HolcombMath

Wednesday, February 28, 2007

Geometry (Class 53)

Announcements
Quiz Friday-- focuses on Chapter 8 Opener, Chapter 8 Lesson 1, Proof by Contradiction

Overview
In this class we apply what we have learned about similarity, ratios, and proportions in order to solve some applied problems.
Textbook Sections
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving in Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
Similarity can be used to determine relationships between lengths in similar figures.

Key Skills
Using a scale factor to enlarge or reduce a triangle
Writing proportions when given two similar triangles
Calculating a scale factor when given two similar triangles
Measurement
Working with equivalent fractions

Handouts
Chapter 8: Lesson 3
Chapter 8: Lesson 4

Assignment
Finish Ch. 8 Lesson 3- Finish
Finish Ch. 8 Lesson 4 #1, 2
8.2 Challenge: Skills and Applications #10-13

Tuesday, February 27, 2007

Algebra (Class 54)

Overview
Today Mr. Holcomb is out sick. The focus will be to correct last weeks quiz and to work the review worksheets. He will be back for the next class-- just has a cold.
Textbook Sections
No New Sections

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Algebraic expressions can be simplified.

Key Skills
Simplifying algebraic expressions
Solving first degree equations.

Handouts
No Handouts Posted

Assignment
Two review worksheets-- Both sides, all. Show clear and complete work. Extra paper is suggested.

Monday, February 26, 2007

Geometry (Class 52)

Announcements
Quiz Friday-- focuses on Chapter 8 Opener, Chapter 8 Lesson 1, Proof by Contradiction

Overview
In today’s class we practice applying what we have learned about similar triangles and the proportions related to their corresponding sides. If the weather permits, we will apply these ideas to the indirect measurement of at least one object on campus that cannot easily be measured directly. Otherwise we will this work off until a future date and continue with our study of similarity while staying indoors.
Textbook Sections
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving in Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
When triangles are similar, proportions that relate the lengths of their corresponding sides can be written and used to calculate missing lengths.
Two methods for determining if triangles are similar: 1) two angles are congruent, 2) corresponding sides are proportional

Key Skills
Using a scale factor to enlarge or reduce a triangle
Writing proportions when given two similar triangles
Calculating a scale factor when given two similar triangles
Measurement
Working with equivalent fractions

Handouts
Chapter 8- Lesson 2: Using Similarity
Chapter 8- Lesson 3: Putting Similarity to Work
8.2 Challenge: Skills and Applications

Assignment
Lesson 8.2- Challenge: Skills and Applications

Friday, February 23, 2007

Algebra (Class 53)

Announcements
The second quiz for the second semester will be next Friday (2/23)— make sure to review your homework assignments and your corrections from your last quiz!

Overview
In this class we extend our methods of finding the Least Common Multiple (LCM) of two numbers to finding the LCM of two algebraic expressions. This lays the groundwork for adding and subtracting algebraic expressions.
Textbook Sections
§6-4 (Txt. p.259) Least Common Denominators

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The LCM of two numbers can be created by using the prime factors of the numbers.

Key Skills
Finding the least common multiple (denominator) of two numbers or two algebraic expressions.
Factoring numbers and algebraic expressions

Vocabulary
LCM
LCD

Handouts
No Handouts Posted

Assignment
§6-4 (Txt. p.262) #21-26
§6-3 (Txt. p.256) #13-18
§6-2 (Txt. p.253) #17-20

Thursday, February 22, 2007

Geometry (Class 51)

Announcements
Quiz next Friday-- focuses on Chapter 8 Opener, Chapter 8 Lesson 1, Proof by Contradiction

Overview
In the last class we established what we mean by the word “similar” and saw that we would be convinced that two triangles are similar if we new that at least two angles were congruent or if we knew that we could enlarge all of the sides by the same scale factor.

In this lesson we extend these ideas and apply them to create similar triangles, to determine if two triangles are similar, and to solve for missing lengths of sides in two similar triangles.
Textbook Sections
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving in Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
Determining if two triangles are similar.
When triangles are similar, you can match up sides so that the ratio of the lengths between the two triangles are the same.

Key Skills
Using a scale factor to enlarge or reduce a triangle
Writing proportions when given two similar triangles
Calculating a scale factor when given two similar triangles
Measurement
Working with equivalent fractions

Vocabulary
ratio
proportion
geometric mean

Handouts
No Handouts Posted

Assignment
Chapter 8 Lesson 1--Through Practice Problem 15.

Wednesday, February 21, 2007

Algebra (Class 52)

Announcements
The second quiz for the second semester will be next Friday (2/23)— make sure to review your homework assignments and your corrections from your last quiz!

Overview
Today we extend our work with simplifying fractions to include the operations of multiplication and division. A key for success remains the students ability to factor algebraic expressions.
Textbook Sections
§6-2 (Txt. p.251) Multiplying Fractions
§6-3 (Txt. p.255) Dividing Fractions

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
To multiply fractions you multiply the numerators and the denominators “straight across”.
To divide fractions, you “keep, change, flip” and then multiply.
You can simplify the fraction after multiplication or division, or you may simplify before.

Key Skills
Finding the prime factors of a number
Factoring using the GCF of the terms of a polynomial
Factoring trinomials into the product of monomials
Multiplying polynomial expressions
Simplifying fractions

Handouts
No Handouts Posted

Assignment
§6-2 (Txt. p.253) #12-16, 35-38
§6-3 (Txt. p.256) #7-12, 21-24
Algebra Practice Worksheets 12.11 & 13.9

Tuesday, February 20, 2007

Geometry (Class 50)

Overview
Today we begin our study of similarity by discussing what is required to be convinced that two triangles are the same shape, though not necessarily the same size. We then extend these ideas to include the concept of a scale factor, a number by which you can multiply all of the sides of a triangle to produce another triangle similar in shape to the first. We then investigate the implications of this enlargement.
In addition, we take our first quiz for the second semester.
Textbook Sections
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving in Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
If the angles of two triangles are equal, the triangles are similar.
If the sides of two triangles have the same scale factor, the triangles are similar.
If you multiply the sides of a triangle by the same amount and then use these measurements to construct a new triangle, the two triangles will be similar

Key Skills
Using a scale factor to enlarge or reduce a triangle
Writing proportions when given two similar triangles
Calculating a scale factor when given two similar triangles
Measurement
Working with equivalent fractions

Vocabulary
Scale factor
ratio
proportion

Handouts
Chapter 8- Lesson 1

Assignment
Chapter 8 Lesson 1 #1-5
Txt. p.796 #1, 2, 9, 10
Txt. p.812 #18, 21, 23, 26, 29
Txt. p.811 #6

Friday, February 16, 2007

Algebra (Class 51)

Announcements
The second quiz for the second semester will be next Thursday (2/22)— make sure to review your homework assignments and your corrections from your last quiz!

Overview
Today we work to generalize our understanding of simplifying fractions to algebraic symbols. A key concept is to understand how the factors of the numerator and denominators play a role in determining if a fraction is simplified and then being able to factor algebraic expressions.
Textbook Sections
§6.1 (Txt. p.247) Simplifying Fractons

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Fractions are simplified when the numerators and denominators are relatively prime-- when they share no common factors.

Key Skills
Finding the prime factors of a number
Factoring using the GCF of the terms of a polynomial
Factoring trinomials into the product of monomials
Simplifying fractions

Vocabulary
Relatively Prime
Prime Factors
Simplify

Handouts
No Handouts Posted

Assignment
Fraction Practice Worksheets p.76 and 77
§6.1 (Txt. p.248) #1-8

Thursday, February 15, 2007

Geometry (Class 49)

Overview
Today we analyze the data we collected during last class in order to find a way to describe a relationship between height and head circumference.
As time permits, we begin our study of similarity by discussing what is required to be convinced that two triangles are the same shape, though not necessarily the same size. We then extend these ideas to include the concept of a scale factor, a number by which you can multiply all of the sides of a triangle to produce another triangle similar in shape to the first. We then investigate the implications of this enlargement.
In addition, we take our first quiz for the second semester.
Textbook Sections
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving in Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
If the angles of two triangles are equal, the triangles are similar.
If the sides of two triangles have the same scale factor, the triangles are similar.
If you multiply the sides of a triangle by the same amount and then use these measurements to construct a new triangle, the two triangles will be similar

Key Skills
Using a scale factor to enlarge or reduce a triangle
Writing proportions when given two similar triangles
Calculating a scale factor when given two similar triangles
Measurement
Working with equivalent fractions

Handouts
Chapter 8 Opener

Assignment
Proofs by Contradiction practice.

Wednesday, February 14, 2007

Algebra (Class 50)

Announcements
The first quiz for the second semester will be this Friday— make sure to review your homework assignments and your corrections from the final exam!

Overview
The focus of our lesson remains the review and deepening of our understanding of fractions as we move towards working with fractions which involve algebra.
Textbook Sections

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
In order to compare quantities a common unit is needed.
A common unit for fractions can be created by using the prime factors of the denominators.

Key Skills
Converting units
Naming fractions
Finding equivalent fractions
Simplifying fractions

Handouts
No Handouts Posted

Assignment
Fraction Practice Worksheets

Tuesday, February 13, 2007

Geometry (Class 48)

Announcements
Quiz-- Thursday focusing on areas of quadrilaterals, proof by contradiction

Overview
We begin our study of similarity by investigating ratios, namely the ratio between the circumference of a person’s head and their height. Students use metric units (cm) to measure head circumference and height. We then collect this data as a class and create a coordinate graph of Height compared to Head Circumference. A line of best fit is added and students compute the slope and y-intercept of the line. Analysis of the relationship is then carried out based on this data.
Textbook Sections
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving in Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
Coordinate graphs and lines can be used to make predictions.
The slope of a line can be used as a tool to describe a relationship between two sets of data (height and head circumference in this case.)

Key Skills
Using a scale factor to enlarge or reduce a triangle
Writing proportions when given two similar triangles
Calculating a scale factor when given two similar triangles
Measurement
Working with equivalent fractions

Handouts
No Handouts Posted

Assignment
Txt. p.808 #17, 19, 21, 22, 29, 32, 35
Txt. p.813 #10-17, 21
B-3 Also needs to compete Proof by Contradiction: Practice 3,4 (Will be collected)

Friday, February 09, 2007

Algebra (Class 49)

Announcements
The first quiz for the second semester will be this Friday— make sure to review your homework assignments and your corrections from the final exam!

Overview
The focus of our lesson remains the review and deepening of our understanding of fractions as we move towards working with fractions which involve algebra. In addition, we take our first quiz for the second semester today.
Textbook Sections

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
In order to compare quantities a common unit is needed.
A common unit for fractions can be created by using the prime factors of the denominators.

Key Skills
Converting units
Naming fractions
Finding equivalent fractions
Simplifying fractions

Handouts
No Handouts Posted

Assignment
Fraction Practice Assignment Handouts

A Mistake on Proof 2 for Geometry

There is a mistake in the givens for proof two of the practice assignment. It reads “Given: P is not the midpoint of HK; segment HK is congruent to segment JK”. IT SHOULD READ “Given: P is not the midpoint of HK; segment HJ is congruent to segment JK” Sorry. Please pass this on to other students if you read this.

Thursday, February 08, 2007

Geometry (Class 47)

Announcements
Quiz-- Next Thursday focusing on areas of quadrilaterals, proof by contradiction, and Chapter 8-Lesson 1

Overview
We continue our work learning how to use proof by contradiction (indirect proof). We also begin our work concerning similarity.
Textbook Sections
§5.6 (Txt. p.302) Indirect Proof
§8.1 (Txt. p.457) Ratio and Proportion
§8.2 (Txt. p.465) Problem Solving IN Geometry with Proportions
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
Some statements only have two possibilities-- either they are true or they are false.
If a statement can only be either true or false, then if you show that the statement is false, its opposite (negation) must be true.
If two figures are the same shape, then their corresponding sides are proportional-- in the same ratio-- and their corresponding angles are equal.

Key Skills
Proving statements using a proof by contradiction-- knowing the format of these proofs is critical.
Measurement
Working with equivalent fractions

Vocabulary
ratio
proportion
similar shapes
similarity

Handouts
No Handouts Posted

Assignment
Proof by Contradiction: Practice 1-4 (Will be collected)

Wednesday, February 07, 2007

Algebra (Class 48)

Announcements
The first quiz for the second semester will be this Friday— make sure to review your homework assignments and your corrections from the final exam!

Overview
The focus of our lesson remains the review and deepening of our understanding of fractions as we move towards working with fractions which involve algebra
Textbook Sections
No New Text Book Sections

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
In order to compare quantities a common unit is needed.
A common unit for fractions can be created by using the prime factors of the denominators.

Key Skills
Converting units
Naming fractions
Finding equivalent fractions
Simplifying fractions

Handouts
No Handouts Posted

Assignment
Txt. p. 245 #12
Txt. p.243 #20-22, 29-31, 38