends mid-December
Kane and Gierut
2014 AP Consortium
• Ends 1st week of school
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Chapter 2
Limits &
Continuity
AP Calculus…as easy as 3, 4, 5
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Planned out the schedule for the year
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Morton East High School
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2014 AP Consortium
• Ends late-February
Chapter 9 Infinite
Series
• Ends late-March
Kane and Gierut
Chapter 8
L’Hôpital’s Rule &
Improper
Integrals
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Chapter 7
Applications of
Definite Integrals
• Includes polar curves, lengths
of curves, parametric curves,
distance traveled in vector
• Ends mid-February
AP Calculus…as easy as 3, 4, 5
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Chapter 6
Slope Fields
• Includes Euler’s method &
Logistic Growth
• Ends January, before Finals
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Videos &
Website
Resources
Planning
Lessons
Kane and Gierut
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Guided
Notes
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2014 AP Consortium
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Demonstrations
AP Calculus…as easy as 3, 4, 5
Morton East High School
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Wolfram
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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∫
Kane and Gierut
2014 AP Consortium
∫
Morton East High School
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AP Calculus…as easy as 3, 4, 5
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∫
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Kane and Gierut
2014 AP Consortium
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Morton East High School
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AP Calculus…as easy as 3, 4, 5
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www.remind101.com
• Math Is Fun
www.mathsisfun.com/calculus/index.html
apcalculusstillwater.wordpress.com/ap-calculus-videos/
https://sites.google.com/a/lusherschool.org/mrwhitecalc/
www.deeringmath.com/Calculus/calculusbc/
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• Mr. Landry’s Online Learning Math Center
Kane and Gierut
• Mr. White’s AP Calculus AB
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2014 AP Consortium
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• AP Calculus Stillwater
AP Calculus…as easy as 3, 4, 5
Morton East High School
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• Remind 101
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Morton East High School
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36 students
55 students
Series
Review Days
Videos
35 students
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3 preps
Kane and Gierut
2014 AP Consortium
Collegial
Support
AP Calculus…as easy as 3, 4, 5
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Frozen Days
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Morton East High School
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More Teachers
Involved
Kane and Gierut
More Vertical
Teaming
∫
2014 AP Consortium
More AB & BC
AP Calculus…as easy as 3, 4, 5
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Student
Buddy System
100% success
rate
Kane and Gierut
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Morton East High School
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2014 AP Consortium
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J. Sterling Morton East High School
Cicero, IL
AP Calculus…as easy as 3, 4, 5
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Barbara Kane
Patrick Gierut