HolcombMath

Thursday, May 31, 2007

Geometry (Class 83)

Overview
In our last class we learned how to use the Law of Sines to solve triangles which did not include a right angle. However the Law of Sines is only a partial solution. In today’s class we will learn about situations where the Law of Sines will not work. Not to worry-- we have the Law of Cosines to use in case the Law of Sines will not work.
Textbook Sections
Supplementary-- Law of Cosines

Vocabulary
Law of Cosine
Expanded form
Factored form

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
The Law of Cosines is a generalization of the Pythagorean Theorem.

Key Skills
Using inscribed angles, right triangle trigonometry, and algebra to develop the Law of Cosines.
Using the Law of Cosines to solve triangles

Turn-In (#82)
Final Review 3

Handouts
Chapter 13- Lesson 2: Law of Cosines

Assignment
Final Review 4
Finish Law of Sines
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 30, 2007

Algebra (Class 84)

Overview
In today’s class we continue our work examining the relationship between the length of the side and the area of a rectangle with a fixed perimeter in order to develop equations which can be used to describe and predict different measurements of these rectangles.
Textbook Sections
§12-4 (Txt. p.572) Graphs of Quadratic Functions

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Equations can be written to represent quadratic relationships.
Equation can be used to predict key features of a graph of a parabola.

Key Skills
Calculate the area of a rectangle with a fixed perimeter given one dimension.
Graph non-linear data.
Use graphs and equations to make predictions.
Determine the perimeter of a rectangle given a table of values or graph.
Create equations given a graph or a table of values that can be used to predict the area of a rectangle with a fixed perimeter when the length is known.

Turn-In (#83)
Txt. p. 656-657 #1-5 ODD, 15-25 ODD
Txt. p.675 #1-3
Practice Worksheet: Worksheet: Which Member of Fred Ferd’s Family Thinks He’s a Pen?”

Handouts
No Handouts Posted

Assignment
Chapter 12: Quadratic Equations
Txt. p.662-663 #1, 9, Solve #35 and 43 by factoring, Solve #32 and 53 by completing the square, Solve #23 and 31 by using the Quadratic Formula
ACE #3, 6-8, 10, 12-16, 27
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 29, 2007

Geometry (Class 82)

Overview
In today’s class we being our study of solving triangles which do not include a right angle by developing the Law of Sines.
Textbook Sections
Supplementary-- Law of Sines

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
Inscribed angles of the same arc are congruent.

Key Skills
Using inscribed angles and algebra to develop the Law of Sines.
Using the Law of Sines to solve triangles

Turn-In (#81)
Final Review 2
Equations of Circles

Handouts
Chapter 13-Lesson 1: Law of Sines

Assignment
Final Review 3
Law of Sines
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 25, 2007

Algebra (Class 83)

Overview
Today is a review day. I will be absent, but will be back for the next class. For blocks A3 and A4 there will be a quiz. Block A2 will be taking a quiz next Friday instead.
Textbook Sections
No new sections

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas

Turn-In (#82)
Chapter 8: Linear Equations
Txt. p. 653-654 #1, 5, 13-33 EOO, and 27, 45-51 ODD, 57, 59, 63, 65, 67

ACE #1, 4, 5, 19, 20, 23, 26

Handouts
No Handouts Posted

Assignment
Txt. p. 656-657 #1-5 ODD, 15-25 ODD
Txt. p.675 #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.

Thursday, May 24, 2007

Geometry (Class 81)

Overview
In today’s class we return to thinking about circles. In particular we figure out how to write the equation of a circle when we know the location of its center and its radius.
Textbook Sections
§10.6 (Txt. p.636) Equations of Circles

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
A point on a circle must be a fixed distance from the center of the circle.
The equation for a circle is an adaptation of the Pythagorean Theorem.

Key Skills
Writing the equation of a circle centered at the origin when given the radius of the circle.
Writing the equation for a circle that has been translated away from the origin.

Turn-In (#80)
Final Exam Review 1
Chapter 12- Making Cones

Handouts
Chapter 10-Lesson 6: Equations of Circles

Assignment
Final Review 2
Equations of Circles
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 23, 2007

Algebra (Class 82)

Announcements
CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
In today’s class we continue our work examining the relationship between the length of the side and the area of a rectangle with a fixed perimeter in order to develop equations which can be used to describe and predict different measurements of these rectangles.
Textbook Sections
§12-4 (Txt. p.572) Graphs of Quadratic Functions

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The dimensions of a rectangle can be calculated from its perimeter.
Graphs and equations help us to make predictions.

Key Skills
Calculate the area of a rectangle with a fixed perimeter given one dimension.
Graph non-linear data.
Use graphs and equations to make predictions.
Determine the perimeter of a rectangle given a table of values or graph.
Create equations given a graph or a table of values that can be used to predict the area of a rectangle with a fixed perimeter when the length is known.

Turn-In (#81)
Chapter 6: Rational Expressions & Equations
Txt. p.649-651 #1-13 ODD, 17-23 ODD, 27, 33, 37-43 ODD, 73, 75, 79-87 ODD
Investigation 1 ACE #9, 11, 17, 18, 21, 24, 25
Quiz Corrections

Handouts
No Handouts Posted

Assignment
Chapter 8: Linear Equations
Txt. p. 653-654 #1, 5, 13-33 EOO, and 27, 45-51 ODD, 57, 59, 63, 65, 67

ACE #1, 4, 5, 19, 20, 23, 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.

Tuesday, May 22, 2007

Geometry (Class 80)

Overview
In today’s class students complete their work on creating cones from different parameters. We also begin our work on determining the equations of circles.
Textbook Sections
§12.3 (Txt. p.735) Surface Areas of Pyramids and Cones

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
Cones can be constructed from a flat piece of paper.
The radius of the base of a cone and the slant height of the cone are key pieces of information for constructing a pattern for a cone.
The central angle of a cone can be computed using arc length.

Key Skills
Identifying and measuring parts of a cone when given a pattern for the cone.
Creating a pattern for a cone given the radius and slant height.

Turn-In (#79)
No assignments due.

Handouts
No Handouts Posted

Assignment
Final Exam Review 1
Making Cones- Finish as much as you can.
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 21, 2007

Algebra (Class 81)

Announcements
CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
In today’s class we consider the implications of building a rectangular garden given that we only have a fixed amount of fencing material. What will be the best set of dimensions to use? What possibilities will we be able to choose from? Can we develop some mathematics to help us?
Textbook Sections

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Many different shapes can have the same perimeter but different areas.
The dimensions of a rectangle can be calculated from its perimeter.
Graphs and equations help us to make predictions.

Key Skills
Find all of the possible whole number dimensions of a rectangle with a given perimeter.
Calculate the area of a rectangle with a fixed perimeter given one dimension.
Graph non-linear data.
Use graphs and equations to make predictions.

Turn-In (#80)
Nothing to turn in!

Handouts
No Handouts Posted

Assignment
Chapter 6: Rational Expressions & Equations
Txt. p.649-651 #1-13 ODD, 17-23 ODD, 27, 33, 37-43 ODD, 73, 75, 79-87 ODD
Investigation 1 ACE #9, 11, 17, 18, 21, 24, 25
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 18, 2007

Geometry (Class 79)

Overview
In today’s class students can complete Chapter 7: Lesson 2, if needed, and then go on to an investigation into creating patterns for circular cones.
Textbook Sections
§7.3 (Txt. p.412) Rotations
§12.3 (Txt. p.735) Surface Areas of Pyramids and Cones

Vocabulary
central angle of a cone

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
There are relationships between the coordinates of images and pre-images which are the results of reflections across lines. These relationships can be used to make predictions.
Cones can be constructed from a flat piece of paper.
The radius of the base of a cone and the slant height of the cone are key pieces of information for constructing a pattern for a cone.
The central angle of a cone can be computed using arc length.

Key Skills
Determining the location of the vertices of a figure after a reflection across the x-axis, y-axis, line y = x, or line y=-x.
Creating the image of a figure after a rotation about the origin.
Determining the angle of rotation needed to duplicate a reflection across two intersecting lines.
Identifying and measuring parts of a cone when given a pattern for the cone.
Creating a pattern for a cone given the radius and slant height.

Turn-In (#78)
No assignments due.

Handouts
Chapter 12- Making a Cone

Assignment
No Homework-- except for any class work that needs to be completed.
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 17, 2007

Algebra (Class 80)

Announcements
CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
Today we write the second, and last, part of the California Standards Test in Math. Take the Test and Do Your Best!
Textbook Sections
No New Textbook Sections

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas

Turn-In (#79)
Nothing to turn in!

Handouts
No Handouts Posted

Assignment
No homework.
The following IS NOT due next class. You can get a head start if you want.
Review Assignment:
Chapter 6: Rational Expressions & Equations
Txt. p.649-651 #1-13 ODD, 17-23 ODD, 27, 33, 37-43 ODD, 73, 75, 79-87 ODD

Chapter 8: Linear Equations
Txt. p. 653-654 #1, 5, 13-33 EOO, and 27, 45-51 ODD, 57, 59, 63, 65, 67

Chapter 9: Systems of Equations
Txt. p. 656-657 #1-5 ODD, 15-25 ODD

Chapter 12: Quadratic Equations
Txt. p.662-663 #1, 9, Solve #35 and 43 by factoring, Solve #32 and 53 by completing the square, Solve #23 and 31 by using the Quadratic Formula
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 16, 2007

Geometry (Class 78)

Announcements
CST Part 1, Monday May 14
CST Part 2, Wednesday May 16

Overview
Today we write part 1 of the California Standards Test in Math
Textbook Sections
No new textbook sections

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas

Turn-In (#77)
No assignments due.

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.

Tuesday, May 15, 2007

Algebra (Class 79)

Announcements
CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
Today we write the first part of the California Standards Test in Math. Take the Test and Do Your Best!
Textbook Sections
No New Textbook Sections

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas

Turn-In (#78)
§12-3 (Txt. p.569)#4-6, 13-15
Txt. p.558 #1-3

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 14, 2007

Geometry (Class 77)

Announcements
CST Part 1, Monday May 14
CST Part 2, Wednesday May 16

Overview
Today we write part 1 of the California Standards Test in Math
Textbook Sections
No new textbook sections

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas

Turn-In
Cumulative Practice (Txt. p.780) #1-6, 8, 9, 11-14, 16, 17, 24, 27-29, 35-37

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.

Friday, May 11, 2007

Algebra (Class 78)

Announcements
CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
In today’s class we investigate how rectangles with a fixed perimeter in order to determine the best way to build a fence around a garden.
Textbook Sections
§12-4 (Txt. p.572) Graphs of the Quadratic Function

Vocabulary
quadratic relationship
quadratic function

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Rectangles that have the same perimeter can have different areas.
Tables, graphs, and equations can be used to investigate, describe, predict, and help explain patterns.

Key Skills
Create rectangles with a given perimeter.
Create a table of values in order to record data.
Write an equation which describes the data in a table.
Create a graph using data in a table.

Turn In
§12-3 (Txt. p.569)#1-3, 16-18
CST Practice

Handouts
No Handouts Posted

Assignment
§12-3 (Txt. p.569)#4-6, 13-15
Txt. p.558 #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.

Thursday, May 10, 2007

Geometry (Class 76)

Announcements
CST Part 1, Monday May 14
CST Part 2, Wednesday May 16

Overview
Today’s class is the last one before we take the California Standards Test (CST). In this class we finish our practice for the CST, complete our work with slides and reflections, and begin to look more in depth at rotations about a point.
Textbook Sections
§7.3 (Txt. p.412) Rotations

Vocabulary
isometry
rotation
center of rotation
rotation angle

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
A rotation is an isometry-- a way to move the location of a figure without changing its shape.

Key Skills
Rotating a figure about a point.
Determining the angle of rotation for a transformation.

Turn-In
Txt. p.402 #44, 45, and Mixed Review #47, 48, 51-56, 57
§7,4 (Txt. p.425) #15, 16, 31, 32, and Mixed Review #62, 63, 68-70
Correct Quiz 12

Handouts
No Handouts Posted

Assignment
Cumulative Practice (Txt. p.780) #1-6, 8, 9, 11-14, 16, 17, 24, 27-29, 35-37
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.