HolcombMath

Tuesday, September 30, 2008

Geometry (Class 12)

Lesson Title
Segments and their Measures

Overview
The warm-up today continues focusing on having students find the lengths of the sides of polygons and the areas of the polygons. Once this information is found they need to use the information to solve a puzzle. In the lesson today we continue with finding the lengths of segments. In fact we reverse the question so that students are ask to create a segment of a specified length.
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 determien the area of the square on the hypotenuse of a right triangle.
I can determine the length of the side of a square when I know the area of the square.
I can determine the length of a line segment using the locations of the endpoints of the segment.
Turn-In (#11)
Txt. p.790 #35, 36
Txt. p.791 #1-18

Handouts
No Handouts Posted

Assignment
Model Drawing Problem 4
Txt. p. 124 #1-4, 13-15, 28-30, 40, 41
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 29, 2008

Intro to Calculus (Class 12)

Lesson Title
Reading Functions,Thinking Graphs

Overview
The warm-up for today continues the theme of interpreting graphs. The rest of the class time is dedicated to working problems from homework 6 and workshop 3. Both of which are due at the start of the next class. There is a test on Friday which addresses the material we have worked with so far.

Textbook Sections
N/A

Vocabulary
function
domain

Key Attitudes
Math is about thinking creatively.

Key Ideas
You can create functions by combining (compositing) other functions.
It is important to be able to move back and forth fluently between the graph of a function and the equation representing the function.
Key Skills
I can find the composition of two functions.
I can create a function to represent a situation involving area, perimeter, or volume.
I can use interval notation to describe the domain and range of a function (which may or may not be continuous) given the graph of the function.
I can identify expression involving a function as distances on a graph of the function and vide versa.
I can determine if the graph of a function is symmetric about the x-axis, y-axis, or origin.
I can determine if a function is odd or even when given the equation or the graph representing the function.
I can create a graph to represent the speed of a roller coaster car as a function of how far it has moved down the track when given a picture of the roller coaster track.
Turn-In (#11)
Nothing to turn in today.

Handouts
No Handouts Posted

Assignment
Finish Homework 6
Finish Workshop 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.

Friday, September 26, 2008

Geometry (Class 11)

Lesson Title
Segments and their Measures

Overview
The warm-up for today marks the beginning of a new series which requires students to use the skills they have been developing related to calculating the length of a segment on order to solve a puzzle. The lesson for the day continues with working with calculating lengths of segments. During the last 50 minutes of class students will be taking their second test.
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 determien the area of the square on the hypotenuse of a right triangle.
I can determine the length of the side of a square when I know the area of the square.
I can determine the length of a line segment using the locations of the endpoints of the segment.
Turn-In (#10)
Finish “Chapter 1- Lesson 2: Practice Finding Lengths”
Lots of Lots 5

Handouts
No Handouts Posted

Assignment
Txt. p.790 #35, 36
Txt. p.791 #1-18
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, September 25, 2008

Intro to Calculus (Class 11)

Lesson Title
Reading Functions,Thinking Graphs

Overview
In today’s class the warm-up continues the theme of relating position and speed. This time students are asked to examine the path of a roller coaster car and create a graph to represent the speed of the car in relation to how far along the track it has moved.
The lesson for today focuses on interpreting function notation in terms of the graph of a function. In particular students will need to be able to solve “function equations” by using the graph of the function and their reasoning skills.
Textbook Sections
N/A

Vocabulary
function
domain

Key Attitudes
Math is about thinking creatively.

Key Ideas
You can create functions by combining (compositing) other functions.
It is important to be able to move back and forth fluently between the graph of a function and the equation representing the function.
Key Skills
I can find the composition of two functions.
I can create a function to represent a situation involving area, perimeter, or volume.
I can use interval notation to describe the domain and range of a function (which may or may not be continuous) given the graph of the function.
I can identify expression involving a function as distances on a graph of the function and vide versa.
I can determine if the graph of a function is symmetric about the x-axis, y-axis, or origin.
I can determine if a function is odd or even when given the equation or the graph representing the function.
I can create a graph to represent the speed of a roller coaster car as a function of how far it has moved down the track when given a picture of the roller coaster track.
Turn-In (#10)
Finish HW 5

Handouts
Lesson for HW 6
Intro to Calc HW 6

Assignment
Homework 6 #1-7
Workshop 3 #1-5
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 24, 2008

Geometry (Class 10)

Lesson Title
Segments and their Measures

Overview
In today’s class the warm-up continues with Lots of Lots #4 and Model Drawing Problem: Lengths of Segments 2. The lesson for the day focuses on solidifying the ability to find the length of a line segment connecting two points a dot grid by thinking about right triangles and areas of squares.
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 determien the area of the square on the hypotenuse of a right triangle.
I can determine the length of the side of a square when I know the area of the square.
I can determine the length of a line segment using the locations of the endpoints of the segment.
Turn-In (#9)
Chapter 1- Lesson 2: Segments and Their Measure Practice #35-43
Txt. p. 790 #30-34

Handouts
Geometry Model Drawing Problem: Lengths of Segments 2
Chapter 1- Lesson 2: Practice Finding Lengths

Assignment
Finish “Chapter 1- Lesson 2: Practice Finding Lengths”
Lots of Lots 5
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 23, 2008

Intro to Calculus (Class 10)

Lesson Title
Reading Functions,Thinking Graphs

Overview
The warm-up for today asks students “Are Graphs Just Pictures?” and provides them with some opportunities to think about this question. In the lesson today we develop a way to determine if a function is odd or even by examining the equation. Afterwards students will have lots of time to work on workshop 3 in groups of their choice.
Textbook Sections
N/A

Vocabulary
function
domain

Key Attitudes
Math is about thinking creatively.

Key Ideas
You can create functions by combining (compositing) other functions.
It is important to be able to move back and forth fluently between the graph of a function and the equation representing the function.
Key Skills
I can find the composition of two functions.
I can create a function to represent a situation involving area, perimeter, or volume.
I can use interval notation to describe the domain and range of a function (which may or may not be continuous) given the graph of the function.
I can identify expression involving a function as distances on a graph of the function and vide versa.
I can determine if the graph of a function is symmetric about the x-axis, y-axis, or origin.
I can determine if a function is odd or even when given the equation or the graph representing the function.
Turn-In (#9)
Homework 5 #8-12

Handouts or Links
Intro to Calc: Lesson for HW 5
Intro to Calculus Workshop 3
Sketch for Problem 4 on WS 3

Assignment
Finish HW 5
Workshop 3 #1-4
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 22, 2008

Geometry (Class 9)

Lesson Title
Segments and their Measures

Overview
The warm-up for today comes in two parts. The first part is a continuation of the “Lots of Lots” problems we started working last week. The second part of the warm-up is a new type of problem which we will refer to as a “Model Drawing Problem”. In these problems the objective for the student is to translate the English sentences into a drawing which models the situation presented. Solving the problem is then accomplished with the help of this drawing. I am intending to do a lot of these sorts of problems throughout the year.
In the lesson today we continue with developing methods for determining the length of any line segment in the plane. Students created methods during the last class for doing this and we will practice and expand on these methods during this 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 determien the area of the square on the hypotenuse of a right triangle.
I can determine the length of the side of a square when I know the area of the square.
I can determine the length of a line segment using the locations of the endpoints of the segment.
Turn-In (#8)
Chapter 1- Lesson 2: Segments and Their Measure Practice #17-34
Txt. p. 790 #26-29

Handouts
No Handouts Posted

Assignment
Chapter 1- Lesson 2: Segments and Their Measure Practice #35-43
Txt. p. 790 #30-34
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.

Sunday, September 21, 2008

Intro to Calc HW 5 Sketch

Here is a sketch for HW 5 problem 8 that I put together as the result of some student questions (thanks for the questions!). HW 5- Problem 8

Friday, September 19, 2008

Intro to Calculus Test 1 Solutions

Here are my solutions for Test 1A and Test 1B.

Intro to Calculus (Class 9)

Lesson Title
Reading Functions,Thinking Graphs

Overview
In today’s class our warm-up reviews some ideas from homework 4. The lesson for today will be brief due to the test. It will cover some of the remaining material needed for completing homework 5.
Textbook Sections
N/A

Vocabulary
function
domain

Key Attitudes
Math is about thinking creatively.

Key Ideas
You can create functions by combining (compositing) other functions.
It is important to be able to move back and forth fluently between the graph of a function and the equation representing the function.
Key Skills
I can find the composition of two functions.
I can create a function to represent a situation involving area, perimeter, or volume.
I can use interval notation to describe the domain and range of a function (which may or may not be continuous) given the graph of the function.
I can identify expression involving a function as distances on a graph of the function and vide versa.
I can determine if the graph of a function is symmetric about the x-axis, y-axis, or origin.
I can determine if a function is odd or even when given the equation or the graph representing the function.
Turn-In (#8)
Finish WS 2
Homework 5: #1-7

Handouts
No Handouts Posted

Assignment
Homework 5 #8-12
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.

Thursday, September 18, 2008

Geometry (Class 8)

Lesson Title
Segments and their Measures

Overview
In today’s class our warm-up focuses on measuring in centimeters, finding the area and perimeter of shapes, and then using this information to figure out a puzzle. A second part of the warm-up reviews the skills of identifying and naming segments as well as determining the length of segments on a number line. In the lesson we continue working with squares, areas, and measuring the distance between two points. We see that these ideas are actually connected and allow us to calculate the distance when we know the locations (coordinates) of any two points in the plane.
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 determien the area of the square on the hypotenuse of a right triangle.
I can determine the length of the side of a square when I know the area of the square.
I can determine the length of a line segment using the locations of the endpoints of the segment.
Turn-In (#7)
Chapter 1- Lesson 2: Segments and Their Measure Practice #1-16
Txt. p.790 #21-25
Test Corrections for B3 & B4

Handouts
No Handouts Posted

Assignment
Chapter 1- Lesson 2: Segments and Their Measure Practice #17-34
Txt. p. 790 #26-29
For B2 Only-- 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.

Wednesday, September 17, 2008

Intro to Calculus (Class 8)

Lesson Title
Reading functions, thinking graphs

Overview
The warm-up for today gives us a chance to take a second look at some previous ideas. The lesson moves us deeper into working with functions in particular strengthening the link between algebraic representations of functions and the graphs of these functions. We do extensive work on developing fluency with function notation and how this relates to geometric concepts of the graphs of the functions.
Textbook Sections
N/A

Vocabulary
function
domain

Key Attitudes
Math is about thinking creatively.

Key Ideas
You can create functions by combining (compositing) other functions.
It is important to be able to move back and forth fluently between the graph of a function and the equation representing the function.
Key Skills
I can find the composition of two functions.
I can create a function to represent a situation involving area, perimeter, or volume.
I can use interval notation to describe the domain and range of a function (which may or may not be continuous) given the graph of the function.
I can identify expression involving a function as distances on a graph of the function and vide versa.
I can determine if the graph of a function is symmetric about the x-axis, y-axis, or origin.
I can determine if a function is odd or even when given the equation or the graph representing the function.
Turn-In (#7)
Finish HW #4
Work on WS 2 with your group if possible.

Handouts
Homework 5
Lesson for Homework 5

Assignment
Finish WS 2
Homework 5: #1-7
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.

Geometry (Class 7)

Lesson Title
Segments and their Measures

Overview
In today’s class our warm-up focuses on measuring in centimeters, finding the area and perimeter of shapes, and then using this information to figure out a puzzle. A second part of the warm-up reviews the skills of identifying and naming segments as well as determining the length of segments on a number line. In the lesson we continue working with squares, areas, and measuring the distance between two points. We see that these ideas are actually connected and allow us to calculate the distance when we know the locations (coordinates) of any two points in the plane.
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 (#6)
Txt. p.790 #11-20
Txt. p.21 #16-18, 21, 22, 31, 32

Handouts
Chapter 1- Lesson 2: Practice

Assignment
Chapter 1- Lesson 2: Segments and Their Measure Practice #1-16
Txt. p.790 #21-25
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, September 15, 2008

Intro to Calculus (Class 7)

Lesson Title
What breaks a function?

Overview
The warm-up for today continues with interpreting graphs with a few additional practice problems thrown in. We will then finish the lesson for HW 4 by examining what it takes to break a function thereby determining the domain of the function by implication. We will then turn our attention to
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 (#6)
HW 4 as much as you are able to do. I will not be collecting this next class.

Handouts
Intro to Calc- Workshop 2

Assignment
Finish HW #4
Work on WS 2 with your group if possible.
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 12, 2008

Intro to Calculus- Quiz 1 Solutions

Here are my solutions to Quiz 1.
Quiz 1 A Solutions
Quiz 1 B Solutions