HolcombMath

Thursday, January 31, 2008

Geometry (Class 47)

Lesson Title
Types of Quadrilaterals

Overview
In today’s lesson students investigate the different types of quadrilaterals, exploring the specific properties that characterize each type.
Textbook Sections
§6.4 (Txt. p.347) Rhombuses, Rectangles, and Squares

Vocabulary
quadrilateral
rhombus
rectangle
square
parallelogram
trapezoid
isosceles trapezoid

Key Attitudes
Math is about thinking creatively.

Key Ideas
Quadrilaterals can be classified as different types based on angle measures and/or side lengths.

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.

Turn-In (#46)
Turn in #46
Warm-Up 46
§6.1 (Txt. p.325) #12-17, 37, 38, 44, 45
§6.2 (Txt. p.333) #12-19, 30-33

Handouts
Chapter 6- Lesson 2: Types of Quadrilaterals Part 1
Chapter 6- Lesson 2: Types of Quadrilaterals Part 2

Assignment
§6.3 (Txt. p.342) #9-19, 29, 33
Finish Chapter 6- Lesson 1: Defining “Parallelogram”
Chapter 6- Lesson 1: One More Parallelogram
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, January 30, 2008

Algebra (Class 45)

Lesson Title
Simplify Expressions with Exponents

Overview
In today’s class our warm-up reviews skills from previous lessons including using concepts of proportion, finding the equation of a line passing through two points, solving an equation that requires the distributive property, and simplifying radicals with an index of 2.

In the lesson today we review and practice simplifying expressions involving exponents as well as begin to work with graphs relating time and distance.
Textbook Sections
§11-5 (Txt. p.525) Square Roots of Variable Expressions

Key Attitudes
Math is about investigating and confirming

Key Ideas
Rules of exponents can be developed and understood by writing them in expanded form and applying what you already know about multiplication and division

Key Skills
Finding the squares and square roots of numbers.
Writing numbers as the product of the largest square factor.
Simplifying radicals.
Interpreting time and distance graphs

Turn-In (#44)
Turn in #44
§11-4 (Txt. p.522) Irrational Numbers #1-10

Handouts
No Handouts Posted

Assignment
Finish packet through SP 4
§11-4 (Txt. p.522) #11-15
§11-5 (Txt. p.526) #1-4
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.

Tuesday, January 29, 2008

Geometry (Class 46)

Announcements
We will not be having a test on Wednesday.

Lesson Title
Defining Parallelograms

Overview
In today’s class we examine our ideas concerning what information is necessary and what information is sufficient to infer that a given quadrilateral must be a parallelogram. We then apply our proof writing skills to formally establish our conjectures.
Textbook Sections
§6.1 (Txt. p.322) Polygons
§6.2 (Txt. p.330) Properties of Paralelograms

Key Attitudes
Math is about thinking creatively.

Key Ideas
All polygons can be cut up into triangles.
Our knowledge of triangles can be used to make inferences regarding polygons.

Key Skills
Determining if given information is enough to determine if a quadrilateral is, might be, or is not a parallelogram.
Proving that a given shape is a parallelogram.

Turn-In (#45)
Turn in #45
Algebra and Geometry 8

Handouts
Chapter 6- Lesson 1 Part 1: Defining “Parallelogram”
Chapter 6- Lesson 1 Part 2: Defining “Parallelogram”
Chapter 6- Lesson 1 Part 3- Defining “Parallelogram”

Assignment
Finish Warm-Up
§6.1 (Txt. p.325) #12-17, 37, 38, 44, 45
§6.2 (Txt. p.333) #12-19, 30-33
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, January 24, 2008

Final Exam Grades Posted

The grades for the final exams have been posted. I still have some more grading to catch up on and then I will be doing the corrections and drops. Hopefully all grades will be done by 12:00 tomorrow.

Friday, January 18, 2008

Geometry (Class 44)

Announcements
We will not be having a test on Wednesday.

Lesson Title
Defining Parallelograms 2

Overview
In today’s class we examine our ideas concerning what information is necessary and what information is sufficient to infer that a given quadrilateral must be a parallelogram. We then apply our proof writing skills to formally establish our conjectures.
Textbook Sections
§6.1 (Txt. p.322) Polygons
§6.2 (Txt. p.330) Properties of Paralelograms

Key Attitudes
Math is about thinking creatively.

Key Ideas
All polygons can be cut up into triangles.
Our knowledge of triangles can be used to make inferences regarding polygons.

Key Skills
Determining if given information is enough to determine if a quadrilateral is, might be, or is not a parallelogram.
Proving that a given shape is a parallelogram.

Turn-In (#43)
Turn in #43
Txt. p. 388 #3-5,7-21
Finish Chapter 5- Lesson 11

Handouts
Algebra and Geometry 8

Assignment
Finish “Algebra and Geometry 8”
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, January 17, 2008

Algebra (Class 43)

Lesson Title
Simplifying Square Roots (Radicals with Index 2)

Overview
In today’s class our warm-up requires students to use their understanding of the solution to the Locker Problem. Also in the warm-up are a few “Box Puzzles” which help students build skills they will need during the upcoming units. Our lesson today continues from last class-- working on developing the ability to simplify square roots (radicals with an index of 2) as well as other radical expressions.
Textbook Sections
11-3 (Txt. p.517) Rational Square Roots

Vocabulary
index
radical
exponent
root
factor
square number

Key Attitudes
Math is about investigating and confirming

Key Ideas
Radicals can be simplified only if they contain a perfect square factor.
To simplify a radical with an index of 2, the exponent is divided by 2.

Key Skills
Finding the squares and square roots of numbers.
Writing numbers as the product of the largest square factor.
Simplifying radicals.

Turn-In (#42)
Turn in #42
Final Exam Review Packet pages 9-12

Handouts
Simplifying Square Roots (Radicals of Index 2) of Whole Numbers

Assignment
§11-4 (Txt. p.522) Irrational Numbers #1-10
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, January 16, 2008

Geometry (Class 43)

Announcements
We will not be having a test on Wednesday.

Lesson Title
Defining “Parallelogram” 1

Overview
In today’s class we finish the proofs involving the centroid of a triangle. In addition we move our focus to quadrilaterals. This study of four sided polygons begins by developing alternative definitions for “parallelogram”. By developing alternative definitions we uncover what information is necessary to infer that a given quadrilateral is, might be, or is not a parallelogram.
Textbook Sections
§6.1 (Txt. p.322) Polygons
§6.2 (Txt. p.330) Properties of Paralelograms

Vocabulary
quadrilateral
parallelogram
adjacent sides
adjacent angles
opposite sides
opposite angles

Key Attitudes
Math is about thinking creatively.

Key Ideas
A good definition captures the essential characteristics of what it is you are trying to define.

Key Skills
Proving conjectures regarding the centroid of a triangle.
Using the properties of the centroid of a triangle to determine lengths and areas.
Determining if given information is enough to determine if a quadrilateral is, might be, or is not a parallelogram.

Turn-In (#42)
Turn in #42
5.3 (Txt. p.283) #10, 20
Txt. p.314 #1-12

Handouts
Chapter 6- Lesson 1: Defining “Parallelogram”

Assignment
Txt. p. 388 #3-5,7-21
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, January 15, 2008

Algebra (Class 42)

Lesson Title
Simplify Square Roots (Radicals of index 2)

Overview
In class today we will come to a conclusion about the locker problem-- which lockers are open and which are closed. We then turn our attention to learning how to simplify radical expressions. A key for success is being comfortable identifying perfect square factors.
Textbook Sections
11-3 (Txt. p.517) Rational Square Roots

Vocabulary
index

Key Attitudes
Math is about investigating and confirming

Key Ideas
Radicals can be simplified only if they contain a perfect square factor.

Key Skills
Finding the squares and square roots of numbers.
Writing numbers as the product of the largest square factor.
Simplifying radicals.

Turn-In (#41)
Turn in #41
Final Exam Review Packet pages 5-8

Handouts
No Handouts Posted

Assignment
Final Exam Review Packet pages 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.

Monday, January 14, 2008

Geometry (Class 42)

Announcements
We will not be having a test on Wednesday.

Lesson Title
The Centroid of a Triangle

Overview
In today’s class we wrap up Chapter 5 by examining a special property of the centroid of triangles.
Textbook Sections
§5.3 (Txt.p.279) Medians and Altitudes of a Triangle

Vocabulary
median
centroid

Key Attitudes
Math is about thinking creatively.

Key Ideas
The area of a triangle is equal to the length of half base multiplied by the length of the altitude.
If two triangles have equal length bases and altitudes, then their areas are equal.
The medians of a triangle separate a triangle into two triangles of equal area.
The medians of a triangle separate a triangle into six triangles of equal area.
The centroid of a triangle separates each median of that triangle into two smaller line segments whose lengths are in the ratio of 2:1.

Key Skills
Finding the balance point of a triangle.
Constructing altitudes of triangles.
Using the properties of the centroid of a triangle to determine lengths and areas.

Turn-In (#41)
Turn in #41
Txt. p.310 #1-25

Handouts
Chapter 5- Lesson 11: A Special Property of the Centroid

Assignment
5.3 (Txt. p.283) #10, 20
Txt. p.314 #1-12
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.

Friday, January 11, 2008

Algebra (Class 41)

Lesson Title
The Locker Problem 2

Overview
In today’s class we the focus of our warm-up returns to writing the equations and using equations of lines. During the lesson we continue our work on the Locker Problem and come to a final conclusion about which lockers are open and which are closed after the 1000th student has passed through. Finally we write Test 8 focusing on areas of polygons, squares, and square roots.
Textbook Sections
11-3 (Txt. p.517) Rational Square Roots

Vocabulary
factor
multiple
square number
square
exponent
base
power

Key Attitudes
Math is about investigating and confirming

Key Ideas
Perfect squares can be used to solve surprisingly different problems.

Key Skills
Finding the squares and square roots of numbers.
Writing numbers as the product of the largest square factor.
Simplifying square roots.

Turn-In (#40)
Turn in #40
Final Exam Review-- pages 1- 4.

Handouts
No Handouts Posted

Assignment
Final Exam Review Packet pages 5-8
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, January 10, 2008

Geometry (Class 41)

5.8-_Balance_a_Triangle_Part_2.pdf

Lesson Title
Balance a Triangle

Overview
In today’s class students work to develop a procedure that would allow them to balance a triangle on one point.
Textbook Sections
§5.3 (Txt.p.279) Medians and Altitudes of a Triangle

Vocabulary
median of a triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
The balance point of a triangle can be found by applying properties of triangles and balances.

Key Skills
Finding the balance point of a triangle.
Constructing altitudes of triangles.
Plotting points and reading coordinates from a graph.

Turn-In (#40)
Turn in #40
Chapter 5- Lesson 9: A Special Property of the Midpoints of a Triangle
Chapter 5- Lesson 7: Changing Borders, Moving Fences

Handouts
Chapter 5- Lesson 10: Travels with an Orthocenter
Chapter 5- Lesson 8: Balance a Triangle Part 1
Chapter 5- Lesson 8: Balance a Triangle Part 2

Assignment
Txt. p.310 #1-25
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.

Wednesday, January 09, 2008

Algebra (Class 40)

Lesson Title
The Locker Problem

Overview
In today’s class our warm-up focuses on finishing our current packet of work involving areas of polygons, squares and square roots, and rules of exponents. Next we will discuss semester grades and the final exam. We will review the homework from the previous class and then turn our attention to the lesson of the day-- The Locker Problem. As time permits we will work to develop our skills for simplifying square roots by extracting perfect square factors.
Textbook Sections
11-3 (Txt. p.517) Rational Square Roots

Key Attitudes
Math is about investigating and confirming

Key Ideas
The number of factors of a square number is odd.
A square root is simplified if all of its square number factors have been factored out and “square rooted”.

Key Skills
Finding the squares and square roots of numbers.
Writing numbers as the product of the largest square factor.
Simplifying square roots.

Turn-In (#39)
Turn in #39
Finish packet through SP20

Handouts
No Handouts Posted

Assignment
Final Exam Review-- pages 1- 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.

Tuesday, January 08, 2008

Geometry (Class 40)

Lesson Title
Areas of Triangles

Overview
In today’s class we continue our work relating to the area of triangles and apply these concepts and skills.
Textbook Sections
§5.3 (Txt. p.279) Medians and Altitudes of a Triangle

Vocabulary
altitude
incricle
incenter
circumcircle
circumcenter

Key Attitudes
Math is about thinking creatively.

Key Ideas
The area of a triangle depends ONLY on the length of its base and the length of the corresponding altitude of the triangle.
A triangle can be “sheard”, and not have its area changed.

Key Skills
Constructing a circle inscribed in a triangle (an “incircle”).
Constructing a circle that circumscribes a triangle (a “circumcircle”)
Constructing the altitudes of triangles.
Finding the area of a triangle.

Turn-In (#39)
Turn in #39
§5.2 (Txt. p.275) #6, 7, 15, 17, 18, 23

Handouts
No Handouts Posted

Assignment
Chapter 5- Lesson 9: A Special Property of the Midpoints of a Triangle
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, January 07, 2008

Algebra (Class 39)

Lesson Title
Estimating Square Roots

Overview
In today’s class we start off with a puzzle to bring your brain back up to speed. We then do a quick review of the homework from the last class and proceed to developing our ability to estimate the square root of a number to the nearest tenth. Finally we review our understanding of exponents and apply it to working with algebraic symbols.
Textbook Sections
11-3 (Txt. p.517) Rational Square Roots

Vocabulary
exponent
base

Key Attitudes
Math is about investigating and confirming

Key Ideas
An exponent is shorthand for saying multiply a number by itself a certain number of times.

Key Skills
Finding the squares and square roots of numbers.
Estimating square roots of whole numbers to the nearest tenth.

Turn-In (#38)
Turn in #38
Finish packet through SP12

Handouts
Potipher Perkin’s Square Quilt of Squares

Assignment
Finish packet through SP20
Finish Mrs. Perkin’s Quilt
Practice reciting the perfect squares
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.