HolcombMath

Sunday, March 08, 2009

Intro to Calc- Test 6A with solutions

Here is a copy of Test 6A (mistakenly labeled 7A) with solutions. Test 6A with Solutions

Friday, March 06, 2009

Intro to Calculus (Class 59)

Lesson Title
Circular Functions (12)

Overview
Test Today! After the test students may work on Sangaku 13 or other assignments that they need to finish.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent

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

Key Ideas
An identity is an equation which is true for all values of the variable.
You can determine if an equation is an identity by graphing the two sides of the equation separately. If these are the same graphs, then its an identity.
Key Skills
I can simplify an expression involving trigonometric functions.
I can verify that an trigonometric equation is an identity by using a graphing calculator.
I can prove that an trigonometric equation is an identity by using algebra.
I can solve trigonometric equations including ones which require substitution.
Turn-In (#58)
Finish Workshop 18

Handouts
Sangaku 13

Assignment
Workshop 19
Sangaku 13
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, March 05, 2009

Geometry (Class 57)

Lesson Title
Using Congruent Triangles (3)

Overview
During the opener today students will continue to work on the CST practice. In addition, students will solve another construction puzzle involving circumscribing a triangle. The lesson for the day continues with either finishing our work with using congruent triangles to prove other facts or with our initial work with triangles which are the same shape, but not necessarily the same size-- similar triangles.
Textbook Sections
§4.6 (Txt. p.236) Isosceles, Equilateral, and Right Triangles

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS
AAS
HL

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

Key Ideas
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
Triangles which are the same shape always have some key attributes.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can use congruent triangles to prove other facts.
I can use a straight edge and compass to construct geometric shapes.
Turn-In (#56)
Txt. p. 55 #9-20

Handouts
CST Review

Assignment
Txt. p.258 #1-3, 7-9, 13-15, 22, 23, 37, 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.

Wednesday, March 04, 2009

Intro to Calculus (Class 58)

Announcements
Test Friday focusing on circular functions but will also have some logarithms!

Lesson Title
Circular Functions (11)

Overview
Today’s class continues to focus on working problems involving angles of rotation and their relationship to coordinates. There is a test next class focused on these concepts as well as on logarithms.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent

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

Key Ideas
An identity is an equation which is true for all values of the variable.
You can determine if an equation is an identity by graphing the two sides of the equation separately. If these are the same graphs, then its an identity.
Key Skills
I can simplify an expression involving trigonometric functions.
I can verify that an trigonometric equation is an identity by using a graphing calculator.
I can prove that an trigonometric equation is an identity by using algebra.
I can solve trigonometric equations including ones which require substitution.
Turn-In (#57)
Workshop 18

Handouts
Workshop 19

Assignment
Finish Workshop 18
Workshop 19 #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, March 03, 2009

Geometry (Class 56)

Lesson Title
Using Congruent Triangles (2)

Overview
For the opener today students will continue working on the CST review that was started last class. We will then work towards wrapping up our initial work with using congruent triangles and move towards working with similar triangles.
Textbook Sections
§4.6 (Txt. p.236) Isosceles, Equilateral, and Right Triangles

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS
AAS
HL

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

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can use congruent triangles to prove other facts.
I can use a straight edge and compass to construct geometric shapes.
Turn-In (#55)
Opener: Algebra Word Problems- How does a fish…

Handouts
CST Review

Assignment
Txt. p. 55 #9-20
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, March 02, 2009

Intro to Calculus (Class 57)

Announcements
Test Friday focusing on circular functions but will also have some logarithms!

Lesson Title
Circular Functions (10)

Overview
The first 30 minutes of the class has been set aside for students to put finishing touches on the work that is due today. Students then will work on Workshop 18 as part of the preparation for the Test on Friday which will focus on Circular Functions, but will also contain problems involving logarithms.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent

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

Key Ideas
An identity is an equation which is true for all values of the variable.
You can determine if an equation is an identity by graphing the two sides of the equation separately. If these are the same graphs, then its an identity.
Key Skills
I can simplify an expression involving trigonometric functions.
I can verify that an trigonometric equation is an identity by using a graphing calculator.
I can prove that an trigonometric equation is an identity by using algebra.
I can solve trigonometric equations including ones which require substitution.
Turn-In (#56)
Sangaku 12
Workshop 17
Homework 19
All are due 30 minutes into class-- students may use that 30 minutes to tie up any loose ends.

Handouts
Workshop 18

Assignment
Workshop 18
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, February 26, 2009

Geometry (Class 55)

Lesson Title
CST Review 1

Overview
I will not be in class today. Students have the opportunity to work together to review material for the upcoming CST.
Textbook Sections
N/A

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS
AAS
HL

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

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can use congruent triangles to prove other facts.
I can use a straight edge and compass to construct geometric shapes.
Turn-In (#54)
Txt. p.255 #1-20-- turn in next class when I return.

Handouts
No Handouts Posted

Assignment
Finish the Opener: Algebra Word Problems- How does a fish…
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.

Intro to Calculus (Class 56)

Lesson Title
Circular Functions (9)

Overview
I am not in class today. Students have the class to work towards finishing the following:
Sangaku 12
Workshop 17
Homework 19
All of which will be due at the end of class on Monday. Students will have approximately 30 minutes of class time Monday to tie up any loose ends.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent

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

Key Ideas
An identity is an equation which is true for all values of the variable.
You can determine if an equation is an identity by graphing the two sides of the equation separately. If these are the same graphs, then its an identity.
Key Skills
I can simplify an expression involving trigonometric functions.
I can verify that an trigonometric equation is an identity by using a graphing calculator.
I can prove that an trigonometric equation is an identity by using algebra.
I can solve trigonometric equations including ones which require substitution.
Turn-In (#55)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
Sangaku 12
Workshop 17
Homework 19
All are due 30 minutes into class-- students may use that 30 minutes to tie up any loose ends.
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, February 25, 2009

Geometry (Class 54)

Lesson Title
Using Congruent Triangles (2)

Overview
The opener for today will be a construction puzzle. We will then continue with working with using congruent triangles to prove other facts. As time permits we will start to investigate triangles which are the same shape, but not the same size.
Textbook Sections

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS
AAS
HL

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

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can use congruent triangles to prove other facts.
I can use a straight edge and compass to construct geometric shapes.
Turn-In (#53)
Finish Opener
Txt. p.240 #20-25, 34

Handouts
No Handouts Posted

Assignment
Txt. p.255 #1-20
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, February 24, 2009

Intro to Calculus (Class 55)

Lesson Title
Circular Functions (7)

Overview
The opener for today will be Sangaku 12. We will then have a lesson which focuses on trigonometric expressions, equations
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent

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

Key Ideas
An identity is an equation which is true for all values of the variable.
You can determine if an equation is an identity by graphing the two sides of the equation separately. If these are the same graphs, then its an identity.
Key Skills
I can simplify an expression involving trigonometric functions.
I can verify that an trigonometric equation is an identity by using a graphing calculator.
I can prove that an trigonometric equation is an identity by using algebra.
I can solve trigonometric equations including ones which require substitution.
Turn-In (#54)
Homework 18- Finish it

Handouts
Homework 19
Sangaku 12

Assignment
Due Monday March 2
Sangaku 12
Workshop 17
Homework 19
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, February 23, 2009

Geometry (Class 53)

Lesson Title
Using Congruent Triangles (1)

Overview
The class starts with students practicing their algebra skills of multiplying and factoring polynomials as well as of writing the equation of line given two points or give the slope of the line and one point though which it passes. We then turn our attention to geometry and continue our work with proving triangles congruent and using congruent triangles as the basis for proving other facts.
Textbook Sections
§4.4 (Txt. p. 220) Proving Triangles Congruent

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS
AAS
HL

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

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can use congruent triangles to prove other facts.
I can factor a polynomial equation.
I can write the equation of a line given the locations of two points on the line.
I can write the equation of a line given the slope of the line and the location of one point on the line.
Turn-In (#52)
Test 9 Corrections
Txt. p.239 #8-19, 33

Handouts
Chapter 4- Lesson 4: Proving Triangles Congruent

Assignment
Finish Opener
Txt. p.240 #20-25, 34
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, February 20, 2009

Intro to Calculus (Class 54)

Lesson Title
Circular Functions (7)

Overview
Class starts with students having time to work towards finishing Homework 18. They then will be working on Workshop 17. During the last part of the class students will take Quiz 3 focusing on relating coordinates of points on the circumference of a circle with radius 1 and the central angle whose terminal side passes through the point.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function
sine
cosine
tangent
cosecant
secant
cotangent

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

Key Ideas
Given two points on the circumference of a circle, one of the points can be rotated around the center to match up with the other point in an infinite number of ways.
The location of the point of intersection of the terminal side of a central angle and a circle are related to each other. This relationship is what is meant by the term “circular function”.
The sine of a central angle in the unit circle is defined as the y-coordinate of the point of intersection of the terminal side of the angle and the unit circle.
The cosine of a central angle in the unit circle is defined as the y-coordinate of the point of intersection of the terminal side of the angle and the unit circle.
Key Skills
I can explain what a radian is.
I can find the location of a point on the circumference of a circle resulting from a rotation about the center of the circle using radians.
I can determine the quadrant that a point on the circumference of a circle will end up in as the result of a rotation about the center given in radian.
I can determine the measure of coterminal angles.
If I know the location of the point of intersection of the terminal side of an angle, then I can find the location of the point of intersection of the terminal side of “family members” of this angle by thinking geometrically.
I can translate between what I have learned about circular functions and the definition of the sine and the cosine of a central angle.
Turn-In (#53)
Sangaku 11
Workshop 16

Handouts
Workshop 17

Assignment
Homework 18- Finish it
Workshop 17 #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, February 19, 2009

Geometry (Class 52)

Lesson Title
Proving Triangles Congruent (7)

Overview
The class begins with where we left off last class-- creating problems involving the identification of the correct triangle congruence postulate or theorem to use to prove triangles congruent. Students will then take a short quiz focusing on these skills. Afterwards. depending on the class, we will either investigate when, if ever, SSA can be used to prove two triangles congruent or we will move on to extend our proofs so that we can use congruent triangles as a step to further ideas.
Textbook Sections
§4.4 (Txt. p. 220) Proving Triangles Congruent

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS
AAS
HL

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

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can construct parallel lines.
I can construct the midpoint of a segment.
Turn-In (#51)
Finish Test 9 Follow-Up

Handouts
Chapter 4- Lesson 4: Proving Triangles Congruent

Assignment
Test 9 Corrections
Txt. p.239 #8-19, 33
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, February 18, 2009

Intro to Calculus (Class 53)

Lesson Title
Circular Functions (6)

Overview
Students begin the class today by working to finish Sangaku 11. They then can continue their work on Workshop 16. We will then have a lesson to “level up” on circular functions by connecting what we have been working on to two old friends.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation
circular function

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

Key Ideas
Given two points on the circumference of a circle, one of the points can be rotated around the center to match up with the other point in an infinite number of ways.
The location of the point of intersection of the terminal side of a central angle and a circle are related to each other. This relationship is what is meant by the term “circular function”.
The sine of a central angle in the unit circle is defined as the y-coordinate of the point of intersection of the terminal side of the angle and the unit circle.
The cosine of a central angle in the unit circle is defined as the y-coordinate of the point of intersection of the terminal side of the angle and the unit circle.
Key Skills
I can explain what a radian is.
I can give a mathematical reason for why radians are “better” than degrees.
I can find the location of a point on the circumference of a circle resulting from a rotation about the center of the circle using radians.
I can determine the quadrant that a point on the circumference of a circle will end up in as the result of a rotation about the center given in radian.
I can determine the measure of coterminal angles.
If I know the location of the point of intersection of the terminal side of an angle, then I can find the location of the point of intersection of the terminal side of “family members” of this angle by thinking geometrically.
I can translate between what I have learned about circular functions and the definition of the sine and the cosine of a central angle.
Turn-In (#52)
Finish Workshop 15
Workshop 16 #1,2

Handouts
Homework 18

Assignment
Snagaku 11
Workshop 16
Homework 18 #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, February 17, 2009

Geometry (Class 51)

Lesson Title
Proving Triangles Congruent (6)

Overview
The opener for the day continues with the theme of reviewing multiplying and factoring algebraic expressions. We will then continue our work with proving triangles congruent.
Textbook Sections
§4.4 (Txt. p. 220) Proving Triangles Congruent

Vocabulary
construction
straight edge
arc
radius
center
diameter
adjacent
opposite
included
non-included
SSS
ASA
SAS

Key Attitudes
Math is about being convinced a statement is always true.

Key Ideas
A factor answers the question “How many of these are in this”?
Triangles can be constructed out of various combinations of angles and sides.
Only some combinations of angles and sides guarantee that all triangle created with this combination will be congruent-- the same size and the same shape. Other combinations only guarantee triangles which are the same shape, and some combinations guarantee nothing at all!
When multiplying two expressions, if the bases are the same the exponents need to be added.
Key Skills
I can identify key angle and side combinations which force triangles to be congruent.
I can identify and sequence the reasons which establish triangle congruence.
I can construct parallel lines.
I can construct the midpoint of a segment.
Turn-In (#50)
Txt. p. 224 #14, 15, 19, 20

Handouts
Test 9 Follow-Up

Assignment
Finish Test 9 Follow-Up
Test 9 Corrections
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.