HolcombMath

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.

Thursday, April 30, 2009

Intro to Calculus (Class 76)

Lesson Title
CST Math Part 1

Overview
Students will be taking the first CST test. Seniors are not allowed to take the test. On Monday we will be finishing and I am predicting that this will only take the first half of the class. We will be continuing our course work afterwards with a lesson on converting 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

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

Key Ideas

Key Skills

Turn-In (#75)
Polar Tic-Tac-Toe Problems
Finish Rocket Problem

Handouts
No Handouts Posted

Assignment
Finish Polar Tic-Tac-Toe 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, April 29, 2009

Geometry (Class 74)

Lesson Title
Right Triangle Ratios (4)

Overview
The opener for class focuses on putting the skills and concepts students have used to work. Problems require that students interpret situations in terms of right triangles and then apply their knowledge of trigonometric rations to solve them. The lesson for today introduces the code words— sine, cosine, and tangent— for the trigonometric ratios we have been working with.
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
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.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
If triangles are similar, then the ratios of corresponding sides are equal.
If you know that two triangles are both right triangles, and you know the measure of one more angle of each of these triangles, then you can determine if the triangles are simialr.
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 (#73)
Finish Chapter 9- Lesson 4
Txt. p.388 #3-5, 7-9

Handouts
Trig. Practice
Chapter 9- Lesson 5: Code Names

Assignment
Txt. p. 562 #10-15, 28-30, 34, 35
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, April 28, 2009

Intro to Calculus (Class 75)

Lesson Title
Polar Graphing (1)

Overview
The opener for today, Rocket Problem, focuses on deepening student’s understanding of a derivative at a point and the definite integral. The lesson takes a step away from our progression through calculus to work with a different 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

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.
Key Skills
I can plot points on a polar graph.
I can write an equation for a polar graph.
Turn-In (#74)
Workshop 24

Handouts
Rocket Problem
Polar Tic-Tac-Toe

Assignment
Polar Tic-Tac-Toe Problems
Finish Rocket Problem
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, April 27, 2009

Geometry (Class 73)

Lesson Title
Right Triangle Ratios (3)

Overview
The opener for today is focused on working problems in preparation for the CST test. The lesson for the today, continues with working with the relationship between the side lengths and the angle measures of right triangles. More specifically, students work with finding the measures of missing side lengths in right triangles when the measure of one angle and one side is known.

Also, a check out the eyeball game! My average was about 3.6 the first two times I did it.
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
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.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
If triangles are similar, then the ratios of corresponding sides are equal.
If you know that two triangles are both right triangles, and you know the measure of one more angle of each of these triangles, then you can determine if the triangles are simialr.
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 (#72)

Txt. p. 554 #18-20, 22,23

Handouts
No Handouts Posted

Assignment
Finish Chapter 9- Lesson 4
Txt. p.388 #3-5, 7-9
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, April 24, 2009

Intro to Calculus (Class 74)

Lesson Title
Workshop

Overview
Students have the opportunity today to reinforce and deepen their understanding of, and computational ability with, derivatives at a point and definite integrals through working problems. At the end of the period we will work cooperatively on a concept map for calculus so far.
Textbook Sections
N/A

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

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

Key Ideas
The definite integral can be thought of as the area under the graph of a function and above the x-axis.
A definite integral can be approximated by cutting up the area under the curve and above the x-axis into smaller shapes-- rectangles and trapezoids in particular.
The units for a definite integral are the product of the units of the independent (x) and dependent (y) variables.
Key Skills
I can explain the meaning of “definite integral”.
I can estimate the value of a definite integral by using rectangles (left, middle, or right) or by using trapezoids.
I can determine if a situation calls for finding a definite integral.
I can interpret the meaning of the definite integral using its units of measure to help.
Turn-In (#73)
Finish HW 24

Handouts
Workshop 24

Assignment
Workshop 24 #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, April 23, 2009

Geometry (Class 72)

Lesson Title
Right Triangle Ratios (2)

Overview
The opener for today is focused on working problems in preparation for the CST test. The lesson for the today, continues with working with the relationship between the side lengths and the angle measures of right triangles beginning with students determining the angle measures and missing side length when given the measures of two sides of a right triangle and then reversing the process and finding missing side lengths when the measure of one of the acute angles and one side length of a right triangle are known.
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
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.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
If triangles are similar, then the ratios of corresponding sides are equal.
If you know that two triangles are both right triangles, and you know the measure of one more angle of each of these triangles, then you can determine if the triangles are simialr.
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 (#71)
Txt. p. 328 #54-60, 64
Test Corrections

Handouts
Chapter 9- Lesson 3: Finding Angles
Chapter 9- Lesson 4: Solvign for Angles

Assignment
Finish Chapter 9- Lesson 3
Txt. p. 554 #18-20, 22,23
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, April 22, 2009

Intro to Calculus (Class 73)

Lesson Title
Introduction to the Definite Integral (1)

Overview
Students have the first 30 minutes in class to work together to finish Workshop 23. The remainder of the class focuses on further students understanding of and ability to estimate the definite integral.
Textbook Sections
N/A

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

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

Key Ideas
The definite integral can be thought of as the area under the graph of a function and above the x-axis.
A definite integral can be approximated by cutting up the area under the curve and above the x-axis into smaller shapes-- rectangles and trapezoids in particular.
The units for a definite integral are the product of the units of the independent (x) and dependent (y) variables.
Key Skills
I can explain the meaning of “definite integral”.
I can estimate the value of a definite integral by using rectangles (left, middle, or right) or by using trapezoids.
I can determine if a situation calls for finding a definite integral.
I can interpret the meaning of the definite integral using its units of measure to help.
Turn-In (#72)
WS 23

Handouts
Workshop 24

Assignment
Finish HW 24
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, April 21, 2009

Geometry (Class 71)

Lesson Title
Right Triangle Ratios (1)

Overview
The opener for today is focused on working problems in preparation for the CST test. The lesson for the today, “Triangle Magic”, sets the stage for our work with the relationships between the angle measures and the side lengths of right triangles. During the last part of the class students will be taking a test focusing on special right triangles, solving quadratics by completing the square, and applications of similar triangles.
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.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
If triangles are similar, then the ratios of corresponding sides are equal.
If you know that two triangles are both right triangles, and you know the measure of one more angle of each of these triangles, then you can determine if the triangles are simialr.
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 (#70)
Special Right Triangle Problems (Worksheet “p.365”) Written Exercises #21-33

Handouts
Lesson 9.1: Right Triangle Magic

Assignment
Txt. p. 328 #54-60, 64
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, April 20, 2009

Intro to Calculus (Class 72)

Lesson Title
Introduction to the Definite Integral

Overview
In today’s class students will be introduced to another main idea of calculus: the definite integral. Students will learn what this term means, what is can be used for, and how to find an estimate of its value.
Textbook Sections
N/A

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

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

Key Ideas
The definite integral can be thought of as the area under the graph of a function and above the x-axis.
A definite integral can be approximated by cutting up the area under the curve and above the x-axis into smaller shapes-- rectangles and trapezoids in particular.
The units for a definite integral are the product of the units of the independent (x) and dependent (y) variables.
Key Skills
I can explain the meaning of “definite integral”.
I can estimate the value of a definite integral by using rectangles (left, middle, or right) or by using trapezoids.
I can determine if a situation calls for finding a definite integral.
I can interpret the meaning of the definite integral using its units of measure to help.
Turn-In (#71)
Homework 23

Handouts, Links
Intro to Calc: Lesson for Homework 24
Intro to calc: Homework 24
GeoGebra Reimann Sums-- Definite Integral by Rectangles

Assignment
HW 24 #1, 2
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, April 17, 2009

Geometry (Class 70)

Announcements
Test Friday focusing on completing the square, special right triangles, and using right triangles.

Lesson Title
Right Triangle Ratios (1)

Overview
Students will begin the class working problems which require the application of concepts and skills related to special right triangles. The lesson for the today, “Triangle Magic”, sets the stage for our work with the relationships between the angle measures and the side lengths of right triangles. During the last part of the class students will be taking a test focusing on special right triangles, solving quadratics by completing the square, and applications of similar triangles.
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.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
If triangles are similar, then the ratios of corresponding sides are equal.
If you know that two triangles are both right triangles, and you know the measure of one more angle of each of these triangles, then you can determine if the triangles are simialr.
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 (#69)
Special Right Triangle Problems (Worksheet “p.365”) Written Exercises #1-20

Handouts
No Handouts Posted

Assignment
Special Right Triangle Problems (Worksheet “p.365”) Written Exercises #21-33
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.

Thursday, April 16, 2009

Intro to Calculus (Class 71)

Lesson Title
Rate of Change by Table, Graph, or Equation

Overview
Today’s lesson focuses on approximating the rate of change of a function at a point when given a graph of the function, a table of values, or an equation. Students learn that using an average of average rates of change can be an effective tool for estimating the instantaneous rate of change at a point.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
The rate of change for a function at a given point can be approximated by finding averages over very small intervals.
The instantaneous rate of change of a function at a point can be approximated by using an average of average rates of change. This is especially helpful when working with experimental data.
Key Skills
I can use a graphing calculator to examine what is happening to a function on a very small scale.
I can determine what is happening in a situation by examining a graph.
I can sketch a graph to represent the relationship between variables.
Turn-In (#70)
Homework 22 All

Handouts
Lesson for Homework 23
Homework 23
Workshop 23

Assignment
Homework 23- All
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, April 15, 2009

Geometry (Class 69)

Announcements
Test Friday focusing on completing the square, special right triangles, and using right triangles.

Lesson Title
Special Right Triangles (3)

Overview
The opener for today continues to focus on solving quadratic equations by completing the square and also has a few problems intended to help students review how to solve for the lengths of the sides of special right triangles. Students then will have an opportunity for more practice working with special right triangles-- first as a “Partner Challenge” and then by working a new set of problems.
Textbook Sections
§9.4 (Txt. p.551) Special Right Triangles

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.
The fact that the special right triangles are formed either as half of a square or half of an equilateral triangle provides a means to find the length of the other sides when the length of one side is known.
The Pythagorean Theorem can be used to find the length of a missing side of a right triangle when the lengths of two sides are known.
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.
Turn-In (#68)
Txt. p.554 #12-17, 21, 22, 24

Handouts
9.1 Special Right Triangles Problems

Assignment
Special Right Triangle Problems (Worksheet “p.365”) Written Exercises #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, April 14, 2009

Intro to Calculus (Class 70)

Lesson Title
Calculus Overview

Overview
Today’s lesson is focused on giving students an understanding of one of the key ideas in the study of Calculus.
Textbook Sections
N/A

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
The rate of change for a function at a given point can be approximated by finding averages over very small intervals.
Key Skills
I can use a graphing calculator to examine what is happening to a function on a very small scale.
I can determine what is happening in a situation by examining a graph.
I can sketch a graph to represent the relationship between variables.
Turn-In (#69)
No Homework

Handouts
Lesson for HW 22- The motion of a door.
Hoemwork 22

Assignment
Homework 22 All
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.