HolcombMath

Thursday, November 30, 2006

Geometry (Class 31)

Announcements
Mid-Term Make-Up for those who were absent (excused) for the Mid-Term is today in room M100 from 2:50 to 4:30. Bring your materials!

Overview
§5.2 (p.272) Bisectors of a Triangle
In this lesson we investigate where to locate a hospital between three cities such that the distances from each of the cities to the hospital are equal. We see how properties related to bisectors of segments or angles can help.

Key Ideas
The intersection of the perpendicular bisectors of the sides of a triangle is called the circumcenter of the triangle.
A circle can be circumscribed around a triangle by using the circumcenter as the center and the distance from the circumcenter to a vertex of the triangle as the radius.

Key Skills
Construct the perpendicular bisectors of a triangle.
Construct the circumcenter of a triangle (the point equidistant from the vertices of a triangle).
Construct the circumcircle (the circle that only passes through the three vertices) of a triangle.
Using the properties of a perpendicular bisector of the sides of a triangle to solve problems and write proofs.

Vocabulary
concurrent lines
point of concurrency
circumcenter of a triangle
circumcircle
circumscribe

Handouts
Hospital Locator

Assignment
§5-2 (Txt. p.275) #14, 17, 20, 22, 24-26

Wednesday, November 29, 2006

Algebra 1 (Class 31)

Overview
§5-10 (p.224) Factoring by Grouping
We continue our work today with factoring second degree trinomial expressions by learning how to factor by grouping. This will be a key skill when factoring second degree trinomials where the coefficient of the second degree term is not equal to 1. We also spend some time reviewing material from sections 4-7 to 4-9 (word problems!) in preparation for the quiz on Friday.

Key Ideas
Identifying common factors

Vocabulary
Factoring by Grouping

Assignment
§5-10 (Txt. p.225) #1-12
§5-8 (Txt. p.218) #7-12
The following have been assigned before but it would be wise to rework.
§4-7 (Txt. p.170) #5, 8
§4-9 (p.173) #6

Tuesday, November 28, 2006

Geometry (Class 30)

Announcements
The assignment for this

Overview
§5.1 (p.264) Angle Bisectors
In this lesson we finish our proofs concerning perpendicular bisectors of a segment and then turn our focus to answering the question “How can we find the points that are equidistant from the sides of an angle.

Key Ideas
If a point is equidistant from the rays that form the sides of an angle, then the point is on the angle bisector of the angle.
If a point is on the angle bisector of an angle, then the point is equidistant from the sides of the angle.

Key Skills
Construct the angle bisector of an angle.
Determine if a point is one the angle bisector of an angle from information giving in a diagram.
Use Theorem 5.3 (Angle Bisector Theorem) and its converse to prove statements.
Apply the properties of an angle bisectors to find missing measurements.

Vocabulary
Angle Bisector
Equidistant

Handouts
Points Equidistant from the Sides of an Angle

Assignment
§5-2 (Txt. p.275) #8, 9, 14

§5-1 (Txt. p.268) #29, 44, 51

Monday, November 27, 2006

Algebra 1 (Class 30)

Overview
§5-8 Factoring Pattern for x^2+bx+c for negative c.

A Visual Approach to Functions: §7
Factoring second degree trinomials continues.

Our work with distance and time graphs continues to include more quantitative information and methods for organizing this information.

Key Ideas
Using the multiplication table helps you factor second degree trinomials.

Vocabulary

Assignment
§5-8 (Txt. p.218) #1-6
§5-7 (Txt. p.215) 10-14
§5-6 (Txt. p.210) #10-12, 31-33
§5-5 (Txt. p.206) #10-14, 37-41
§5-3 (Txt. p.198) #5

Sunday, November 26, 2006

SIx-Week Grades Posted

Six week progress report grades are now posted on the web and will be posted in the window of M100 on Monday. Grades for my classes are based on a “running total” not an average of each six-week grades. Also, it is a policy of the math department that a semester grade of C- or higher is earned in order for a student to be enrolled in the course for the second semester.
Lastly, please see me promptly if you believe there is a mistake in the records.

Tuesday, November 21, 2006

Geometry (Class 29)

Announcements
The assignment for this class has changed from the one on the assignment sheet.

The Make-Up for the Mid-Term will be on Th. Nov. 30 from 2:50 to 3:30 in M100. This is the only opportunity to take the Mid-Term if you were absent (excused) the day it was given.

Overview
§5.1 (p.264) Perpendicular Bisectors
In this lesson we investigate the properties of a perpendicular bisector of a segment.

Key Ideas
The distance from a point to a line is the length of a segment that is perpendicular to the line passing through the point.
If a point is on the perpendicular bisector of a segment, then the point is equidistant from the endpoints of the segment.
If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

Key Skills
Construct a perpendicular bisector of a segment.
Measure the distance from a point to a line.
Calculate the distance between two points using the distance formula.
Determine if a point is equidistant from the endpoints of a segment.
Use Theorem 5.1 (Perpendicular Bisector Theorem) and the converse of Theorem 5.1 to prove statements.
Justify that a given segment is a perpendicular bisector based on information provided in a diagram.

Vocabulary
Perpendicular Bisector
Equidistant

Handouts
Coffee Shop Problem

Assignment
Note: There are different assignments for different classes.
B3: §5-1 (Txt. p.268) #8-10 14, 16, 30
B4: Coffee Shop Problem Proofs

Monday, November 20, 2006

Geometry Mid-Term Make-Up

Geometry Mid-Term Make-Up is on Thursday, November 30 from 2:50 to 4:30 in M100. This is the only opportunity for a student to take the Mid-Term if they had an excused absence when it was originally given. A score of 0 will be recorded after this date if a student has not taken the mid-term.

Algebra 1 (Class 29)

Overview
§5-7 Factoring Pattern for x^2+bx+c for positive c.

A Visual Approach to Functions: §6
We continue our work with factoring second degree trinomials.

We also continue our work with graphs of Distance v. Time.

Key Ideas
Factoring is the inverse (undoes) expanding.
Division is to multiplication as factoring is to expanding.
To factor a second degree trinomial expression:
1) Draw the multiplication table
2) Reason through what has to go in each cell of the table by thinking about factor pairs.

Vocabulary

Assignment
§5-7 (Txt. p.215) #1-9
§5-6 (Txt. p.210) #5-9, 26-30
§5-5 (Txt. p.206) #10-13, 31-36
§5-3 (Txt. 198) #4

Sunday, November 19, 2006

Grades Updated

Grades, including the Geometry Mid-Term, have been updated. Except for comportment, these are very close (if not exactly) the grades for the 2nd six-week progress reports. Please let me know if you see any mistakes.

Friday, November 17, 2006

Geometry (Class 28)

Overview
Midterm Chapters 1-4
Today the entire class is dedicated to the Mid-term covering Chapters 1-4.

Key Ideas

Vocabulary

Assignment
No Homework

Thursday, November 16, 2006

Algebra 1 (Class 28)

Overview
§5-5 Difference of Two Squares

§5-6 Squares of Binomials

Today we begin our work with factoring second degree (quadratic) trinomial expressions. A key to understanding these problems is to use the area model of multiplication we have been using to multiply binomials but in reverse. In other words, we will be given the inside part of the area models and have to figure out the dimensions of the rectangle. Having a strong grip on multiplication facts is a real asset when factoring! A web-resource for this topic can be found at http://www.classbrain.com/artteensb/publish/factoring_trinomials_interactive.shtml This lesson uses a different approach than what we have used in class, but you might even like it more!

Key Ideas
Factoring is the inverse (undoes) expanding.
Division is to multiplication as factoring is to expanding.
To factor a second degree trinomial expression:
1) Draw the multiplication table
2) Reason through what has to go in each cell of the table by thinking about factor pairs.

Vocabulary
multiplication table
cell (of a table)
factor pairs
second degree trinomial expressions

Assignment
§5-6 (Txt. p.210) #1-4, 21-25
§5-5 (Txt. p.206) #5-9, 26-30
§5-3 (Txt. p.198)#3
§5-2 (Txt. p.192) #3k-1| k = 6 to 10

Wednesday, November 15, 2006

Geometry (Class 27)

Overview
§4.7 (p.243) Triangles and Coordinate Proof

Review for Midterm
Today we continue our work with Analytic Geometry.

We also spend a significant portion of the class working review problems in our groups in order to further prepare for the mid-term exam on Friday November 17.

Key Ideas
Use the coordinates to your advantage!
The main tools that can be used when writing coordinate proofs are the distance formula (to show two segments are of equal length and hence congruent), the midpoint formula (to find the location of the midpoint), the slope of a line (to show lines are parallel or perpendicular), and the Pythagorean Theorem (to show that a triangle is a right triangle).
In order to make the proof as easy as possible, place the figure wisely. For instance, place a vertex at the origin, or use the axes to form a right triangle, or use the symmetry of an isosceles triangle to your advantage by placing the base on the x-axis and the vertex angle on the y-axis.

Vocabulary
No new vocabulary

Assignment
§4.7 (Txt. p.247) #11-13, 18, 24-26

Chapter 4 Test (Txt. p.255) 10 most important problems-- you pick them!

Chapter 4 Standardized Test (Txt. p.256) 10 most important problems-- you pick them!

Tuesday, November 14, 2006

Algebra 1 (Class 27)

Overview
§5-3 (p.197) Writing Expressions for Shaded Regions

A Visual Approach to Functions: §6 and §7
We spend some more time today working with writing expressions for the shaded regions of geometric figures including some created by students. We also dedicate a significant portion of the class to our continuing work with interpreting graphs of Distance v. Time relationships.

Key Ideas
When writing the coordinates of a point on a graph, the back and forth (x) is written first and the up and down (y) is written last. An aide for remembering this is that (x, y) are in alphabetical order.

The rate at which someone is traveling can be determined by using the coordinates from a distance versus time graph.

Vocabulary
coordinates
x-intercept
y-intercept
rate
slope

Assignment
§5-3 (Txt. p.198) #2
§5-3 (Txt. p.196) #3k-2| k = 1 to 6 AND 11 to 13
§5-2 (Txt. p.192) #3k| k=6 to 10

Monday, November 13, 2006

Geometry (Class 26)

Overview
§4.7 (p.243) Triangles and Coordinate Proof

Review for Midterm
In 1637 the French mathematician Rene Descartes linked Algebra and Geometry by inventing the coordinate plane. This invention (or discovery depending on your viewpoint) opened the doors for the development of Analytic Geometry. Today we have an introduction to this “new” type of Geometry and begin to learn how we can use our algebraic skills to prove theorems about geometric shapes. (http://en.wikipedia.org/wiki/Ordinate)

Key Ideas
Use the coordinates to your advantage!
The main tools that can be used when writing coordinate proofs are the distance formula (to show two segments are of equal length and hence congruent), the midpoint formula (to find the location of the midpoint), the slope of a line (to show lines are parallel or perpendicular), and the Pythagorean Theorem (to show that a triangle is a right triangle).
In order to make the proof as easy as possible, place the figure wisely. For instance, place a vertex at the origin, or use the axes to form a right triangle, or use the symmetry of an isosceles triangle to your advantage by placing the base on the x-axis and the vertex angle on the y-axis.

Vocabulary
analytic geometry
coordinate proof

Assignment
§4.7 (Txt. p.247) #7-10, 22, 23, 35, 37, 38, 43

Chapter 4 Review (Txt. p.252) 5 most important problems--you pick them!

Thursday, November 09, 2006

Algebra 1 (Class 26)

Overview
§5-3 (p.197) Writing Expressions for Shaded Regions
A Visual Approach to Functions: §5
Today we focus on writing expressions for the shaded regions of various geometric figures. The key to success for doing these problems is to know the formulas for finding the area of a rectangle (Area = L x W, and the area of a circle (Area = πr^2) and to be able to puzzle through the combining of these formulas in creative ways.

Key Ideas
The formula for finding the area of a rectangle is Area = L x W and the formula for finding the area of a circle is Area = π(r)^2. We will use 22/7 to approximate the value of π.

When writing expressions for shaded regions:
1) breaking the figure up into simple shapes (rectangles, circles, triangles) can often help.
2) it frequently helps to try the problem with numbers first,
3) subtracting the area of one region from another region will often give you an expression for the shaded region.

Vocabulary
shaded region

Assignment
§5-3 (Txt. p.198) #1
§5-3 (Txt. p.196) #3k-1| k= 1 to 6 and 11 to 13
§5-2 (Txt. p.192)#3k-2| k=1 to 5
§4-7 (Txt. p.166) #3k-1| k = 7 to 9