HolcombMath

Friday, November 06, 2009

Algebra 2 (Class 29)

Lesson Title
2.1.4 How can I describe a sequence

Overview
In the bouncy-ball activity form Lesson 2.1.2 students used multiple representations (a table, a rule, and a graph) to represent a discrete situation involving a bouncing ball. In today’s lesson student learn about a new way to represent a discrete pattern, called a “sequence”
Textbook Sections
2.1.4 (Txt. p.69) How can I describe a sequence?

Vocabulary
input
output
relation
function
dependent variable
independent variable
parameters
linear relationship
subscript
exponential relationship
discrete
continuous
sequence
initial value

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can a sequence of numbers be represented?
How can you determine the ”sequence generating machine”?

Key Knowledge
The number of rabbits George and Lenny could have each month could be represented by a seuqence.
There are different types of sequences.

Key Skills
I can create a rule for generating a sequence.
I can classify sequences.

Turn-In (#-1)
2-27 to 2-29, 2-36

Handouts
No Handouts Posted

Assignment
2-37 to 2-41
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.

Math 7 (Class 59)

Lesson Title
Problem 2.4 Day 4 Chincoteague Island to Norfolk

Overview

Textbook Sections
Prb. 2.4 (Txt. p.23) Chincoteague Island to Norfolk

Vocabulary
coordinate graph
quadrant
axis
axes
x-axis
y-axis
coordinates
ordered pair
origin
vertical
horizontal
plot
scale
vertices
coordinate geometry
polygon
quadrilateral
parallelogram
rhombus

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can change be described mathematically?
How are patterns of change related to the behavior of functions?
How do mathematical models/representations shape our understanding of mathematics?
How can change be described mathematically?
How are patterns of change related to the behavior of functions?
How do mathematical models/representations shape our understanding of mathematics?

Key Knowledge
In order to determine if the points in a coordinate graph should or should not be connected depends on the data that is being collected as well as what you are intending to show or find out.
A graph can be used to make predictions about what could have occurred between the collected data.
The speed at which something is moving can be inferred from a graph comparing distance and time.

Key Skills
I can determine if it is, or is not, appropriate to connect the points on a coordinate graph.
I can use a coordinate graph to make inferences about a situation.

Turn-In (#-1)
ACE p. 26 #2, 11

Handouts
No Handouts Posted

Assignment
ACE p. 26 #2, 11 (Same as the other day due to confusion with what the assignment was and my late posting)
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.

Math 6 (Class 59)

Lesson Title
Investigation 2: Types of Data

Overview
In today’s class students are presented with categorical and numerical data organized in frequency tables and bar graphs. By using these tables and graphs they are asked to answer questions.
Textbook Sections
Problem 2.2 (Txt. p.23) Counting Pets

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
What is average?
What makes a data representation useful?

Key Knowledge
Data comes in two man types: categorical and numberical

Key Skills
I can determine if data is numerical or categorical.
I can determine if a question is asking for numerical or categorical data.
I can use a frequency table or bar graph to answer questions.

Turn-In (#-1)
ACE p. 26 #1-8

Handouts
No Handouts Posted

Assignment
No Homework
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, November 05, 2009

IB Math HL (Class 29)

Lesson Title
Lesson 10: A Formula for Derivatives (3)

Overview
I was absent for this lesson. Students finished Lesson 10: A Formula for Derivatives and then spent the remainder of the time working on Problem Set 10.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can an equation for the derivative of a function be created?
What does it mean for a function to be its own derivative?
Is possible for a function to be its own derivative?

Key Knowledge
A function exists such that it is its own derivative function.

Key Skills
I can find the derivative of functions involving the natural exponential.

Turn-In (#-1)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
Problem Set 9-- Finish it
Problem Set 10 #As much as you can handle
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.

Math 7 (Class 58)

Lesson Title
Problem 2.3: Day 3 Lewes to Chincoteague Island

Overview
In today’s class students reverse the process of making a report from data and instead make a table of data and a graph given a story.
Textbook Sections
Problem 2.3 (Txt. p.23) Day 3 Lewes to Chincoteague Island

Vocabulary
coordinate graph
quadrant
axis
axes
x-axis
y-axis
coordinates
ordered pair
origin
vertical
horizontal
plot
scale
vertices
coordinate geometry
polygon
quadrilateral
parallelogram
rhombus

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can change be described mathematically?
How are patterns of change related to the behavior of functions?
How do mathematical models/representations shape our understanding of mathematics?

Key Knowledge
In order to determine if the points in a coordinate graph should or should not be connected depends on the data that is being collected as well as what you are intending to show or find out.
A graph can be used to make predictions about what could have occurred between the collected data.
The speed at which something is moving can be inferred from a graph comparing distance and time.

Key Skills
I can determine if it is, or is not, appropriate to connect the points on a coordinate graph.
I can use a coordinate graph to make inferences about a situation.

Turn-In (#-1)
ACE p. 26 #1, 10

Handouts
No Handouts Posted

Assignment
ACE p. 26 #2, 11
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.

IB Math SL (Class 29)

Lesson Title
Lesson for PS 7: The Derivative Function (5)

Overview
In today’s class students will write a short quiz focusing on the last lesson. They will then continue to work on Workshop 6.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can you use what you know about the transformation of functions to predict how the derivatives of two functions will be related?
When differentiating a function, what can you ignore? What do you have to pay attention to?

Key Knowledge
What are the four basic ways in which a function can be transromed?
How do each of the four basic function transformations effect the derivative of the function?

Key Skills
I can match a derivative and a function.
I can sketch the graph of the derivative of a function.

Turn-In (#-1)
PS 7- Finish it.

Handouts
No Handouts Posted

Assignment
Workshop 6- Complete as much as 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.

Math 6 (Class 58)

Lesson Title
Investigation 2

Overview
In today’s class students explore the two different types of data-- Numerical and Categorical.

Note: I was absent again today.
Textbook Sections
Problem 2.1 (Txt. p.22) Counting Pet

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
What is average?
What makes a data representation useful?

Key Knowledge
The median is a measure of the center of a set of data.
The median is a type of average.
The median is found by organizing the data in sequential order then finding the “middle” value.

Key Skills
I can explain what a median is.
I can find the median of a set of data.
I can explain what happens to the median of a set of data as the result of adding or removing values from the data set.
I can create a set of data to match a given median.

Turn-In (#-1)
ACE p.17 #16-21

Handouts
No Handouts Posted

Assignment
ACE p. 26 #1-8
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, November 04, 2009

Algebra 2 (Class 28)

Lesson Title
2.1.3 What is the Pattern

Overview
In the last class students used the data they collected and the graph they made from this data to make predictions about how high the successive bounces of a ball would be. In today’s class students will have a chance to check their predictions. They will then examine their data and create an equation which can be used to model the height of each bounce.
Textbook Sections
2.1.3 (Txt. p.64) What is the Pattern?

Vocabulary
input
output
relation
function
dependent variable
independent variable
parameters
linear relationship
subscript

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
What do we need to measure?
How should we organize our data?
How can we be confident that our data is accurate?

Key Knowledge
A graph can be used to make predictions.
As the ball bounces, what was the bounce height becomes the drop height.

Key Skills
I can create a graph from data.
I can use my graph to make predictions.
I can explain why an exponential equation is appropriate to model the successive bounce heights of a ball.
I can create an exponential equation to model the successive bounce heights of a ball.

Turn-In (#-1)
2-18, 2-19, 2-24, 2-26

Handouts
No Handouts Posted

Assignment
2-27 to 2-29, 2-36
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.

Math 7 (Class 57)

Lesson Title
Investigation 2: Graphing Change

Overview
In today’s class student are asked to analyze and interpret a distance compared to time graph in greater depth.

Note: I was absent from class today.
Textbook Sections
Problem 2.2 (Txt. p.20) Atlantic City to Lewes

Vocabulary
coordinate graph
quadrant
axis
axes
x-axis
y-axis
coordinates
ordered pair
origin
vertical
horizontal
plot
scale
vertices
coordinate geometry
polygon
quadrilateral
parallelogram
rhombus

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can change be described mathematically?
How are patterns of change related to the behavior of functions?
How do mathematical models/representations shape our understanding of mathematics?

Key Knowledge
In order to determine if the points in a coordinate graph should or should not be connected depends on the data that is being collected as well as what you are intending to show or find out.
A graph can be used to make predictions about what could have occurred between the collected data.
The speed at which something is moving can be inferred from a graph comparing distance and time.

Key Skills
I can determine if it is, or is not, appropriate to connect the points on a coordinate graph.
I can use a coordinate graph to make inferences about a situation.

Turn-In (#-1)
Post Card

Handouts
No Handouts Posted

Assignment
ACE p. 26 #1, 10
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.

Math 6 (Class 57)

Lesson Title
Investigation 1: Organizing Your Data

Overview
In class today students will be working numerous problems in order to help them become more fluent with the concepts and skills they have been studying.

Note: I was absent today.
Textbook Sections
Problem 1.5 (Txt. p.13) Experimenting with the Median

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
What is average?
What makes a data representation useful?

Key Knowledge
The median is a measure of the center of a set of data.
The median is a type of average.
The median is found by organizing the data in sequential order then finding the “middle” value.

Key Skills
I can explain what a median is.
I can find the median of a set of data.
I can explain what happens to the median of a set of data as the result of adding or removing values from the data set.
I can create a set of data to match a given median.

Turn-In (#-1)
ACE p.15 #7 (Note: It does not ask you to actually make a list of names!)

Handouts
No Handouts Posted

Assignment
ACE p.17 #16-21
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, November 03, 2009

IB Math HL (Class 28)

Lesson Title
Lesson 10: A Formula for Derivatives (2)

Overview
In today’s class students continue developing their skills of creating a derivative function.

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can an equation for the derivative of a function be created?

Key Knowledge
An equation for the derivative a function can be created by generalizing the process of finding the slope between two points.

Key Skills
I can use the difference quotient to find an equation for the derivative of a function.
I can use the power rule to find the derivative of a function.

Turn-In (#-1)
IA

Handouts
No Handouts Posted

Assignment
PS 9 #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.

Math 7 (Class 56)

Lesson Title
Investigation 2: Graphing Change

Overview
In today’s class students share their drafts of the “reports” they wrote as homework. They then create a coordinate graph using data organized in a table for Day 2 of the bike trip. Finally they are asked to analyze the data in the table and graph and to write a postcard to their parents from the perspective of a rider on the trip. These postcards and and the graphs they created will be mailed out to parents.
Textbook Sections
Problem 2.2 (Txt. p.20) Atlantic City to Lewes

Vocabulary
coordinate graph
quadrant
axis
axes
x-axis
y-axis
coordinates
ordered pair
origin
vertical
horizontal
plot
scale
vertices
coordinate geometry
polygon
quadrilateral
parallelogram
rhombus

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can change be described mathematically?
How are patterns of change related to the behavior of functions?
How do mathematical models/representations shape our understanding of mathematics?

Key Knowledge
A table of values can be read to answer questions about the situation from which the numbers came.
A table of values can tell a story about what happened.

Key Skills
I can use a table of values to answer questions about the situation from which the numbers came.
I can use a table of values to make inferences about the situation from which the numbers came.
I can create a properly labeled coordinate graph from a table of values.
I can write a paragraph describing patterns of change in data which was organized in a graph.

Turn-In (#-1)
Rough draft of paragraph for Problem 2.1

Handouts
No Handouts Posted

Assignment
Final Draft of Problem 2.1
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.

Math 6 (Class 56)

Lesson Title
Investigation 1: Organizing Your Data

Overview
In today’s class students investigate what happens to the median of a set of data as the result of adding or removing values from the set.
Textbook Sections
Problem 1.5 (Txt. p.13) Experimenting with the Median

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
What is average?
What makes a data representation useful?

Key Knowledge
The median is a measure of the center of a set of data.
The median is a type of average.
The median is found by organizing the data in sequential order then finding the “middle” value.

Key Skills
I can explain what a median is.
I can find the median of a set of data.
I can explain what happens to the median of a set of data as the result of adding or removing values from the data set.
I can create a set of data to match a given median.

Turn-In (#-1)
ACE p.15 #7 (Note: It does not ask you to actually make a list of names!)

Handouts
No Handouts Posted

Assignment
ACE p.15 #7 (Note: It does not ask you to actually make a list of names!)
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.

IB Math SL (Class 28)

Lesson Title
Lesson for PS 7: The Derivative Function (4)

Overview
In today’s class student continue developing their understanding of the meaning of “the derivative function”.
Derivative Function 1
Derivative matching game
Derivative Functions 2
Sketching a Derivative Video

Practice Sketching a Derivative

Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
How can a function be created to represent the derivatives of another function?

Key Knowledge
A function can be made out of the values of the derivatives of another function.
The values of a derivative function is the slopes of the tangent line of another function.
You can think of a derivative function as the “child” of another function.

Key Skills
I can match a derivative and a function.
I can sketch the graph of the derivative of a function.

Turn-In (#-1)
IA

Handouts
No Handouts Posted

Assignment
PS 7- Finish it.
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, November 02, 2009

Algebra 2 (Class 27)

Lesson Title
2.1.2 Rebound Ratios

Overview
In today’s class students will organize the data they collected during the last class for the bounciness of the ball.
Textbook Sections
2.1.2 (Txt. p.60) Rebound Ratios

Vocabulary
input
output
relation
function
dependent variable
independent variable
parameters
linear relationship
subscript

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Change is fundamental to understanding functions.
Mathematical relationships can be represented in 4 main ways: Graphical, Numerical, Algebraic, Verbal (written and oral).

Essential Question
What do we need to measure?
How should we organize our data?
How can we be confident that our data is accurate?

Key Knowledge
A graph, or a table, can be used to organize and interpret data.

Key Skills
I can use a meter stick to measure how high a ball bounces.
I can organize the data I collect using a table.
I can create a properly labeled coordinate graph of the data I have collected.
I can find, describe, and generalize patterns.
I can identify the independent and dependent variable in an experiment.
I can determine the “rebound ratio” of a ball

Turn-In (#-1)
2-15 to 2-17

Handouts
No Handouts Posted

Assignment
2-18, 2-19, 2-24, 2-26
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.