HolcombMath

Monday, March 31, 2008

Algebra (Class 63)

Announcements
Test Friday focusing on linear inequalities, systems of linear inequalities, and the Pythagorean Theorem

Lesson Title
Applications of the Pythagorean Theorem

Overview
In today’s class, our first since spring break, we will pick up where we left off with the Pythagorean Theorem, seeing how it can be used to solve various problems. The warm-up today, Puzzle Grid (E), continues to focus on developing algebraic reasoning.
Textbook Sections
11-6 (Txt. p.529) The Pythagorean Theorem
UCLA Materials- Unit 6: Week 24

Vocabulary
hypotenuse
legs
Pythagorean theorem
mean
median
mode
outlier
range
right triangle

Key Attitudes
Math is about investigating and confirming

Key Ideas
The Pythagorean theorem relates the lengths of the sides of a right triangle.
The Pythagorean theorem can be used to find the length of a side of a right triangle when the lengths of two sides are known.
Radicals are simplified if they contain no perfect square factors.
The hypotenuse of a right triangle is always across from the right angle.
In order to be able to use the Pythagorean theorem for solving a problem you need to be able to answer “yes” to both of the following questions: 1) Do you see right triangles, 2) Do you have the lengths of two sides?
Key Skills
Find the area of rectangles or triangles.
Simplify algebraic expressions by combining like terms.
Find the area of shapes on dot paper.
Simplify radicals.
Use the Pythagorean Theorem to find the lengths of a missing side of a right triangle when given the lengths of two other sides.
Turn-In (#62)
ACE p.78 #18
Extra Practice 26 #26, 27
Skill Builder 2C (SP15)

Handouts/Links
Pythagorean Theorem Practice Problems

Assignment
Skill Builder 1
Extra Practice 26 #28, 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.

Friday, March 21, 2008

Geometry (Class 64)

Announcements
Test today. Focus will be on Chapter 8: Lesson 1 through Chapter 9: Lesson 2

Lesson Title
Right Triangle Magic

Overview
In today’s class we continue our work with the surface area and volume of solids by examining another pattern that creates a pyramid,— this time with a triangular base. During the lesson we wrap up “Chapter 9- Lesson 2: Right Triangle Magic” by explaining how the trick worked, creating some tricks of our own, and thinking about the things we know so far about right triangle trigonometry and the things we would like to find out. Finally, during the last hour or so of the class we will take Test 10
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios
Chapter 9- Lesson 2: Right Triangle Magic

Vocabulary
special right triangle
isosceles right triangle
45-45-90 triangle
30-60-90 triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
All right triangle with an acute angle of measure x˚ are similar.
The ratios of the sides of all right triangles with an acute angle of measure x˚ are equal.
The measure of the reference angle determines the ratios of the sides of a right triangle.
If you know the ratios of two sides of a right triangle, you can use trigonometric ratios to figure out the measure of the angles of the triangle.
The surface area and volume of a triangular based pyramid can be found in the same way as a square based pyramid, the only difference is that the area of the base is a triangle.
Key Skills
I can explain how trigonometry is connected to similar triangles.
I can draw a right triangle in standard position, identify the reference angle, adjacent side, opposite side, and hypotenuse.
I can use a trigonometric ratios table to find the measure of the reference angle when I know the ratio of the adjacent : hypotenuse, opposite : hypotenuse, or opposite : adjacent.
Find the surface area and volume of a triangular based pyramid.
Turn-In (#63)
§9.4 (Txt. p.554) #12-17, 24-27
§9.3 (Txt. p.546) #8-10, 14-17

Handouts
Chapter 12- Solid 6

Assignment
Finish Warm-Up (Solid 5)
§9.4 (Txt. p.554) #18-20
§9.3 (Txt. p.546) #11-13, 18-20, 26, 27

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, March 20, 2008

Algebra (Class 62)

Announcements
Test today focusing on work from Investigation 3 and Investigation 5. Rework the hard problems from the ACE and the warm-ups!

Lesson Title
Using the Pythagorean Theorem

Overview
We continue to build our algebraic fluency through solving the puzzle grids during our warm-up. Our lesson for today continues to focus on the Pythagorean theorem. We discuss the dissection puzzle and see a animation of one possible solution to the puzzle. We focus down to building fluency for using the Pythagorean theorem to solve for the missing lengths of sides of right triangles. We also discuss ways to to recognize a Pythagorean theorem problem-- you need to be able to answer the following questions “yes”: 1) Do you see right triangles?, 2) Do you know the lengths of two sides?
Textbook Sections
11-6 (Txt. p.529) The Pythagorean Theorem
UCLA Materials- Unit 6: Week 24

Vocabulary
hypotenuse
legs
Pythagorean theorem
mean
median
mode
outlier
range
right triangle

Key Attitudes
Math is about investigating and confirming

Key Ideas
The Pythagorean theorem relates the lengths of the sides of a right triangle.
The Pythagorean theorem can be used to find the length of a side of a right triangle when the lengths of two sides are known.
Radicals are simplified if they contain no perfect square factors.
The hypotenuse of a right triangle is always across from the right angle.
In order to be able to use the Pythagorean theorem for solving a problem you need to be able to answer “yes” to both of the following questions: 1) Do you see right triangles, 2) Do you have the lengths of two sides?
Key Skills
Find the area of rectangles or triangles.
Simplify algebraic expressions by combining like terms.
Find the area of shapes on dot paper.
Simplify radicals.
Use the Pythagorean Theorem to find the lengths of a missing side of a right triangle when given the lengths of two other sides.
Turn-In (#61)
ACE p.78 #17
Extra Practice 26 #19-21, 24, 25
Skill Builder 2B (SP14)

Handouts
No Handouts Posted

Assignment
ACE p.78 #18
Extra Practice 26 #26, 27
Skill Builder 2C (SP15)
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, March 19, 2008

Geometry (Class 63)

Announcements
Test Friday. Focus will be on Chapter 8: Lesson 1 through Chapter 9: Lesson 2

Lesson Title
Special Right Triangles 2

Overview
In today’s class our warm-up continues to extend the skills and concepts necessary to find surface area and volume. Our focus today is on pyramids and we see how the work we did with the Yang Ma can be generalized to all pyramids. During the lesson part of the class we wrap up the development of special right triangles.
Textbook Sections
§9.4 (Txt.p.551) Special Right Triangles

Vocabulary
special right triangle
isosceles right triangle
45-45-90 triangle
30-60-90 triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
A special right triangle can be created from a square. This results in an isosceles right triangle whose angle measures are 45˚, 45˚, and 90˚.
A special right triangle can be created from folding an equilateral triangle. This creates a triangle with 30˚, 60˚, and 90˚ angles- a 30-60-90 triangle
30-60-90 and 45-45-90 triangles are special because we can easily related the lengths of the sides of the triangle to the measures of the interior angles of the triangle.
Key Skills
Recognize special right triangels.
Explain what makes a right triangle special.
Justify the relationships between angle measures and side lengths in special right triangles.
Use the relationships between the angle measures and side lengths in special right triangles to find missing side lengths or angle measures. http://www.youtube.com/watch?v=_eBIuP9pugM
Simplify radicals including rationalizing the denominator. http://www.youtube.com/watch?v=N8MkTuLlgOg&feature=email
Turn-In (#62)
§9.2 (Txt. p.538) 7-9, 16-18, 25-27, 31
Chapter 8- Lesson 7

Handouts
Chapter 12- Solid 5 (Square Based Pyramid)

Assignment
§9.4 (Txt. p.554) #12-17, 24-27
§9.3 (Txt. p.546) #8-10, 14-17
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, March 18, 2008

Algebra (Class 61)

Announcements
Test today focusing on work from Investigation 3 and Investigation 5. Rework the hard problems from the ACE and the warm-ups!

Lesson Title
The Pythagorean Theorem 2

Overview
The Warm-Up for today’s class (Puzzle Grid (C)) continues the theme of using algebraic reasoning to solve a problem. The lesson for the class carries on our development of the Pythagorean Theorem, seeing how it is related to the lengths and areas of squares on the sides of right triangles. We will develop a geometric justification of the theorem to help us understand how and why the Pythagorean Theorem works as well as work on developing our skills at using the the Pythagorean Theorem for finding missing lengths of sides of right triangles. Our skills for simplifying radicals will come in handy! Also during the class Test 11 will be returned and students will have an opportunity to correct their test.
Textbook Sections
11-6 (Txt. p.529) The Pythagorean Theorem
UCLA Materials- Unit 6: Week 24

Vocabulary
hypotenuse
legs
Pythagorean theorem
mean
median
mode
outlier
range
right triangle

Key Attitudes
Math is about investigating and confirming

Key Ideas
The Pythagorean theorem relates the lengths of the sides of a right triangle.
The Pythagorean theorem can be used to find the length of a side of a right triangle when the lengths of two sides are known.
Radicals are simplified if they contain no perfect square factors.
The hypotenuse of a right triangle is always across from the right angle.
Key Skills
Find the area of rectangles or triangles.
Simplify algebraic expressions by combining like terms.
Find the area of shapes on dot paper.
Simplify radicals.Video for Simplifying Radicals
Use the Pythagorean Theorem to find the lengths of a missing side of a right triangle when given the lengths of two other sides.

Turn-In (#60)
ACE p.78 #10, 12
Extra Practice 26 #13-18, 22, 23

Handouts
No Handouts Posted

Assignment
ACE p.78 #17
Extra Practice 26 #19-21, 24, 25
Skill Builder 2B (SP14)
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, March 17, 2008

Geometry (Class 62)

Announcements
Test Friday. Focus will be on Chapter 8: Lesson 1 through Chapter 9: Lesson 2

Lesson Title
Special Right Triangles

Overview
In today’s class we use our warm-up time to finish up the second proof of the Pythagorean theorem. The lesson for the day marks the start of our study concerning the angle measures and side lengths of right triangles learning about special right triangles, what makes them special, and how we can use this “specialness” to solve problems.
Textbook Sections
§9.4 (Txt.p.551) Special Right Triangles

Vocabulary
special right triangle
isosceles right triangle
45-45-90 right triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
A special right triangle can be created from a square. This results in an isosceles right triangle whose angle measures are 45˚, 45˚, and 90˚.
A special right triangle can be created from folding an equilateral triangle. This creates a triangle with 30˚, 60˚, and 90˚ angles- a 30-60-90 triangle
30-60-90 and 45-45-90 triangles are special because we can easily related the lengths of the sides of the triangle to the measures of the interior angles of the triangle.

Key Skills
Recognize special right triangels.
Explain what makes a right triangle special.
Justify the relationships between angle measures and side lengths in special right triangles.
Use the relationships between the angle measures and side lengths in special right triangles to find missing side lengths or angle measures.
Simplify radicals including rationalizing the denominator.Video for Rationalizing the Denominator

Turn-In #61
§9.1 (Txt. p.531)#22-24, 28-31, 35
Finish Warm-Up (Solid 4- Yangma)
Finish Chapter 8- Lesson 6

Handouts
Chapter 9: Preview
Chapter 9- Lesson 1: Special Right Triangles

Assignment
§9.2 (Txt. p.538) 7-9, 16-18, 25-27, 31
Chapter 8- Lesson 7
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, March 14, 2008

Algebra (Class 60)

Announcements
Test today focusing on work from Investigation 3 and Investigation 5. Rework the hard problems from the ACE and the warm-ups!

Lesson Title
The Pythagorean Theorem 1

Overview
In today’s class both our warm-up and lesson focus on new material. The warm-up focuses on logical reasoning and algebraic skills to solve a “puzzle grid”, while our lesson returns to a geometric focus to develop the Pythagorean theorem.
Textbook Sections
11-6 (Txt. p.529) The Pythagorean Theorem
UCLA Materials- Unit 6: Week 24

Vocabulary
hypotenuse
legs
Pythagorean theorem
mean
median
mode
outlier
range
right triangle

Key Attitudes
Math is about investigating and confirming

Key Ideas
The Pythagorean theorem relates the lengths of the sides of a right triangle.
The Pythagorean theorem can be used to find the length of a side of a right triangle when the lengths of two sides are known.
Key Skills
Find the area of rectangles or triangles.
Simplify algebraic expressions by combining like terms.
Find the area of shapes on dot paper.
Turn-In (#59)
ACE p.42 #41, 47
ACE p.78 #6, 7, 9, 11
Extra Practice 26 #1, 2, 7-12

Handouts
No Handouts Posted

Assignment
ACE p.78 #10, 12
Extra Practice 26 #13-18, 22, 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.

Thursday, March 13, 2008

Geometry (Class 61)

Announcements
Test Friday. Focus will be on Chapter 8 Lesson 1- Lesson 5.

Lesson Title
A Useful Little Theorem

Overview
In today’s class the warm-up focuses on finding the volume of a very special pyramid, one with a square base and a vertex over one of the vertices of the square. Finding the volume of this solid will lead us to finding a general formula for all pyramids and cones.
During the lesson we finish developing the concepts related to similar right triangles in right triangles, seeing how a table can help us organize the data. We then apply these concepts to proving the Pythagorean Theorem.
Textbook Sections
9.2 (Txt. p.536) The Pythagorean Theorem

Vocabulary
similar, similarity statement
ratio
proportion
scale factor
statement of proportionality
geometric mean
golden section
golden rectangle
altitude
hypotenuse
right triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
Inside any right triangle there exists other right triangle which are similar to the original.
Since the right triangles created by constructing an altitude to the hypotenuse are similar, the corresponding sides are proportional.
If you are given a geometric mean, you only need two values to solve the proportion.
Since some of the proportions share the length of a side, and that side length is across from itself in the proportion, a geometric mean is created.
Key Skills
Creating similar right triangles inside a right triangle.
Solve problems involving similar right triangles formed by the altitude drawn from the hypotenuse of the right triangle
Creating and using geometric means to solve problems.
Matching corresponding pieces of similar triangles.
Turn-In (#60)
§9.1 (Txt. p.531)#11-21, 25-27
Test Corrections

Handouts
Chapter 8- Lesson 7: A Useful Little Theorem

Assignment
§9.1 (Txt. p.531)#22-24, 27-31, 35
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, March 12, 2008

Algebra (Class 59)

Announcements
Test Friday focusing on work from Investigation 3 and Investigation 5. Rework the hard problems from the ACE and the warm-ups!

Lesson Title
Systems of Linear Inequalities

Overview
In today’s class our warm-up continues to focus on using tables and patterns to organize data and to help us find patterns we can use for writing equations. In the lesson for the day we continue our work with linear inequalities by learning how a system of two linear inequalities can be used to solve a problem.
Textbook Sections
§10-7 (Txt. p.490) Graphing Linear Inequalities
The Shapes of Algebra- Investigation 5.4 (p. 76)

Vocabulary
inequality
systems of linear inequalities
region
constraint

Key Attitudes
Math is about investigating and confirming

Key Ideas
Inequalities are used to represent situations where there is a limiting value.
Solutions to inequalities can be graphed on a number line when there is only one variable.
Solutions to inequalities are represented by a region on a two axis graph when two variables are involved.
When multiplying or dividing by a negative value, the direction of the inequality switches.
In equalities can include or not include the limiting value. We use a closed circle on the number line to represent including the limiting value and an open circle to represent not including the limiting value.
To find the solution to a system of two (or more) linear inequalities you need to find where the shaded regions overlap.
Key Skills
Find ordered pairs which satisfy two sets of constraints.
Graph a linear inequality on a coordinate plane.
Determine the region that satisfies a system of inequalities by trying points.
Match a linear inequality to its graph.
Solve a system of two linear inequalities by graphing.
Turn-In (#58)
ACE p.78 #2, 4, 5
ACE p.42 #40, 46

Handouts
Extra Practice 26- Inequalities in Two Variables

Assignment
ACE p.42 #41, 47
ACE p.78 #6, 7, 9, 11
Extra Practice 26 #1, 2, 7-12
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.

Tuesday, March 11, 2008

Geometry (Class 60)

Announcements
Test Friday. Focus will be on Chapter 8 Lesson 1- Lesson 5.

Lesson Title
Triangles in Right Triangles 2

Overview
In the last class we saw how similar right triangles are hiding inside any right triangle. We also learned how to find the corresponding sides and angles of these triangles and saw that many statements of proportionality between the triangles can be written. In today’s class we build on these ideas and use them to solve some related problems, including a proof of the Pythagorean Theorem.
Textbook Sections

Vocabulary
similar, similarity statement
ratio
proportion
scale factor
statement of proportionality
geometric mean
golden section
golden rectangle
altitude
hypotenuse
right triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
Inside any right triangle there exists other right triangle which are similar to the original.
Since the right triangles created by constructing an altitude to the hypotenuse are similar, the corresponding sides are proportional
If you are given a geometric mean, you only need two values to solve the proporion.
Key Skills
Creating similar right triangles inside a right triangle.
Solve problems involving similar right triangles formed by the altitude drawn from the hypotenuse of the right triangle
Creating and using geometric means to solve problems.
Turn-In (#59)
Txt. p.522 #16-18, 53-58
Txt. p.801 #1-3

Handouts
Chapter 12- Solid 3 (Right Triangular Prism)

Assignment
§9.1 (Txt. p.531)#11-21, 25-27
Test Corrections
Finish Chapter 8- Lesson 6 through #9b
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, March 10, 2008

Algebra (Class 58)

Announcements
Test Friday focusing on work from Investigation 3 and Investigation 5. Rework the hard problems from the ACE and the warm-ups!

Lesson Title
Graphs of Linear Inequalities

Overview
In today’s class our warm-up continues to focus on using tables to organize information as a tool for writing equations. The lesson for today extends our work with linear inequalities focusing on being able to match a graph of a linear inequality with an equation.
Textbook Sections
§10-7 (Txt. p.490) Graphing Linear Inequalities
The Shapes of Algebra- Investigation 5.3 (p. 73)

Vocabulary
inequality
systems of linear inequalities
region
constraint

Key Attitudes
Math is about investigating and confirming

Key Ideas
Inequalities are used to represent situations where there is a limiting value.
Solutions to inequalities can be graphed on a number line when there is only one variable.
Solutions to inequalities are represented by a region on a two axis graph when two variables are involved.
When multiplying or dividing by a negative value, the direction of the inequality switches.
In equalities can include or not include the limiting value. We use a closed circle on the number line to represent including the limiting value and an open circle to represent not including the limiting value.
Key Skills
Find ordered pairs which satisfy two sets of constraints.
Graph a linear inequality on a coordinate plane.
Determine the region that satisfies a system of inequalities by trying points.
Match a linear inequality to its graph.
Turn-In (#57)
ACE p.78 #1, 3, 14
ACE p.42 #34, 35, 39, 45

Handouts
No Handouts Posted

Assignment
ACE p.78 #2, 4, 5
ACE p.42 #40, 46
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, March 07, 2008

Geometry (Class 59)

Announcements
Test Friday. Focus will be on Chapter 8 Lesson 1- Lesson 5.

Lesson Title
Right Triangles in Right Triangles 1

Overview
In today’s class our warm-up focuses on creating a cylinder from a net, calculating the surface area of the cylinder and its volume. During the lesson we use the triangles we made at the end of the last class to explore the relationships inside of a right triangle. During the last part of the class we take Test 10 which focuses on concepts and skills related to similar figures.
Textbook Sections
§9.1 (Txt. p.527) Similar Right Triangles

Vocabulary
similar, similarity statement
ratio
proportion
scale factor
statement of proportionality
geometric mean
golden section
golden rectangle
altitude
hypotenuse
right triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
Inside any right triangle there exists other right triangle which are similar to the original.
Since the right triangles created by constructing an altitude to the hypotenuse are similar, the corresponding sides are proportional
If you are given a geometric mean, you only need two values to solve the proporion.
Key Skills
Creating similar right triangles inside a right triangle.
Solve problems involving similar right triangles formed by the altitude drawn from the hypotenuse of the right triangle
Creating and using geometric means to solve problems.
Turn-In (#58)
Txt. p.519 #1-9, 10-15, 17
Txt. p.522 #1-3, 13-15

Handouts
Chapter 12- Lesson 2- Solid 2 (Cylinder)

Assignment
Txt. p.522 #16-18, 53-58
Txt. p.801 #1-3
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, March 06, 2008

Algebra (Class 57)

Assignment
ACE p.78 #1, 3, 14
ACE p.42 #34, 35, 39, 45
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.

Lesson Title
Limiting Carbon Dioxide Emissions- Solving Linear Inequalities by Graphing

Overview
In today’s class we continue to work with situations which can be modeled with linear inequalities. In particular we work to further our ability to write systems that represent a situation being careful to define the variables in the situation. Graphs again play a crucial role finding a solution.
Textbook Sections
§10-7 (Txt. p.490) Graphing Linear Inequalities
The Shapes of Algebra- Investigation 5.1 (p. 69)

Vocabulary
inequality
systems of linear inequalities
region
constraint

Key Attitudes
Math is about investigating and confirming

Key Ideas
Inequalities are used to represent situations where there is a limiting value.
Solutions to inequalities can be graphed on a number line when there is only one variable.
Solutions to inequalities are represented by a region on a two axis graph when two variables are involved.
When multiplying or dividing by a negative value, the direction of the inequality switches.
In equalities can include or not include the limiting value. We use a closed circle on the number line to represent including the limiting value and an open circle to represent not including the limiting value.
Key Skills
Solve a linear inequality and graph its solution on a number line.
Find ordered pairs which satisfy two sets of constraints.
Graph a linear inequality on a coordinate plane.
Determine the region that satisfies a system of inequalities by trying points.
Write a system of linear inequalities to model a situation.
Turn-In (#56)
Test Corrections
ACE p.42 #28-33, 38, 44
ACE p. 78 #13, 15

Handouts
No Handouts Posted

Assignment
ACE p.78 #1, 3, 14
ACE p.42 #34, 35, 39, 45
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, March 05, 2008

Geometry (Class 58)

Chapter 8- Lesson 5: Donald Duck in Mathmagic Land

Announcements
Test Friday. Focus will be on Chapter 8 Lesson 1- Lesson 5.

Lesson Title
The Golden Rectangle

Overview
In today’s class we develop the concept of a “geometric mean” and how this relates to the golden section and to golden rectangles. As time permits we will also begin work examining proportional relationships inherent in right triangles.
Textbook Sections
§8.2 (Txt. p.465) Problems Solving in Geometry with Proportions
§9.1 (Txt. .527) Similar Right Triangles

Vocabulary
similar, similarity
similarity statement
scale factor
statement of proportionality
geometric mean
golden section
golden rectangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
A “golden section” is created when a line segment of length a is divided into two segments of length b and c such that b/a=c/b.
The golden section gives rise to a quadratic equation.
Quadratic equations can be solved by using the quadratic formula
Key Skills
Create a golden rectangle.
Simplify an algebraic proportion.
Solve a quadratic equation using the quadratic formula.
Turn-In (#57)
Complete Warm-Up
§8.6 (Txt. p.502) #25-28, 39a-c
Txt. p.517 #8-17

Handouts
Chapter 8-Lesson 5: The Golden Rectangle and the Geometric Mean
Chapter 8- Lesson 6: Seeing Similarities

Assignment
Txt. p.519 #1-9, 10-15, 17
Txt. p.522 #1-3, 13-15
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.

Tuesday, March 04, 2008

Algebra (Class 56)

Lesson Title
Limiting Driving Miles

Overview
Our class today focuses on learning how to solve inequalities involving one and two variables and to create a system of inequalities to represent a situation.
Textbook Sections
§10-7 (Txt. p.490) Graphing Linear Inequalities
The Shapes of Algebra- Investigation 5.1 (p. 69)

Vocabulary
inequality
systems of linear inequalities
region
constraint

Key Attitudes
Math is about investigating and confirming

Key Ideas
Inequalities are used to represent situations where there is a limiting value.
Solutions to inequalities can be graphed on a number line when there is only one variable.
Solutions to inequalities are represented by a region on a two axis graph when two variables are involved.
When multiplying or dividing by a negative value, the direction of the inequality switches.
Key Skills
Solve a linear inequality and graph its solution on a number line.
Find ordered pairs which satisfy two sets of constraints.
Determine the region that satisfies a system of inequalities by trying points.
Write a system of linear inequalities to model a situation
Turn-In (#55)
ACE p.42 #3, 11, 13, 17, 18, 23, 24, 48-52, 58-62

Handouts
No Handouts Posted

Assignment
Test Corrections
ACE p.42 #28-33, 38, 44
ACE p. 78 #13, 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.