HolcombMath

Friday, May 22, 2009

Intro to Calculus (Class 84)

Lesson Title
Lesson for HW 28: Who’s the Boss (2)

Overview
Students begin class today with Workshop 26. Then we will work towards finishing the Lesson for Homework 28.
Textbook Sections
§2.2 (p.85) The Limit of a Function

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Limits involving the x-value going to infinity can often be evaluated by determining which part of the function dominates.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
I can evaluate the limit of a function which involves the x-value approaching infinity.
Turn-In (#83)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
WS 26 All
HW 28 #TBA
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, May 21, 2009

Geometry (Class 82)

Announcements
Test Friday: Right Triangle Trigonometry, Lines

Lesson Title
Circles (1): Inscribed Arcs

Overview
The opener for today is a short problem which requires the students to apply their trigonometric skills. The lesson picks up where we left off last class with our investigation into the relationships between the measures of inscribed angles, central angles, and their arcs. We will finish this lesson and then have time to work a variety of related problems.
Textbook Sections
§10.3 (Txt. p.613) Inscribed Angles

Vocabulary
circle
central angle
arc
arc length
arc angle
inscribed angle
inscribed arc

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
The measure of a central angle is equal to the measure of the arc it insribes.
If a central angle and an inscribed angle inscribe (capture) the same arc, then the measure of the central angle is twice the measure of the inscribed angle.
Key Skills
I can use correct terminology to describe parts of a circle.
I can determine the measures of central angles and inscribed arcs using the relationship between them.
Turn-In (#81)
Test Corrections
Trig. Problems

Handouts
Chapter 10- Lesson 1: Practice 1

Assignment
Chapter 10- Lesson 1 Problems #TBA
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Wednesday, May 20, 2009

Intro to Calculus (Class 83)

Lesson Title
Lesson for HW 27: Know Your Limits (4)

Overview
Students have time during the opener to continue their work on WS 26. The lesson for today, “Who’s the Boss”, focuses on working with limits involving x-values which head to infinity.
Textbook Sections
§2.2 (p.85) The Limit of a Function

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Limits involving the x-value going to infinity can often be evaluated by determining which part of the function dominates.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
I can evaluate the limit of a function which involves the x-value approaching infinity.
Turn-In (#82)
WS 25

Handouts
Lesson for HW 28: Who’s the Boss?

Assignment
WS #26 #1-9
HW 28 #1,2
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Tuesday, May 19, 2009

Geometry (Class 81)

Announcements
Test Friday: Right Triangle Trigonometry, Lines

Lesson Title
Circles (1): Inscribed Arcs

Overview
During the opener today students will have the opportunity to continue their work on the latest trig. problems. Afterwards we will begin our study of circles by investigating the relationship between angles and arcs.
Textbook Sections
§10.3 (Txt. p.613) Inscribed Angles

Vocabulary
circle
central angle
arc
arc length
arc angle
inscribed angle
inscribed arc

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
The measure of a central angle is equal to the measure of the arc it insribes.
If a central angle and an inscribed angle inscribe (capture) the same arc, then the measure of the central angle is twice the measure of the inscribed angle.
Key Skills
I can use correct terminology to describe parts of a circle.
I can determine the measures of central angles and inscribed arcs using the relationship between them.
Turn-In (#80)
Trig. Practice Problems

Handouts
Chapter 9- Lesson 7: Putting Trig. to Work

Assignment
Test Corrections
Trig. Problems
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Monday, May 18, 2009

Intro to Calculus (Class 82)

Lesson Title
Lesson for HW 27: Know Your Limits (3)

Overview
The opener for the class will be used for work time on WS 25. The remaining time will then be used to WS 26. Here is a link for a good site with trig. identities SOS Math Trig. Identities
Textbook Sections
§2.2 (p.85) The Limit of a Function

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
Turn-In (#81)
HW 27

Handouts
Workshop 26

Assignment
WS 26 #TBA
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Friday, May 15, 2009

Geometry (Class 80)

Announcements
Test Friday: Right Triangle Trigonometry, Lines

Lesson Title
Right Triangle Ratios (7)

Overview
The opener today will be used for students to continue working on problems involving the creative use of trigonometry. The rest of the class will be spent working on Test 13 which focuses on these skills.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#79)
Txt. p.585 #1-6, 8-13, 15, 16

Handouts
Chapter 9- Lesson 7.1 More Trig Problems (3)

Assignment
Trig. Practice Problems
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, May 14, 2009

Intro to Calculus (Class 81)

Lesson Title
Lesson for HW 27: Know Your Limits (1)

Overview
Students have an opportunity to further their work on Workshop 25 during the first 30 minutes of class. We will then turn our attention to finishing the lesson for HW 27. During the remaining class time students can continue their work on HW 27.
Textbook Sections
§2.2 (p.85) The Limit of a Function

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
Turn-In (#80)
HW 27 #1-4

Handouts
No Handouts Posted

Assignment
HW 27- Finish It
WS 25-- Note: Problems 8 and 9 are really hard as written. Change them so that you do not have to isolate r, then they are not bad at all and will graph fine, but not on your calculator!
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Wednesday, May 13, 2009

Geometry (Class 79)

Announcements
Test Friday: Right Triangle Trigonometry, Lines

Lesson Title
Right Triangle Ratios (6)

Overview
The opener today again focuses on lines and the coordinates of points on the line. Students will then have an opportunity to continue to develop their ability to use trigonometry to solve problems. As time permits we will begin our study of the relationships between circles, segments, and angles.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#78)
Txt. p.562 #16-19, 31-33, 36-38

Handouts
Chapter 9: Lesson 7- Putting Trig. to Work

Assignment
Txt. p.585 #1-6, 8-13, 15, 16
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Tuesday, May 12, 2009

Intro to Calculus (Class 80)

Lesson Title
Lesson for HW 27: Know Your Limits

Overview
During the fist part of class today students will have the opportunity to continue their work on WS 25. We most likely will do this again on Th. We will then begin our work on our next topic-- Limits. We will develop an understanding of what they are, why we need them, and how to compute them using both a graph and algebra.
Textbook Sections
§2.2 (p.85) The Limit of a Function

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
Turn-In (#79)
Finish HW 26: Problems from “To the Pole and Back”

Handouts
Lesson for HW 27: Know Your Limits
HW 27: Know Your Limits
Assignment
HW 27 #TBA
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Monday, May 11, 2009

Geometry (Class 78)

Lesson Title
Right Triangle Ratios (5)

Overview
The opener for today focuses on equations of lines. Students will then learn how to use their calculator instead of a trig. table to solve problems, Students will then have time to work a new set of problems requiring the creative use of trigonometry. As time permits we will begin our study of the relationship between angles, segments, and circles.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#77)
Trig. Practice Problems

Handouts
Chapter 9: Lesson 6- Using your calculator

Assignment
Txt. p.562 #16-19, 31-33, 36-38
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Saturday, May 09, 2009

Intro to Calc Test 7 Grades Posted

The grades for Test 7 have been posted. Also, you can find a copy and the answers to Test 7B version B here. Go to the bottom of the page and click on “Check Your Answers” to see the solutions.

Friday, May 08, 2009

Intro to Calculus (Class 79)

Lesson Title
Test 7

Overview
Students write Test 7 today focusing on approximating the derivative at a point, approximating the definite integral, interpreting each of these in terms of a given situation, and working with the basics of the polar coordinate system.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
Our work with trigonometry and circular functions gives us the necessary tools for converting between the polar coordinate system and the rectangular (Cartesian) coordinate system.
Key Skills
I can convert polar coordinates into rectangular coordiantes.
I can convert rectangular coordinates into polar coordinates.
I can convert a polar equation into a rectangular (Cartesian) equation.
Turn-In (#78)
Homework 26: To the Pole and Back #TBA

Handouts
Workshop 25

Assignment
Finish HW 26: Problems from “To the Pole and Back”
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, May 07, 2009

Geometry (Class 77)

Lesson Title
Right Triangle Ratios (5)

Overview
The opener for today is to continue to work on the Trig. Practice problems. This will be the last day in class for these. Students may continue to work with their partners outside of class. This assignment is due at the start of class Monday.
The lesson for today focuses on using a calculator instead of a table of values to solve trig. problems.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#76)
No Homework

Handouts
Chapter 9: Lesson 6- Using your calculator

Assignment
Trig. Practice Problems
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Wednesday, May 06, 2009

Intro to Calculus (Class 78)

Lesson Title
To the Pole and Back

Overview
In today’s class we will learn how to convert between polar and rectangular coordinate systems.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
Our work with trigonometry and circular functions gives us the necessary tools for converting between the polar coordinate system and the rectangular (Cartesian) coordinate system.
Key Skills
I can convert polar coordinates into rectangular coordiantes.
I can convert rectangular coordinates into polar coordinates.
I can convert a polar equation into a rectangular (Cartesian) equation.
Turn-In (#77)
The Leaky Balloon

Handouts
Lesson and Homework 26: To the Pole and Back

Assignment
Homework 26: To the Pole and Back #TBA
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Tuesday, May 05, 2009

Geometry (Class 76)

Lesson Title
CST Geometry Part 2

Overview
Students take the second part of the math portion of the CST today. As an opener we will review terminology related to parallel lines as well as the code names and how to use trigonometric ratios.
Textbook Sections
N/A

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

Key Attitudes
Math is about building up understanding one idea at a time.

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#75)
No Homework

Handouts
No Handouts Posted

Assignment
No Homework
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.