PreCalculus
4.6 Graphs of Other Trig Functions p. 298
Check word problems from yesterday.
p.296 (75, 76)
Discuss that the Tangent function is created by the quotient of Sine over Cosine.
Since the Cos can equal zero, this influences our Domain and also introduces vertical asymptotes to the graph
Show how a sin/cos Unit Circle can easily be used to find the tan values at the main angles.
Note that the Period of Tan(x) is pi... look at how the positive and negative sin/cos values in the 4 quadrants make this so. Remind them that the period of the Tan function is pi ---> half that of the sin/cos -2 pi.
Quickly look at the graph of the tangent and cotangent functions
Discuss how to indicate that the vertical asymptotes are given by x = pi/2 + npi
Discuss the Domain being x not equal to pi/2 + npi
Discuss how the Range is all Reals (pos infinity to neg infinity)
Work p. 305 (3,5,7-10, 29, 67, 69)
Bridge Math
Using Formulas
Convert between Celcius and Faren. in various problems
Work problems from worksheet 01, worksheet 02, and worksheet 03.
Geometry
Finish Constructions worksheet from yesterday.
Focus on constructing
Perpendicular Bisector of line segment
Perp. line thru a given point not on the line
Parallel line thru a point not on the line.
Finish worksheet. Also provide additional related problems from board.
Wednesday, September 30, 2015
Tuesday, September 29, 2015
Tuesday Sept 29 2015
PreCalculus
Finish problems from yesterday. Check selected problems on board.
Applied problems (multi-step and multiple questions. Calculator needed.)
page 296 (74, 75, 76)
Bridge Math
Formulas.
Solve for other variables in formulas. Worksheet.
Solve selected formulas involving exponents.
Geometry
G-CO 12
Continue with constructions -- Bisecting a segment and now an angle.. copying a segment and angle. Perpendicular bisectors.
Worksheet (segments, perp. bisectors)
Worksheet (angles)
Finish problems from yesterday. Check selected problems on board.
Applied problems (multi-step and multiple questions. Calculator needed.)
page 296 (74, 75, 76)
Bridge Math
Formulas.
Solve for other variables in formulas. Worksheet.
Solve selected formulas involving exponents.
Geometry
G-CO 12
Continue with constructions -- Bisecting a segment and now an angle.. copying a segment and angle. Perpendicular bisectors.
Worksheet (segments, perp. bisectors)
Worksheet (angles)
Monday, September 28, 2015
Monday Sept 28 2015
PreCalculus
warm up Solve an exponential equation and a logarithmic equation (CH03)
4.5 Basic Sine/Cosine Functions p.287
p. 288 Locate Max/min/intercepts for sin/cos in radians Note the Period is 2*pi
Note general formula/equation for sin/cos : y = asin(bx - c) + d
Note/define a,b,c,d in general equation:
Amplitude p.289, specific period = 2*pi / b, Horizontal translation interval p.292
Work 1 - 50 p.294/295
Bridge Math
W-SM-05
Manipulate exponents and formulas with exponents
Exponents Handout PDF
Worksheet
Geometry
G-CO-10
Median of Triangle: What is it?
Note: There are several "breaks" in the video. But no break-dancing.
Construction : Median of a Triangle
Woksheet :Median and Centroid constructions
Proof: Triangle Medians all meet at a common point (centroid)
Homework: watch informal proof (Triangle Medians and Centroid), copy down diagrams and work, turn in for quiz grade tomorrow.
warm up Solve an exponential equation and a logarithmic equation (CH03)
4.5 Basic Sine/Cosine Functions p.287
p. 288 Locate Max/min/intercepts for sin/cos in radians Note the Period is 2*pi
Note general formula/equation for sin/cos : y = asin(bx - c) + d
Note/define a,b,c,d in general equation:
Amplitude p.289, specific period = 2*pi / b, Horizontal translation interval p.292
Work 1 - 50 p.294/295
Bridge Math
W-SM-05
Manipulate exponents and formulas with exponents
Exponents Handout PDF
Worksheet
Geometry
G-CO-10
Median of Triangle: What is it?
Note: There are several "breaks" in the video. But no break-dancing.
Construction : Median of a Triangle
Woksheet :Median and Centroid constructions
Proof: Triangle Medians all meet at a common point (centroid)
Homework: watch informal proof (Triangle Medians and Centroid), copy down diagrams and work, turn in for quiz grade tomorrow.
Thursday, September 24, 2015
Thursday Sept 24 2015
PreCalculus
Warm-up p. 276 # 57
4.4 Trig Functions of Any Angle p. 278
Discuss trig functions of unit circle vs. non-unit circle
Sin x = y/r, etc...
Notes: chart page 278, pos/neg of trig functions in each quadrant
Def. Reference Angle
Work through examples 1 - 4
Work 1-4, 45 - 50 p. 284/285
Bridge Math
Work examples (after pausing video) then check...
work problems from worksheet:
Worksheet
Geometry
G-CO-10 Prove Properties of Triangles:
Work through following videos, pausing and discussing steps
Warm-up p. 276 # 57
4.4 Trig Functions of Any Angle p. 278
Discuss trig functions of unit circle vs. non-unit circle
Sin x = y/r, etc...
Notes: chart page 278, pos/neg of trig functions in each quadrant
Def. Reference Angle
Work through examples 1 - 4
Work 1-4, 45 - 50 p. 284/285
Bridge Math
Work examples (after pausing video) then check...
work problems from worksheet:
Worksheet
Geometry
G-CO-10 Prove Properties of Triangles:
Work through following videos, pausing and discussing steps
Wednesday, September 23, 2015
Wednesday Sept 23 2015
Precalculus
Continue from Monday. Work and check the following applied problems on
Text p. 276( 55, 57, 58, 59, 63)
Bridge Math
Watch and take notes on what defines an irratonal number... how they are used, and graphical visualizations of them.
Geometry
Parallel Line Proofs
3.3 p. 155
Define Postulate, Axiom, Theorem
Corresponding Angles postulate p. 157
Rework similar theorem and check
Rework similar theorem
Work problems from video below, pause, then check.
Work p. 161 37-44
p.165 18 -24
Continue from Monday. Work and check the following applied problems on
Text p. 276( 55, 57, 58, 59, 63)
Bridge Math
Watch and take notes on what defines an irratonal number... how they are used, and graphical visualizations of them.
Geometry
Parallel Line Proofs
3.3 p. 155
Define Postulate, Axiom, Theorem
Corresponding Angles postulate p. 157
Rework similar theorem and check
Rework similar theorem
Work problems from video below, pause, then check.
Work p. 161 37-44
p.165 18 -24
Tuesday, September 22, 2015
Tuesday September 22 2015
Note: 80% of classes gone due to LMU field trip and other absences.
Classes work on finishing assignments from previous day.
SSmith
Classes work on finishing assignments from previous day.
SSmith
Monday, September 21, 2015
Monday Sept 21 2015
PreCalculus
Work through HW problem 59 p.265
Trigonometry of the Unit Circle
Define sin, cos, tan and their inverses.
SOH CAH TOA
Show how to find opposite, adjacent, and tangent sides of triangle.
Work through Examples 1 - 3, 6, 7)
Work 1-7, 17 - 27 ODD
Bridge Math
M-SG
Graphically solve systems of equations
Work problems from overhead using TI Inspire's to solve a system of linear equations graphically.
Problems
Geometry
8.4 The Side-Splitting Theorem (Triangle Parallel Theorem. p.525
Previously partially covered in previous lesson - work thru Examples 1, 2, Work and check p. 528 (6.7.8. 13 - 17)
Work Problems p.531 (39) p. 523 (35-38)
Work through HW problem 59 p.265
Trigonometry of the Unit Circle
Define sin, cos, tan and their inverses.
SOH CAH TOA
Show how to find opposite, adjacent, and tangent sides of triangle.
Work through Examples 1 - 3, 6, 7)
Work 1-7, 17 - 27 ODD
Bridge Math
M-SG
Graphically solve systems of equations
Work problems from overhead using TI Inspire's to solve a system of linear equations graphically.
Problems
Geometry
8.4 The Side-Splitting Theorem (Triangle Parallel Theorem. p.525
Previously partially covered in previous lesson - work thru Examples 1, 2, Work and check p. 528 (6.7.8. 13 - 17)
Work Problems p.531 (39) p. 523 (35-38)
Friday, September 18, 2015
Friday Sept 18 2015
PreCalculus
4.2 Unit Circle p. 259
Complete blank unit circle handout with assistance of video.
Define sine, cosine, tangent function in terms of unit circle
Quick geometry review of special triangles (45-45-90 and 30-60-90 triangle side length relationships)
HW p. 264 1 - 39 ODD
Bridge Math
Perimeter and Area of complex figures handouts
Geometry
Perimeter and Area of Complex figures handout
4.2 Unit Circle p. 259
Complete blank unit circle handout with assistance of video.
Define sine, cosine, tangent function in terms of unit circle
Quick geometry review of special triangles (45-45-90 and 30-60-90 triangle side length relationships)
HW p. 264 1 - 39 ODD
Bridge Math
Perimeter and Area of complex figures handouts
Geometry
Perimeter and Area of Complex figures handout
Thursday, September 17, 2015
Thursday Sept 17 2015
PreCalculus
4.1 Radian and Degree Measure p. 248
notes from p. 248 - 254
Examples 6 and 7 p. 254
HW p. 255 (1-59 ODD)
Bridge Math
Solve word problems involving scientific notation
Geometry
Solve word problems involving similar figures + review of prior concepts.
4.1 Radian and Degree Measure p. 248
notes from p. 248 - 254
Examples 6 and 7 p. 254
HW p. 255 (1-59 ODD)
Bridge Math
Solve word problems involving scientific notation
Geometry
Solve word problems involving similar figures + review of prior concepts.
Wednesday, September 16, 2015
Wednesday, Sept 16 2015
PreCalculus
Quiz
Page 244 15-20
CH 4.1 Radia Measure p.248
Bridge Math
Scientific Notation
Operations in Sci Not.
Begin Word Problems
Geometry
Similar Triangles
Continue solving for unknown lengths given similar triangles
Focus on word problems and short task style problems.
Quiz
Page 244 15-20
CH 4.1 Radia Measure p.248
Bridge Math
Scientific Notation
Operations in Sci Not.
Begin Word Problems
Geometry
Similar Triangles
Continue solving for unknown lengths given similar triangles
Focus on word problems and short task style problems.
Tuesday, September 15, 2015
Tuesday, Sept 15 2015
PreCalculus
Solving logarithmic and exponential equations - real life problems
Bridge Math
Scientific Notation : adding, subtracting
Work problems from selected worksheets
Geometry
Similar Triangles
Work problems from board
HW p. 528 (13-25)
Solving logarithmic and exponential equations - real life problems
Bridge Math
Scientific Notation : adding, subtracting
Work problems from selected worksheets
Geometry
Similar Triangles
Work problems from board
HW p. 528 (13-25)
Monday, Sept 14 2015
PreCalculus
Logarithmic and Exponential Equations
Solving more complex equations
Bridge Math
Scientific Notation
multiplication and division
Geometry
Similar Triangles p. 517
Congruency vs. Similarity
Work problems from board
HW p. 524 (39-42; 48 -51)
Logarithmic and Exponential Equations
Solving more complex equations
Bridge Math
Scientific Notation
multiplication and division
Geometry
Similar Triangles p. 517
Congruency vs. Similarity
Work problems from board
HW p. 524 (39-42; 48 -51)
Friday, September 11, 2015
Friday, September 11, 2015
In progress...
PreCalculus
p.217 graphs, equations into notes, Work through examples 1-4.
Bridge Math
Intro to Scientific Notations
Geometry
PreCalculus
p.217 graphs, equations into notes, Work through examples 1-4.
Bridge Math
Intro to Scientific Notations
Geometry
Thursday, September 10, 2015
Thursday September 10, 2015
In progress...
PreCalculus
p.214 73-87 ODD, p.116 ( look at Example 10 p.195), problems from board.
Work through problems and discuss, correct, etc.
Bridge Math
Solving equations with radical expressions
Geometry
Solve word problems involving Special Triangles (30,60,90 and 45,45,90 Triangles)
PreCalculus
p.214 73-87 ODD, p.116 ( look at Example 10 p.195), problems from board.
Work through problems and discuss, correct, etc.
Bridge Math
Solving equations with radical expressions
Geometry
Solve word problems involving Special Triangles (30,60,90 and 45,45,90 Triangles)
Wednesday, September 9, 2015
Wednesday Sept 09 2015
PreCalculus
2 handouts - solving exponential equations & solving logarithm equations
Work through problems solving various kinds of equations. Check answers.
Bridge Math
2 worksheets - Simplifying rational expreassions & operations with rational expressions
Geometry
2 Handouts - Using the Midpoint Formula and the Distance Formula
2 handouts - solving exponential equations & solving logarithm equations
Work through problems solving various kinds of equations. Check answers.
Bridge Math
2 worksheets - Simplifying rational expreassions & operations with rational expressions
Geometry
2 Handouts - Using the Midpoint Formula and the Distance Formula
Tuesday, September 8, 2015
Tuesday Sept 08 2015
PreCalculus
3.4 Solving Exponential and Logarithmic Equations (p.206)
Properties page 206
Examples 1 - 7 p.206-209
Page 213 (17 - 37ODD 38-45 all)
Bridge Math
Operations involving Radical expressions (-, +, mult, div)
Simplify and solve expressions involving radicals ie. square roots.
Students work problems from overhead
Note: review rationalizing denominator
Geometry
5.5 Special Triangles (p.331)
illustrate the relationships between side length in 45-45-90 triangles and 30-60-90 triangles.
Work several examples of 45-45-90 triangles via Pythagoraean Theorem. Show how the hypotenuse is always SQRT(2) times the leg length.
Work several 30-60-90 problems. Work on how to remember the relationships.
p.335 (5 - 33; 44, 45)
3.4 Solving Exponential and Logarithmic Equations (p.206)
Properties page 206
Examples 1 - 7 p.206-209
Page 213 (17 - 37ODD 38-45 all)
Bridge Math
Operations involving Radical expressions (-, +, mult, div)
Simplify and solve expressions involving radicals ie. square roots.
Students work problems from overhead
Note: review rationalizing denominator
Geometry
5.5 Special Triangles (p.331)
illustrate the relationships between side length in 45-45-90 triangles and 30-60-90 triangles.
Work several examples of 45-45-90 triangles via Pythagoraean Theorem. Show how the hypotenuse is always SQRT(2) times the leg length.
Work several 30-60-90 problems. Work on how to remember the relationships.
p.335 (5 - 33; 44, 45)
Friday, September 4, 2015
Friday Sep 04 2015
PreCalculus
Logarithm and Exponential Functions
Continue learning Log properties and using in problems p. 188 - 201
Example 8 p. 192
Graphs of log functions p. 190 - 191
Example 10, 11 p. 184
HW p. 203 (9, 15, 23-37ODD) + videos below
Bridge Math
Adding and subtracting, multiplying and dividing rational expressions
Review meaning of rational number/expression (fractions)
review multiplying and adding rational numbers
Relate those examples to examples with rational expressions (simplify after factoring, etc)
Work problems from the following worksheets: Mult. & Div Add & Subt.
Geometry
Pythagorean word problems
Work Problems from p.327-329 and from this: PDF
Logarithm and Exponential Functions
Continue learning Log properties and using in problems p. 188 - 201
Example 8 p. 192
Graphs of log functions p. 190 - 191
Example 10, 11 p. 184
HW p. 203 (9, 15, 23-37ODD) + videos below
Bridge Math
Adding and subtracting, multiplying and dividing rational expressions
Review meaning of rational number/expression (fractions)
review multiplying and adding rational numbers
Relate those examples to examples with rational expressions (simplify after factoring, etc)
Work problems from the following worksheets: Mult. & Div Add & Subt.
Geometry
Pythagorean word problems
Work Problems from p.327-329 and from this: PDF
Thursday, September 3, 2015
Thursday Sep 03 2015
PreCalculus
FIre drill and pictures day. Since we are studying solving equations involving the natural number, e, and logarithms, that we learn more about e and it's properties.
Bridge Math
(GM)
Solving Quadratic equations in standard for by graphing.
Note: some equations aren't in standard form. Work examples were you algebraically put the epression in standard form.
Sketch graph, and locate the zeros of each equation...
Problems used to solve graphically: PDF
Geometry
Warm Up p. 319 #33, 34, 35 (Circle word problems)
5.4 The Pythagorean Theorem p. 321
Notes p. 323 - 325
Ladder problem p.323
Classwork p. 323 14-33
FIre drill and pictures day. Since we are studying solving equations involving the natural number, e, and logarithms, that we learn more about e and it's properties.
Bridge Math
(GM)
Solving Quadratic equations in standard for by graphing.
Note: some equations aren't in standard form. Work examples were you algebraically put the epression in standard form.
Sketch graph, and locate the zeros of each equation...
Problems used to solve graphically: PDF
Geometry
Warm Up p. 319 #33, 34, 35 (Circle word problems)
5.4 The Pythagorean Theorem p. 321
Notes p. 323 - 325
Ladder problem p.323
Classwork p. 323 14-33
Wednesday, September 2, 2015
Wednesday Sep 02 2015
PreCalculus
3.1 Exponential and Logarithmic Functions p. 175
Start with exponential function 2^x = 17. How do we get the x "out" of the exponent area and solve??
Enter Exponential and Exp. Functions. They are Inverse Functions and thus "undo" one another. So the log or ln functions can be used to "undo" an exponential function and solve for x.
Homework:
Bridge Math
Repeat Tuesday's lesson since class was ended so students could sign up for TN Promise
Geometry
GM
p310 46, 47 for Warmup -- determine pattern for sidle lengths and Max area for triangles, Parall.
5.3 Circumference and Area of Circle p. 314
Define Circumference/Area of Circle
Classwork: p.317 (8-29)
Homework Below:
3.1 Exponential and Logarithmic Functions p. 175
Start with exponential function 2^x = 17. How do we get the x "out" of the exponent area and solve??
Enter Exponential and Exp. Functions. They are Inverse Functions and thus "undo" one another. So the log or ln functions can be used to "undo" an exponential function and solve for x.
Homework:
Bridge Math
Repeat Tuesday's lesson since class was ended so students could sign up for TN Promise
Geometry
GM
p310 46, 47 for Warmup -- determine pattern for sidle lengths and Max area for triangles, Parall.
5.3 Circumference and Area of Circle p. 314
Define Circumference/Area of Circle
Classwork: p.317 (8-29)
Homework Below:
Tuesday, September 1, 2015
Tuesday Sep 01 2015
PreCalculus
Work review problems for Quiz
Work two examples- Factorization of Polynomial Function: One with all Real Solutions, One with Complex Solutions & One Real Solution
Bridge Math
W-GM 2(Graphing Mathematics)
Graphing Quadratics...
Watch Intro to Quadratics video (standard and vertex form)
Work problems from overhead - Problems ( PDF )
Note: Class was stopped just after video as students were signed up for TN Promise
Geometry
Area of Triangles, Trapezoids and Parallelograms p.303
Warm up p.301 # 39
Work/check/correct
Copy formulas for area p. 303 - 306
Discuss Altitudes for the various figures and how it plays into area
Show that a triangle is half a rectangle thus 1/2 the area...
Show a trapezoid has two bases so you have to average them...
Work area problems with each
problems p. 308/309 (10 - 34)
word problems as warm up tomorrow
Work review problems for Quiz
Work two examples- Factorization of Polynomial Function: One with all Real Solutions, One with Complex Solutions & One Real Solution
Bridge Math
W-GM 2(Graphing Mathematics)
Graphing Quadratics...
Watch Intro to Quadratics video (standard and vertex form)
Work problems from overhead - Problems ( PDF )
Note: Class was stopped just after video as students were signed up for TN Promise
Geometry
Area of Triangles, Trapezoids and Parallelograms p.303
Warm up p.301 # 39
Work/check/correct
Copy formulas for area p. 303 - 306
Discuss Altitudes for the various figures and how it plays into area
Show that a triangle is half a rectangle thus 1/2 the area...
Show a trapezoid has two bases so you have to average them...
Work area problems with each
problems p. 308/309 (10 - 34)
word problems as warm up tomorrow
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