HolcombMath

Friday, September 12, 2008

Geometry (Class 6)

Lesson Title
Segments and their Measures

Overview
The warm-up for today starts a new series of problems which require students to measure lengths using centimeters and then calculate areas and perimeters. Students then need to use this derived information to solve a puzzle.
The lesson for the day continues working towards being able to calculate the distance between two coplanar points.
During the last part of the class students will be taking the first test for the class.
Textbook Sections
§1.3 (Txt. p.17) Segments and their Measures

Vocabulary
length
distance
coordinates
ordered pair
diagonal
right triangle
leg(s) of a right triangle
hypotenuse
polygon

Key Attitudes
Math is about thinking creatively.

Key Ideas
The distance between points can be calculated.
The length of a line can be determined by thinking about it as a right triangle.
Key Skills
I can create a non-square rectangle, right triangle, or non-rectangular parallelogram on the coordinate plane when given the locations of two vertices of the shape.
I can determine the area of a figure drawn on dot paper.
I can create any of the possible squares whose vertices are on the dots of a 5 by 5 grid of dot paper.
I can predict the area of the square on the hypotenuse of a right triangle.
I can determine the length of a segment connecting two points on the coordinate plane.
I can create a segment to represent an irrational length.
Turn-In (#5)
Txt. p.790 #1-10
Txt. p.21 #13-15, 19, 20, 23-30

Handouts
No Handouts Posted

Assignment
Txt. p.790 #11-20
Txt. p.21 #16-18, 21, 22, 31, 32
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 11, 2008

Intro to Calculus (Class 6)

Lesson Title
Is it a Function? Three Ways to Tell.

Overview
In place of the Warm-Up today students have time to continue their work on Workshop 1. Those groups who are finished may use this time to work on “Replacement Assignment 2”
Textbook Sections
N/A

Vocabulary
function
domain

Key Attitudes
Math is about thinking creatively.

Key Ideas
Function notation is a different form of representing relationships between quantities. This is not a new idea, just a new way to represent an idea (equations) which you have been dealing with for a long time.
Not all relationships are functions. A relationship is a function if and only if for any x-value in the domain of the function there is only one corresponding y-value.
Three ways to determine if a relationship is a function: graphs, tables of values, equations.
The domain of a function are the values which do not “break” the function.
Key Skills
I can evaluate a function given a numeric value or another function
I can write an algebraic formula for a function described in English.
I can determine if a graph, table of values, map diagram, or equation represents a function.
I can determine the domain of a function algebraically.
I can create a function to represent a situation.
Turn-In (#5)
Homework 3- #6-11 (Back Side)

Handouts
Intro to Calculus Homework 4
Replacement Assignment 2

Assignment
HW 4 as much as you are able to do. I will not be collecting this next class.
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 10, 2008

Geometry (Class 5)

Lesson Title
Segments and their Measures

Overview
In today’s class our warm up will be the last in the “Maps” series before the test. The lesson for the day will continue to investigate how to find the measure of segments.
Textbook Sections

Vocabulary
length
distance
coordinates
ordered pair
diagonal
right triangle
leg(s) of a right triangle
hypotenuse
polygon

Key Attitudes
Math is about thinking creatively.

Key Ideas
The distance between points can be calculated.
The length of a line can be determined by thinking about it as a right triangle.
Key Skills
I can create a non-square rectangle, right triangle, or non-rectangular parallelogram on the coordinate plane when given the locations of two vertices of the shape.
I can determine the area of a figure drawn on dot paper.
I can create any of the possible squares whose vertices are on the dots of a 5 by 5 grid of dot paper.
I can predict the area of the square on the hypotenuse of a right triangle.
I can determine the length of a segment connecting two points on the coordinate plane.
I can create a segment to represent an irrational length.
Turn-In (#4)
Txt. p.13 #9-31, 36-39, 44-50, 61-64, 74-76.

Handouts
No Handouts Posted

Assignment
Txt. p.790 #1-10
Txt. p.21 #13-15, 19, 20, 23-30
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 09, 2008

Intro to Calculus (Class 5)

Lesson Title
Using Graphs and Equations

Overview
The warm-up today remains focused on interpreting points on a graph. In addition we have a few problems concerning absolute value. During the remainder of the class students will work in groups on their first Workshop. The workshops are intended to provide more in depth problems than those on homework assignments and are intended to be done in groups. Finally, when after students have turned in Workshop 1 they will have the remainder of the time to work together on Homework 3.

We’ll have a quiz next class addressing topics from the summer review and homework 1 through 3.
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 (#4)
Workshop 1

Handouts
Intro to Calculus Workshop 1

Assignment
Homework 3- #6-11 (Back Side)
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, September 08, 2008

Geometry (Class 4)

Lesson Title
Segments and their Measures

Overview
The warm-up for the day continues to focus on measurement skills and logical reasoning. We will finish up Lesson 1:  Points, Lines, and Planes and move into working with the distance between points.
Textbook Sections

Vocabulary
length
distance
coordinates
ordered pair
diagonal
right triangle
leg(s) of a right triangle
hypotenuse
postulate

Key Attitudes
Math is about thinking creatively.

Key Ideas
The distance between points can be calculated.
The length of a line can be determined by thinking about it as a right triangle.
Key Skills
I can give an example of when measuring the length of a segment (directly, using coordinate, or indirectly) would be important.
I can calculate the lengths of segments using geometric reasoning, arithmetic, and algebraic skills.
I can state, in my own words, the segment addition postulate.
I can create a square on a coordinate grid given the coordinates of two of the vertices of the square.
Turn-In (#3)
Txt. p.789 #1-24
Chapter 1- Lesson 1: Points, Lines, and Planes

Handouts
Chapter 1: Lesson 2- Segments and their Lengths

Assignment
Txt. p.13 #9-31, 36-39, 44-50, 61-64, 74-76.
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, 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.