HolcombMath

Monday, June 08, 2009

Intro to Calculus (Class 89)

Lesson Title
Lesson for HW 30 (2): The Derivative Function from a Graphical Perspective

Overview
Today is the last day of regular class! (Even Function!!!!) The main focus is becoming better at sketching the graph of derivative functions when given an original function. Students have the opportunity to continue work in the Library with the computers in order to finish Lesson for HW 30, can work together to finish HW 30, or can play a game in class designed to help them become better derivative function artists.
Textbook Sections
§3.1 (Txt. p. 128) An Introduction to the Derivative: Tangents

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian
f’(x)

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

Key Ideas
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
Key Skills
I can explain what is meant by “derivative function”.
I can determine over what interval a function is differentiable given the graph of the function.
When given four graphs, I can determine if any two represent a function and its derivative function.
I can sketch the graph of the derivative function when given the graph of a function.
I can sketch the graph of a function without using a calculator and then create a graph of the derivative function.
Turn-In (#88)
Nothing to turn in

Handouts
No Handouts Posted

Assignment
Lesson for Homework 30
Homework 30
Workshop 27
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, June 06, 2009

Intro to Calc- Sketching the Derivative of a Function

Here is a GeoGebra dynamic worksheet, Derivatives 2- Sketching the Derivative Function, I created to help with sketching the derivative function.

I think playing the Derivative Matching Game is also a really good tool for getting ready to be able to sketch the graphs of the derivative function.

Also, this video, Sketching the Derivative of a Function, could also be helpful.

Friday, June 05, 2009

Geometry (Class 87)

Lesson Title
Circles (5): Outside or Inside

Overview
The opener today gives students the opportunity to continue their work with the practice problems from Chapter 10- Lesson 2, Lesson 3, and Lesson 4. We then will work to finish our lesson from last class concerning the relationships between the angles of intersecting segments and the arcs which they capture.

Also, as posted previously, students may earn extra credit by studying for the final exam in the following manner:
1) Print a copy of an old test (see links below).
2) Work the problems correctly.
3) Turn in the test on the day of the final-- al of the ones you do.
For each test completed as described above, students will receive 10 points of extra credit (Learning Skills).
Geometry Test 1A
Geometry Test 2A
Geometry Test 3A
Geometry Test 4A
Geometry Test 5A
Geometry Test 6A
Geometry Test 7A
Geometry Test 8A
Geometry Test 9A
Geometry Test 10A
Geometry Test 11A
Geometry Test 12A
Geometry Test 13A

Textbook Sections
§10.4 (Txt. p.621) Other Angle Relationships

Vocabulary
circle
circumference
diameter
radius
chord
secant
tangent
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 an exterior angle of a triangle is equal to the sum of the remote interior angles.
The measure of a inscribed angle is half of the measure of the arc it captures.
If two extended chords intersect at a point outside a circle, then the measure of the angle between these extended chords is equal to half of the difference of the arcs the extended segments capture.
The angle between a tangent and a chord drawn from teh point of tangency is half of the intercepted arc.
The angle between two tangents is half of the difference of the intercepted arcs.
The angle between two intersecting chords is equal to half the sum of the measures of the intercepted arcs.
Key Skills
I can solve problems related to segments which intersect inside, on, or outside of a circle.
Turn-In (#86)
Chapter 10- Lesson 3: Practice 2

Handouts
Chapter 10: Lesson 5- Inside or Outside-- Measuring Angles

Assignment
Chapter 10- Lesson 5: Practice 1 (At the end of the Chapter 10- Lesson 5).
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, June 04, 2009

Geometry Final Exam Review

Below are links to each of the 13 tests we have had this year. You should have corrected copies of each. In order to study for the final, you may earn extra credit by doing the following:
1) Print a test
2) Work the problems correctly
3) Turn it in on the day of the final

For each test for which you do the above, you will receive 10 points of extra credit (Learning Skills Category).
Geometry Test 1A
Geometry Test 2A
Geometry Test 3A
Geometry Test 4A
Geometry Test 5A
Geometry Test 6A
Geometry Test 7A
Geometry Test 8A
Geometry Test 9A
Geometry Test 10A
Geometry Test 11A
Geometry Test 12A
Geometry Test 13A

Intro to Calculus (Class 88)

Lesson Title
Lesson for HW 30 (1): The Derivative Function from a Graphical Perspective
Geogebra Worksheet for the Lesson for Homework 30: The Derivative of a Function
”Derivative Matching Game”.

Overview
Today and Monday’s class are both focused on developing an understanding of the derivative function-- in other words, a function which represents the derivatives of another function for any value of x. In order to develop this concept students will begin from a graphical perspective aided by a dynamic worksheet.
Textbook Sections
§3.1 (Txt. p. 128) An Introduction to the Derivative: Tangents

Vocabulary
derivative function
differentiable

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

Key Ideas
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
Key Skills
I can explain what is meant by “derivative function”.
I can determine over what interval a function is differentiable given the graph of the function.
When given four graphs, I can determine if any two represent a function and its derivative function.
I can sketch the graph of the derivative function when given the graph of a function.
I can sketch the graph of a function without using a calculator and then create a graph of the derivative function.
Turn-In (#87)
HW 29

Handouts
Lesson for Homework 30: The Derivative Function
Homework 30

Assignment
The Lesson for HW 30 and HW 30 are both due the day of the final
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, June 03, 2009

Geometry (Class 86)

Lesson Title
Circles (5): Outside or Inside

Overview
The opener today gives students the opportunity to continue their work with the practice problems from Chapter 10- Lesson 2, Lesson 3, and Lesson 4. We then either finish up Lesson 4 or go straight into working with some other surprising angle relationships resulting from intersecting segments whose point of intersection is either outside or inside the circle.
Textbook Sections
§10.4 (Txt. p.621) Other Angle Relationships

Vocabulary
circle
circumference
diameter
radius
chord
secant
tangent
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 an exterior angle of a triangle is equal to the sum of the remote interior angles.
The measure of a inscribed angle is half of the measure of the arc it captures.
If two extended chords intersect at a point outside a circle, then the measure of the angle between these extended chords is equal to half of the difference of the arcs the extended segments capture.
The angle between a tangent and a chord drawn from teh point of tangency is half of the intercepted arc.
The angle between two tangents is half of the difference of the intercepted arcs.
The angle between two intersecting chords is equal to half the sum of the measures of the intercepted arcs.
Key Skills
I can solve problems related to segments which intersect inside, on, or outside of a circle.
Turn-In (#85)
Chapter 10- Lesson 3: Practice 1

Handouts
Chapter 10: Lesson 5- Inside or Outside-- Measuring Angles

Assignment
Chapter 10- Lesson 3: Practice 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, June 02, 2009

Intro to Calculus (Class 87)

Lesson Title
Lesson for HW 29 (2): Continuity and the Intermediate Value Theorem

Overview
The opener is given over to students to continue their work on Workshop 27. The lesson will focus on finishing up Lesson for HW 29- Continuity and the Intermediate Value Theorem. As time permits, students may begin their work on the Lesson for HW 30 which is computer based.
Textbook Sections
§2.4 (Txt. p.107) Continuity

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 function is continuous if it’s graph can be drawn without lifting the pencil.
In order to analytically determine if a function is continuous at a point, the left-hand and right-hand limit must be equal and the value of the function at the point in question must be equal to this limit.
If a function is continuous on some closed interval, [a,b], then the function takes on every value between f(a) and f(b).
Key Skills
I can explain what it means for a function to be continuous.
I can determine if a function is continuous at a point.
I can determine if a function is continuous on the domain in which it is defined.
I can explain the Intermediate Value Theorem.
I can use the Intermediate Value Theorem to solve problems.
Turn-In (#86)
HW 29 #1-5

Handouts
Monk Problem Solution
HW 29 Continuity and the Intermediate Value Theorem

Assignment
Finish HW 29
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, June 01, 2009

Intro to Calc- The Derivaitve as a Function

Here is the link for the Geogebra Worksheet for the Lesson for Homework 30: The Derivative of a Function

Here is a link for the ”Derivative Matching Game”.

Geometry (Class 85)

Lesson Title
Circles (4): Intersecting Chords

Overview
Students have the opportunity to do their final work on the problems from Chapter 10 Lesson 1 and Chapter 10 Lesson 2 during the first 25 minutes of class. These assignments will then be turned in. The lesson for the day continues with Chapter 10- Lesson 3: Intersecting Chords of a Circle and Chapter 10- Lesson 4: Extended Chords of Circle
Textbook Sections
§10.2 (Txt. p.606) Arcs and Chords

Vocabulary
circle
circumference
diameter
radius
chord
secant
tangent
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
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
In the same circle, or in congruent circles, tow minor arcs are congruent if an only if their corresponding chords are congruent.
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
If one chord is a perpendicular bisector of another, then the first chord is a diameter.
In the same circle, or congruent circles, two chords are congruent if and only if they are equidistant from the center of the circle.
Key Skills
I can use properties of intersecting chords to solve problems.
I can use properties of extended chords to solve problems.
Turn-In (#84)
Chapter 10- Lesson 2 and Lesson 3

Handouts
Chapter 10: Lesson 3- Intersecting Chords
Chapter 10- Lesson 3: Intersecting Chords Practice 1

Assignment
Chapter 10- Lesson 3: Practice
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.

Sunday, May 31, 2009

Intro to Calc- Key Concepts and Key Skills

I have complied a list of the key concepts and a list of key skills for the course. Looking over these list in conjunction with working the previously posted tests should help ensure that you do well on the final. It is a lot of material.

Friday, May 29, 2009

Intro to Calc Tests

Here are links to the tests for the course. You can earn 2 points extra credit (on Homework) for each test you complete and turn in on the day of the final. Yea, 2 points might not seem like a lot, but depending on your current grade, it can move the HW grade up about .2 percent per test. That’s a lot in comparison to the amount of work already done! Oh yea, and it is a really good way to study for the final exam!
Test 1A
Test 2A
Test 3A
Test 4A
Test 5A
Test 6A
Test 7A
Test 8A
Second Semester Mid-Term Part 1A
Second Semester Mid-Term Part 2A

Intro to Calculus (Class 86)

Announcements
Test on Limits this Friday.

Lesson Title
Lesson for HW 29 (1): Continuity and the Intermediate Value Theorem

Overview
Class today will be begin with a puzzle that leads us into a closer inspection of what it means for a function to be continuous and examine an implication of continuity. This implication, the Intermediate Value Theorem, will provide us a new tool which (surprisingly) can be used to help solve the puzzle. During the last 45 minutes of class students will work Test 8 focusing on limits.
Textbook Sections
§2.4 (Txt. p.107) Continuity

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 function is continuous if it’s graph can be drawn without lifting the pencil.
In order to analytically determine if a function is continuous at a point, the left-hand and right-hand limit must be equal and the value of the function at the point in question must be equal to this limit.
If a function is continuous on some closed interval, [a,b], then the function takes on every value between f(a) and f(b).
Key Skills
I can explain what it means for a function to be continuous.
I can determine if a function is continuous at a point.
I can determine if a function is continuous on the domain in which it is defined.
I can explain the Intermediate Value Theorem.
I can use the Intermediate Value Theorem to solve problems.
Turn-In (#85)
WS 27 #1-4

Handouts
Lesson for HW 29
HW 29
Assignment
HW 29 #1-5
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 28, 2009

Geometry (Class 84)

Lesson Title
Circles (4): Intersecting Chords

Overview
The opener today provides time for students to continue working on problems involving central angles, inscribed angles, and tangents. The lesson focuses on the relationships resulting from chords which intersect.
Textbook Sections
§10.2 (Txt. p.606) Arcs and Chords

Vocabulary
circle
circumference
diameter
radius
chord
secant
tangent
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
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
In the same circle, or in congruent circles, tow minor arcs are congruent if an only if their corresponding chords are congruent.
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
If one chord is a perpendicular bisector of another, then the first chord is a diameter.
In the same circle, or congruent circles, two chords are congruent if and only if they are equidistant from the center of the circle.
Key Skills
I can use properties of intersecting chords to solve problems.
Turn-In (#83)
Chapter 10- Lesson 1: Practice 2- ALL

Handouts
Chapter 10: Lesson 3- Intersecting Chords
Chapter 10- Lesson 3: Intersecting Chords Practice 1

Assignment
Work towards finishing the problems at the end of Lessons 1, 2, and 3 for Chapter 10
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 27, 2009

Intro to Calculus (Class 85)

Announcements
Test on Limits this Friday.

Lesson Title
Lesson for HW 28: Who’s the Boss (3)

Overview
Today is a minimum day so we will forgo the opener and finish the lesson for HW 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 (#84)
WS 26 All
HW 28 All but 5b, c

Handouts
Workshop 27

Assignment
WS 27 #1-4
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 26, 2009

Geometry (Class 83)

Lesson Title
Circles (3): Tangents to Circles

Overview
The opener today continues to focus on the application of right triangle trigonometry. The lesson moves students further into the study of the relationships between angles and segments related to circles. Today the focus on lines which are tangent to a circle.
Textbook Sections
§10.1 (Txt. p.595) Tangents to Circles

Vocabulary
circle
circumference
diameter
radius
chord
secant
tangent
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
A line which is tangent to a circle touches the circle in exactly one point.
A radius drawn to the point of tangency is perpendicular to the tangent line.
If two segments from the same exterior point are tangent to a circle, then the segments are congruent.
Key Skills
I can construct a line tangent to a circle.
I can prove use congruent triangles to prove theorems about tangents.
I can use concepts of tangents to solve puzzles.
Turn-In (#82)
Chapter 10- Lesson 1 Practice 1- ALL

Handouts
Chapter 10- Lesson 2: Tangents to Circles

Assignment
Chapter 10- Lesson 1: Practice 2- ALL
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.