CalculusAB First Six Weeks
Week 1 8/27/07 to 8/31/07
Monday / Tuesday / Wednesday / Thursday / FridayPre - Cal / 1C / 1D / 1A,B
2A,B / 1A,B
2A,B
CAL / 1A / 1A / 1A / 1A
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Orientation
Class rules
Course expectations and requirements. / T.L.W:
Sketch the graph of an equation.
Find the intercepts of a graph.
Find the points of intersection of two graphs.
Interpret mathematical models for real –life data. / T.L.W:
Find the slope of a line passing through two points.
Write the equation of a line with a given point and slope.
Interpret slope as a ratio or as a rate of change in real –life application.
Write equations of lines that are parallel or perpendicular to a given line. / T.L.W:
Use function notation to represent and evaluate a function.
Find domain and range of a function.
Sketch the graph of a function.
Identify different types of transformations of functions. / T.L.W:
Classify functions and recognize combinations of functions.
Test a graph for symmetry with respect to an axis and the origin.
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages / Text Pages 17 – 22 / Text Pages 25 – 30 / Text Pages 34 – 41 / Text Pages 20 – 21
40 – 41
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Functions.
Intercepts / Slope, Rate of change, Parallel, Perpendicular. / Parent Graph, Domain, Range, Interval notation. / Symmetry, Odd and Even function
Strategies / Strategies / Strategies / Strategies / Strategies
Analyze graph sketched both manually and with calculator.
Finding points of intersection by solving equations algebraically, and graphically. / Find slope of a line when given two points.
Find equation of a line from two points or one point and a slope.
Discuss slope-intercept, and standard form of an equation for a line.
Relate slope to a rate of change
and its applications. / Identify domain and range of a function in both interval form and set notation form.
Sketch parent graphs and perform transformations. / Find composite and inverse functions.
Recognize Even and Odd functions.
Discuss tests for symmetry with respect to axis and Origin.
Use properties of Odd, Even, and Inverse function to complete the graph of a function.
Assessment / Assessment
Pages 23
Problems 1 – 16
27 – 30
52 - 66 / Assessment
Pages 23 – 24
Problems 53 – 56
Pages 31
Problems 1 – 54 / Assessment
Pages 42
Problems 1 – 42 / Assessment
Pages 23
Problems 17 – 26
Pages 43
Problems 53 – 56
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB First Six Weeks
Week 2 9/3/07 to 9/7/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / 2C, 3A / 2C, 3A / 1A,B,C,D / 1A,B,C,D
2A,B,C, 3A / 1A,B,C,D
2A,B,C, 3A
CALC / 1A / 1A / 1A / 1A / 1A
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Review trigonometric identities.
Solve special right triangles. / T.L.W:
Graph trig. Functions.
Solve trig. Functions. / T.L.W:
Quiz over algebra review / T.L.W:
Review last two weeks objectives / T.L.W:
Major assessment.
Chapter review test.
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages 45 – 52 / Text Pages 45 – 52 / Text Pages Hand outs / Text Pages Hand outs / Text Pages Hand outs
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Standard position, Co terminal, Special right triangles, Identities, Period, Amplitude.
Strategies / Strategies / Strategies / Strategies / Strategies
Review basic trigonometric identities including sum, difference, double, and half angles.
Review graphing of trig. functions including reciprocal, quotient, and Pythagoras.
Evaluate exact value of a trig. Function using special right triangle.
Solving trigonometric functions algebraically and graphically. / Sketch all six trig. Function in
[ – 2 , 2
Use graphing calculator to graph trig. Functions.
Use special right triangle to solve trig. Function.
Use graphing calculator to find zeros of trig. Functions. / Answer student’s questions. / Answer student’s questions.
Assessment
Page 53
Problems 13 – 46 / Assessment
Page 55
Problems 51 – 77 / Assessment / Assessment / Assessment
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB First Six Weeks
Week 3 9/10/07 to 9/14/07
Monday / Tuesday / Wednesday / Thursday / FridayPre -Cal / Holiday / 1D / 1D / 1D, 1E
CALC / I – B – 1 / I – B – 2 / I – B – 2
I – B –3 / I – B – 1, 2, 3
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
Holiday / T.L.W:
Estimate a limit using a numerical or graphical approach
Learn different ways that a limit can fail to exist / T.L.W:
Evaluate a limit using properties of limits / T.L.W:
Develop and use a strategy for finding limits
Evaluate a limit using dividing out and rationalizing techniques / T.L.W:
Evaluate a limit using properties of limits
Develop and use a strategy for finding limits
Evaluate a limit using dividing out and rationalizing techniques
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages / Text Pages
61-65 / Text Pages
70-74 / Text Pages
76-79 / Text Pages
Various AP questions from past tests and other resources.
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Limit / Scalar multiple / Rationalization
Strategies / Strategies / Strategies / Strategies / Strategies
Find limits of functions through table (as x approaches a value) and graphically / Find limits of function by direct substitution / Find limits by using algebra to get equivalent expressions for which limits are defined / Quiz students over objectives covered up to date over limits
Assessment / Assessment
p. 68: 1-18, 35, 36 / Assessment
p.74: 1-34 / Assessment
p. 82: 1-24 / Assessment
Teacher made quiz
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB First Six Weeks
Week 4 9/17/07 to 9/21/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / 1 – D / 1 – D / 1 – D / 1 – D
E
B – 2
C – 3 / 1 - D
CALC / I – B – 1
I – B – 2 / I – B – 1, 2 / I – B – 1, 2 / I – B – 1, 2 / I – D – 3
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Evaluate a limit using properties of limits
Develop and use a strategy for finding limits
Evaluate a limit using dividing out and rationalizing techniques / T.L.W:
Evaluate a limit using the squeeze theorem / T.L.W:
Evaluate a limit using properties of limits
Develop and use a strategy for finding limits
Evaluate a limit using dividing out and rationalizing techniques
Evaluate a limit using the squeeze theorem / T.L.W:
Review all objectives covered to date / T.L.W:
Determine one-sided limits and continuity on a closed interval
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages / Text Pages
80-81 / Text Pages
81-83 / Text Pages
Various AP questions from tests / Text Pages
86-87
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Squeeze theorem / One sided limits
Strategies / Strategies / Strategies / Strategies / Strategies
Correct Friday’s quiz, review concepts of limits that were not mastered / Find limit as x approaches 0 of sin x/x by applying squeeze theorem / Review more trig concepts to help find limits involving trig functions.
Find all limits of a piece-wise.
Review all function objectives on limits covered to date. / Test students on objectives covered up to this point / Find one sided limits using previous objectives
Assessment
Oral evaluation / Assessment
p.82: 25-40 / Assessment
p.83: 43-48, 51-52 / Assessment
Teacher made test / Assessment
p.92: 1-13
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB First Six Weeks
Week 5 9/24/07 to 9/28/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / 1 – E / 1 – E / 1 – E
2 – B / 1 – E
2 – B / 1 – E
3 – C
CALC / I – B – 1
I – B – 2 / I – D – 1, 2 / I – D – 1, 2 / I – D – 3 / I – D – 1, 2, 3
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Determine continuity at a point and continuity on an open interval
Determine one-sided limits and continuity on a closed interval / T.L.W:
Use properties of continuity / T.L.W:
Determine continuity at a point and continuity on an open interval
Determine one-sided limits and continuity on a closed interval
Use properties of continuity / T.L.W:
Understand and use the intermediate value theorem / T.L.W:
Determine continuity at a point and continuity on an open interval
Determine one-sided limits and continuity on a closed interval
Use properties of continuity
Understand and use the intermediate value theorem
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages
84-85 / Text Pages
86-88 / Text Pages
89-90 / Text Pages
91-92 / Text Pages
Quiz
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Removable and non removable discontinuities / Removable and non removable discontinuities / Removable and non removable discontinuities / Mean value theorem
Strategies / Strategies / Strategies / Strategies / Strategies
Discuss limits of functions by examining functions graphically / Discuss continuity of functions by examining functions graphically / Use various methods to find limits of functions including one-sided and non-existent. / Discuss intermediate value theorem and give applications / Give quiz over concepts covered up to this point.
Assessment
p.93: 14-26 / Assessment
p.93: 27-46 / Assessment
p.93: 49-50 / Assessment
p.93: 67-74 / Assessment
Quiz
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB First Six Weeks
Week 6 10/1/07 to 10/5/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / 1 – E / 1 – E / 1 – E / 1 – E / 1 – E
1 – D
CALC / I – C – 1, 2 / I – C – 1, 2 / I – B
I – C – 1, 2 / I – B
I – C – 1, 2 / I – B, C, D
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Determine infinite limits from the left and from the right
Find and sketch the vertical asymptotes of the graph of a function / T.L.W:
Determine finite limits at infinity
Determine the horizontal asymptotes, if any, of the graph of a function / T.L.W:
Determine infinite limits from the left and from the right
Find and sketch the vertical asymptotes of the graph of a function
Determine finite limits at infinity
Determine the horizontal asymptotes, if any, of the graph of a function / T.L.W:
Determine infinite limits from the left and from the right
Find and sketch the vertical asymptotes of the graph of a function
Determine finite limits at infinity
Determine the horizontal asymptotes, if any, of the graph of a function / T.L.W:
Determine infinite limits from the left and from the right
Find and sketch the vertical asymptotes of the graph of a function
Determine finite limits at infinity
Determine the horizontal asymptotes, if any, of the graph of a function
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages
96-100 / Text Pages
198-201 / Text Pages
102-103 / Text Pages
Test / Text Pages
Test
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Vertical asymptote / Horizontal asymptote
Strategies / Strategies / Strategies / Strategies / Strategies
Relate infinite limits to vertical asymptote / Find limits as x approaches infinity and relate to horizontal asymptote / Review all methods of finding limits discussing continuity, finding vertical and horizontal asymptotes / 6 week test / 6 week test
Assessment
p.101: 9-42 / Assessment
p.203: 1-30 / Assessment
p.102: 1-40 / Assessment
Test / Assessment
Test
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB Second Six Weeks
Week 7 10/8/07 to 10/12/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / 1 – E / 1 – E / 1 – E / 1 – E / 1 – E
CALC / II – A – 1
II – A – 3 / II – A – 2
II – A – 4 / II – A – 1, 2, 3, 4 / II – A – 1, 2, 3, 4 / II – A – 1
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function / T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity / T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity / T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity / T.L.W:
Find the derivative of a function using the constant rule.
Find the derivative of a function using the power rule.
Find the derivative of a function using the sum and difference rule.
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages
105-110 / Text Pages
110-112 / Text Pages / Text Pages
Teacher made test / Text Pages
115-117
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Secant line
Tangent line
Derivative
Rate of change / Differentiability
Differentiable
Differentiation / Instantaneous rate of change / Constant rule
Power rule
Sum and difference rules
Strategies / Strategies / Strategies / Strategies / Strategies
Find slopes of secant lines then relate to slope of tangent line using limits
Define the derivative of a function / Discuss derivatives of functions with sharp turns, vertical tangent lines, and discontinuities / Answer questions.
Incorporate calculators to discuss continuity and differentiability / Administer test over intro to derivatives / Demonstrate constant rule, basic power rule, and sum/difference rules.
Have students relate back to definition of a limit with limits to compare answers with rules.
Assessment
p.112: 1-16 / Assessment
p.113: 17-32 / Assessment
p.114: 39-65 / Assessment
Test / Assessment
p.123: 1-12, 17-28
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
Calculus AB Second Six Weeks
Week 8 10/15/07 to 10/19/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / Professional
Development
Day / 2 – B / 2 – B, 2 – C / 2 – B, 2 – C / 2 – B, 2 - C
CALC / II – A – 1
II – F – 1, 2 / II – A – 2
II – B – 1, 2
II – F – 1, 2 / II – A – 2
II – B – 1, 2
II – F – 1, 2 / II – A – 2
II – B – 1, 2
II – F – 1, 2
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
Professional development day / T.L.W:
Find the derivatives of the sine and cosine function / T.L.W:
Use derivatives to find rates of change / T.L.W:
Use derivatives to find rates of change / T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity
Find the derivatives of the sine and cosine functions
Use derivatives to find rates of change
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages / Text Pages
p. 120 / Text Pages
p. 121 / Text Pages
p. 121 / Text Pages
Quiz
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Linear approximations / Average rate of change
Strategies / Strategies / Strategies / Strategies / Strategies
Derive formulas for derivatives of sine and cosine and apply to various functions / Find equation of tangent and normal lines, points with horizontal tangent lines, apply linear approximations / Compare average rate of change to instantaneous rate of change / Administer quiz
Assessment / Assessment
p.123: 13-16, 29, 30, 41, 47 / Assessment
p.124:43-59 / Assessment
p.124: 61-70
p.126: 81-88 / Assessment
Quiz
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB Second Six Weeks
Week 9 10/22/07 to 10/26/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal / 1 – D
1 – E / 1 – D
1 – E
2 – B / 1 – D
1 – E
2 – B / 2 – B / 1
CALC / II – E – 5 / II – A – 2
II – B – 1
II – C – 2
II – E – 5
II – F – 1, 2 / II – A – 2
II – B – 1
II – C – 2
II – E – 5
II – F – 1, 2 / II – F – 2 / II – F – 1, 2
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Use derivatives to find rates of change / T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity
Find the derivatives of the sine and cosine functions
Use derivatives to find rates of change / T.L.W:
Find the slope of the tangent line to a curve at a point
Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity
Find the derivatives of the sine and cosine functions
Use derivatives to find rates of change / T.L.W:
Find the derivative of functions using the product and quotient rules / T.L.W:
Find the derivative of functions using the product and quotient rules
Find the derivative of trigonometric functions
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages
p.122 / Text Pages
p.161 / Text Pages / Text Pages
p.127-130 / Text Pages
p.131-132
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Free fall / Product and quotient rules / Secant, cosecant, tangent, cotangent
Strategies / Strategies / Strategies / Strategies / Strategies
Discuss free fall formula and apply to various situations (metric and customary) / Review all concepts of differentiation up to this point / Administer test / Use quotient and product rule to find derivatives / Use rules to find derivatives of trig functions other than sine and cosine with product and quotient rules
Assessment
p.125: 71-79 / Assessment
Oral evaluation / Assessment
Teacher made test / Assessment
p.134: 1-20 / Assessment
p.134: 21-56
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB Second Six Weeks
Week 10 10/29/07 to 11/2/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal
CALC / II – F – 1 / II – F – 3 / II – F – 1, 3 / II – F – 1, 3 / II – F – 1, 3
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Find the derivative using the general power rule
Simplify the derivative of a function using algebra / T.L.W:
Find the derivative of a function using the chain rule
Simplify the derivative of a function using algebra / T.L.W:
Find the derivative of trigonometric functions using the chain rule
Simplify the derivative of a function using algebra / T.L.W:
Find the derivative using the general power rule
Simplify the derivative of a function using algebra
Find the derivative of a function using the chain rule
Find the derivative of trigonometric functions using the chain rule / T.L.W:
Find the derivative using the general power rule
Simplify the derivative of a function using algebra
Find the derivative of a function using the chain rule
Find the derivative of trigonometric functions using the chain rule
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages
139-141 / Text Pages
137-138 / Text Pages
142 / Text Pages
137-142 / Text Pages
137-142
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
General power rule / Chain rule
Strategies / Strategies / Strategies / Strategies / Strategies
Find the derivative of functions of the form y = (f(x))n
Quiz on product and quotient rules and trig derivatives / Find the derivative of functions using the chain rule / Find the derivatives of functions of higher power trig functions / Use the chain to find rate of change in application problems / Teacher made quiz on general power rule, chain rule, and trig rules
Assessment
p.143: 7-30
Quiz / Assessment
p.144: 53-62 / Assessment
p.143: 1-6
p.144: 39-52 / Assessment
p.145: 79-91 / Assessment
Quiz
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
Calculus AB Second Six Weeks
Week 11 11/5/07 to 11/9/07
Monday / Tuesday / Wednesday / Thursday / FridayPre Cal
CALC / II – F – 3 / II – F – 1, 2, 3 / II – F – 1, 2, 3 / II – F – 1, 2, 3 / II – E – 3
II – E – 5
Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations / Learner Expectations
T.L.W:
Distinguish between functions written in implicit form and explicit form
Use implicit differentiation for find the derivative of a function / T.L.W:
Distinguish between functions written in implicit form and explicit form
Use implicit differentiation for find the derivative of a function / T.L.W:
Review all derivative rules covered up to this point / T.L.W:
Administer test / T.L.W:
Find a related rate
Use related rates to solve real life problems
Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources / Suggested Resources
Text Pages
146-149 / Text Pages
150 / Text Pages / Text Pages / Text Pages
153-156
Vocabulary / Vocabulary / Vocabulary / Vocabulary / Vocabulary
Implicit functions / Related rate
Strategies / Strategies / Strategies / Strategies / Strategies
Discuss differences between implicit and explicit functions
Find derivatives implicitly / Find 2nd derivatives implicitly being sure to substitute y into the first derivative / Review all derivative rules covered up to this point / Administer test / Find rate of change of functions with 2 or more variables
Assessment
p.151: 1-34 / Assessment
p.151: 35-52 / Assessment / Assessment
Test / Assessment
p.158: 11-21
Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions / Scaffolding Questions
CalculusAB Second Six Weeks