HolcombMath

Monday, May 11, 2009

Geometry (Class 78)

Lesson Title
Right Triangle Ratios (5)

Overview
The opener for today focuses on equations of lines. Students will then learn how to use their calculator instead of a trig. table to solve problems, Students will then have time to work a new set of problems requiring the creative use of trigonometry. As time permits we will begin our study of the relationship between angles, segments, and circles.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

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

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#77)
Trig. Practice Problems

Handouts
Chapter 9: Lesson 6- Using your calculator

Assignment
Txt. p.562 #16-19, 31-33, 36-38
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.

Saturday, May 09, 2009

Intro to Calc Test 7 Grades Posted

The grades for Test 7 have been posted. Also, you can find a copy and the answers to Test 7B version B here. Go to the bottom of the page and click on “Check Your Answers” to see the solutions.

Friday, May 08, 2009

Intro to Calculus (Class 79)

Lesson Title
Test 7

Overview
Students write Test 7 today focusing on approximating the derivative at a point, approximating the definite integral, interpreting each of these in terms of a given situation, and working with the basics of the polar coordinate system.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

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

Key Ideas
Our work with trigonometry and circular functions gives us the necessary tools for converting between the polar coordinate system and the rectangular (Cartesian) coordinate system.
Key Skills
I can convert polar coordinates into rectangular coordiantes.
I can convert rectangular coordinates into polar coordinates.
I can convert a polar equation into a rectangular (Cartesian) equation.
Turn-In (#78)
Homework 26: To the Pole and Back #TBA

Handouts
Workshop 25

Assignment
Finish HW 26: Problems from “To the Pole and Back”
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Thursday, May 07, 2009

Geometry (Class 77)

Lesson Title
Right Triangle Ratios (5)

Overview
The opener for today is to continue to work on the Trig. Practice problems. This will be the last day in class for these. Students may continue to work with their partners outside of class. This assignment is due at the start of class Monday.
The lesson for today focuses on using a calculator instead of a table of values to solve trig. problems.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

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

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#76)
No Homework

Handouts
Chapter 9: Lesson 6- Using your calculator

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

Wednesday, May 06, 2009

Intro to Calculus (Class 78)

Lesson Title
To the Pole and Back

Overview
In today’s class we will learn how to convert between polar and rectangular coordinate systems.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian

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

Key Ideas
Our work with trigonometry and circular functions gives us the necessary tools for converting between the polar coordinate system and the rectangular (Cartesian) coordinate system.
Key Skills
I can convert polar coordinates into rectangular coordiantes.
I can convert rectangular coordinates into polar coordinates.
I can convert a polar equation into a rectangular (Cartesian) equation.
Turn-In (#77)
The Leaky Balloon

Handouts
Lesson and Homework 26: To the Pole and Back

Assignment
Homework 26: To the Pole and Back #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, May 05, 2009

Geometry (Class 76)

Lesson Title
CST Geometry Part 2

Overview
Students take the second part of the math portion of the CST today. As an opener we will review terminology related to parallel lines as well as the code names and how to use trigonometric ratios.
Textbook Sections
N/A

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

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

Key Ideas
If the length of two sides of a right triangle are known, then you can figure out the measure of the angles of the triangle using trigonometric ratios.
If the length of one side and the measure of one angle in a right triangle are known, then you can figure out the measures of the other sides and angle using right triangle trigonometry.
All right triangles which have equal acute angles will be similar and hence the ratios of theirs sides (opp./adj., opp/hyp, adj/hyp) will be equal.
The terms sine, cosine, and tangent are code names for the ratios of sides of right triangles.
Key Skills
I can translate between the ratios of sides of right triangles and their code names (sine, cosine, tangent).
I can find the measure of the missing sides of a right triangle when given the measure of one acute angle and the measure of one side.
I can find the measure of an acute angle of a right triangle when given the measures of two sides of the right triangle.
Turn-In (#75)
No Homework

Handouts
No Handouts Posted

Assignment
No Homework
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, May 04, 2009

Intro to Calculus (Class 77)

Lesson Title
CST Math Part (2)

Overview
Students take the second part of the math CST today. As time permits we will continue our work with the polar coordinate systems-- learning how to convert polar coordinates and equations to rectangular coordinates and the inverse.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph

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

Key Ideas
Polar graphs are a different coordinate system.
The coordinates of a polar graph are the radius and the angle of rotation. The angle of rotation is considered the independent variable and the radius is considered the dependent variable.
Polar coordinates and equations can be converted to rectangular ones.
Key Skills
I can plot points on a polar graph.
I can write an equation for a polar graph.
I can convert polar coordinates and equations into rectangular coordinates and equations.
Turn-In (#76)
§ (Txt. p.)

Handouts
The Leaky Balloon

Assignment
The Leaky Balloon
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, May 01, 2009

Geometry (Class 75)

Lesson Title
CST Geometry Part 1

Overview
The opener for today is a partner challenge focusing on knowing the code names (sine, cosine, tangent) for the three main trigonometric ratios. Students then will take the first part of the Geometry CST. In the time they have left after the test students will be continuing their work on the trigonometry practice problems.
Textbook Sections
N/A

Vocabulary
right triangle
leg
hypotenuse
special right triangle
trigonometry
isosceles right triangle
equilateral triangle
equiangular triangle
45-45-90 triangle
30-60-90 triangle
standard position
reference angle
adjacent side
opposite side
hypotenuse
ratio
trigonometry

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

Key Ideas

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.
I can use properties of special right triangles to solve problems.
I can use the ratio of the adjacent side to the hypotenuse of a right triangle to predict the measure of the included angle.
Turn-In (#74)
Txt. p. 562 #10-15, 28-30, 34, 35

Handouts
No Handouts Posted

Assignment
No Homework
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.