HolcombMath

Friday, November 30, 2007

Geometry (Class 32)

Overview
In today’s class we take Test 5 which focuses on classes 25-31 whose main focus was using congruent triangles as tools for proving other facts, proving right triangles congruent using the Leg-Leg Theorem or the Hypotenuse-Leg Theorem. After the test, as time permits, we take a look at using another approach for proving theorems-- Proof by Contradiction (Indirect Proof)
Textbook Sections
§4.6 (Txt. p.236) Isosceles, Equilateral, and Right Triangles
§5.0 (Not in Text) Locus of Points

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Right triangles can be proved congruent using either the Leg-Leg Theorem or the Hypotenuse-Leg Theorem.
A figure can be thought of as a collection of points that meet a given set of requirements. This is called a “locus” of points.

Key Skills
Deciding if two triangles can be proved congruent from the given information.
Identifying which triangle congruence postulate can be used to prove triangles congruent.
Proving triangles congruent using HL or LL.
Constructing right trinagles.

Turn-In (#31)
Algebra & Geometry 5.5 (Optional)
Algebra & Geometry 6
§4.6 (Txt. p.239) #8, 9, 11-13, 17, 18, 20, 21, 33, 34

Handouts
Chapter 4- Lesson 6: Proof By Contradiction
Warm-Up 11/30

Assignment
§4.7 (Txt. p.247) #6-19
§4.6 (Txt. p.239) #10, 14-16, 19, 22, 23
Finish Chapter 4- Lesson 5: Proving Right Triangles Congruent
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, November 29, 2007

Algebra (Class 31)

Overview
In today’s class we continue to work with problems involving percents. In particular we examine the concept of simple interest and learn how to solve problems involving simple interest.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method
§3-1 (Txt. p.95) Transforming Equations

Vocabulary
Interest
Principal
Rate of interest
Time
Total
I=PRT
A=P+I

Key Attitudes
Math is about investigating and confirming

Key Ideas
Interest is computed as a percent.
Calculating simple interest involves using the principal, the rate, and the amount of time.

Key Skills
Setting up and solving simple interest problems

Turn-In (#30)
§9-1 (Txt. p.415) #4-6 (Accurate graphs required! Use graph paper if needed.)
Packet through SP5
Test Corrections
Finish writing the equation of the lines for the sides of the square from the warm-up.

Handouts
No Handouts Posted

Assignment
§9-1 (Txt. p.415) #7-10, 19 (Accurate graphs required! Use graph paper if needed.)
Finish packet through SP 10
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, November 28, 2007

Geometry (Class 31)

Overview
In today’s class we work to solidify our abilities for using algebra to solve geometric problems-- in particular the finding the point of intersection of two lines.
Textbook Sections

Vocabulary
Locus

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
An equation for a line can be determined from the coordinates of two points.
In order to write the equation in slope-intercept form from two points, the slope of the line and the y-intercept needs to be determined.
In order to fins the point of intersection of two lines a system of two linear equations needs to be written and solved.
The key step in solving a system of equations is turning the two equations involving two variables into one equation with only one variable.
Two approaches for solving a system of two linear equations are 1) by using substitution, 2) by adding or subtracting the two equations.

Key Skills
Writing the equation of a line from two points.
Writing and solving a system of two linear equations.

Turn-In (#30)
§4.4 (Txt. p.223)#8-13, 19, 20
§4.5 (Txt. p.234) #17, 18
Chapter 4- Lesson 4.5

Handouts
Algebra and Geometry 5.5
Algebra and Geometry 6

Assignment
Algebra & Geometry 5.5 (Optional)
Algebra & Geometry 6
§4.6 (Txt. p.239) #8, 9, 11-13, 17, 18, 20, 21, 33, 34
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, November 27, 2007

Algebra (Class 30)

Overview
The class today focuses on correcting Test 6 as well as moving on to Unit 5, Week 18: Ratio, Proportion, and Percent. In this unit we examine problems involving finding the percent increase or decrease, understanding and calculating simple interest, as well as solving general problems involving percent. We also continue to develop our skills for writing the equations of lines during the daily warm-ups
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method

Key Attitudes
Math is about investigating and confirming

Key Ideas
“percent” means “out of 100”
Percent problems are proportion problems

Key Skills
Setting up and solving proportions.
Computing percents.

Turn-In (#29)
§9-1 (Txt. p.415) #1-3 (Accurate graphs required! Use graph paper if needed.)

Handouts
No Handouts Posted

Assignment
§9-1 (Txt. p.415) #4-6 (Accurate graphs required! Use graph paper if needed.)
Packet through SP5
Test Corrections
Finish writing the equation of the lines for the sides of the square from the warm-up.
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, November 26, 2007

Geometry (Class 30)

Overview
In today’s class we finish up our work proving some useful theorems and then take a look at proving right triangles congruent.

Also, a substantial number of students are struggling with finding the intersection of two lines. Please come get some help with this at lunch or after school. You can also check out http://www.regentsprep.org/Regents/math/math-topic.cfm?TopicCode=syslin

New Theorems
Hypotenuse-Leg Theorem: If two triangles are right triangles with congruent hypotenii and a pair of congruent legs, then the triangles are congruent.
Leg-Leg: If two triangles are right triangles and the legs of these triangles are congruent, then the triangles are congruent.
Textbook Sections
§4.6 (Txt. p.236) Isosceles, Equilateral, and Right Triangles

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Right triangles can be proved congruent using different information.

Key Skills
Deciding if two triangles can be proved congruent from the given information.
Identifying which triangle congruence postulate can be used to prove triangles congruent.
Proving triangles congruent using HL or LL.
Constructing right trinagles.

Turn-In (#29)
Algebra & Geometry 5

Handouts
Chapter 4- Lesson 5: Proving Right Triangles Congruent

Assignment
§4.4 (Txt. p.223)#8-13, 19, 20
§4.5 (Txt. p.234) #17, 18
Finish Chapter 4- Lesson 4.5
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, November 20, 2007

Algebra (Class 29)

Overview
In today’s class we finish Unit 5: Week 17- Ratio, Proportion, and Percent. In addition extend our knowledge of the graphs of lines by starting to examine how we could find the point of intersection of two lines. Finally, we take out 6th test whose focus remains writing and using equations of lines.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method

Key Attitudes
Math is about investigating and confirming

Key Ideas
Ratio, rates, proportions, and percents are all ways to compare the relative size of two quantites.

Key Skills
Setting up and solving proportions.
Computing percents.
Finding factors of numbers.
Graphing lines

Turn-In (#28)
Nothing to turn in today.

Handouts
No Handouts Posted

Assignment
§9-1 (Txt. p.415) #1-3 (Accurate graphs required! Use graph paper if needed.)
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, November 19, 2007

Geometry (Class 29)

Overview
In today’s class we use congruent triangles to develop some new theorems which will be useful.

New Theorems
Sum of the Interior Angles of a Triangle, Third Angle Theorem, Base Angles Theorem, AAS, Converse of Base Angles Theorem, Equilateral Triangle if and only if Equiangular Triangle.
Textbook Sections
§4.6 (Txt. p.236) Isosceles, Equilateral, and Right Triangles
§4.4 (Txt. p.220) Proving Triangles are Congruent: ASA and AAS

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
The definitions, postulates, and theorems we have developed can be used to create new theorems.

Key Skills
Deciding if two triangles can be proved congruent from the given information.
Identifying which triangle congruence postulate can be used to prove triangles congruent.
Proving triangles congruent using SSS, SAS, or ASA.

Turn-In (#28)
Finish Chapter 4- Lesson 3: Proving Triangles Congruent.
§4.3 (Txt. p.216) #6-8, 12-17, 21, 22
Txt. p.210 #1-6

Handouts
Chapter 4- Lesson 4.5: Some Theorems You May Find Useful

Assignment
Finish Chapter 4- Lesson 4.5: Some Theorems You May Find Useful Through #5
Algebra & Geometry #5
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, November 16, 2007

Algebra (Class 28)

Overview
I will be absent for today’s class. Not to worry, I’ll be back on Monday. Mr. Haddow will be the replacement teacher for today. The class will focus on learning a game involving the factors of numbers. In addition, students will need to finish the current packet of work-- Unit 5- Week 17.
Textbook Sections
§7-2 (Txt. p.293) Proportions

Key Attitudes
Math is about investigating and confirming

Key Ideas
A number, a, is said to be a factor of another number, b, if b can be divided by a without having a remainder. For example, 2 is a factor of 8, but 3 is not a factor of 8.

A number, a, is a multiple of a number b if there exists some whole number k such that kb=a. For example, 15 is a multiple of 3 since 5(3)=15.

Key Skills
Setting up and solving proportions.
Computing percents.
Finding factors of numbers.

Turn-In (#27)
Txt. p.373 Self-Test #1-6
Txt. p.369 #37

Handouts
No Handouts Posted

Assignment
Finish Packet-- Get parent signature
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, November 15, 2007

Geometry (Class 28)

Overview
In today’s class we learn how to use congruent triangles as a tool for proving other facts. A key skill will be using SSS, ASA, and SAS as tools for proving triangles congruent.

New Definitions, Postulates, or Theorems
If two radii are in the same circle, then they are congruent.
Textbook Sections
§4.5 (Txt. p.229) Using Congruent Triangles

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
If triangles are congruent, then the corresponding parts of the triangle are congruent.

Key Skills
Deciding if two triangles can be proved congruent from the given information.
Identifying which triangle congruence postulate can be used to prove triangles congruent.
Proving triangles congruent using SSS, SAS, or ASA.

Turn-In (#27)
Finish Chapter 4- Lesson 3: Proving Triangles Congruent.
§4.3 (Txt. p.216) #6-8, 12-17, 21, 22
Txt. p.210 #1-6

Handouts
Chapter 4- Lesson 4: Using Congruent Triangles
What’s Wrong #1
Construction Design

Assignment
Finish Chapter 4- Lesson 4
Construction Design
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, November 14, 2007

Algebra (Class 27)

Overview
In today’s class we continue our work with proportions, ratios, and percents.
Textbook Sections
§7-2 (Txt. p.293) Proportions

Key Attitudes
Math is about investigating and confirming

Key Ideas
Finding 10% of a number is the equivalent to moving the decimal point one place to the left (make the number smaller).
Finding 10% of a number can be used as the basis for finding other percents of the number.

Key Skills
Setting up and solving proportions.
Computing percents.

Turn-In (#26)
§8-5 (Txt. p.372) #15, 16, 31-34
§7-2 (Txt. p.295) #9-12, 24, 25

Handouts
No Handouts Posted

Assignment
Txt. p.373 Self-Test #1-6
Txt. p.369 #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.

Tuesday, November 13, 2007

Geometry (Class 27)

Overview
In today’s class we continue our work with proving triangles congruent. As time permits we will also examine various diagrams analyzing what is wrong with them based on our geometric knowledge so far.
Textbook Sections
§4.3 (Txt. p.212) Proving Triangles are a Congruent: SSS and SAS

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A unique triangle can be constructed from three segments (SSS), two segments and an included side (SAS), or two angles and the included side (ASA).
Triangles can be proved congruent by showing SSS, SAS, or ASA.

Key Skills
Proving lines are parallel.
Finding the equation of a line given two points.
Determining if two lines are parallel or perpendicular based on the equations of the lines.
Finding the distance between two points.

Turn-In (#26)
§3.6 (Txt. p.168)#11-13, 17-20, 24, 25, 33, 34, 36, 37 (Easy practice with equations of lines
§3.7 (Txt. p.175) #7-9, 13-15, 21, 22, 25, 26, 29, 30, 42, 43
Finish Chapter 4- Lesson 2: Constructing Triangles

Handouts
No Handouts Posted

Assignment
Finish Chapter 4- Lesson 3: Proving Triangles Congruent.
§4.3 (Txt. p.216) #6-8, 12-17, 21, 22
Txt. p.210 #1-6
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, November 09, 2007

Algebra (Class 26)

Overview
In today’s class we continue to work with ratio and proportion, reviewing how percents are related and using percents to solve problems. In addition, we keep working on building our skills for writing and using equations of lines. Lastly, we take Test 5 which focuses on equations of line.
Textbook Sections
§7-2 (Txt. p.293) Proportions

Vocabulary
percent

Key Attitudes
Math is about investigating and confirming

Key Ideas
Percents are ratios were the denominator is always 100.
A ratio is a way to compare the relative size of two quantities.
A proportion is a comparison of two equal ratios.
If a proportion has three values, the fourth value can be found.
Cross multiplication can be used to solve proportions.

Key Skills
Finding the equation of a line when given two points.
Finding the equation of a line when given one point and the slope of the line.
Sketching a graph of a line given its equation in y=mx+b form.
Determining if a point is on a line when given the coordinates of the point and the equation of the line.
Setting up and solving proportions.
Computing percents.

Turn-In (#25)
§7-2 (Txt. p.293) #1-8, 22, 23
§8-5 (Txt. p.372) #13, 14, 26-30

Handouts
No Handouts Posted

Assignment
§8-5 (Txt. p.372) #15, 16, 31-34
§7-2 (Txt. p.295) #9-12, 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.

Thursday, November 08, 2007

Geometry (Class 26)

Overview
In today’s class we learn how to construct triangles when given different angle or side combinations. Once again The Open Math Reference has very useful demonstrations for how to make these constructions. If time permits, we will begin our work with proving triangles congruent.
Textbook Sections
§4.3 (Txt. p.212) Proving Triangles Congruent

Vocabulary
included side
included angle

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A unique triangle can be constructed from three segments (SSS), two segments and an included side (SAS), or two angles and the included side (ASA).

Key Skills
Proving lines are parallel.
Finding the equation of a line given two points.
Determining if two lines are parallel or perpendicular based on the equations of the lines.
Finding the distance between two points.

Turn-In (#25)
§4.1 (Txt. p.198) #10-21, 31-39, 62-65
Test 4 Corrections

Handouts
Chapter 4- Lesson 2: Constructing Triangles
Chapter 4- Lesson 3: Proving Triangles Congruent

Assignment
§3.6 (Txt. p.168)#11-13, 17-20, 24, 25, 33, 34, 36, 37 (Easy practice with equations of lines
§3.7 (Txt. p.175) #7-9, 13-15, 21, 22, 25, 26, 29, 30, 42, 43
Finish Chapter 4- Lesson 2: Constructing Triangles
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, November 07, 2007

Algebra (Class 25)

Announcements
Test Friday!

Overview
In today’s class we continue reviewing and strengthening our understanding of ratio and proportions. In addition, we continue our work with writing and using equations of lines.
Textbook Sections
§7-2 (Txt. p.293) Proportions

Vocabulary
x-axis
y-axis
∆y
∆x
slope
x-intercept
y-intercept
substitute
evaluate
solve
x-value
y-value
solve for x
solve for y
solve for b
coordinates
standard form
slope-intercept form

Key Attitudes
Math is about investigating and confirming

Key Ideas
A ratio is a way to compare the relative size of two quantities.
A proportion is a comparison of two equal ratios.
If a proportion has three values, the fourth value can be found.
Cross multiplication can be used to solve proportions.

Key Skills
Finding the equation of a line when given two points.
Finding the equation of a line when given one point and the slope of the line.
Sketching a graph of a line given its equation in y=mx+b form.
Determining if a point is on a line when given the coordinates of the point and the equation of the line.

Turn-In (#24)
§8-5 (Txt. p.372) #7-12, 23-25
Packet

Handouts
No Handouts Posted

Assignment
§7-2 (Txt. p.293) #1-8, 22, 23
§8-5 (Txt. p.372) #13, 14, 26-30
Finish through SP __ in the packet.
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, November 06, 2007

Geometry (Class 25)

Overview
In today’s class we finish our work investigating how to determine if a triangle can be made when given the lengths of its sides. In addition, Test 4 is returned and corrected.
Textbook Sections
§4.1 (Txt. p.194) Triangles and Angles

Vocabulary
Triangle inequality

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
It is not always possible to construct a triangle given three segments!
A triangle can be constructed only when the sum of the two shortest sides is greater than the longest side.

Key Skills
Proving lines are parallel.
Finding the equation of a line given two points.
Determining if two lines are parallel or perpendicular based on the equations of the lines.
Finding the distance between two points.

Turn-In (#24)
Algebra & Geometry 4

Handouts
No Handouts Posted

Assignment
§4.1 (Txt. p.198) #10-21, 31-39, 62-65
Test 4 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.