HolcombMath

Friday, January 30, 2009

Geometry (Class 46)

Lesson Title
Proving Triangles Congruent (2)

Overview
During the opener for today’s class students have the opportunity to analyze, and make corrections to, two “student” proofs from the first semester final. The lesson for the day focuses on proving triangles congruent by identifying angle and side combinations that force congruence: SSS, SAS, ASA
Textbook Sections
§4.3 (Txt. p.212) Proving Triangles Congruent

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

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

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!
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 a triangle given given two sides and a non-included angle (SSA).

I can construct parallel lines.
I can construct the midpoint of a segment.
I can construct a triangle given the lengths of its three sides (SSS).
I can construct a triangle given its three angles (AAA).
I can construct a triangle given two adjacent sides and an included angle (SAS).
I can construct a triangle given two angles and the included side (ASA)
I can construct a triangle given two angles and the non-included side (AAS).
I can construct parallel lines.
I can construct the midpoint of a segment.
I can construct a triangle given the lengths of its three sides (SSS).
I can construct a triangle given its three angles (AAA).
I can construct a triangle given two adjacent sides and an included angle (SAS).
I can construct a triangle given two angles and the included side (ASA)
I can construct a triangle given two angles and the non-included side (AAS).
Turn-In (#45)
Txt. p.298 #6-20

Handouts
Chapter 4- Lesson 3: Proving Triangles Congruent

Assignment
Final Exam Free Response Corrections
Txt. p.298 #21-25, 42-46
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, January 29, 2009

Intro to Calculus (Class 47)

Lesson Title
Circular Functions (2)

Overview
The warm-up for today is Sangaku 9. Our lesson will continue working with rotations of points on the circumference of a circle about the center.
Textbook Sections
N/A

Vocabulary
radian
central angle
terminal side
circumference
rotation

Key Attitudes
Math is about connecting ideas.

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.
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.
Turn-In (#46)
Homework 16 #1-7

Handouts
Homework 16

Assignment
Homework 16: Finish it.
Workshop 13 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, January 28, 2009

Geometry (Class 45)

Announcements
Test Wed. 12/17 focusing on proving lines parallel.

Lesson Title
Proving Triangles Congruent (1)

Overview
The opener for the class today is a construction puzzle requiring the ability to construct parallel lines and find the midpoints of segments. The lesson continues with the construction theme by practicing the construction of triangles given various pieces of a triangle: SSS, SAS, ASA, AAS, AAA, SSA. Some of these combinations result in a “fixed” triangle while other combinations allow the triangle to be altered while the initial conditions are still being met.
Textbook Sections
§4.3 (Txt. p.212) Proving Triangles Congruent

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

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

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!
Key Skills
I can construct parallel lines.
I can construct the midpoint of a segment.
I can construct a triangle given the lengths of its three sides (SSS).
I can construct a triangle given its three angles (AAA).
I can construct a triangle given two adjacent sides and an included angle (SAS).
I can construct a triangle given two angles and the included side (ASA)
I can construct a triangle given two angles and the non-included side (AAS).
I can construct a triangle given given two sides and a non-included angle (SSA).

Turn-In (#45)
§ (Txt. p.)

Handouts
No Handouts Posted

Assignment
Txt. p.298 #6-20
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.

Saturday, January 17, 2009

Intro to Calculus (Class 44)

Lesson Title
Final Exam Preparation

Overview
Today’s class is the last before the semester final. Students will have the opportunity to begin work on Sangaku 8, but this will not be due until after the final exam-- studying for exams can be tedious and I wanted something to help you keep minds fresh. During the class students will be able to continue their reworking material from the semester.
Textbook Sections

Vocabulary
exponent
base
negative exponent
discrete growth
continuous growth
e
limit
asymptote

Key Attitudes
Math is about connecting ideas.

Key Ideas
There are two types of questions we can ask concerning exponential: 1) Given the number of growth cycles, determine the quantity; 2) Given the quantity, determine the number of growth cycles. These questions are inverses of each other.
A logarithm is an exponential equation in disguise.
Problems involving logarithms can be solved by first translating the problem into one invovling exponents and then solving this exponent problem.
There are three fundamental properties of logarithms: the multiplication property, the division property, and the power property.
Key Skills
I can explain the meaning of a logarithm in both mathematical terms and real world situations.
I can solve problems which involve logarithms by translating them into exponent problems.
I can justify and use the multiplication property of logarithms.
I can justify and use the division property of logarithms.
I can justify and use the power property of logarithms.
Turn-In (#43)
Workshop 12

Handouts
Sangaku 8

Assignment
Work the problems you missed from previous tests. Fresh copies of the tests can be found here:
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, January 16, 2009

Intro to Calculus (Class 43)

Lesson Title
Final Exam Preparation

Overview
Today’s class is the last before the semester final. Students will have the opportunity to begin work on Sangaku 8, but this will not be due until after the final exam-- studying for exams can be tedious and I wanted something to help you keep minds fresh. During the class students will be able to continue their reworking material from the semester.
Textbook Sections

Vocabulary
exponent
base
negative exponent
discrete growth
continuous growth
e
limit
asymptote

Key Attitudes
Math is about connecting ideas.

Key Ideas
There are two types of questions we can ask concerning exponential: 1) Given the number of growth cycles, determine the quantity; 2) Given the quantity, determine the number of growth cycles. These questions are inverses of each other.
A logarithm is an exponential equation in disguise.
Problems involving logarithms can be solved by first translating the problem into one invovling exponents and then solving this exponent problem.
There are three fundamental properties of logarithms: the multiplication property, the division property, and the power property.
Key Skills
I can explain the meaning of a logarithm in both mathematical terms and real world situations.
I can solve problems which involve logarithms by translating them into exponent problems.
I can justify and use the multiplication property of logarithms.
I can justify and use the division property of logarithms.
I can justify and use the power property of logarithms.
Turn-In (#43)
Workshop 12

Handouts
No Handouts Posted

Assignment
Work the problems you missed from previous tests. Fresh copies of the tests can be found here:
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, January 15, 2009

Intro to Calc First Semester Tests

A number of students have requested clean copies of the tests from the first semester to rework as part of getting ready for the final. Here they are:
Quiz 1
Test 1
Test 2
Test 3
Test 4
Test 5

Geometry (Class 43)

Announcements
Test Wed. 12/17 focusing on proving lines parallel.

Lesson Title
Constructions 4

Overview
The warm-up for the day is the second construction puzzle. Our lesson focuses on using angles and segments to construct triangles.
Textbook Sections
§5.5 (txt. p.295) Inequalities in One Triangle

Vocabulary
construction
straight edge
arc
radius
center
diameter

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

Key Ideas
A straight edge and compass can be used to create geometric figures.
A compass is used to measuring lengths by making circles and arcs.
Some parts of a construction can be places wherever you want, while others have to be determined.
If you want a line to be in a specific location, then you have to have two points that it goes through. These points can be created by the intersection of two lines, two arcs, or a line and an arc.
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!

Key Skills
I can construct a triangle given a side and the two adjacent angles (ASA).
I can construct a triangle given two sides and the included angle (SAS).
I can copy a triangle.
I can construct a triangle given two sides and the non-included angle (SSA)
Turn-In (#42)
Constructions 3.7
Txt. p.175 #7-9, 13-16, 21, 22, 25, 26, 32, 33, 38, 39

Handouts
Constructions 4

Assignment
Constructions 4
Txt. p.175 #7-9, 13-16, 21, 22, 25, 26, 32, 33, 38, 39 (For B3 and B4 Only)
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, January 14, 2009

Intro to Calculus (Class 43)

Lesson Title
Exponents and Logarithms (10)

Overview
We will start the class today with sharing approaches and results to Sangaku 7. If time permits, and students are willing, we can start working on Sangaku 8. All remaining time will be used to finish workshop 12 as well as identify and rework problems from the past in preparation for the final exam.
Textbook Sections
N/A

Vocabulary
exponent
base
negative exponent
discrete growth
continuous growth
e
limit
asymptote

Key Attitudes
Math is about connecting ideas.

Key Ideas
There are two types of questions we can ask concerning exponential: 1) Given the number of growth cycles, determine the quantity; 2) Given the quantity, determine the number of growth cycles. These questions are inverses of each other.
A logarithm is an exponential equation in disguise.
Problems involving logarithms can be solved by first translating the problem into one invovling exponents and then solving this exponent problem.
There are three fundamental properties of logarithms: the multiplication property, the division property, and the power property.
Key Skills
I can explain the meaning of a logarithm in both mathematical terms and real world situations.
I can solve problems which involve logarithms by translating them into exponent problems.
I can justify and use the multiplication property of logarithms.
I can justify and use the division property of logarithms.
I can justify and use the power property of logarithms.
Turn-In (#42)
Workshop 12
Review past Tests, Homeworks, and Workshops to collect important problems to study.

Handouts
No Handouts Posted

Assignment
Workshop 12
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, January 13, 2009

Geometry (Class 42)

Announcements
Test Wed. 12/17 focusing on proving lines parallel.

Lesson Title
Constructions 3.7

Overview
The warm-up for the day asks students to figure out a way to construct a figure. The lesson for the day continues to focus on constructing triangles given using the lengths of three segments. As time permits we will begin to investigate constructing triangles using combinations of angles and sides.
Textbook Sections
§5.5 (txt. p.295) Inequalities in One Triangle

Vocabulary
construction
straight edge
arc
radius
center
diameter

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

Key Ideas
A straight edge and compass can be used to create geometric figures.
A compass is used to measuring lengths by making circles and arcs.
Some parts of a construction can be places wherever you want, while others have to be determined.
If you want a line to be in a specific location, then you have to have two points that it goes through. These points can be created by the intersection of two lines, two arcs, or a line and an arc.
It is not possible to construct a triangle out of just any three line segments!
Key Skills
I can construct a triangle from three line segments.
I can determine if it is possible to construct a triangle when given three line segments, or the lengths of three line segments.
I can determine the possible lengths for the third side of a triangle when given the lengths of two of the triangles sides.
I can determine if a triangle will be acute, right, or obtuse based on the lengths of the sides of the triangle.
I can determine the location of the smallest or the location of the largest angle when given the lengths of the sides of a triangle.
Turn-In (#41)
Finish Constructions 3.5

Handouts
Constructions 3.7
Geometry Key Concepts Fall 2008/2009
Geometry Key Skills Fall 2008/2009

Assignment
Constructions 3.7
Txt. p.175 #7-9, 13-16, 21, 22, 25, 26, 32, 33, 38, 39

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, January 12, 2009

Intro to Calculus (Class 42)

Lesson Title
Exponents and Logarithms (9)

Overview
Students will have time during the warm-up today to further their work on Sangaku 7. This will be due next meeting
Textbook Sections
N/A

Vocabulary
exponent
base
negative exponent
discrete growth
continuous growth
e
limit
asymptote

Key Attitudes
Math is about connecting ideas.

Key Ideas
There are two types of questions we can ask concerning exponential: 1) Given the number of growth cycles, determine the quantity; 2) Given the quantity, determine the number of growth cycles. These questions are inverses of each other.
A logarithm is an exponential equation in disguise.
Problems involving logarithms can be solved by first translating the problem into one invovling exponents and then solving this exponent problem.
There are three fundamental properties of logarithms: the multiplication property, the division property, and the power property.
Key Skills
I can explain the meaning of a logarithm in both mathematical terms and real world situations.
I can solve problems which involve logarithms by translating them into exponent problems.
I can justify and use the multiplication property of logarithms.
I can justify and use the division property of logarithms.
I can justify and use the power property of logarithms.
Turn-In (#41)
HW 15

Handouts
Workshop 12
I2C Key Concepts Fall 2008/2009
I2C Key Skills Fall 2008/2009

Assignment
Workshop 12
Review past Tests, Homeworks, and Workshops to collect important problems to study.
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, January 09, 2009

Geometry (Class 41)

Announcements
Test Wed. 12/17 focusing on proving lines parallel.

Lesson Title
Constructions 3.5

Overview
The warm-up today asks students to determine the needed length for a missing side, or sides, of a triangle in order for the triangle to turn out to be a specific type. For instance, if two sides of a triangle were 3 cm and 5 cm, what could be the length of the third side so that the triangle was a right triangle?
The lesson for today will focus on developing student’s problem solving skills.
Textbook Sections
§5.5 (txt. p.295) Inequalities in One Triangle

Vocabulary
construction
straight edge
arc
radius
center
diameter

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

Key Ideas
A straight edge and compass can be used to create geometric figures.
A compass is used to measuring lengths by making circles and arcs.
Some parts of a construction can be places wherever you want, while others have to be determined.
If you want a line to be in a specific location, then you have to have two points that it goes through. These points can be created by the intersection of two lines, two arcs, or a line and an arc.
It is not possible to construct a triangle out of just any three line segments!
Key Skills
I can construct a triangle from three line segmetns.
I can determine if it is possible to construct a triangle when given three line segments, or the lengths of three line segments.
I can determine the possible lengths for the third side of a triangle when given the lengths of two of the triangles sides.
Turn-In (#40)
Finish “Constructions 3”
Chapter 3 Practice: Proving Lines Parallel All

Handouts
Constructions 3.5

Assignment
Finish Constructions 3.5
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, January 08, 2009

Intro to Calculus (Class 41)

Lesson Title
Exponents and Logarithms (8)

Overview
The warm-up for today is Sangaku 7. The lesson will focus on extending our understanding of logarithms to include some general properties concerning the multiplication, division, and exponentiation of expressions involving logarithms.
Textbook Sections
N.A

Vocabulary
exponent
base
negative exponent
discrete growth
continuous growth
e
limit
asymptote

Key Attitudes
Math is about thinking creatively.

Key Ideas
There are two types of questions we can ask concerning exponential: 1) Given the number of growth cycles, determine the quantity; 2) Given the quantity, determine the number of growth cycles. These questions are inverses of each other.
A logarithm is an exponential equation in disguise.
Problems involving logarithms can be solved by first translating the problem into one invovling exponents and then solving this exponent problem.
Key Skills
I can explain the meaning of a logarithm in both mathematical terms and real world situations.
I can solve problems which involve logarithms by translating them into exponent problems.
Turn-In (#40)
HW 15 #1-3

Handouts
Sangaku 7

Assignment
HW 15
Sangaku 7 is not due next class-- it will be due the following class.
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, January 07, 2009

Geometry (Class 40)

Announcements
Test Wed. 12/17 focusing on proving lines parallel.

Lesson Title
Constructions 3

Overview
The warm-up today asks students to practice proving lines parallel. The lesson for today continues working with constructions and introduces students to constructing and copying triangles.
Textbook Sections
§5.5 (txt. p.295) Inequalities in One Triangle

Vocabulary
construction
straight edge
arc
radius
center
diameter

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

Key Ideas
A straight edge and compass can be used to create geometric figures.
A compass is used to measuring lengths by making circles and arcs.
Some parts of a construction can be places wherever you want, while others have to be determined.
If you want a line to be in a specific location, then you have to have two points that it goes through. These points can be created by the intersection of two lines, two arcs, or a line and an arc.
It is not possible to construct a triangle out of just any three line segments!
Key Skills
I can construct a triangle from three line segmetns.
I can determine if it is possible to construct a triangle when given three line segments, or the lengths of three line segments.
I can determine the possible lengths for the third side of a triangle when given the lengths of two of the triangles sides.
Turn-In (#39)
Test Corrections
Constructions Practice
Txt. p. 63 #1-15

Handouts
Constructions 3
Constructions 4

Assignment
Finish “Constructions 3”
Chapter 3 Practice: Proving Lines Parallel #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, January 06, 2009

Intro to Calculus (Class 40)

Announcements
There will be a test next class focusing on exponential growth and working with logarithms as represented by homework assignments 12 to 14 and workshops 10 and 11.

Lesson Title
Exponents and Logarithms (7)

Overview
During the warm-up today we will discuss discuss aspects of how our memory works and the implications this has on studying for exams. We will then share solutions to Sangaku 6. The lesson for today will turn our attention back to logarithms, what they mean, and how we can work with them.
Textbook Sections
N/A

Vocabulary
exponent
base
negative exponent
discrete growth
continuous growth
e
limit
asymptote

Key Attitudes
Math is about thinking creatively.

Key Ideas
There are two types of questions we can ask concerning exponential: 1) Given the number of growth cycles, determine the quantity; 2) Given the quantity, determine the number of growth cycles. These questions are inverses of each other.
A logarithm is an exponential equation in disguise.
Problems involving logarithms can be solved by first translating the problem into one invovling exponents and then solving this exponent problem.
Key Skills
I can explain the meaning of a logarithm in both mathematical terms and real world situations.
I can solve problems which involve logarithms by translating them into exponent problems.
Turn-In (#39)
Sangaku 6

Handouts
Homework 15
What Will Improve Memory?

Assignment
HW 15 #1-3
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, January 05, 2009

Geometry (Class 39)

Announcements
Test Wed. 12/17 focusing on proving lines parallel.

Lesson Title
Constructions 2

Overview
During the warm-up today students will participate in an activity which helps to explain how our memory works. We will discuss the implications as they relate to studying for finals. After this we will score two example proofs from the last test. The lesson for the day focuses on straight edge and compass constructions. During the last part of the class the last test will be returned and students will have some time to make corrections.
Textbook Sections
§3.4 (Txt. p.150) Proving Lines Parallel

Vocabulary
implication
deduction
syllogism
two-column proof
statement
reason
auxiliary line

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

Key Ideas
A converse of an If, then statement can be created by switching the position of the hypothesis (if) and conclusion (then).
Not all converses are true.
If an if, then statement and its converse are true, then the statement is a biconditional.
Key Skills
I can create and solve a problem involving parallel lines and a “bent” transversal.
I can prove lines parallel.
Turn-In (#38)
Constructions 1 #TBA

Handouts
Constructions 2

Assignment
Test Corrections
Constructions Practice
Txt. p. 63 #1-15
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.