HolcombMath

Wednesday, October 31, 2007

Geometry (Class 23)

Overview
In today’s class we practice writing proofs which show that two lines are parallel. We also being our study of congruent triangles by thinking about the requirements for the lengths of the sides of triangles-- can you make a triangle out of any three segments?
Textbook Sections
§3.4 (Txt. p.150) Proving Lines Parallel

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
When proving lines parallel you always use one of the “Converse” theorems.
The lengths of the sides of a triangle are related to each other.

Key Skills
Proving lines are parallel

Turn-In (#22)
Finish Chapter 3-Lesson 2 (Including the textbook work)
Algebra & Geometry 2

Handouts
Algebra and Geometry 3
Proving More Lines Parallel
Reason Cards

Assignment
Algebra & Geometry 3
More Proving Lines Parallel

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, October 30, 2007

Algebra (Class 22)

Overview
In today’s class Test 4 is returned and correct. We also continue our work with equations of lines and looking at functions related to the area and perimeter of rectangles.
Textbook Sections
§8-5 (Txt. p.371) Determining an Equation of a Line

Key Attitudes
Math is about investigating and confirming

Key Ideas
In order to write an equation of a line you need two pieces of information-- the “change per month” (m) and the “amount started with” (b).
An equation of a line can always be written in the form y=mx+b.

Key Skills
Finding the equation of a line when given two points.
Sketching a graph of a line given its equation in y=mx+b form.

Turn-In (#21)
§8-2 (Txt. p.356) Oral Exercises #5-8, 17-20
§8-3 (Txt. p.363) #4-6, 16-18

Handouts
No Handouts Posted

Assignment
§8-5 (Txt. p.372) #1-6, 17-22
Packet SP 15
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, October 29, 2007

Geometry (Class 22)

Overview
Today’s class continues with our work of proving the converse of our parallel line theorems in order to develop the tools we will need to prove that lines are parallel.
Textbook Sections
§3.4 (Txt. p.150) Proving Lines Parallel

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
The converse of an implication is formed by switching the position of the hypothesis and conclusion.
Not all converses of true statements are true.

Key Skills
Proving lines are parallel

Turn-In (#21)
More Practice Proofs #3
Chapter 3- Lesson 1: Your problem,

Handouts
Algebra and Geometry 2

Assignment
Finish Chapter 3-Lesson 2 (Including the textbook work)
Algebra & Geometry 2
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, October 26, 2007

Algebra (Class 21)

Overview
In today’s class we continue to build our fluency with writing equations for lines. In addition, we investigate the relationships inherent in family’s of rectangles which all have the same perimeter. Finally, we take our fourth test of the year focusing on writing equations of lines and dividing fractions.
Textbook Sections

Key Attitudes
Math is about investigating and confirming

Key Ideas
In order to write an equation of a line you need two pieces of information-- the “change per month” (m) and the “amount started with” (b).
An equation of a line can always be written in the form y=mx+b.

Key Skills
Finding the equation of a line when given two points.
Sketching a graph of a line given its equation in y=mx+b form.

Turn-In (#20)
§8-2 (Txt. p.356) Oral Exercises #5-8, 17-20
§8-3 (Txt. p.363) #4-6, 16-18

Handouts
No Handouts Posted

Assignment
§8-3 (Txt. p.363) #7-9, 21-24
Skill builder 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, October 25, 2007

Geometry (Class 21)

Overview
In today’s class we develop theorems which we can use to prove that two lines are parallel.
Textbook Sections
§3.4 (Txt. p.150) Proving Lines Parallel

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
The converse of an implication is formed by switching the position of the hypothesis and conclusion.
Not all converses of true statements are true.

Key Skills
Proving lines are parallel

Turn-In (#20)
More Practice Proofs #3
Chapter 3- Lesson 1: Your problem,

Handouts
Algebra and Geometry 1
Chapter 3- Lesson 2: Proving Lines Parallel

Assignment
Algebra & Geometry Problem 1
§3.3 (Txt. p.147) #13-16, 24-26, 29
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, October 24, 2007

Algebra (Class 20)

Announcements
Test next class-- writing equations of lines, dividing fractions.

Overview
In today’s class (a minimum day) we practice writing equations for lines when we have to sets of ordered pairs of data in our table. We also work on making a graph when given an equation in y=mx+b form.
Textbook Sections
§8-3 (Txt. p.360) Linear Equations

Vocabulary
ordered pair

Key Attitudes
Math is about investigating and confirming

Key Ideas
In order to write an equation of a line you need two pieces of information-- the “change per month” (m) and the “amount started with” (b).
An equation of a line can always be written in the form y=mx+b.

Key Skills
Finding the equation of a line when given two points.
Sketching a graph of a line given its equation in y=mx+b form.

Turn-In (#19)
§8-2 (Txt. p.356) Oral Exercises #1-4, 13-16
§8-3 (Txt. p.363) #1-3, 13-15

Handouts
No Handouts Posted

Assignment
§8-2 (Txt. p.356) Oral Exercises #5-8, 17-20
§8-3 (Txt. p.363) #4-6, 16-18
Skill Builder 2
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, October 23, 2007

Geometry (Class 20)

Overview
In today’s class we apply our understandings of parallel lines and transversals to a new type of problem, one involving transversal with a “bend”. Students see how constructing an auxiliary line can help them solve these types of problems. Students also work together to create problems involving parallel lines and transversals with bends, then trade and solve each others. Test 3 is also returned-- corrections are due next class.
Textbook Sections

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Auxiliary lines can help to solve problems.

Key Skills
Creating and solving parallel line problems which require an auxiliary line to solve.

Turn-In (#19)
Construction Collection 1

Handouts
More Proofs for Practice #3
New versions of Reason Cards Reason Cards 1 and Reason Cards 2

Assignment
More Practice Proofs #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.

Monday, October 22, 2007

Algebra (Class 19)

Announcements
All word problems need to be solved so that I can see “GUESS” from your work.

Overview
In today’s class we continue to work with concepts and skills related to area and perimeter. We see how an equation can be written to represent the various tables of data we have constructed (width v. length, perimeter v. length, area v. length) and develop our understanding of when a function will be linear and when it will not. We also formalize our definition of slope ∆y/∆x) and the y-intercept (the y-value when x=0).
Textbook Sections

Vocabulary
Slope
y-intercept
Slope-intercept form of a linear equation

Key Attitudes
Math is about investigating and confirming

Key Ideas
The amount saved each month is the slope of the linear equation.

Key Skills
Finding all of the rectangles possible for a given area.
Graphing data.
Finding the equation of a line when given two points.

Turn-In (#18)
Nothing to turn in!

Handouts
No Handouts Posted

Assignment
§8-2 (Txt. p.356) Oral Exercises #1-4, 13-16
§8-3 (Txt. p.363) #1-3, 13-15
Skill Builder 2 or 1c, whichever you have not finished.
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, October 19, 2007

Geometry (Class 19)

Overview
In today’s class we review writing equations for lines given two points, the relationship between the slope of perpendicular lines, and practice writing proofs. We then take Test 3 which focuses on writing proofs.
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Proofs can be thought of as a game. The game pieces are the geometric facts we have been given, or have proved, and the game rules are the rules of logic.

Key Skills
Writing two column proofs.

Turn-In (#18)
Additional Worksheet for Proof Practice

Handouts
Chapter 3- Lesson 1: Parallel Line Puzzles
Construction Collection 1

Assignment
Construction Collection 1
Chapter 3 Lesson 1 #1
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, October 18, 2007

Algebra (Class 18)

Announcements
All word problems need to be solved so that I can see “GUESS” from your work.

Overview
In today’s class we investigate the number of rectangles that can be made having an area of 24 square units. We create and analyze graphs that represent this activity.
Textbook Sections
§8-3 (Txt. p.360) Slope of a Line

Vocabulary
area
perimeter
minimum point
maximum point
function of

Key Attitudes
Math is about investigating and confirming

Key Ideas
Shapes can have the same perimeter and different areas.
The perimeter of a rectangle can be determined if you know its area and the length of one of its sides.

Key Skills
Finding all of the rectangles possible for a given area.
Graphing data.
Finding the equation of a line when given two points.

Turn-In (#17)
Test Corrections

Handouts
No Handouts Posted

Assignment
Skill Builder 1C
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, October 17, 2007

Geometry (Class 18)

Announcements
Test 3 is this Friday. It will focus on writing proofs.

Overview
In today’s class we continue getting better at writing proofs. In groups we will use “reason cards” to arrange the reasons for proofs. You will want to create your own “Reason Cards” for the test. Here are mine:Reason Cards 1, Reason Cards 2
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Proofs can be thought of as a game. The game pieces are the geometric facts we have been given, or have proved, and the game rules are the rules of logic.

Key Skills
Writing two column proofs.

Turn-In (#17)
Additional Worksheet for Proof Practice

Handouts
No Handouts Posted

Assignment
§3.3 (Txt. p.146) #8-12, 17, 21-23, 27
Three vertices of a rhombus are A(3,2), B(3,7), C(7,4). What is the coordinate of the fourth vertex? What are the equations of the lines that form the sides? What are the equations of the lines that form the diagonals?
Create “Reason Cards”
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, October 16, 2007

Algebra (Class 17)

Announcements
All word problems need to be solved so that I can see “GUESS” from your work.

Overview
I today’s class we discuss and correct our test from last week as well as start a new unit (Unit 4: Week 13) focusing on Length, Area, and Volume.
Textbook Sections
§8-3 (Txt. p.360) Slope of a Line

Vocabulary
area
perimeter
minimum point
maximum point
function of

Key Attitudes
Math is about investigating and confirming

Key Ideas
Shapes can have the same perimeter and different areas.
The perimeter of a rectangle can be determined if you know its area and the length of one of its sides.

Key Skills
Finding all of the rectangles possible for a given area.
Graphing data.

Turn-In (#16)
Packet-- Unit 3: Week 12

Handouts
No Handouts Posted

Assignment
Focus on Vocabulary
Skill Builder 1A and 1B
Test 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.

Monday, October 15, 2007

Geometry (Class 17)

Announcements
Test 3 is this Friday. It will focus on writing proofs.

Overview
Today’s class remains focused on writing proofs. In addition, we learn two new constructions: Construct a perpendicular to a line through a point on the line and Construct a perpendicular to a line from a point not on the line

Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Proofs can be thought of as a game. The game pieces are the geometric facts we have been given, or have proved, and the game rules are the rules of logic.

Key Skills
Writing two column proofs.

Turn-In (#16)
Additional Worksheet for Proof Practice

Handouts
No Handouts Posted

Assignment
Practice each of the constructions we learned today as well as the dividing line construction we learned last week.
Proof from class.
Warm-up problem #1-- finding the equation of the lines that form the side of a square where the vertices are A:(2,3) and B:(4,8)
§3.2 (Txt. p.138) #14-16, 19
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, October 12, 2007

Algebra (Class 16)

Announcements
Test Friday covering classes 11-15.

Overview
In today’s class we take our third test which focuses on solving equations, creating equations to represent saving money in the bank (Ex: you started with $10 in the bank and save $40 each month gives the equation y = 40x+10), making tables using the equation, creating graphs from the tables, as well as using graphing calculators to make graphs and tables. After the test students work to finish the current packet (Unit 3: Week 12) and play the Factor Game
Textbook Sections
§8-3 (Txt. p.360) Slope of a Line

Key Attitudes
Math is about investigating and confirming

Key Ideas
The slope can be determined from the graph.
The coefficient of x in the equation, y=mx+b, is the slope of the line.
The y-intercept can be determined from the graph.
The y-intercept is the “b” in the equation of a line written as y=mx+b.

Key Skills
Finding the equation of a line from verbal descriptions or from the graph of the line.

Turn-In (#15)
§3-2 (Txt. p.105) #8, 9
§3-3 (Txt. p.110) #53, 54

Handouts
No Handouts Posted

Assignment
Finish 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.

Thursday, October 11, 2007

Geometry (Class 16)

Announcements
Test corrections are due for all students-- even if you didn’t take the test! In that case, just work the test and it will count as corrections.

Overview
In today’s class we continue to work on writing proofs.
Textbook Sections
§3.3 (Txt. p.143) Parallel Lines and Transversals

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
Proofs can be thought of as a game. The game pieces are the geometric facts we have been given, or have proved, and the game rules are the rules of logic.

Key Skills
Writing two column fill in the blank proofs.

Turn-In (#15)
Txt. p.134 #43-46
Txt. p.141 #29-36

Handouts
No Handouts Posted

Assignment
Additional Worksheet for Proof Practice #8-10
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.