HolcombMath

Thursday, November 12, 2009

IB Math SL (Class 31)

Lesson Title
Lesson 8: Derivatives and Transformations (2)

Overview
In today’s class student will continue with their work exploring the relationships between the transformations of functions and their derivatives.
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)
Problem Set 8 #TBA

Handouts
No Handouts Posted

Assignment
Problem Set 8—You can now work all but a few of the problems on PS 8. We will pick up the last few tomorrow!
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 63)

Lesson Title
Investigation 3: Using Graphs to Group Data

Overview
In today’s class we examine the data we collected and organized yesterday and use it to answer the question “What is the typical age of a person in the family of someone in our class?” Students then turn their attention to another method of displaying data-- the double stem and leaf plot.
Textbook Sections
Problem 3.2 (Txt. p.34) Jumping Rope

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median
numerical data
categorical data
tally
tally marks
Intervals
Stem and Leaf Plot
ones digit
tens digit
vertical

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
A Stem-and-Leaf Plot is one way to display data.

Key Skills
I can create a Stem-and_Leaf plot for a set of data.
I can use a Stem-and-Leaf plot to answer factual questions about the data.
I can use a Stem-and-Leaf plot to determine what is “typical”.
I can help to design and carry out a survey.
I can organize and interpret data.

Turn-In (#-1)
ACE p.38 #1-10 due Friday.

Handouts
No Handouts Posted

Assignment
ACE p.38 #1-10 due Friday.
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 63)

Lesson Title
Problem 2.5: Norfolk to Williamsburg

Overview
In class today students continue to explore a graph which compares speed to distance. They are then given a graph showing the speed of the wind as a function of time and are asked to create a graph of the speed of a bicyclist compared to time assuming the wind was at his back.
Textbook Sections
Problem 2.5 (Txt. p.24) Day 5: Norfolk to Williamsburg

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
annotate
rate of change
positive rate of change
negative rate of change
average rate of change
per
speed
speedometer
acceleration

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
A graph of speed compared to time is different than a graph of distance compared to time.

Key Skills
I can use a graph of speed compared to time to determine when the fastest or slowest speed occured.
I can describe the changes is speed by analyzing a graph of speed compared to time.
I can explain in writing the meaning of the shape of a graph of speed compared to time in terms of the bicycle race.
I can explain what the slope of a speed compared to time graph represents.
I can explain what the slope of a distance compared to time graph represents.

Turn-In (#-1)
ACE p.26 #4

Handouts
No Handouts Posted

Assignment
ACE p.26 #6, 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.

Wednesday, November 11, 2009

Math 7 (Class 62)

Lesson Title
Problem 2.5: Norfolk to Williamsburg

Overview
In today’s class students share the tables of values and graphs they made based on Malcolm and Sarah’s notes. They then analyze a graph showing the relationship between the speed and time collected from a bike race. Students use this graph to answer factual questions as well as make inferences about what happened during the race.
Textbook Sections
Problem 2.5 (Txt. p.24) Day 5: Norfolk to Williamsburg

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
annotate
rate of change
positive rate of change
negative rate of change
average rate of change
per
speed
speedometer
acceleration

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
A graph of speed compared to time is different than a graph of distance compared to time.

Key Skills
I can use a graph of speed compared to time to determine when the fastest or slowest speed occured.
I can describe the changes is speed by analyzing a graph of speed compared to time.
I can explain in writing the meaning of the shape of a graph of speed compared to time in terms of the bicycle race.
I can explain what the slope of a speed compared to time graph represents.
I can explain what the slope of a distance compared to time graph represents.

Turn-In (#-1)
ACE p.26 #3,

Handouts
No Handouts Posted

Assignment
ACE p.26 #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.

Algebra 2 (Class 31)

Lesson Title
2.1.4 How can I describe a sequence

Overview
Two thirds of class was absent for the entire class today and one-third was absent for half of the class. Hence, we postponed moving forward and took a side trip to investigate organizing squares.
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
There are two main types of sequences: arithmetic and geometric.
Arithmetic sequences and linear functions are closely connected.

Key Skills
I can determine if a sequence is arithmetic or geometric.
I can determine the initial value of a sequence.
I can determine the common difference between terms in an arithmetic sequence.
I can create a generating rule for an arithmetic sequence.
I can create a graph to represent the relationship between terms and term numbers of an arithmetic sequence.
I can explain how the common difference is related to the graph and to the rule for generating arithmetic sequences.

Turn-In (#-1)
2-46 to 2-50

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.

Math 6 (Class 62)

Lesson Title
Investigation 3: Using Graphs to Group Data

Overview
In today’s class students consider the question: “What is the typical age of a person in the family of someone in this class?” They decide what data they need to collect to answer this question, figure out a way to collect the data, organize and display the data, and then use the data to answer the original question.
Textbook Sections
Problem 3.1 (Txt. p.30) Traveling to School

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median
numerical data
categorical data
tally
tally marks
Intervals
Stem and Leaf Plot
ones digit
tens digit
vertical

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
A Stem-and-Leaf Plot is one way to display data.

Key Skills
I can create a Stem-and_Leaf plot for a set of data.
I can use a Stem-and-Leaf plot to answer factual questions about the data.
I can use a Stem-and-Leaf plot to determine what is “typical”.
I can help to design and carry out a survey.
I can organize and interpret data.

Turn-In (#-1)
ACE p.26 #9 to 17 (Due Wed.)

Handouts
No Handouts Posted

Assignment
ACE p.38 #1-10 due Friday.
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 10, 2009

IB Math HL (Class 30)

Lesson Title
Lesson 11: Somethings Are Just Natural (1)

Overview
In today’s class we continue on our journey into developing equations for derivative function of a given function. Today we investigate the question ”Could a function be its own derivative?”

Some Things are just Natural
http://holcombmath.com/sketches/I2C_geogebra_sketches/Somethings_are_just_natural.html
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)
Problem Set 9-- Finish it
Problem Set 10 #TBA

Handouts
No Handouts Posted

Assignment
Continue to work on PS 10. Due Tue.
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 61)

Lesson Title
Problem 2.4 Day 4 Chincoteague Island to Norfolk

Overview
In today’s class we continue with Problem 2.4 but take a different perspective. Students are asked to analyze tables of values and determine why each table is not a good match for the written description of the journey.
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.
I can examine a table of values and determine if the table is a good representation of a written description of an event.

Turn-In (#-1)
ACE p.26 #5

Handouts
No Handouts Posted

Assignment
ACE p.26 #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.

IB Math SL (Class 30)

Lesson Title
Lesson 8: Derivatives and Transformations (1)

Overview
In today’s class students will begin investigating how transformations of functions effect the derivative of a function.

Dynamic Worksheets (DWS)
Derivatives and Transformations 1
http://holcombmath.com/sketches/I2C_geogebra_sketches/Derivatives_and_Transformations_1.html

Derivatives and Transformations 2
http://holcombmath.com/sketches/I2C_geogebra_sketches/Derivatives_and_Transformations_2.html

Derivatives and Transformations 3
http://holcombmath.com/sketches/I2C_geogebra_sketches/Derivatives_and_Transformations_3.html
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)
Problem Set 8 #TBA

Handouts
No Handouts Posted

Assignment
Problem Set 8 #1, 2, 4, 5, 6
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 61)

Lesson Title
Investigation 3: Using Graphs to Group Data

Overview
In today’s class students explore another type of graphical representation of data— the Stem-and_Leaf plot. Students learn how to make such a plot and then use it to answer factual questions about the data.
Textbook Sections
Problem 3.1 (Txt. p.30) Traveling to School

Vocabulary
typical
variable
frequency
frequently
table
line plot
bar graph
axis
scale
bell shaped
clustered/ grouped
range
mode
median
numerical data
categorical data
tally
tally marks
Intervals
Stem and Leaf Plot
ones digit
tens digit
vertical

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
A Stem-and-Leaf Plot is one way to display data.

Key Skills
I can create a Stem-and_Leaf plot for a set of data.
I can use a Stem-and-Leaf plot to answer factual questions about the data.
I can use a Stem-and-Leaf plot to determine what is “typical”.
I can help to design and carry out a survey.
I can organize and interpret data.

Turn-In (#-1)
ACE p.26 #9 to 17 (Due Wed.)

Handouts
No Handouts Posted

Assignment
ACE p.26 #9 to 17 (Due Wed.)
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 09, 2009

IB Math SL (Class 30)

Lesson Title
Lesson 8: Derivatives and Transformations (1)

Overview
In today’s class students will begin investigating how transformations of functions effect the derivative of a function.

Dynamic Worksheets (DWS)
Derivatives and Transformations 1
http://holcombmath.com/sketches/I2C_geogebra_sketches/Derivatives_and_Transformations_1.html

Derivatives and Transformations 2
http://holcombmath.com/sketches/I2C_geogebra_sketches/Derivatives_and_Transformations_2.html

Derivatives and Transformations 3
http://holcombmath.com/sketches/I2C_geogebra_sketches/Derivatives_and_Transformations_3.html
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)
Problem Set 8 #TBA

Handouts
No Handouts Posted

Assignment
Problem Set 8 #TBA
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 HL (Class 30)

Lesson Title
Lesson 11: Somethings Are Just Natural

Overview
In today’s class we continue on our journey into developing equations for derivative function of a given function. Today we investigate the question ”Could a function be its own derivative?”

Some Things are just Natural
http://holcombmath.com/sketches/I2C_geogebra_sketches/Somethings_are_just_natural.html
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)
Problem Set 9-- Finish it
Problem Set 10 #TBA

Handouts
No Handouts Posted

Assignment
Continue to work on PS 10
PS 11 #TBA
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.

Algbera 2 (Class 30)

Lesson Title
2.1.4 How can I describe a sequence

Overview
In today’s class student continue examining their sequences of numbers by making graphs.
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.
Some sequences represent functions I already know!

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

Turn-In (#-1)
2-37 to 2-41

Handouts
No Handouts Posted

Assignment
2-46 to 2-50
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 60)

Lesson Title
Investigation 2: Types of Data

Overview
In today’s class student continue working on answering the questions we began last time using the data presented in bar graphs and frequency tables.
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
numerical data
categorical data
tally
tally marks

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)
No Homework

Handouts
No Handouts Posted

Assignment
ACE p.26 #9 to 17 (Due Wed.)
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 60)

Lesson Title
Problem 2.4 Day 4 Chincoteague Island to Norfolk

Overview
In today’s class we continue with making a table of values and a graph to represent a written description of a bicycle trip.
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 (Same as the other day due to confusion with what the assignment was and my late posting)

Handouts
No Handouts Posted

Assignment
ACE p.26 #5, Rough Draft of Problem 2.4
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.