HolcombMath

Wednesday, December 17, 2008

Geometry (Class 38)

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

Lesson Title
Constructions 1

Overview
During the warm-up today students are introduced to constructions using a straight edge and compass. Detailed instructions for making these constructions can be found at the Math Open Reference. As time permits, students will have another opportunity to improve their skills of writing proofs to show that lines are parallel. Finally, students will take Test 7 focusing on proving lines parallel.
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 (#37)
Txt. p.154 #27, 28, 34, 35
Txt. p. 160 #11, 12, 15, 16, 18, 19, 21, 22

Handouts
Constructions 1

Assignment
Constructions 1 #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, December 16, 2008

Intro to Calculus (Class 38)

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 (5)

Overview
The warm-up today asks students to examine what happens to $1 invested in an account which pays 50% annual interest as a function of the number of compoundings. The remainder of the class time will be dedicated to working on Workshop 11.
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 (#37)
Homework 14
Sangaku 5

Handouts
Workshop 12
Money Changes Everything- 50% Annual Growth

Assignment
Workshop 11
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, December 15, 2008

Geometry (Class 37)

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

Lesson Title
Proving Lines Parallel

Overview
The warm-up for the day is another problem involving parallel lines and a bent transversal. These problems require the addition of an auxiliary line-- placement of which is often the hardest part of the problem. The lesson for the day continues with proving lines parallel. Students will work more complicated proofs, thereby building understanding and fluency. We do have a test Wed. focusing on proving lines parallel.
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 (#36)
Txt. p.153 #10-18, 20-26

Handouts
More Proving Liens Parallel

Assignment
Txt. p.154 #27, 28, 34, 35
Txt. p. 160 #11, 12, 15, 16, 18, 19, 21, 22
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, December 12, 2008

Intro to Calculus (Class 37)

Announcements
The next test is going to be moved to Thursday December 18 (we need more time) and will focus on Homework 14 or 15, Workshops 10 and possibly 11.

Lesson Title
Exponents and Logarithms (4)

Overview
The warm-up for today is a Sangaku involving two equilateral triangles and a circle. The rest of the class will be spent on develop greater fluency in working with 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 (#36)
Sangaku 4

Handouts
Workshop 10
Sangaku 5

Assignment
Finish Homework 14
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, December 11, 2008

Geometry (Class 36)

Lesson Title
Proving Lines Parallel

Overview
Students solve student problems created last class concerning parallel lines and a “bent” transversal as their warm-up for the day. The lesson for the day focuses on how to prove lines parallel.
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 (#35)
Txt. p.168 #26, 30-34, 36-38, 42, 43

Handouts
Chapter 3- Lesson 2: Proving Lines Parallel

Assignment
Txt. p.153 #10-18, 20-26
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, December 10, 2008

Intro to Calculus (Class 36)

Announcements
The next test is going to be moved to Thursday December 18 (we need more time) and will focus on Homework 14 or 15, Workshops 10 and possibly 11.

Lesson Title
Exponents and Logarithms (3)

Overview
A sangaku returns for a warm-up today. The lesson focuses on understanding what a logarithm is, how it is related to exponents, and how to translate a problem involving logarithms into one involving exponents and then solving it.
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 (#35)
Homework 13

Handouts
Lesson for Homework 14: Working with Logs
Sangaku 4

Assignment
Homework 14 #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, December 09, 2008

Geometry (Class 35)

Lesson Title
Investigating Parallel Lines (1)

Overview
The warm-up for today consists of scoring two proofs modeled on student work from the test last class. The lesson for the day invites students to solve a curious parallel line problem and then to invent and solve one of their own. Finally students will trade the problems they create with others and solve them.
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

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
Proofs can be thought of as a game where the game pieces are definitions, postulates, and theorems and the objective is to build a logical chain of conditional statements (a syllogism) using these pieces to connect the “given” to the “prove”.
Key Skills
I can use properties of parallel lines to solve problems.
I can create auxiliary lines to help solve problems.
I can create a parallel line problem which requires the addition of auxiliary lines to solve.
Turn-In (#34)
Txt. p.168 #11-22, 24, 25, 27-29

Handouts
Chapter 3- Lesson 1: Parallel Lines Puzzles

Assignment
Txt. p.168 #26, 30-34, 36-38, 42, 43
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, December 08, 2008

Intro to Calculus (Class 35)

Announcements
The next test is going to be moved to Thursday December 18 (we need more time) and will focus on Homework 14 or 15, Workshops 10 and possibly 11.

Lesson Title
Exponents and Logarithms (2)

Overview
The warm-up for the day is
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
Exponential growth and decay are characterized by a constant multiplier.
Exponential growth and decay arise from situations where each “individual” creates new “individuals”.
Exponential growth or dcay can be modeled by the function f(t) = Cb^t where C represents the starting value or initial population, b represents the exponential constant, and t represents the # of cycles of growth.
Exponential growth can be either discrete, happening all at once, or continuous, changing all the time.
Growth of money in an investment gaining interest can be thought of as continuous growth-- the principal is accumulating interest, and the interest is accumulating interest, and the interest on the interest is accumulating interest on a continuous basis.
The number e can be thought of as the total amount of money in an account which started with $1, was growing at a rate of 100% per year, and had an infinite number of compounding periods (compounded continuously) at the end of one year.
Key Skills
I can explain the meaning of the number e in terms of exponential growth
Turn-In (#34)
Sangaku 3

Handouts
Money Changes Everything— An investigation into the number e.

Assignment
Finish Homework 14
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, December 05, 2008

Geometry Test 7 Solutions

Here are the solutions to Test 7. You will need to scroll to the bottom of the page and hit check your answers. Then scroll down to the bottom of the next page.

Geometry (Class 34)

Lesson Title
The Game of Proof (6)

Overview
The warm-up for today is a practice proof and we will then work on some more proofs in order to prepare for the test at the end of the class.
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Vocabulary
implication
deduction
syllogism
two-column proof
statement
reason

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

Key Ideas
Proofs can be thought of as a game where the game pieces are definitions, postulates, and theorems and the objective is to build a logical chain of conditional statements (a syllogism) using these pieces to connect the “given” to the “prove”.
Key Skills
I can build a syllogism (an If…, then… chain of reasons).
I can label a diagram with the information given in a proof.
I can use my knowledge of angle relationships to figure out a plan for proving a statement.
I can organize the angle relationships to build a logical chain of reasoning going from what is given to what is to be proved.
I can use the definitions, postulates, and theorems the class has developed to justify steps I take to solve a missing angle puzzle.
I can write a two column proof to represent the process of solving a missing angle puzzle.

Turn-In (#33)
Txt. p.806 #30, 37
Txt. p.807 #14-17, 26, 27, 29, 30

Handouts
No Handouts Posted

Assignment
Txt. p.168 #11-22, 24, 25, 27-29
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.

Thursday, December 04, 2008

Intro to Calculus (Class 34)

Announcements
The next test is scheduled for Friday Dec. 12 and will focus on Homework 12- Homework 14 or 15, Workshops 10 and possibly 11.

Lesson Title
Exponents and Logarithms (1)

Overview
The warm-up today is a sangaku. We will also have some time for students to present their solutions to the sangaku’s from the last class.
The lesson for today, Noodle Analysis, works towards providing a foundation for working with exponential and logarithmic functions, expressions, and equations. Here is a video of a Beijing noodle maker which we will use to get started with our Noodle Analysis:
Textbook Sections
N/A

Vocabulary
exponent
base
negative exponent

Key Attitudes
Math is about thinking creatively.

Key Ideas
Exponential growth and decay are characterized by a constant multiplier.
Exponential growth and decay arise from situations where each “individual” creates new “individuals”.
Exponential growth or dcay can be modeled by the function f(t) = Cb^t where C represents the starting value or initial population, b represents the exponential constant, and t represents the # of cycles of growth.
Key Skills
I can describe why a given situation would or would not represent exponential growth.
I can give an example of where an example of exponential growth would arise.
I can explain what it means for growth to be exponetial.
I can create, and use, a function to model exponential growth or decay.
I can explain the difference between exponential growth and exponential decay.
I can create, and use, a function to model exponential decay.
Turn-In (#33)
Sangaku 2
Homework 12

Handouts
Sangaku 3
Homework 13

Assignment
Homework 13 #1,2, 5 - 8
Sangaku 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.

Wednesday, December 03, 2008

Geometry (Class 33)

Announcements
Test Friday- Proofs

Lesson Title
The Game of Proof (4)

Overview
Today the class will focus on writing proofs in preparation for the test on Friday.
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Vocabulary
implication
deduction
syllogism
two-column proof
statement
reason

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

Key Ideas
Proofs can be thought of as a game where the game pieces are definitions, postulates, and theorems and the objective is to build a logical chain of conditional statements (a syllogism) using these pieces to connect the “given” to the “prove”.
Key Skills
I can build a syllogism (an If…, then… chain of reasons).
I can label a diagram with the information given in a proof.
I can use my knowledge of angle relationships to figure out a plan for proving a statement.
I can organize the angle relationships to build a logical chain of reasoning going from what is given to what is to be proved.
I can use the definitions, postulates, and theorems the class has developed to justify steps I take to solve a missing angle puzzle.
I can write a two column proof to represent the process of solving a missing angle puzzle.

Turn-In (#32)
Txt. p.807 #1-13 (Do the proof following the rules from the class, not the textbook)

Handouts
No Handouts Posted

Assignment
Txt. p.806 #30, 37
Txt. p.807 #14-17, 26, 27, 29, 30
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, December 02, 2008

Intro to Calculus (Class 33)

Announcements
The next test is scheduled for Friday Dec. 12 and will focus on Homework 12- Homework 14 or 15, Workshops 10 and possibly 11.

Lesson Title
Simplifying Expressions (1)

Overview
The warm-up for today consists of two Sangaku. The lesson focuses on simplifying expressions and solving equations involving exponents— including negative ones.
Textbook Sections
N/A

Vocabulary
exponent
base
negative exponent

Key Attitudes
Math is about thinking creatively.

Key Ideas
A negative exponent represent the reciprocal of the base.
When multiplying expressions with the same base, the exponents can be added.
When dividing expressions with the same base, the exponents can be subtracted.
Key Skills
I can simplify expressions involving negative exponents.
I can solve equations involving exponents.
I can apply what I have learned about factoring quadratic expressions to situations involving exponents.
Turn-In (#32)
Sangaku 1

Handouts
Homework 12
Sangaku 2

Assignment
Sangaku 2
Homework 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.

Monday, December 01, 2008

Geometry (Class 32)

Announcements
Test Friday- Proofs

Lesson Title
The Game of Proof (4)

Overview
The warm-up today is a recap of Test 6. Students are asked to use a scoring guide and score two different proofs modeled after student work from the test. They then have to write their own proof.
The lesson for the day continues to a focus of learning how to write proofs.
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Vocabulary
implication
deduction
syllogism
two-column proof
statement
reason

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

Key Ideas
Proofs can be thought of as a game where the game pieces are definitions, postulates, and theorems and the objective is to build a logical chain of conditional statements (a syllogism) using these pieces to connect the “given” to the “prove”.
Key Skills
I can build a syllogism (an If…, then… chain of reasons).
I can label a diagram with the information given in a proof.
I can use my knowledge of angle relationships to figure out a plan for proving a statement.
I can organize the angle relationships to build a logical chain of reasoning going from what is given to what is to be proved.
I can use the definitions, postulates, and theorems the class has developed to justify steps I take to solve a missing angle puzzle.
I can write a two column proof to represent the process of solving a missing angle puzzle.

Turn-In (#31)
Txt. p.138 #7-13
Txt. p. 141 Mixed Review #29-36

Handouts
No Handouts Posted

Assignment
Txt. p.807 #1-13 (Do the proof following the rules from the class, not the textbook)
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.