HolcombMath

Thursday, March 15, 2007

Algebra (Class 60)

Overview
Today we practice using polynomial long division and we return to take another look at equations of lines-- in particular we find how to determine the slope when given the coordinates of two points.
Textbook Sections
§6-7 (Txt. p274) Polynomial Long Division
§8-3(Txt. p.360) Slope of a Line

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Polynomial division works like long division with numbers
Place holders need to be used when the dividend is missing terms.
The slope of a line can be found by calculating the ∆y/∆x
The slope of a line can be used to find other points on a line.

Key Skills
Polynomial division
Finding the slope of a line given two points
Finding other points on a line when given two points

Vocabulary
Slope
∆y
∆x
y-intercept
slope-intercept form of an equation
dividend
divisor
quotient

Handouts
No Handouts Posted

Assignment
§8-3 (Txt. p.363) #1-5
§6-7 (Txt. p.276) #7, 8
§6-6 (Txt. p.271) #17-19

Wednesday, March 14, 2007

Geometry (Class 58)

Announcement
Quiz Friday focusing on Chapter 8 Lessons 3 to 5 and Chapter 9 Lesson 1

Overview
Today we start the development of the three key trigonometric ratios, what they mean, where they come from, why they work, and how to put them to work.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios

Key Attitudes
Mathematics is about justification.

Key Ideas
If two right triangles have one additional congruent pair of angles, then the triangles are similar.
If two right triangles are similar, then the ratios of their sides are equal.
If you know the measure of one non-right angle in a right triangle and the length of one side, then you can find the lengths of the other sides and the measures of the other angles.
If you know the length of two sides of a right triangle, then you can find the lengths of all of the sides of the right triangle

Key Skills
Using trigonometric ratios to solve right triangles.

Handouts
Chapter 9-Lesson 2: An Introduction to Right Triangle Trigonometry
Chapter 9-Lesson 2: Trigonometric Ratios Record Sheet

Assignment
§9.1 (Txt. p.531)#13, 14, 17, 18, 19, 20, 33
§8.6 (Txt. p.503)#23, 24

Tuesday, March 13, 2007

Algebra (Class 59)

Overview
In today’s call we work extend our skills involving algebraic fractions to include working with mixed numbers. In addition, we also learn how to generalize our method of doing long division involving whole numbers to doing long division involving algebraic expressions.
Textbook Sections
§6.6 (Txt. p.270) Mixed Expressions
§6.7 (Txt. p274) Polynomial Long Division

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
In order to add fractions, you have to have the same size pieces; you have to have common denominators.
Finding a common denominator requires that you adjust the numerator.
Long division of polynomials works just like long division of whole numbers.

Key Skills
Finding the LCD
Adding expressions
Multiplying expressions

Handouts
No Handouts Posted

Assignment
§6-6 (Txt. p.271) 5-16
§6-7 (Txt. p.276) #1-6

Monday, March 12, 2007

Geometry (Class 57)

Overview
Today we begin our work with trigonometry. We start by investigating relationships in right triangles.
Textbook Sections
§9.1 (Txt. p.527) Similar Right Triangles
§9.5 (Txt. p.558) Trigonometric Ratios

Key Attitudes
Mathematics is about justification.

Key Ideas
Right triangles contain other right triangles which are similar.

Key Skills
Proving triangles similar
Writing and using proportions based on similarity statements

Handouts
Chapter 9- Lesson 1: Seeing Similarities

Assignment
Txt. p.519 #1, 4-13
Chapter 9- Lesson 1

Sunday, March 11, 2007

Six Week Grades Posted

Grades for the first six weeks of the second semester are posted. Please let me know if you think you see a mistake-- printing the progress report from the web and bringing in the incorrectly recorded papers is very helpful.

Friday, March 09, 2007

Algebra (Class 58)

Overview
In today’s call we work extend our skills involving algebraic fractions to include working with mixed numbers. In addition, we also learn how to generalize our method of doing long division involving whole numbers to doing long division involving algebraic expressions.
Textbook Sections
§6.6 (Txt. p.270) Mixed Expressions
§6.7 (Txt. p274) Polynomial Long Division

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
In order to add fractions, you have to have the same size pieces; you have to have common denominators.
Finding a common denominator requires that you adjust the numerator.
Long division of polynomials works just like long division of whole numbers.

Key Skills
Finding the LCD
Adding expressions
Multiplying expressions

Handouts
No Handouts Posted

Assignment
§6-6 (Txt. p.271) 5-16
§6-7 (Txt. p.276) #1-6

Thursday, March 08, 2007

Geometry (Class 56)

Overview
Today we focus on proving triangles simialr.
Textbook Sections
§8.5 (Txt. p.488) Proving Triangles Similar

Key Attitudes
Mathematics is about justification.

Key Ideas
Triangles can be proved to be similar by showing that:
two angles are congruent (AA Similarity Theorem)
the sides of the triangles are proportional (SSS Similarity Theorem)
two sides are proportional and the included angle is congruent (SAS Similarity Theorem)

Key Skills
Proving triangles similar

Handouts
Chpater 8: Lesson 5- Are they Similar?

Assignment
Chapter 8 Lesson 5- Similarity Proofs

Wednesday, March 07, 2007

Algebra (Class 57)

Announcements
Wednesday we have a school wide problem solving quiz-- the score can only help your grade.

Overview
After reviewing student work from last class, I have decided to postpone the quiz until next week. Instead we will practice adding and subtracting rational expressions today.
Textbook Sections
§6-5 (Txt. p.264) Adding and Subtracting Fractions

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
In order to add fractions, you have to have the same size pieces; you have to have common denominators.
Finding a common denominator requires that you adjust the numerator.

Key Skills
Finding the LCD
Adding expressions
Multiplying expressions

Handouts
No Handouts Posted

Assignment
Practice Worksheets 17.9, 17.10, 17.11, 17.12

Tuesday, March 06, 2007

Geometry (Class 55)

Overview
Today we wrap-up our work on Chapter 8: Lesson 4 where we examine a different method for setting up proportions involving similar triangles formed when a line intersects the sides of a triangle and is parallel to the third side. As time permits we also begin our work with proving triangles similar.
Textbook Sections
§8.4 (Txt. p.480) Similar Triangles
§8.5 (Txt. p.488) Proving Triangles SImilar

Key Attitudes
Mathematics is about justification.

Key Ideas
If a line intersects the sides of a triangle, and the line is parallel to the third side, then the line divides the other lines into 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
No Handouts Posted

Assignment
Finish Chapter 8 Lesson 4 (Due next class)
§8.4 (Txt. p.485) #40, 41, 45, 46
Quiz Corrections
Weekly Summary

Monday, March 05, 2007

Algebra (Class 56)

Announcements
Wednesday we have a school wide problem solving quiz-- the score can only help your grade.

Overview
Today we continue our work with adding and subtracting algebraic fractions with a focus on getting common denominators involving variables.
Textbook Sections
§6-5 (Txt. p.264) Adding and Subtracting Fractions

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
In order to add fractions, you have to have the same size pieces; you have to have common denominators.
Finding a common denominator requires that you adjust the numerator.

Key Skills
Finding the LCD
Adding expressions
Multiplying expressions

Handouts
No Handouts Posted

Assignment
§6-5 (Txt. p.267) #7-12, 38-43
§6-4 (Txt. p.262) #33-38

Friday, March 02, 2007

Geometry (Class 54)

Overview
Today, which looks like it will be sunny, students will take quiz 7 which focuses on using the ideas related to similar triangles. In addition, they will be going outside to put similarity to work in order to measure the height of the gym and the flag pole.
Textbook Sections
§8.4 (Txt. p.480) Similar Triangles

Key Attitudes
Mathematics is about justification.

Key Ideas
If triangles are similar, their corresponding sides are proportional.
If you know three values in a proportion, you can solve for the fourth value.

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
§8.4 (Txt. p.483)18-26, 39-42, 53
Chapter 8: Lesson 2

Thursday, March 01, 2007

Algebra (Class 55)

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 pull together many of the skills we have been building-- factoring, finding LCD’s, multiplying expressions, adding expressions, and simplifying expressions.
Textbook Sections
§6.5 (Txt.  p.264) Adding and Subtracting Fractions

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
In order to add two fractions, the denominators need to be the same.

Key Skills
Finding the LCD
Adding expressions
Multiplying expressions

Handouts
No Handouts Posted

Assignment
§6-5 (Txt. p.264) #1-6, 35-37
§6-4 (Txt. p.262) #27-32
§6-3 (Txt. p.256) #19-22

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