HolcombMath

Friday, February 29, 2008

Algebra (Class 55)

Lesson Title
Mathematical Reflection- Systems of Linear Equations

Overview
in today’s class the warm-up focuses on making a table to represent a given situation and then using patterns in the table to make predictions. The lesson for the day is focuses on summarizing the concepts and skills related to systems of linear equations and continuing to practice putting these skills and concepts to work. Also during the class we take test 10 focusing on systems of linear equations.
Textbook Sections
Structure and Method §9-4 ( p.426) The Addition-or-Subtraction Method

Vocabulary
systems of equations
eliminate variable
isolate
solution to an equation

Key Attitudes
Math is about investigating and confirming

Key Ideas
An equation with two variables has many solutions.
In order for a number(s) to be a solution(s) to an equation, the numbers must make the equation true when substituted into the equation.
Equations can be written in different forms.
Two equations can be equivalent but be in different forms.
In order for a point to be the solution of a system of equations, the point must be located at the intersection of the graphs.
Lines only intersect once, all the time, or not at all.
Key Skills
Creating an equation with two variables to represent a situation.
Graphing equations in standard form or slope intercept form.
Estimate the location of the point of intersection of two lines from a graph.
Solving a system of two linear equations using graphing, substitution, or combination
Turn-In (#54)
§9-2 (Txt. p.419)#6
§9-3 (Txt. p. 427) #6
ACE p.42 #2, 4, 42, 43

Handouts
No Handouts Posted

Assignment
ACE p.42 #3, 11, 13, 17, 18, 23, 24, 48-52, 58-62
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, February 28, 2008

Geometry (Class 56)

Announcements
Check out the crossword for this chapter’s vocabulary!

Lesson Title
Some Surprising Relations

Overview
The warm-up for today’s class focuses on the relationships between perimeter, area, and volume of similar shapes as well as using logic to solve a puzzle related to distances on a map. The lesson for today focuses on two proportional relationships, one related to triangles and the other to parallel lines. We will investigated, conjecture, and then prove these relationships. As time permits, we will then begin looking more closely at a special type of proportion, the “Geometric Mean”.
Textbook Sections
§8.6 (Txt. p. 498) Proportions and Similar Triangles

Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality

Key Attitudes
Math is about thinking creatively.

Key Ideas
Triangles are similar if and only if all of the corresponding sides of the triangles are in equal ratios. (Definition of Similarity)
Triangles are similar if and only if two pairs of angles are congruent. (AA Similarity Theorem and Converse of AA Similarity Theorem)
Triangles are similar if and only if a pair of angles are congruent and both pairs of adjacent sides are in the same ratio (SAS Similarity Thm. and Converse of SAS Similarity Theorem)
If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. (Angle Bisector Proportionality Theorem)
If three parallel lines intersect two transversals, then they divide the transversals proportionally. (Parallel Lines Proportionality Theorem)
Key Skills
Use the Angle Bisector Proportionality Theorem to find missing lengths.
Use the Parallel Lines Proportionality Theorem to find missing lengths.
Turn-In (#55)
Test Corrections
Complete warm-up (Analyzing Proofs from Test 8)
Chapter 8- Lesson 3 Problems

Handouts
Chapter 8- Lesson 4: Some Surprising Relations

Assignment
§8.6 (Txt. p.502) #11, 12, 15, 16, 21-24, 34, 40
Finish the first proof from Chapter 8 Lesson 4
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, February 27, 2008

Algebra (Class 54)

Announcements
Test next class focusing on solving systems of equations by substitution or combination, changing equations from slope-intercept into standard form and back, finding slopes and intercepts,

Lesson Title
Intersections of Lines

Overview
In today’s class we continue our work with solving systems of linear equations. We develop equations from a situation involving membership to a school club and see how solving a system of equations can be used to answer key questions about this situation.
Textbook Sections
Structure and Method §9-4 ( p.426) The Addition-or-Subtraction Method
The Shapes of Algebra- Investigation 3.3 (p. 41)

Vocabulary
systems of equations
eliminate variable
isolate
solution to an equation

Key Attitudes
Math is about investigating and confirming

Key Ideas
An equation with two variables has many solutions.
In order for a number(s) to be a solution(s) to an equation, the numbers must make the equation true when substituted into the equation.
Equations can be written in different forms.
Two equations can be equivalent but be in different forms.
In order for a point to be the solution of a system of equations, the point must be located at the intersection of the graphs.
Lines only intersect once, all the time, or not at all.
Key Skills
Creating an equation with two variables to represent a situation.
Graphing equations in standard form or slope intercept form.
Estimate the location of the point of intersection of two lines from a graph.
Turn-In (#53)
§9-2 (Txt. p.419)#5
§9-3 (Txt. p. 427) #5
ACE p.42 #1, 7, 21, 22

Handouts or Links
Investigation 3 Crossword

Assignment
§9-2 (Txt. p.419)#6
§9-3 (Txt. p. 427) #6
ACE p.42 #2, 4, 42, 43
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, February 26, 2008

Geometry (Class 55)

Chapter 8- Lesson 3: A Triangle in a Triangle (The A-Level proofs and hint cards are at the end.)

Lesson Title
A Triangle in a Triangle 1

Overview
In today’s class our warm-up focuses on the two proofs from the test. For one of the proofs students will need to edit and score “student” work. For the second proof, which had a mistake on the test, students will work to create a proof of their own. We will switch papers and edit each others work as part of the warm-up for the next class.

The lesson for the class continues our work from last Friday where we are examining the relationships created when from a triangle created inside of another triangle by constructing a parallel line.
Textbook Sections
§8.6 (Txt. p. 498) Proportions and Similar Triangles

Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality

Key Attitudes
Math is about thinking creatively.

Key Ideas
Triangles are similar if and only if all of the corresponding sides of the triangles are in equal ratios. (Definition of Similarity)
Triangles are similar if and only if two pairs of angles are congruent. (AA Similarity Theorem and Converse of AA Similarity Theorem)
Triangles are similar if and only if a pair of angles are congruent and both pairs of adjacent sides are in the same ratio (SAS Similarity Thm. and Converse of SAS Similarity Theorem)
If a line is parallel to one side of a triangle and intersects the other two sides, then the line divides the two sides proportionally. (Triangle Proportionality, or Side-Splitter, Theorem)
If a line divides two sides of a triangle proportionally, then the line is parallel to the third side of the triangle. (Converse of the Triangle Proportionality, or Side-Splitter, Theorem)
Key Skills
Determine if two triangles are similar using shortcuts (AA, SAS)
Prove triangles similar.
Use the “side-splitter” theorem to solve problems.
Turn-In (#54)
Chapter 8- Lesson 2: Proving Triangles Similar using SAS
§8.5 (Txt. p.492) #13, 14, 26-28, 32, 33

Handouts
Chapter 8- Lesson 3: A Triangle in a Triangle (The A-Level proofs and hint cards are at the end.)

Assignment
Test Corrections
Complete warm-up
Chapter 8- Lesson 3 Problems
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, February 25, 2008

Algebra (Class 53)

Announcements
Test Friday: Graphing equations, solving systems using substitution or combination, using systems to solve applied problems.

Lesson Title
Many Ways to Reach a Goal

Overview
In today’s class our warm-up focuses on solving systems of equations while our lesson will work towards putting systems of equations to work.
Textbook Sections
Structure and Method §9-4 ( p.426) The Addition-or-Subtraction Method
The Shapes of Algebra- Investigation 3.1 (p. 37)

Vocabulary
systems of equations
eliminate variable
isolate
solution to an equation

Key Attitudes
Math is about investigating and confirming

Key Ideas
An equation with two variables has many solutions.
In order for a number(s) to be a solution(s) to an equation, the numbers must make the equation true when substituted into the equation.
Key Skills
Finding pairs of values that make an equation with two variables true.
Creating an equation with two variables to represent a situation.
Graphing ordered pairs
Turn-In (#51)
§9-2 (Txt. p.419)#1-3
§9-3 (Txt. p. 427) #1-3
Test 9 Corrections
Packet SP20 (The Packet is due next class-- make sure you have completed all of the problems!)

Handouts
No Handouts Posted

Assignment
ACE p.42 #5, 6, 9, 15, 16, 36, 37
§9-2 (Txt. p.419)#5
§9-3 (Txt. p. 427) #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, February 22, 2008

Geometry (Class 54)

Lesson Title
A Triangle in a Triangle 1

Overview
The warm-up for today’s class focuses on proving triangles similar using the SAS similarity theorem. The lesson for the class continues this focus on similarity to examine relationships created by having a triangle in a triangle.
Textbook Sections
§8.6 (Txt. p. 498) Proportions and Similar Triangles

Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality

Key Attitudes
Math is about thinking creatively.

Key Ideas
Triangles are similar if and only if all of the corresponding sides of the triangles are in equal ratios. (Definition of Similarity)
Triangles are similar if and only if two pairs of angles are congruent. (AA Similarity Theorem and Converse of AA Similarity Theorem)
Triangles are similar if and only if a pair of angles are congruent and both pairs of adjacent sides are in the same ratio (SAS Similarity Thm. and Converse of SAS Similarity Theorem)
Key Skills
Determine if two triangles are similar using shortcuts (AA, SAS)
Prove triangles similar.
Turn-In (#53)
Chapter 8- Lesson 2: Proofs
§8.5 (Txt. p.492) #6-12, 19-25

Handouts
Chapter 8- Lesson 2: Proving Triangles Similar using SAS
Chapter 8- Lesson 3: A Triangle in a Triangle

Assignment
Chapter 8- Lesson 2: Proving Triangles Similar using SAS
§8.5 (Txt. p.492) #13, 14, 26-28, 32, 33
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, February 21, 2008

Algebra (Class 52)

Lesson Title
Many Ways to Reach a Goal

Overview
In today’s class our warm-up focuses on solving systems of equations while our lesson will work towards putting systems of equations to work.
Textbook Sections
The Shapes of Algebra- Investigation 3.1 (p. 37)

Vocabulary
systems of equations
eliminate variable
isolate
solution to an equation

Key Attitudes
Math is about investigating and confirming

Key Ideas
An equation with two variables has many solutions.
In order for a number(s) to be a solution(s) to an equation, the numbers must make the equation true when substituted into the equation.
Key Skills
Finding pairs of values that make an equation with two variables true.
Creating an equation with two variables to represent a situation.
Graphing ordered pairs
Turn-In (#51)
§9-2 (Txt. p.419)#1-3
§9-3 (Txt. p. 427) #1-3
Test 9 Corrections
Packet SP20 (The Packet is due next class-- make sure you have completed all of the problems!)

Handouts
No Handouts Posted

Assignment
ACE p.42 #5, 6, 9, 15, 16, 36, 37
§9-2 (Txt. p.419)#4
§9-3 (Txt. p. 427) #4
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, February 20, 2008

Geometry (Class 53)

Lesson Title
Shortcuts to Similarity- Proofs

Overview
In today’s class our warm-up again focuses on editing and scoring a proof while the in the lesson we pin down the shortcuts to similarity and then use these shortcuts to determine if two triangles are similar.
Textbook Sections
§8.5 (Txt. p.488) Proving Triangles are Similar

Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality

Key Attitudes
Math is about thinking creatively.

Key Ideas
Triangles are similar if and only if all of the corresponding sides of the triangles are in equal ratios. (Definition of Similarity)
Triangles are similar if and only if two pairs of angles are congruent. (AA Similarity Theorem and Converse of AA Similarity Theorem)
Triangles are similar if and only if a pair of angles are congruent and both pairs of adjacent sides are in the same ratio (SAS Similarity Thm. and Converse of SAS Similarity Theorem)
Key Skills
Determine if two triangles are similar using shortcuts (AA, SAS)
Prove triangles similar.
Turn-In (#52)
§8.4 (Txt. p.483) #9-26, 29, 30

Handouts
Chapter 8- Lesson 2: Shortcuts to Similarity
Chapter 8- Lesson 3: A Triangle in a Triangle

Assignment
Chapter 8- Lesson 2: Proofs
§8.5 (Txt. p.492) #6-12, 19-25
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.

Tuesday, February 19, 2008

Algebra (Class 51)

Lesson Title
Systems of Two Linear Equations- Part 3

Overview
In today’s class we continue working with systems of two linear equations and how to solve them. We extend our use of the combination method (adding the two equations) by learning how to transform the equations into forms which will allow for the elimination of a variable.
Textbook Sections
§9-4 (Txt. p.426) The Addition or Subtraction Mehtod

Vocabulary
systems of equations
eliminate variable
isolate

Key Attitudes
Math is about investigating and confirming

Key Ideas
Two equations have the same values only at their points of intersection.
Two lines can intersect at one point, no points, or all points.
A solution to a system of two linear equations is equivalent to the coordinates of the point of intersection of the two lines.
An equation with a single variable has a unique solution
In order to solve a system of equations you must eliminate variables until you end up with one equation and one variable
Since equations mean that the expressions on each side of the equal sign are equal, we can add or subtract other equations to eliminate a variable.
Key Skills
Solving first degree equations of one variable.
Verify that a point is the solution to the system of equations.
Solving a system of two linear equations by combination.
Turn-In (#50)
Two systems of equations to solve.
Graphing practice for equations in standard form.

Handouts
No Handouts Posted

Assignment
§9-2 (Txt. p.419)#1-3
§9-3 (Txt. p. 427) #1-3
Test 9 Corrections
Packet SP20 (The Packet is due next class-- make sure you have completed all of the problems!)
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, February 15, 2008

Geometry (Class 52)

Lesson Title
Shortcuts to Similarity

Overview
In today’s class our warm-up focuses on the midsegment of a trapezoid. while the lesson for the day focuses on shortcuts for proving that two triangles are similar.
Textbook Sections
§8.5 (Txt. p.488) Proving Triangles are Similar

Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality

Key Attitudes
Math is about thinking creatively.

Key Ideas
Triangles are similar if and only if all of the corresponding sides of the triangles are in equal ratios. (Definition of Similarity)
Triangles are similar if and only if two pairs of angles are congruent. (AA Similarity Theorem and Converse of AA Similarity Theorem)
Triangles are similar if and only if a pair of angles are congruent and both pairs of adjacent sides are in the same ratio (SAS Similarity Thm. and Converse of SAS Similarity Theorem)
Key Skills
Determine if two triangles are similar.
Write similarity statements.
Write statements of proportionality.
Find missing side lengths or angle measures of similar triangles.
Turn-In (#51)
§6.7 (Txt. p.376) 14-18, 35-38, 41, 42, 50, 51

Handouts
Chapter 6- Lesson 5: Midsegments of a Trapezoid
Chapter 8- Lesson 2: Shortcuts to Similarity

Assignment
§8.4 (Txt. p.483) #9-26, 29, 30
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, February 14, 2008

Algebra (Class 50)

Lesson Title
Systems of Two Linear Equations- Part 2

Overview
In today’s class our warm-up changes focus from working with ratios and proportions to interpreting time and distance graphs-- review of older material is still included of course!
The lesson for the class focuses on solving a system of equations using a new method-- “combination”-- where adding or subtracting the two equations in the system allows us to eliminate a variable.
Textbook Sections
§9-4 (Txt. p.426) The Addition or Subtraction Mehtod

Vocabulary
systems of equations
eliminate variable
isolate

Key Attitudes
Math is about investigating and confirming

Key Ideas
Two equations have the same values only at their points of intersection.
Two lines can intersect at one point, no points, or all points.
A solution to a system of two linear equations is equivalent to the coordinates of the point of intersection of the two lines.
An equation with a single variable has a unique solution
In order to solve a system of equations you must eliminate variables until you end up with one equation and one variable
Since equations mean that the expressions on each side of the equal sign are equal, we can add or subtract other equations to eliminate a variable.
Key Skills
Graphing equations of lines.
Solving first degree equations of one variable.
Verify that a point is the solution to the system of equations.
Solving a system of two linear equations by combination.
Turn-In (#49)
Two systems of equations to solve

Handouts
No Handouts Posted

Assignment
Two systems of equations to solve.
Graphing practice for equations in standard form.
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, February 13, 2008

Geometry (Class 51)

Lesson Title
What is “similarity”?

Overview
In today’s class our warm-up focuses on analyzing, editing, and evaluating two proofs written by “students”. During the lesson we share and validate area formulas the students derived for the areas of polygons. For homework students will apply these formulas to various situations. We then turn our attention to the next section of work which focus on “similarity”. We begin by investigating what is meant when we say that two triangles are similar.
Textbook Sections
§8.3 (Txt. p.473) Similar Polygons

Vocabulary
diagonal
bisect
vertex
opposite angle
opposite side
adjacent angle
adjacent side
attributes
similar, similarity

Key Attitudes
Math is about thinking creatively.

Key Ideas
A formulas for the area of a quadrilateral can be created by breaking the quadrilateral into triangles.
If two shapes look the same but are not necessarily the same size, we say that the shapes are similar.
All similar shapes share important attributes.
Key Skills
Be able to find the area of any quadrilateral.
Create similar triangles from given information.
Describe the attributes of similar shapes.
Turn-In (#50)
Turn in #50
Finish Chapter 6: Lesson 4

Handouts
Chapter 6- Lesson 7: Analyzing Proofs
Chapter 8- Lesson 1: “Similarity"- What does it mean?
Chapter 8- Lesson 2: Shortcuts to Similarity

Assignment
§6.7 (Txt. p.376) 14-18, 35-38, 41, 42, 50, 51
Test Corrections
Finish Chapter 8- Lesson 1: “Similar”- What does it mean?
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, February 12, 2008

Algebra (Class 49)

Lesson Title
Systems of Two Linear Equations- Part 2

Overview
In the last class we saw how the solution to such a system can be thought of as the point of intersection of the graphs of the two equations. When we deal with linear equations, the graphs will be lines, and hence the point of intersection of the lines will be the solution to the system. We also saw how to “set equations equal” in order to eliminate a variable. Once we had one equation with one variable we were able to solve the equation. Afterwards we could substitute the value back into the other equation and solve. We could then verify our solution by examining the graph as well as by substituting and evaluating each equation to make sure the point really was on both lines.
In today’s class we continue to develop our ability to solve a system of two linear equations by examining systems where at least one equation does not have an isolated variable.
Textbook Sections
§9-1 (Txt. p.413) Solving Systems of Linear Equations

Vocabulary
systems of equations
eliminate variable
isolate

Key Attitudes
Math is about investigating and confirming

Key Ideas

Key Skills
Graphing equations of lines.
Solving first degree equations of one variable.

Turn-In (#48)
Turn in #48
Packet SP15
§11-5 (Txt. p.526)#9-12

Handouts
No Handouts Posted

Assignment
Three systems of equations to solve:

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, February 08, 2008

Geometry (Class 50)

Lesson Title
Areas of Quadrilaterals 1

Overview
In today’s class our warm-up focuses on clarifying the hierarchy and interrelationships between quadrilaterals. We then turn our attention to developing formulas for the area of quadrilaterals based on breaking quadrilaterals up into triangles. Finally during the last 40 minutes of class we will be writing Test 7.
Textbook Sections
§6.7 (Txt. p.371) Area of Triangles and Quadrilaterals

Vocabulary
diagonal
bisect
vertex
opposite angle
opposite side
adjacent angle
adjacent side

Key Attitudes
Math is about thinking creatively.

Key Ideas
A formulas for the area of a quadrilateral can be created by breaking the quadrilateral into triangles.

Key Skills
Be able to classify quadrilaterals based on side lengths and/or angle measures.
Be able to identify and describe the essential elements of a given type of quadrilateral.
Be able to classify the type of quadrilateral based on the arrangement of the diagonals.

Turn-In (#49)
Turn in #49
Chapter 6- Lesson 3
§6.5 (Txt. p.359) #16, 17, 28, 29, 31, 32, 40

Handouts
Chanpter 6- Lesson 6: Classification Review
Chapter 6- Lesson 4: Areas of Quadrilaterals Part 1

Assignment
Finish Chapter 6: Lesson 4
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, February 07, 2008

Algebra (Class 48)

Lesson Title
Systems of Equations1

Overview
In today’s class we begin our study of solving systems of linear equations by algebraic methods. We learn that: 1) solving a system of linear equations is the same as finding the intersection of two lines, 2) that the coordinates of a point of intersection will make both equations true, 3) to find a solution means we have to first eliminate a variable.
Textbook Sections
§9-1 (Txt. p.413) Solving Systems of Linear Equations

Vocabulary
systems of equations
eliminate variable

Key Attitudes
Math is about investigating and confirming

Key Ideas
Two equations have the same values only at their points of intersection.
Two lines can intersect at one point, no points, or all points.
An equation with a single variable has a unique solution

Key Skills
Graphing equations of lines.
Solving first degree equations of one variable.

Turn-In (#47)
Turn in #47
Graphing practice (Except if you took the CAHSEE)

Handouts
No Handouts Posted

Assignment
Packet SP15
§11-5 (Txt. p.526)#9-12
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.