HolcombMath

Tuesday, March 31, 2009

Geometry (Class 66)

Lesson Title
Special Right Triangles

Overview
The opener for today is focused on helping students see how to use their knowledge about perfect square trinomials to find the solutions to any quadratic equation, i.e., by “completing the square”. The lesson for the day is our first in a series looking at the relationships between the angles and the sides of right triangles. More specifically, we ask the question “Is it possible to know anything about the lengths of the sides of right triangles based on the measures of the angles in a right triangle?” Answering this question brings the study of special right triangles and right triangle trigonometry into focus.
Textbook Sections

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle

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

Key Ideas
Certain right triangles are special-- we can figure out the lengths of all three sides when we know the length of only one side.
A 30-60-90 triangle can be created by folding an equilateral triangle.
A 45-45-90 triangle can be created by folding a square.
Key Skills
I can find the length of the missing two sides of a 45-45-90 right triangle when I know the length of the remaining side.
I can find the length of the missing two sides of a 30-60-90 right triangle when I know the length of the remaining side.
Turn-In (#65)
Txt. p.493 #6-14, 29

Handouts
Chapter 9- Lesson 1: Special Right Triangles

Assignment
Txt. p.493 #15-25, 32, 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.

Monday, March 30, 2009

Intro to Calculus (Class 67)

Announcements
Test next Friday (150 points) covering logs to sinusoidals. It will take the entire block.

Lesson Title
Circular Functions (20)

Overview
The class time today, as well as on Wednesday, is focused on preparing for the Mid-Term on Friday. Students will first finish Homework 21 and then begin work on Workshop 22.
Textbook Sections
N/A

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

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

Key Ideas
A point rotating on the circumference of a circle can be used to generate a sine or cosine graph by plotting the height of the sine (or cosine) as a function of the measure of the central angle.
Graphs of sinusoidal functions can be stretched, compressed, shifted, and reflected in the same way that graphs of any function can.
A point rotating on the circumference of a circle can be used to generate a sine or cosine graph by plotting the height of the sine (or cosine) as a function of time when the point of on the circumference of the circle is rotating at some speed.
Increasing the speed at which the point on the circumference of a circle is rotating makes the graph of the sine or cosine have more “bump” in a given time. In other words, increasing the rotation speed shortens the period of the function. Decreasing the speed, increases the period.
Key Skills
I can determine the transformations needed to change the graph of one function into another.
I can deduce the necessary graphical translations needed to change the graph of a sine or cosine function into a graph which will accurately represent a situation.
Turn-In (#66)
Lesson for Homework 21 by end of class

Handouts
Workshop 22

Assignment
Homework 21- Finish it.
Workshop 22 #TBA

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

Friday, March 27, 2009

Geometry (Class 65)

Lesson Title
Similar Triangles (7)

Overview
The opener for the day focuses on simplifying and unsimplifying square roots. Students also apply these skills to right triangles via the Pythagorean Theorem. The lesson for the day focuses on proving triangles similar using SAS. During the last part of the class students will be taking Test 11 which focuses on proving triangles similar, using similar triangles, perfect square trinomials.
Textbook Sections
§8.5 (Txt. p.488) Proving Triangles are Similar

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.
Squaring binomials creates a pattern which can be used to solve certain types of quadratic equations.
Key Skills
I can recognize a perfect square trinomial.
I can factor a perfect square trinomial by inspection quickly.
I can solve a perfect square trinomial equation by factoring.
I can simplify square roots.
I can match angles and sides of similar triangles.
I can write similarity statements for two similar triangles.
I can write a proportionality statement for two similar triangles.
I can translate between similarity statements and proportionality statements as related to similar triangles.
I can determine which of the triangle similarity postulates (SSS, AA, SAS) can be used to show that two triangles are similar
I can prove two triangles are similar by using SSS, AA, or SAS.
Turn-In (#64)
Txt. p.483 #39-45-47

Handouts
Proving Triangles Similar using SAS

Assignment
Txt. p.493 #6-14, 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, March 26, 2009

Intro to Calculus (Class 66)

Announcements
Test next Friday (150 points) covering logs to sinusoidals. It will take the entire block.

Lesson Title
Circular Functions (19)

Overview
The opener for today focuses students on how to stretch or compress a sinusoidal function in order to force it to have the period desired. The remaining class will be focused on developing the skills needed to create sinusoidal functions to model periodic relationships.
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
A point rotating on the circumference of a circle can be used to generate a sine or cosine graph by plotting the height of the sine (or cosine) as a function of the measure of the central angle.
Graphs of sinusoidal functions can be stretched, compressed, shifted, and reflected in the same way that graphs of any function can.
A point rotating on the circumference of a circle can be used to generate a sine or cosine graph by plotting the height of the sine (or cosine) as a function of time when the point of on the circumference of the circle is rotating at some speed.
Increasing the speed at which the point on the circumference of a circle is rotating makes the graph of the sine or cosine have more “bump” in a given time. In other words, increasing the rotation speed shortens the period of the function. Decreasing the speed, increases the period.
Key Skills
I can determine the transformations needed to change the graph of one function into another.
I can deduce the necessary graphical translations needed to change the graph of a sine or cosine function into a graph which will accurately represent a situation.
Turn-In (#65)
Homework 21 #1-6

Handouts
Homework 21

Assignment
Homework 21 #7-12
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.

Wednesday, March 25, 2009

Geometry (Class 64)

Handouts
Proving Triangles Similar using SAS

Assignment
Txt. p.483 #39-45-47
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.

Announcements
Test Friday-- proving triangles similar, using similar triangles, perfect square trinomials.

Lesson Title
Similar Triangles (6)

Overview
The opener today focuses on simplifying radicals and solving perfect square trinomials. The lesson works focuses on proving triangles similar using the Side-Angle-Side similarity postulate.
Textbook Sections
§8.5 (Txt. p.488) Proving Triangles are Similar

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.
Squaring binomials creates a pattern which can be used to solve certain types of quadratic equations.
Key Skills
I can recognize a perfect square trinomial.
I can factor a perfect square trinomial by inspection quickly.
I can solve a perfect square trinomial equation by factoring.
I can simplify square roots.
I can match angles and sides of similar triangles.
I can write similarity statements for two similar triangles.
I can write a proportionality statement for two similar triangles.
I can translate between similarity statements and proportionality statements as related to similar triangles.
I can determine which of the triangle similarity postulates (SSS, AA, SAS) can be used to show that two triangles are similar
I can prove two triangles are similar by using SSS, AA, or SAS.
Turn-In (#63)
Txt. p.483 #21-29, 33-38

Handouts
Proving Triangles Similar using SAS

Assignment
Txt. p.483 #39-47
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 24, 2009

Intro to Calculus (Class 65)

Lesson Title
Circular Functions (18)

Overview
Students will share their results for Snagaku 14 as the opener today. We will then begin to work with using circular functions as tools for modeling periodic situations.
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
Arguments of angles have to agree.
The arguments of trigonometric functions can be changed.
The rules for changing the arguments of trigonometric expressions are derived from the rules you already know and cleverness.
Key Skills
I can work with trigonometric expressions and equations involving the sum or difference of arguments.
Turn-In (#64)
Finish Workshop 21 and Sangaku 14

Handouts
Lesson for Chapter 21
Homework 21

Assignment
Homework 21 #1-6
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 23, 2009

Geometry (Class 63)

Announcements
Test Friday-- proving triangles similar, using similar triangles, perfect square trinomials.

Lesson Title
Similar Triangles (5)

Overview
The opener today continues to focus on quadratic trinomials which are perfect squares-- both factoring and using the factored form to solve equations. The lesson for the day continues with similar triangles, finishing proofs started in the last class as well as extending the work to include using the Side-Angle-Side similarity postulate.
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
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.
Squaring binomials creates a pattern which can be used to solve certain types of quadratic equations.
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.
I can square a binomial by inspections.
I can recognize a perfect square trinomial.
I can factor a perfect square trinomial by inspection quickly.
Turn-In (#62)
Txt. p.483 #9-20

Handouts
No Handouts Posted

Assignment
Txt. p.483 #21-29, 33-38
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.

Thursday, March 19, 2009

Geometry (Class 62)

Lesson Title
Similar Triangles (5)

Overview
The opener today examines squaring binomials and recognizing the pattern that this generates. This provides the foundation for solving perfect square trinomials as well as for developing the technique of completing the square-- all very important algebra for next year!
The lesson for the day continues to focus on similar triangles, writing and using proportions, and then proving triangles similar.
Textbook Sections
§8.4 (Txt. p. 480) Similar 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.
Squaring binomials creates a pattern which can be used to solve certain types of quadratic equations.
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.
I can square a binomial by inspections.
I can recognize a perfect square trinomial.
I can factor a perfect square trinomial by inspection quickly.
Turn-In (#61)
Finish 8.21 and 8.22 Worksheets
Test Corrections

Handouts
Chapter 8 Lesson 2 Proving Triangles Similar

Assignment
Txt. p.483 #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.

Wednesday, March 18, 2009

Intro to Calculus (Class 63)

Announcements
Quiz Friday focusing on working with trig. expressions and equations which do not have matching arguments.

Lesson Title
Circular Functions (16)

Overview
The agenda for the day is for students to work towards finishing Sangaku 14 as well as Workshop 21 which they will receive. There will be a quiz addressing the material from Homework 20 and Workshop 21 on friday.
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
Arguments of angles have to agree.
The arguments of trigonometric functions can be changed.
The rules for changing the arguments of trigonometric expressions are derived from the rules you already know and cleverness.
Key Skills
I can work with trigonometric expressions and equations involving the sum or difference of arguments.
Turn-In (#62)
Homework 20- Finish it
Sangaku 14 due Friday

Handouts
Workshop 21

Assignment
Workshop 21
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 17, 2009

Geometry (Class 61)

Lesson Title
Similar Triangles (4)

Overview
The opener today has students correct two proofs from the test last week as well as work on concepts and skills related to solving absolute value equations. The lesson continues to focus on similar triangles: writing statements of proportionality, proving triangles similar.
Textbook Sections
§8.4 (Txt. p. 480) Similar 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 (#60)
Finish worksheets 8.4B and 8.5A

Handouts
8.21 Working with Similar Triangles
8.22 Working with Similar Triangles

Assignment
Finish 8.21 and 8.22 Worksheets
Test 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.

Monday, March 16, 2009

Intro to Calculus (Class 62)

Announcements
Quiz Friday focusing on working with trig. expressions and equations which do not have matching arguments.

Lesson Title
Circular Functions (15)

Overview
The opener today is Sangaku 14. This is one of the few Sangaku created by a women. The remainder of the class will be used for working on homework 20.
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
Arguments of angles have to agree.
The arguments of trigonometric functions can be changed.
The rules for changing the arguments of trigonometric expressions are derived from the rules you already know and cleverness.
Key Skills
I can work with trigonometric expressions and equations involving the sum or difference of arguments.
Turn-In (#61)
Homework 20 #TBA

Handouts
Sangaku 14

Assignment
Homework 20- Finish it
Sangaku 14 due Friday
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, March 13, 2009

Geometry (Class 60)

Lesson Title
Similar Triangles (3)

Overview
The opener today will be an algebra review. The lesson will focus on how the lengths of the corresponding sides of similar triangles are related. During the last part of the class students will take Test 10 which focuses on using congruent triangles
Textbook Sections
§8.4 (Txt. p. 480) Similar 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 (#59)
Txt. p.250 #1, 2 (Hint: Do you see isosceles triangles?)
Txt. p.258 #28-30, 43-48

Handouts
No Handouts Posted

Assignment
Finish worksheets 8.4B and 8.5A
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 12, 2009

Intro to Calculus (Class 61)

Lesson Title
Circular Functions (14)

Overview
The opener today is a short video that gives an interesting perspective on the pace at which the world is changing. Students will then work through a lesson which focuses on the sine and cosine of the sum of two angles. The remainder of the time will be used to work on problems related to these concepts.
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
Arguments of angles have to agree.
The arguments of trigonometric functions can be changed.
The rules for changing the arguments of trigonometric expressions are derived from the rules you already know and cleverness.
Key Skills
I can work with trigonometric expressions and equations involving the sum or difference of arguments.
Turn-In (#60)
Workshop 20

Handouts
Lesson for Homework 20
Homework 20

Assignment
Homework 20 #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, March 11, 2009

Geometry (Class 59)

Announcements
Test Friday- Using Congruent Triangles

Lesson Title
Similar Triangles (2)

Overview
The opener today reviews solving quadratic equations by factoring as well as gives students another opportunity to use proving triangles congruent to prove another fact. The lesson will continue with working with Similar triangles.
Textbook Sections
§8.4 (Txt. p. 480) Similar 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 (#58)
Txt. p.258 #16-18, 24-27, 39-42
Chapter 4- Lesson 4
CST Review

Handouts
No Handouts Posted

Assignment
Txt. p.250 #1, 2 (Hint: Do you see isosceles triangles?)
Txt. p.258 #28-30, 43-48
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 10, 2009

Intro to Calculus (Class 60)

Lesson Title
Circular Functions (13)

Overview
During the opener students have a chance to confirm their solutions for Sangaku 13. Afterwards students will continue to work to build a stronger connections between relationships between angles and coordinates and the mathematical notation used to represent these relationships. During the last part of class, Test 6 will be returned. Solutions to version A of the test have been previously posted on the class website.
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.
I can translate between mathematical notation and English with regards to trigonometric functions and their inverses.
Turn-In (#59)
Workshop 19
Sangaku 13

Handouts
Workshop 20

Assignment
Workshop 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.