HolcombMath

Monday, June 09, 2008

Geometry (Class 89)

Lesson Title
All Together Now

Overview
The warm-up for today’s class asks students to create a mind map with a triangle at the center. The map is intended to represent what was studied this year and how it all centers around the triangle.
The lesson for the day asks students to think through all of the various methods we have developed for solving a triangle (finding angle and length measurements). Students then make a flow chart to represent a process for determining which method to use for any given situation. Finally, students are presented with a number of “solve the triangle” problems on which they can put their flow chart to the test.
Textbook Sections
Supplemental

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
inscribe
cyclic quadrilateral
law of sines
apothem
oblique triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
This course centers around the triangle and all concepts and skills can be tied to this shape.
A triangle can be solved in many different ways.
Key Skills
I can create a map of what I have learned to show how the concepts and skills are related.
I can create a flow chart to help in deciding which method I should use to solve a triangle.
I can recognize a “solve the triangle” problem from a situation.
I can recognize the best method for solving a triangle.
I can solve triangles using any one of the methods we have studied.
Turn-In (#88)
Benchmark Test 6
Grade Corrections and Drop Sheet (Due day of final)
Optional review (Due day of final)
Ch. 13 Lesson 3: Perfecting the Pythagorean Theorem: For an A-- ALL, B -> 10, C ->8

Handouts
Last Day Warm-Up
Chapter 13- Lesson 4: All Together Now (with answers!)

Assignment
Finish Ch. 13- Lesson 4: All Together Now
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, June 06, 2008

Algebra (Class 87)

Lesson Title
Completing the Square 2

Overview
This is our last class before the final! Yippee!
Our warm-up is one more problem involving using measurement, scale, and reasoning skills to solve a problem involving maps. The lesson will focus first on building fluency with solving quadratic equations by completing the square and then will move into understanding these solutions from a graphical perspective.
Textbook Sections
§12-2 (Txt. p.564) Completing the Square

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
first difference
second difference
complete the square
matrix

Key Attitudes
Math is about investigating and confirming

Key Ideas
A quadratic equation can be solved by completing the square.
The process of completing the square requires that the quadratic equation is a perfect square trinomial.
Any quadratic equation can be forced to become a perfect square trinomial equation by the process called “completing the square”.
The solution to a quadratic equation can be represented by the intersection of a lines and a parabola.
The solution to a quadratic equation can be represented by the location of the x-intercepts.
Key Skills
I can use a ruler to accurately measure.
I can use a scale on a map to convert measurements.
I can use a matrix of distance values.
I can complete the square.
I can solve a quadratic equation by completing the square where the coefficient of the second degree term is 1.
I can turn a quadratic equation whose coefficient of the second degree term is not 1 into a quadratic equation where the second degree coefficient is 1.
I can use a graphing calculator to solve a quadratic equation.
Turn-In (#86)
Standards Mastery (p.481)

Handouts
No Handouts Posted

Assignment
Standards Mastery- Skip: 8-11, 15, 16, 21, 28, 29, 36, 39, 40, 44, 45, 50, 53, 54
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, June 05, 2008

Geometry (Class 88)

Lesson Title
Using the Law of Cosines

Overview
The warm-up for today’s class asks students to reflect on what they learned from the last class. The lesson for today provides many chances to clarify and apply the concepts and skills from the last class-- using the law of cosines to solve problems.
Textbook Sections
Supplemental

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
inscribe
cyclic quadrilateral
law of sines
apothem
oblique triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
The area of a triangle can be found using the Law of Sines
The Pythagorean Theorem can be “perfected” so that it can be sued with oblique as well as right triangles.
The sum of the two squares is smaller than the area of the third side when the included angle is obtuse and is larger when the included angle is acute.
The amount the Pythagorean Theorem needs to be adjusted depends on the size of the included angle and the lengths of the adjacent sides. (This implies the use of the cosine function.)
The amount the Pythagorean Theorem needs to be adjusted can be figured out using right triangle trigonometry.
In order to use the Law of Cosines, you need the measures of two sides and the included angle or the measures of all three sides of a triangle.
Key Skills
I can explain how and why the Pythagorean Theorem needs to be adjusted for oblique triangles.
I can use the Law of Cosines to solve for a missing side of a triangle.
I can use the Law of Cosines to solve for an angle in a triangle.
I can recognize a situation in which the Law of Cosines can be used.
Turn-In (#87)
End of Year Test A

Handouts
Chapter 13- Lesson 3: Warm-Up
Semester Grades: Corrections and Drops
Semester 2 Optional Review
Benchmark Test 6 Answers

Assignment
Benchmark Test 6
Grade Corrections and Drop Sheet (Due day of final)
Optional review (Due day of final)
Ch. 13 Lesson 3: Perfecting the Pythagorean Theorem: For an A-- ALL, B -> 10, C ->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.

Wednesday, June 04, 2008

Algebra (Class 86)

Lesson Title
Completing the Square 2

Overview
The warm-up today continues in the same theme as last class-- using maps and logic to identify landmarks.

In the last class we saw how numbers and expressions can be written in equivalent ways, and how squaring a number can be represented by finding the area of a rectangle. Further we saw that some quadratic trinomials are in fact perfect squares and we learned how to decide to identify them. From this we learned how to use perfect squares to solve quadratic equations. Wow! That’s a lot!

Now today we extend these ideas, learning how to turn any quadratic equation into one involving a perfect square trinomial and then use what we learned in the previous class to solve it-- this is called solving a quadratic equation by completing the square.
Textbook Sections
§12-2 (Txt. p.564) Completing the Square

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
first difference
second difference
complete the square
matrix

Key Attitudes
Math is about investigating and confirming

Key Ideas
A quadratic equation can be solved by completing the square.
The process of completing the square requires that the quadratic equation is a perfect square trinomial.
Any quadratic equation can be forced to become a perfect square trinomial equation by the process called “completing the square”.
Key Skills
I can use a ruler to accurately measure.
I can use a scale on a map to convert measurements.
I can use a matrix of distance values.
I can complete the square.
I can solve a quadratic equation by completing the square where the coefficient of the second degree term is 1.
I can turn a quadratic equation whose coefficient of the second degree term is not 1 into a quadratic equation where the second degree coefficient is 1.
Turn-In (#85)
ACE p.66 #9, 10, 29a, 31, 33

Handouts
No Handouts Posted

Assignment
Standards Mastery (p.481)
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, June 03, 2008

Geometry (Class 87)

Lesson Title
Perfecting the Pythagorean Theorem

Overview
The warm-up for today asks students to come up with three methods for finding the diameter of the circumcircle for a triangle. The lesson for today takes us into the last main concept for the year— how to generalize the Pythagorean Theorem so that it works on oblique triangles as well as right triangles.
Textbook Sections
Supplemental

Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
inscribe
cyclic quadrilateral
law of sines
apothem
oblique triangle

Key Attitudes
Math is about thinking creatively.

Key Ideas
The area of a triangle can be found using the Law of Sines
The Pythagorean Theorem can be “perfected” so that it can be sued with oblique as well as right triangles.
The sum of the two squares is smaller than the area of the third side when the included angle is obtuse and is larger when the included angle is acute.
The amount the Pythagorean Theorem needs to be adjusted can be figured out using right triangle trigonometry.
In order to use the Law of Cosines, you need the measures of two sides and the included angle or the measures of all three sides of a triangle.
Key Skills
I can find the area of a triangle by using the law of sines.
I can explain how why the Pythagorean Theorem needs to be adjusted for oblique triangles.
I can use the Law of Cosines to solve for a missing side of a triangle
I can use the Law of Cosines to solve for an angle in a triangle.
Turn-In (#86)
Benchmark Test 5
Finish Area of Regular Polygon Warm-Up
Finish Chapter 13- Lesson 2: Careful with the Law

Handouts
Chapter 13- Lesson 3: Perfecting the Pythagorean Theorem
Warm-Up: Trigonometry and the Area of Triangles
End of Year Test A Answers

Assignment
Finish Warm-Up
End of Year Test A-- make sure to correct it! You can skip problems 46, 48, 55, 56
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, June 02, 2008

Algebra (Class 85)

Announcements
Next Test-- date TBA (the calendar has really thrown us off our regular testing schedule).

Lesson Title
Completing the Square

Overview
The warm-up today is the first in a new series, Maps 1. This series of problems requires that students use their measuring, ratio, data analysis, and logical reasoning skills to figure out the names of the landmarks on a map.
In the lesson for the day students learn another method for solving quadratic equations which is based on a geometric understanding of the situation— completing the square.
Textbook Sections
§12-2 (Txt. p.564) Completing the Square

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
first difference
second difference
complete the square
matrix

Key Attitudes
Math is about investigating and confirming

Key Ideas
A quadratic equation can be solved by completing the square.
The process of completing the square requires that the quadratic equation is a perfect square trinomial.
Any quadratic equation can be forced to become a perfect square trinomial equation by the process called “completing the square”.
Key Skills
I can use a ruler to accurately measure.
I can use a scale on a map to convert measurements.
I can use a matrix of distance values.
I can complete the square.
Turn-In (#84)
ACE p.64 #1, 11, 15-17, 21, 22
Standards Mastery (p.421) #1-25 (Don’t do “Chapter 9 Test” on the back yet)

Handouts
No Handouts Posted

Assignment
ACE p.66 #9, 10, 29a, 31, 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.