HolcombMath

Friday, September 05, 2008

Intro to Calculus (Class 4)

Lesson Title
Using Graphs AND Equations

Overview
Our warm-up today continues to focus on interpreting points on graphs. The lesson for the day extend the concept of distance to examining the locus of points in the plane equidistant from a given point-- circles in other words! The purpose will be to help students develop their skills of using graphs in conjunction with equations to solve problems.
Textbook Sections
N/A

Vocabulary
inequality
number line graph
absolute value
interval
open interval
closed interval
infinity
union
critical point
inclusive
exclusive

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs and equations can be used in conjunction to help solve problems.
Many concepts are connected to the Pythagorean Theorem.
Key Skills
I can determine the length of a segment connecting two points in the cartesian plane.
I can draw segments to represent specified lengths by connecting integer valued points in the plane.
I can draw and find the equation of a circle when given the locations where the circle intersects axes, a points through which the circle passes, or the endpoints of the diameter of the circle.
I can determine where a circle intersects an axis when given the equation of a circle, completing the square when necessary.
I can determine the equation of a line tangent to a circle given the equation of the circle in various forms and the point of tangency.
Turn-In (#3)
Homework 2

Handouts
Intro to Calculus Homework 3

Assignment
HW 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, September 04, 2008

Geometry (Class 3)

Lesson Title
Points, Lines, and Planes

Overview
The warm-up for today continues the theme from the last class where students need to measure the lengths of segments using an inch ruler, scale these measurements based on a map, and then solve a puzzle based on these measurements. The lesson for the class is a continuation from last class. We justify why the sum of the measures of the interior angles of a triangle will always equal 180˚ using
Textbook Sections
§1.2 (Txt. p.10) Points, Lines, and Planes

Vocabulary
point
line
plane
undefined terms
line
line segment
ray
opposite ray
collinear
coplanar
distance
perpendicular
right angle
interior angle
exterior angle

Key Attitudes
Math is about thinking creatively.

Key Ideas
The shortest distance from a line to a point not on the line is equal to the length of the perpendicular segment from the point to the line.
Not sets of three line segments will make a triangle.
The sum of the interior angles of a triangle is 180˚.
Key Skills
I can determine the distance between a point and a line.
I can create a triangle using three line segments.
I can recognize and use basic geometry terminology.
I can sketch and uses sketches which represent a plane and the basic geometric objects related to the plane.
Turn-In (#2)
Txt. p.786 #2-24 Even
Txt. p.787 #2-30 Even

Handouts
No Handouts Posted

Assignment
Txt. p.789 #1-24
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, September 03, 2008

Intro to Calculus (Class 3)

Lesson Title
Absolute Value Equations and Inequalities

Overview
The warm-up today continues to focus on interpreting the points on a graph. The lesson for the day focuses on absolute value equations and inequalities and how working with these concepts is made significantly easier when you think geometrically about what the symbols mean.
Textbook Sections
N/A

Vocabulary
inequality
number line graph
absolute value
interval
open interval
closed interval
infinity
union
critical point
inclusive
exclusive

Key Attitudes
Math is about thinking creatively.

Key Ideas
Translating mathematical symbols into English can make solving problems easier.
Absolute value can be used to represent the distance between two points.
Key Skills
I can translate between a number line graph, an inequality, and interval notation.
I can translate between absolute value expressions and English statements about numbers on the number line.
I can solve equations and inequalities involving absolute value by translating the equations or inequalities first into “suto math” and then into an English sentence about numbers on the number line.
Turn-In (#2)
Homework 1

Handouts
Intro to Calc Homework 2

Assignment
Homework 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.

Tuesday, September 02, 2008

Geometry (Class 2)

Lesson Title
Points, Lines, and Planes

Overview
In the warm-up today students need to use a ruler to accurately measure the lengths of distances on a map, and then use these measurements along with some clues to figure out a puzzle.
During the lesson today students are introduced to some of the fundamental concepts and skills related to points, lines, and planes including how to measure the distance from a point to a line as well as the measures of the interior and exterior angles of a triangle.
Textbook Sections
§1.2 (Txt. p.10) Points, Lines, and Planes

Vocabulary
point
line
plane
undefined terms
line
line segment
ray
opposite ray
collinear
coplanar
distance
perpendicular
right angle

Key Attitudes
Math is about thinking creatively.

Key Ideas
The shortest distance from a line to a point not on the line is equal to the length of the perpendicular segment from the point to the line.
Not sets of three line segments will make a triangle.
The sum of the interior angles of a triangle is 180˚.
Key Skills
I can determine the distance between a point and a line.
I can create a triangle using three line segments.
I can recognize and use basic geometry terminology.
I can sketch and uses sketches which represent a plane and the basic geometric objects related to the plane.
Turn-In (#1)
Get materials.
Letter signed by parent
“Practice A” and “Assessment” #2-32 even

Handouts
Chapter 1- Lesson 1: Points, Lines, and Planes

Assignment
Txt. p.786 #2-24 Even
Txt. p.787 #2-30 Even

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, August 29, 2008

Intro to Calculus (Class 2)

Lesson Title
Interval Notation

Overview
The warm-up today is the first in a series of problems which helps students develop a deeper understanding of coordinate graphs. In this activity students work on matching the points on a coordinate graph comparing the age and height of a person to a drawing of the people.

Our lesson today focuses on
Textbook Sections
N/A

Vocabulary
inequality
number line graph
absolute value
interval
open interval
closed interval
infinity

Key Attitudes
Math is about thinking creatively.

Key Ideas
Translating mathematical symbols into English can make solving problems easier.
Absolute value can be used to represent the distance between two points.
Key Skills
I can translate between a number line graph, an inequality, and interval notation.
I can translate between absolute value expressions and English statements about numbers on the number line.
I can solve equations and inequalities involving absolute value by translating the equations or inequalities first into “suto math” and then into an English sentence about numbers on the number line.
Turn-In (#1)
Get materials.
Letter signed by parent
Summer Review or Replacement Assignment (1)

Handouts
Intro to Calculus: Homework 1

Assignment
Homework 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.

Thursday, August 28, 2008

Geometry (Class 1)

Lesson Title
Class Introduction/ Diagnostic Testing

Overview
In today’s class students learn will meet the other students in the class, learn about the details of the course, take a diagnostic test, and work to finish the summer review packet or work on “Replacement Assignment (1)” which they can later trade out for another assignment.

Textbook Sections
§1.1 (Txt. p.3) Patterns and Inductive Reasoning

Key Attitudes
Math is about thinking creatively.

Turn-In (#1)
Get materials.
Letter signed by parent
“Practice A” and “Assessment” #2-32 even

Handouts
No Handouts Posted

Assignment
Txt. p.13 #9-31, 36-39, 44-50, 61-64, 74-76.
Txt. p.786 #2-24 Even
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, August 27, 2008

Intro to Calculus (Class 1)

Lesson Title
Math Diagnostic Testing Project

Overview
In today’s class students learn will meet the other students in the class, learn about the details of the course, take a diagnostic test, and work to finish the summer review packet or work on “Replacement Assignment (1)” which they can later trade out for another assignment.
Textbook Sections
N/A

Turn-In (#0)
Finish Ch. 13- Lesson 4: All Together Now

Handouts
Replacement Assignment

Assignment
Get materials.
Letter signed by parent
Summer Review or Replacement Assignment (1)
Pick up your textbook from the Library- Pre-Calculus with Limits, Larson, Hostetler, Edwards; Second Edition
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, August 15, 2008

Intro to Calculus Summer Review

I have created a couple of interactive sketches that might help you with a couple of the problems. Here they are:
Problem 2: Circle and Tangent Line
Problem 5: The Light Pole and the Shadow
Problem 6: The Parabola and the Line

Also, send me an email if you need some additional hints.

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.

Friday, May 30, 2008

Geometry (Class 86)

Lesson Title
Law of Sines 4

Overview
The warm-up today requires that students apply their knowledge of the areas of polygons, angle relationships of polygons, and right triangle trigonometry to create a regular octagon with an area of 96 square cm.
We will then push on further into seeing the implications, and limitations, of the Law of Sines by working on Chapter 13- Lesson 2: Careful with the Law. As time permits we will begin our work to find a way to solve triangles for which the Law of Sines does not apply— The Law of Cosines!
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

Key Attitudes
Math is about thinking creatively.

Key Ideas
The Law of Sines is a consequence of relationships between arcs and angles of circles.
Th eLaw of Sines can be sued to find missing side lengths or angle measures of triangle including those which are not right triangles.
The Law of Sines is a proportion stating that the ratio of the side length and the sine of the opposite angle is the same for all side/opposite angle pairs in any triangle.
For any obtuse angle their is a corresponding acute angle with the same sine.
In the case of knowing the measure of two sides and a non-included angle (SSA), the law of sines gives zero, one, or two possible solutions.
The law of sines can only be applied if the triangle in question has an angle and opposite side pair of measurements.
Key Skills
I can use right triangle trigonometry to solve a problem.
I can show how the Law of Sines is a consequence of the relationships between arcs, angles, and segment lengths in a circle.
I can use the Law of Sines to solve for missing length sides and angles in a triangle.
I can recognize a situation where using the Law of Sines would be useful.
I can translate a situation into an equation involving the Law of Sines and solve that equation.
I can recognize when I need to be extra careful with the Law of Sines.
I can create a regular polygon of a specified area.
Turn-In (#85)
Benchmark Test 4
Finish Chapter 13- Lesson 1: Law of Sines (Class Work)
Finish Chapter 13- Lesson 1: Law of Sines (Problems)
Test Corrections

Handouts
Areas of Regular Polygons Warm-Up
Chapter 13- Lesson 2: Being Careful with the Law
law of Cosines Problem 1
Chapter 13- Lesson 3: Law of Cosines
Benchmark Test 5 Answers

Assignment
Benchmark Test 5 (Skip #26)
Finish Area of Regular Polygon Warm-Up
Finish Chapter 13- Lesson 2: Careful with the Law
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.