HolcombMath

Thursday, December 20, 2007

Geometry (Class 39)

Lesson Title
Altitudes of a Triangle

Overview
In today’s class students examine the altitudes of triangles, learning that every triangle has three altitudes. Students use their construction skills to create each of the three altitudes to specific triangles and make observations regarding when the altitude of a triangle will be inside or outside of the triangle. As time permits, students apply their knowledge of the altitudes of triangles to the problem of finding the area of triangles.
Textbook Sections
§5.3 (Txt. p.279) Medians and Altitudes of a Triangle

Vocabulary
altitude

Key Attitudes
Math is about thinking creatively.

Key Ideas
An altitude of a triangle is a perpendicular line segment connecting a vertex of a triangle with its opposite side.
All triangles have three altitudes

Key Skills
Constructing a circle inscribed in a triangle (an “incircle”).
Constructing a circle that circumscribes a triangle (a “circumcircle”)

Turn-In (#38)
Turn in #38
§5.1 (Txt. p.268) #8-13, 16-18, 21-26
§5.2 (Txt. p.275) #5, 10-14
Test Corrections

Handouts
Chapter 5- Lesson 5: Altitudes of a Triangle

Assignment
§5.2 (Txt. p.275) #6, 7, 15, 17, 18, 23
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, December 19, 2007

Algebra (Class 38)

Lesson Title
Area Formulas of Polygons

Overview
In today’s class our we will take a quiz focusing on the work we have done on the “Plane Shapes” problems we have been working with over the last few weeks. In addition, we will continue our work with areas of polygons. In particular we will focus on the relationship between the area and side length of squares, learning about the square root operation, how to approximate the value of the square root of a number, when the square root of a number will be whole, when it is “irrational”, and when it is “imaginary”. We will also work towards memorizing the first 25 perfect squares and will see how thinking about area can help use with this task.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method

Vocabulary
irrational numbers
imaginary numbers
perfect squares
square roots

Key Attitudes
Math is about investigating and confirming

Key Ideas
The coordinates of the point of intersection of two lines is the solution to both equations simultaneously.
Equations can be used to verify the point of intersection by substituting and evaluating the equations. If both equations “work” with these values, then the point is the point of intersection of both lines-- otherwise it is not.
The length of the side of a square can be found by taking the square root of the area of the square.
Only “perfect squares” have whole number square roots.
Only positive numbers have square roots, but all numbers can be squared.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Finding the area of a polygon using a formula.
Finding the perimeter of a polygon using a formula.

Turn-In (#37)
Turn in #37
Txt. p.653 #19, 20, 30-34, 60, 66
Packet through SP11
Plane Shapes 8

Handouts
No Handouts Posted

Assignment
Finish packet through SP17
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, December 18, 2007

Geometry (Class 38)

Lesson Title
Locating a Hospital

Overview
In today’s class our warm-up will further our understanding of angle bisectors. During the lesson we will examine another applied problem, finding the best location for a regional hospital, by applying geometry.
Textbook Sections
§5.2 (Txt. p.272) Bisectors of a Triangle

Vocabulary
incircle
circumcircle

Key Attitudes
Math is about thinking creatively.

Key Ideas
If a point is equidistant from the three vertices of a triangle, then the point is at the intersection of the three perpendicular bisectors of the sides of the triangle.
If a point is equidistant from the three sides of a triangle, then the point is at the intersection of the angle bisectors of the triangle.

Key Skills
Constructing a circle inscribed in a triangle (an “incircle”).
Constructing a circle that circumscribes a triangle (a “circumcircle”)

Turn-In (#37)
Turn in #37
Practice After Test 6 worksheet.

Handouts
Chapter 4- Lesson 5: Locating a Hospital
Chapter 5- Lesson 4 Warm-Up (Angle Bisectors)

Assignment
§5.1 (Txt. p.268) #8-13, 16-18, 21-26
§5.2 (Txt. p.275) #5, 10-14
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, December 17, 2007

Algebra (Class 37)

Lesson Title
Area Formulas of Polygons

Overview
In today’s class students continue to refine their ability to write and use equations of lines. In addition we continue our work with area formulas and use the concept of area to establish the relationship between the area and length of the side of a square. Students then learn to approximate the value of the square root of a number by comparison to perfect squares and by using a calculator.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method

Key Attitudes
Math is about investigating and confirming

Key Ideas
The coordinates of the point of intersection of two lines is the solution to both equations simultaneously.
Equations can be used to verify the point of intersection by substituting and evaluating the equations. If both equations “work” with these values, then the point is the point of intersection of both lines-- otherwise it is not.
The length of the side of a square can be found by taking the square root of the area of the square.
Only “perfect squares” have whole number square roots.
Only positive numbers have square roots, but all numbers can be squared.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Finding the area of a polygon using a formula.
Finding the perimeter of a polygon using a formula.

Turn-In (#36)
Turn in #36
Txt. p.653 #16-18, 25, 26, 28, 29, 35, 38, 39
Finish Plane Shapes 7
Finish Packet through SP 6

Handouts
Plane Shapes 8

Assignment
Txt. p.653 #19, 20, 30-34, 60, 66
Packet through SP11
Plane Shapes 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.

Friday, December 14, 2007

Geometry (Class 37)

Lesson Title
Building an Addition

Overview
In today’s class we investigate a problem involving finding the optimal location for building an addition on a house. Our geometric skills will be useful for finding the solution. As time permits, we will also investigate a problem involving finding the optimal location for a hospital. Again our geometric skills will be useful. During the last part of the class we will take Test 6.
Textbook Sections
§5.2 (Txt. p.272) Bisectors of a Triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
The concepts of locus can be applied to triangles.

Key Skills
Applying concepts and skills to new problems.

Turn-In (#36)
Turn in #36
§5.6 (Txt. p.305) #13-15, 19, 20, 27
Chapter 5- Lesson 2, Including Perpendicular Bisector Practice

Handouts
Chapter 5- Lesson 3: Building an Addition

Assignment
Practice After Test 6 worksheet.
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, December 13, 2007

Algebra (Class 36)

Lesson Title
Area Formulas of Polygons

Overview
During today’s class our warm-up continues to focus on develop our abilities to write and use equations of lines. A new concept we deal with is reflecting a shape across and axis. During our lesson focus on the area and perimeter of some common polygons by using our ability to dissect a polygon as the foundation for deriving formulas for area and perimeter.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method

Key Attitudes
Math is about investigating and confirming

Key Ideas
If a point is on a line, then it makes the equation for the line true.
The slopes of two lines are equal if and only if the lines are parallel.
The slopes of two lines are opposite reciprocals if and only if the two lines are perpendicular
The area formula for shapes can be figured out by cutting up the shape and rearranging it to form a rectangle or parallelogram.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Finding the area of a polygon using a formula.
Finding the perimeter of a polygon using a formula.

Turn-In (#35)
Turn in #35
Txt. p.653 #13-15, 22-24, 53, 59, 65
Finish Packet through page SP 5
Finish Warm-Up (Plane Shapes #6)
Test Corrections

Handouts
Plane Shapes 7

Assignment
Txt. p.653 #16-18, 25, 26, 28, 29, 35, 38, 39
Finish Plane Shapes 7
Finish SP7 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.

Wednesday, December 12, 2007

Geometry (Class 36)

Lesson Title
Coffee Shop Problem

Overview
In today’s class we finish our work on the Coffee Shop problem and then apply the concepts we have learned about perpendicular bisectors of a segment.
Textbook Sections
§5.1 (p.264) Perpendicular Bisectors

Vocabulary
perpendicular bisector

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Key Skills
Using properties of perpendicular bisectors while writing proofs.

Turn-In (#35)
Turn in #35
§5.6 (Txt. p.305) #7-12, 18, 19, 26, 27
§5.1 (Txt. p.268) 14, 15

Handouts
Warm-Up 12/11 (Perpendicular Bisectors)
Assignment
§5.6 (Txt. p.305) #13-15, 19, 20, 27
Chapter 5- Lesson 2, Including Perpendicular Bisector Practice
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, December 11, 2007

Algebra (Class 35)

Lesson Title
Area Formulas of Polygons

Overview
In today’s class the warm-up (Plane Shapes 6) remains to focused on the graphs and equations of lines. During the lesson we switch our focus to the areas of polygons and develop the formulas for the areas and perimeters of common ones.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method

Vocabulary
area
perimeter
formula
altitude
height
base
width
dimensions

Key Attitudes
Math is about investigating and confirming

Key Ideas
The area of a polygon can be determined by turning it into triangles.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Finding the area of a polygon using a formula.

Turn-In (#34)
Turn in #34
§9-1 (Txt. p.415) 11-13, 21
Finish Packet-- Unit 5: Week 18

Handouts
No Handouts Posted

Assignment
Txt. p.653 #13-15, 22-24, 53, 59, 65
Finish Packet through page SP 5
Finish Warm-Up (Plane Shapes #6)
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, December 10, 2007

Geometry (Class 35)

Lesson Title
Locus of Points

Overview
In today’s class we apply our skills of proof by contradiction to develop two new theorems: Hinge Theorem and Converse of the Hinge Theorem. In addition we finish Chapter 5- Lesson 1: Locus and start to use these skills to uncover special properties of triangles.
Textbook Sections
§5.6 (Txt. p.302) Indirect Proof

Vocabulary
locus of points

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A locus of points is a set of points that fits a given description.

Key Skills
Proving a statement is true by contradiction.
Writing the negation of a statement.
Using the proof by contradiction format to write a proof by contradiction.

Turn-In (#34)
Turn in #34
Finish Chapter 4- Lesson 6
Txt. p. 255 (Chapter Test) #1-10, 15, 18

Handouts
Chapter 5- Lesson 2: The Coffee Shop Problem

Assignment
§5.6 (Txt. p.305) #7-12, 18, 19, 26, 27
§5.1 (Txt. p.268) 14, 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.

Friday, December 07, 2007

Algebra (Class 34)

Lesson Title
Test 7

Overview
In today’s class we finish our work with percents and simple interest (for now) and take Test 7.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method
§3-1 (Txt. p.95) Transforming Equations

Vocabulary
exponent
square number
linear interpolation
exponential notation
square root
multiplicative identity property
base
positive square root
product

Key Attitudes
Math is about investigating and confirming

Key Ideas
I=PRT
A=P+I
You can determine which formula to use by matching the information given in a problem to what the variables in a formula mean. If you have data for all but one of the variables in a formula, then that formula can be used to find the missing data.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Setting up and solving simple interest problems.
Determining the appropriate formula to use in a given situation.

Turn-In (#33)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
§9-1 (Txt. p.415) 11-13, 21
Finish Packet-- Unit 5: Week 18
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, December 06, 2007

Geometry (Class 34)

Lesson Title
Indirect Proof 2

Overview
In today’s class we practice using proofs by contradiction. These proofs take the form of making an assumption, then showing that the negation of this assumption leads to an obviously false outcome. (Note: This obviously false outcome frequently is a contradiction of something from the “given”.)
Textbook Sections
§5.6 (Txt. p.302) Indirect Proof

Vocabulary
contradiction
assumption
negate, negation
syllogism
proof by contradiction
indirect proof

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A statement can be proved true by first assuming that it is false and then showing that this leads to an impossible result.

Key Skills
Proving a statement is true by contradiction.
Writing the negation of a statement.
Using the proof by contradiction format to write a proof by contradiction.

Turn-In (#33)
§4.7 (Txt. p.247) #6-19
§4.6 (Txt. p.239) #10, 14-16, 19, 22, 23

Handouts
No Handouts Posted

Assignment
Finish Chapter 4- Lesson 6
Txt. p. 255 (Chapter Test) #1-10, 15, 18
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, December 05, 2007

Algebra (Class 33)

Overview
In today’s class we our warm-up continues to focus on graphing and finding the equations of lines. During the lesson for the day we being a new packet which focuses on areas of polygons, squares and square roots, and working with exponents.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method
§3-1 (Txt. p.95) Transforming Equations

Vocabulary
exponent
square number
linear interpolation
exponential notation
square root
multiplicative identity property
base
positive square root
product

Key Attitudes
Math is about investigating and confirming

Key Ideas
Equations of lines can be written using two the coordinates of two points.
The area of a shape is the number of square units it encloses.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Setting up and solving simple interest problems.

Turn-In (#32)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
Unit 5- Week 18: SP14- SP16
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, December 04, 2007

Geometry (Class 33)

Overview
In today’s class we focus on learning a different approach for proving theorems-- Proof by Contradiction.
Textbook Sections
§5.6 (Txt. p.302) Indirect Proof

Vocabulary
Proof by contradiction
contrdiction

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A statement can be proved true by first assuming that it is false and then showing that this leads to an impossible result.

Key Skills
Proving a statement is true by contradiction.
Writing the negation of a statement.
Using the proof by contradiction format to write a proof by contradiction.

Turn-In (#32)
§4.7 (Txt. p.247) #6-19
§4.6 (Txt. p.239) #10, 14-16, 19, 22, 23

Handouts
Chapter 4- Lesson 6: Proof By Contradiction

Assignment
Test Corrections
§4.6 (Txt. p.242) Mixed review #45, 46, 48, 49, 54, 55
Txt. p.250 #1, 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.

Monday, December 03, 2007

Announcements

Announcements
Get your packet’s signed by a parent!

Overview
In today’s class we work on our skills of graphing and writing equations of lines during our warm-up while we continue our work with simple interest during the lesson for the day. In particular we examine a situation involving the buying of a car and calculating the monthly payment based on its initial cost, down payment, interest rate, and the length of time needed to repay the loan.
Textbook Sections
§9-1 (Txt. p.413) The Graphing Method
§3-1 (Txt. p.95) Transforming Equations

Key Attitudes
Math is about investigating and confirming

Key Ideas
Interest is the amount of money paid to use money.
Interest depends on the principal, rate of interest and time.
The total amount to repay a loan depends on the principal and the interest.

Key Skills
Writing and using equations of lines.
Parallel lines have equal slope.
Setting up and solving simple interest problems.

Turn-In (#31)
§9-1 (Txt. p.415) #7-10, 19 (Accurate graphs required! Use graph paper if needed.)
Finish packet through SP 10

Handouts
No Handouts Posted

Assignment
Skill Builder 1A and 1B (SP12, 13)
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.