HolcombMath

Wednesday, April 30, 2008

Algebra (Class 74)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Quadratic Formula

Overview
In today’s class the we finish the “Block Balance” series of warm-ups which have dealt with solving systems of linear equations. Our lesson for the day reviews factoring quadratic expressions and introduces the quadratic formula as a tool for factoring quadratic expressions and finding the location of the x-intercepts.
Textbook Sections
12-3 (Txt. p.567) The Quadratic Formula

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form
standard form of a quadratic equation
quadratic formula

Key Attitudes
Math is about investigating and confirming

Key Ideas
Quadratic expressions can be written in expanded or factored form.
An expression is written in expanded form when the expression is the sum or difference of terms.
An expression is written in factored form when the expression is the product of factors.
Quadratic equations written in expanded or factored form contain clues that can be used to create a graph of the equation.
The x-intercepts, line of symmetry, vertex, (and y-intercept) determine a the graph of a quadratic equation (a parabola)
The quadratic formula is a tool that can be used for finding the x-intercepts of a quadratic equation when the equation can not be factored.
Key Skills
I can change a quadratic equation from factored form to expanded form, or from expanded form to factored form.
I can find the x-intercepts from a quadratic equation written in factored form.
I can find the y-intercept of a graph of a quadratic equation when given a quadratic equation.
I can find the line of symmetry of a graph of a quadratic equation when given a quadratic equation.
I can find the vertex of a graph of a quadratic equation when given a quadratic equation.
I can match a graph of a quadratic equation to its equation written in expanded or factored form.
I can write a quadratic expression in standard form.
I can find the value of the discriminant (b^2-4ac).
I can use the quadratic formula to factor and find the x-intercepts of a quadratic equation.
Turn-In (#73)
ACE p.30 #30-33, 40, 44-47

Handouts/ Links
Using the Quadratic Formula Video 1
Using the Quadratic Formula Video 2
Using the Quadratic Formula Video 3

Assignment
Finish Worksheet 10.5 Practice B #1-33
Finish Worksheet 9.5 Practice A #1-27
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.

Tuesday, April 29, 2008

Geometry (Class 75)

Announcements
Next test is next Friday, April 26. The following test will not be until May 23 due to STAR testing-- that test will cover a lot of material!

Lesson Title
Volume of Sphere
Extended Chords of a Circle

Overview
In today’s class our warm-up focuses on developing the formula for the volume of a sphere. We view a demonstration, analyze what we saw, and draw a conclusion about the relationship between the radius and volume of a sphere. We then confirm our experimental evidence through mathematical analysis. Our lesson for the day continues with our work on segment and arc relationships of circles. In particular we examine the relationship between the lengths of extended chords.
Textbook Sections
§10.5 (Txt. p.629) Segment Lengths in Circles

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
Cavalieri’s Principle

Key Attitudes
Math is about thinking creatively.

Key Ideas
If two extended chords intersect outside of a circle, then the lengths of the entire extended cords is proportional to the lengths of the sections of the chords exterior to the circle.
The volume of a sphere is equal to four-thirds of the cube of the radius of the shpere.
Key Skills
I can recognize extnded chords and recall the relationship between their lengths.
I can use the relationship between the lengths of the sections of extended chords to solve problems.
I can explain why the relationship between the lengths of extend chords works.
I can recall and use the volume formula for a sphere to solve problems.
I can develop the volume formula of a sphere based on what I know about cones and cylinders.
Turn-In (#74)
Finish Warm-Up (Finding the surface area of an Octagonal Pyramid)
Finish Chapter 10- Lesson 3

Handouts
Chapter 12- Volume of a Sphere
Chapter 10- Lesson 4: Extended Chords of a Circle

Assignment
Finish Chapter 10 Lesson 4
Finish Volume of a Sphere.
Txt. p.632 #10-18, 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.

Monday, April 28, 2008

Algebra (Class 73)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
A Closer Look At Parabolas

Overview
In today’s class our warm-up continues to focus on solving systems of equations in the form of a balance puzzle. The lesson for today brings us back to focus on the graphs of quadratic expressions and learn how the equations tell us the critical information we need in order to create a graph.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Problem 2.5:  A Closer Look at Parabolas

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form

Key Attitudes
Math is about investigating and confirming

Key Ideas
Quadratic expressions can be written in expanded or factored form.
An expression is written in expanded form when the expression is the sum or difference of terms.
An expression is written in factored form when the expression is the product of factors.
Key Skills
I can change a quadratic equation from factored form to expanded form, or from expanded form to factored form.
I can find the x-intercepts from a quadratic equation written in factored form.
I can find the y-intercept of a graph of a quadratic equation when given a quadratic equation.
I can find the line of symmetry of a graph of a quadratic equation when given a quadratic equation.
I can find the vertex of a graph of a quadratic equation when given a quadratic equation.
I can match a graph of a quadratic equation to its equation written in expanded or factored form.
Turn-In (#72)
ACE p.30 #14, 15, 26-29, 50a, c (skip b)
Partner Challenge with someone

Handouts
No Handouts Posted

Assignment
ACE p.30 #30-33, 40, 44-47
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, April 25, 2008

Geometry (Class 74)

Announcements
Next test is next Friday, April 26. The following test will not be until May 23 due to STAR testing-- that test will cover a lot of material!

Lesson Title
Intersecting Chords of a Circle

Overview
The warm-up for today focuses on using the concepts and skills related to surface area and volume to find the surface area of an octagonal pyramid. During the lesson we continue to develop the ideas related to the lengths of intersecting chords of a circle. During the last part of the class we write test 11.
Textbook Sections
§10.5 (Txt. p.629) Segment Lengths in Circles

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords

Key Attitudes
Math is about thinking creatively.

Key Ideas
If two chords intersect in the interior of a circle, then the products of the lengths of the sections of one chord is equal to the product of the lengths of the sections of the other chord.
The volume of a cone is equal to one-third the product the area of its base and height.
Key Skills
I can recognize intersecting chords and recall the relationship between their lengths.
I can explain why the product of the sections of intersecting chords is equal.
I can use the relationship between the lengths of the sections of intersecting chords to solve problems.
I can identify the various parts of a cone.
I can use the formula for the volume of a cone to solve applied problems.
Turn-In (#73)
Finish Cone 5- Problems
Txt. 600 #36-41, 46-48
Txt. p.608 #32-41
CST Practice 4 All (Problems 64-74)

Handouts
Surface Area of Octagonal Pyramid
Chapter 10- Lesson 3: Intersecting Chords
Assignment
Finish Warm-Up (Finding the surface area of an Octagonal Pyramid)
Finish Chapter 10- Lesson 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, April 24, 2008

Algebra (Class 72)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Factoring Quadratic Expressions

Overview
The warm-up for today remains focused on solving balance problems which require converting units. In the lesson we continue working with quadratic relationships by learning how to reverse the expanding process in order to factor quadratic expressions.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Problem 2.4 Factoring Quadratic Expressions

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form

Key Attitudes
Math is about investigating and confirming

Key Ideas
Quadratic expressions can be written in expanded or factored form.
An expression is written in expanded form when the expression is the sum or difference of terms.
An expression is written in factored form when the expression is the product of factors.
Key Skills
I can make a rectangle diagram to help me factor a quadratic expression.
I can use a rectangle model to factor a quadratic expression
I can use the distributive property (in reverse) to rewrite an expression given in expanded form in factored form.
Turn-In (#71)
ACE p.30 #6, 7, 10, 11, 17, 19, 20, 21, 23-25, 56-58
Test Corrections

Handouts
No Handouts Posted

Assignment
ACE p.30 #10, 11, 14, 15, 26-29, 50a, c (skip b)
Partner Challenge with someone
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, April 23, 2008

Geometry (Class 73)

Announcements
Next test is next Friday, April 26. The following test will not be until May 23 due to STAR testing-- that test will cover a lot of material!

Lesson Title
Intersecting Chords of a Circle

Overview
The warm-up today focuses on applications of the formula for the volume of a cone. In our lesson we will learn how the lengths of chords which intersect inside a circle are related.
Textbook Sections
§10.5 (Txt. p.629) Segment Lengths in Circles

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords

Key Attitudes
Math is about thinking creatively.

Key Ideas
If two chords intersect in the interior of a circle, then the products of the lengths of the sections of one chord is equal to the product of the lengths of the sections of the other chord.
The volume of a cone is equal to one-third the product the area of its base and height.
Key Skills
I can recognize intersecting chords and recall the relationship between their lengths.
I can explain why the product of the sections of intersecting chords is equal.
I can use the relationship between the lengths of the sections of intersecting chords to solve problems.
I can identify the various parts of a cone.
I can use the formula for the volume of a cone to solve applied problems.
Turn-In (#72)
Finish Warm-Up (Cone 5)
Finish Chapter 10-Lesson 2
Txt. p.599 #9, 13, 17, 18-25

Handouts
Chapter 12- Cone 5
Chapter 10- Lesson 3: Intersecting Chords

Assignment
Finish Cone 5- Problems
Txt. 600 #36-41, 46-48
Txt. p.608 #32-41
CST Practice 4 All (Problems 64-74)
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, April 22, 2008

Algebra (Class 71)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Changing Two Dimensions

Overview
The warm-up for today’s class deals with solving a balance problem which requires converting units. In the lesson today we focus on factoring and expanding quadratic expressions.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Problem 2.3 Changing Two Dimensions

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form

Key Attitudes
Math is about investigating and confirming

Key Ideas
Quadratic expressions can be written in expanded or factored form.
An expression is written in expanded form when the expression is the sum or difference of terms.
An expression is written in factored form when the expression is the product of factors.
Key Skills
I can write an expression to represent the area of a rectangle in two different ways-- as the product of the length and the width (factored) or as the sum of the individual areas (expanded)
I can use the distributive property to expand an expression written in factored form.
Turn-In (#70)
ACE p.30 #2 - 5, 8, 9, 12, 13, 16, 18

Handouts
No Handouts Posted

Assignment
ACE p.30 #6, 7, 10, 11, 17, 19, 20, 21, 23-25, 56-58
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, April 21, 2008

Geometry (Class 72)

Announcements
Next test is next Friday, April 26. The following test will not be until May 23 due to STAR testing-- that test will cover a lot of material!

Lesson Title
Tangents to a Circle

Overview
The warm-up today focuses on developing a formula for calculating the volume of a cone. The development of our formula is a sneak preview into calculus! The lesson for the day continues to develop student understanding of the relationships between the arcs and angles of circles. We finish our work related to lengths of intersecting tangent segments and begin to examine relationships between the lengths of intersecting chords.
Textbook Sections
§10.1 (Txt. p.595) Segments Tangent to a Circle

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter

Key Attitudes
Math is about thinking creatively.

Key Ideas
A circle is the locus of points equidistant from a given point.
All radii of a circle are congruent.
Any triangle constructed with one vertex at the center of a circle and both other vertices on the circumference of the circle will be an isosceles triangle.
If a triangle is inscribed in a circle such that one side of the triangle is a diameter of the circle, then the triangle is a right triangle.
Key Skills
Use the relationships related to tangent segments to find lengths
I recognize and construct a tangent to a circle.
I can recall and use the fact that a radius is perpendicular to a line tangent to the circle.
I can use pyramid slices of a cone to show that the volume of a cone is equal to the one-third of the area of its base times its height.
I can quickly recall the formula for the volume of a cone and use it to quickly and accurately find the volume of a cone.
Turn-In (#71)
CST Practice
Finish Warm-up
Finish Chapter 10- Lesson 1

Handouts
Chapter 12- Cone 5: Volume of a Cone
Chapter 10- Lesson 2: Tagent to a Circle

Assignment
Finish Warm-Up (Cone 5)
Finish Chapter 10-Lesson 2
Txt. p.599 #9, 13, 17, 18-25
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.

Friday, April 18, 2008

Algebra (Class 70)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Changing One Dimension

Overview
In today’s class our warm-up shifts its focus back to dealing with balance scales and figuring out the weight of different objects— solving a system of equations in disguise! The lesson for the class continues to focus on quadratic relationships. We see how to model changing one dimension of a rectangle effects the area of the rectangle, and how to write expressions and equations for these situations.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Problem 2.2 Changing One Dimension

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form

Key Attitudes
Math is about investigating and confirming

Key Ideas
Quadratic expressions can be written in expanded or factored form.
The factored form of a quadratic equation can be easily used to find the x-intercepts of the graph of that equation.
The expanded form of a quadratic equation can be easily used to find the y-intercept of the graph of that equation.
The vertex of a parabola is always located on a vertical line half-way between the x-intercepts.
Key Skills
I can enter a quadratic equation into a graphing calculator.
I can use a graphing calculator to make a table of values, including adjusting the starting value and the increment between “x” values.
I can use a table of value to find the maximum or minimum of a quadratic relationship.
I can use a table of values relating the area to the length of a side of rectangles with a fixed perimeter to determine the perimeter of the rectangle.
I can describe a graph of a quadratic equation using x-intercepts, y-intercept, location of the line of symmetry, location of the vertex, and the direction of the opening of the parabola.
I can describe the important features of a parabola (x-int, y-int., L.O.S., vertex, opens up or opens down)
I can create expressions to represent to represent the relationship between the side length and the area of a rectangle with fixed area.
Turn-In (#69)
ACE p.11 #29
ACE p.30 #1

Handouts
No Handouts Posted

Assignment
ACE p.30 #2 - 5, 8, 9, 12, 13, 16, 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, April 17, 2008

Geometry (Class 71)

Announcements
Next test is next Friday, April 26. The following test will not be until May 23 due to STAR testing-- that test will cover a lot of material!

Lesson Title
The Measure of an Inscribed Angle

Overview
The warm-up for today focuses on understanding how the altitude of a cone is related to the radius of the base and the slant height of the cone. Our lesson continues from last class, focusing on inscribed angles of a circle and the inherent relationships.
Textbook Sections
§10.3 (Txt. p.613) Inscribed Angles

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter

Key Attitudes
Math is about thinking creatively.

Key Ideas
A circle is the locus of points equidistant from a given point.
All radii of a circle are congruent.
Any triangle constructed with one vertex at the center of a circle and both other vertices on the circumference of the circle will be an isosceles triangle.
If a triangle is inscribed in a circle such that one side of the triangle is a diameter of the circle, then the triangle is a right triangle.
Key Skills
Find the surface area of a cone when given the height of the cone and another piece of information which allows for the finding of the radius of the base or the slant height of the cone.
Use relationships of inscribed angles to find missing angle measures.
Turn-In (#70)
§9.5 (Txt. p.563) #55
CST Practice #22- 49
Finish Warm-Up
Test Corrections

Handouts
12.11- Cone 4: Finding the Altitude of a Cone

Assignment
CST Practice
Finish Warm-up
Finish Chapter 10- Lesson 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.

Wednesday, April 16, 2008

Algebra (Class 69)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Trading Land

Overview
The Warm-Up for today’s class remains focused on using concepts of scale, ratio, proportion, and logical reasoning to puzzle out the locations of various places on a map. Clues today include having to deal with the speed a person is traveling!

In the lesson today we work on writing expressions to represent a situation involving the trading of land. These expressions turn out to be quadratic and we will see how we can express the area of the land in two different forms-- expanded and factored. The transforming of quadratic equations from factored to expanded form and back will turn out to be a very useful tool in the near future.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Problem 2.1 Trading Land

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form

Key Attitudes
Math is about investigating and confirming

Key Ideas
Quadratic expressions can be written in expanded or factored form.
The factored form of a quadratic equation can be easily used to find the x-intercepts of the graph of that equation.
The expanded form of a quadratic equation can be easily used to find the y-intercept of the graph of that equation.
The vertex of a parabola is always located on a vertical line half-way between the x-intercepts.
Key Skills
I can enter a quadratic equation into a graphing calculator.
I can use a graphing calculator to make a table of values, including adjusting the starting value and the increment between “x” values.
I can use a table of value to find the maximum or minimum of a quadratic relationship.
I can use a table of values relating the area to the length of a side of rectangles with a fixed perimeter to determine the perimeter of the rectangle.
I can describe a graph of a quadratic equation using x-intercepts, y-intercept, location of the line of symmetry, location of the vertex, and the direction of the opening of the parabola.
I can describe the important features of a parabola (x-int, y-int., L.O.S., vertex, opens up or opens down)
I can create expressions to represent to represent the relationship between the side length and the area of a rectangle with fixed area.
Turn-In (#68)
ACE p. 11 #11-20, 26, 27
Get “Course Selection for Next Year” signed by a parent

Handouts
No Handouts Posted

Assignment
ACE p.11 #29
ACE p.30 #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.

Tuesday, April 15, 2008

Geometry (Class 70)

Announcements
Test today focusing on right triangle trigonometry. Take a look at your Chapter 9 Preview for specifics.

Lesson Title
The Measure of an Inscribed Angle

Overview
In today’s class the focus of the Warm-Up returns to dealing with surface area and volumes of solids. In particular we focus on learning how to compute the surface area of a cone. The lesson for the day marks the start of Chapter 10 and our work with the geometry of chords, tangents, secants and various angles of circles.
Textbook Sections
§10.3 (Txt. p.613) Inscribed Angles

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter

Key Attitudes
Math is about thinking creatively.

Key Ideas
A circle is the locus of points equidistant from a given point.
All radii of a circle are congruent.
Any triangle constructed with one vertex at the center of a circle and both other vertices on the circumference of the circle will be an isosceles triangle.
If a triangle is inscribed in a circle such that one side of the triangle is a diameter of the circle, then the triangle is a right triangle.
Key Skills
Find the surface area of a cone when given the radius of the base and the slant height.
Use relationships of inscribed angles to find missing angle measures.
Turn-In (#69)
§9.5 (Txt. p.563) #37-42

Handouts
Chapter 12- Cone 3
Chapter 10- Student Outline
Chapter 10- Lesson 1: The Measure of an Inscribed Angle

Assignment
§9.5 (Txt. p.563) #55
§9.5 (Txt. p.563) #55
CST Practice #22- 49
Finish Warm-Up
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, April 14, 2008

Algebra (Class 68)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Trading Land

Overview
The Warm-Up for today’s class remains focused on using concepts of scale, ratio, proportion, and logical reasoning to puzzle out the locations of various places on a map. We don’t have a new lesson today, instead we spend the time working problems from the ACE section in order to solidify and deepen what we have recently studied.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Reading Graphs and Tables 1.3 ACE Problems

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola
expression
factored form
expanded form

Key Attitudes
Math is about investigating and confirming

Key Ideas
Relationships can be categorized as linear or non-linear.
A quadratic relationship is a special type of non-linear relationship.
Graphs of non-linear relationships will be curved-- not striaght.
The graphs of quadratic relationships are “U” shaped, open up or down, are symmetrical about a vertical line half-way between the x-intercepts.
Key Skills
I can enter a quadratic equation into a graphing calculator.
I can use a graphing calculator to make a table of values, including adjusting the starting value and the increment between “x” values.
I can use a table of value to find the maximum or minimum of a quadratic relationship.
I can use a table of values relating the area to the length of a side of rectangles with a fixed perimeter to determine the perimeter of the rectangle.
I can describe a graph of a quadratic equation using x-intercepts, y-intercept, location of the line of symmetry, location of the vertex, and the direction of the opening of the parabola.
I can describe the important features of a parabola (x-int, y-int., L.O.S., vertex, opens up or opens down)
I can create expressions to represent to represent the relationship between the side length and the area of a rectangle with fixed area.
Turn-In (#67)
ACE p.11 #4-20, 24-28

Handouts
No Handouts Posted

Assignment
ACE p. 11 #11-20, 26, 27
Get “Course Selection for Next Year” signed by a parent
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, April 11, 2008

Geometry (Class 69)

Announcements
Test today focusing on right triangle trigonometry. Take a look at your Chapter 9 Preview for specifics.

Lesson Title
Applications of Trigonometry

Overview
We take a break from working with solids during the warm-up today and instead do one of the “Partner Challenges” from the last class. The lesson focuses on using right triangle trigonometry to solve some applied problems. During the last part of the class students take Test 11
Textbook Sections
§9.6 (p. 567) Solving Right Triangles

Vocabulary
special right triangle
isosceles right triangle
45-45-90 triangle
30-60-90 triangle
right triangle trigonometry
trigonometric ratios
trigonometric ratios
sine ratio
cosine ratio
tangent ratio
secant ratio
cosecant ratio
cotangent ratio
inverse trigonometric functions
angle of depression
angle of elevation

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.
Key Skills
I can quickly and accurately recall the sides used to make the sine, cosine, or tangent ratio.
I can use my calculator instead of a table of trigonometric ratio values to solve right triangle trigonometry problems.
I can keep the answers to a problem as precise as possible when using a calculator and round my answer to reflect the correct number of significant figures.
I can use a diagram to organize the information I am given and what I am trying to find.
I can recognize right triangles in an applied situation and determine if the problem can be solved with the Pythagorean Theorem, Right Triangle Trigonometry, or both.
I can set-up and solve trigonometric equations representing an applied problem.
Turn-In (#68)
Partner Challenge with someone.
Lesson 9.6 Practice B- All
Review the Chapter 9- Preview

Handouts
No Handouts Posted

Assignment
§9.5 (Txt. p.563) #37-42
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, April 10, 2008

Algebra (Class 67)

Announcements
Test Friday, April 18 focusing on quadratic relationships.

Lesson Title
Using What We Know

Overview
The Wram-Up for today’s class remains focused on using concepts of scale, ratio, proportion, and logical reasoning to puzzle out the locations of various places on a map. In the lesson today we work on consolidating the concepts and skills we have learned so far in this unit.
Textbook Sections
Supplemental
Connected Math: Frogs, Fleas, and Painted Cubes- Reading Graphs and Tables 1.3 ACE Problems

Vocabulary
rectangle
area
perimeter
maximum
quadratic relationship
parabolas
function
symmetry
line of symmetry
x-intercepts
roots
y-intercepts
parabola

Key Attitudes
Math is about investigating and confirming

Key Ideas
Relationships can be categorized as linear or non-linear.
A quadratic relationship is a special type of non-linear relationship.
Graphs of non-linear relationships will be curved-- not striaght.
Quadratic relationships have unique patterns.
Key Skills
I can sketch a generalized rectangle to represent all rectangles with a given perimeter.
I can write a declare and use variable to represent the width in terms of the length of the fixed perimeter recatngle.
I can write an equation for the are in terms of the length of the fixed perimeter recatngle.
I can enter a quadratic equation into a graphing calculator.
I can use a graphing calculator to make a table of values, including adjusting the starting value and the increment between “x” values.
I can use a table of value to find the maximum or minimum of a quadratic relationship.
I can use a table of values relating the area to the length of a side of rectangles with a fixed perimeter to determine the perimeter of the rectangle.
I can describe a graph of a quadratic equation using x-intercepts, y-intercept, location of the line of symmetry, location of the vertex, and the direction of the opening of the parabola.
Turn-In (#66)
Test Corrections
ACE p.11 #1, 3
Skill Builder (Pythagorean packet) 3B

Handouts
No Handouts Posted

Assignment
ACE p.11 #4-20, 24-28
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.