HolcombMath

Friday, October 30, 2009

Math 6 (Class 53)

Lesson Title
Investigation 1: Organizing Your Data

Overview
In today’s class work Quiz 7 focusing on the last unit, Prime Time. This is our last quiz for that unit.
Textbook Sections
Problem 1.4 (Txt. p.11) Identifying the Median

Vocabulary
typical
variable
frequency
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.

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
No Homework (However, ACE p. 18 #15 is due Tuesday)
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 27)

Lesson Title
Lesson 10: A Formula for Derivatives (1)

Overview
In today’s class students begin to develop shortcuts for finding an equation for the derivative function when given a function.
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 create?

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)
Finish Lesson 9
WS 6 #1
IA

Handouts
No Handouts Posted

Assignment
IA
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 53)

Lesson Title
Investigation 1: Variables and Coordinate Graphs

Overview
In today’s class students create a graph to represent how the number of daylight hours change as a function of the month. In addition, they write the final quiz focusing on operations with integers.
Textbook Sections
Problem 1.1 (Txt. p.5): Preparing for a Bicycle Tour

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 used to organize and analyze data.
A table of values, or a coordinate graph, need to be setup properly in order to be understood.

Key Skills
I can setup a coordinate graph: numbers (scale), unit names, variable names, title
I can collect and organize data for an experiment.
I can organize the data I collect using a properly labeled table.
I can plot data I have collected on a coordinate graph.

Turn-In (#-1)
ACE p. 11 #3, 7

Handouts
No Handouts Posted

Assignment
No homework (However-- ACE p.15 #8 is due Tuesday)
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 27)

Lesson Title
Lesson for PS 7: The Derivative Function (3)

Overview
In today’s class students work to deepen their understanding of a derivative function.

Derivative Function 1
Derivative matching game
Derivative Functions 2
Sketching a Derivative Video
Sketching a Derivative Function Practice

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
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
A function can be created using the derivatives (slopes) 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)
Finish PS 7 #4, 5
Continue with IA

Handouts
No Handouts Posted

Assignment
PS 7 #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.

Thursday, October 29, 2009

Math 6 (Class 53)

Lesson Title
Investigation 1: Organizing Your Data

Overview
In today’s class we explore creating a list of class names to fit a given the range and mode of the lengths of the names.
Textbook Sections
Problem 1.3 (Txt. p.9) Identifying the Mode and Range

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

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
One way to describe what is typical, or average, about a set of data is to give the value that occurs most frequently.
The value that occurs most frequently is called the “mode”.
It is often helpful to talk about how data is spread out.
The “range” of a set of data is one way to describe how a set of data is spread out.

Key Skills
I can create a set of data to fit a specified range and have a given mode.
I can make a line plot to display data.
I can describe the shape of data using a line plot.

Turn-In (#-1)
ACE p.15 #11, 12, 13

Handouts
No Handouts Posted

Assignment
Problem 1.3- Class Names (using the handout from 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.

Math 7 (Class 53)

Lesson Title
Investigation 1: Variables and Coordinate Graphs

Overview
Student continue to work problems focusing on using tables and coordinate graphs to organize and interpret data.
Textbook Sections
Problem 1.1 (Txt. p.5): Preparing for a Bicycle Tour

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 used to organize and analyze data.
A table of values, or a coordinate graph, need to be setup properly in order to be understood.

Key Skills
I can setup a coordinate graph: numbers (scale), unit names, variable names, title
I can collect and organize data for an experiment.
I can organize the data I collect using a properly labeled table.
I can plot data I have collected on a coordinate graph.

Turn-In (#-1)
ACE p.10 #TBA

Handouts
No Handouts Posted

Assignment
ACE p. 11 #3, 6 - 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.

IB Math SL (Class 26)

Lesson Title
Lesson for PS 7: The Derivative Function (2)

Overview
In today’s class we continue with our exploration of the derivative as a function unto itself. Students learn to match a function with its derivative by playing the derivative matching game.

Derivative Function 1

Derivative matching game

Derivative Functions 2

Sketching 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 a function be created to represent the derivatives of another function?

Key Knowledge
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
A function can be created using the derivatives (slopes) 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)
PS 7 #1-3
WS 6 #4

Handouts
No Handouts Posted

Assignment
PS 7 #4, 5
Continue with IA
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 26)

Derivatives of the Sums or Differences of Functions
Product of Two Functions

Lesson Title
Lesson 9: Sums, Differences, Products and Quotients

Overview
Suppose we were to add two functions together. What would happen to the derivatives of these function? In today’s class we will explore this idea along with others using GeoGebra to help.

Derivatives of the Sums or Differences of Functions
Product of Two Functions

Textbook Sections
N/A

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
When differentiating a function, what can you ignore? What do you have to pay attention to?
What happens to the derivatives of two functions as the result of adding, subtracting, multiplying, or dividing two functions?

Key Knowledge
What is the relationship between the derivatives of two functions and the derivative of the sum of the two functions?
What is the relationship between the derivatives of two functions and the derivative of the difference of the two functions?
What is the relationship between the derivatives of two functions and the derivative of the product of the two functions?
What is the relationship between the derivatives of two functions and the derivative of the quotient of the two functions?

Key Skills
I can explain the effect that adding or subtracting two functions has on the derivatives of these two functions.
I can demonstrate that what happens to the derivatives of two functions as the result of multiplying or dividing the two functions is different from what happens when you add or subtract the two functions.

Turn-In (#-1)
Finish Lesson 8.5
WS 5- Finish it
Problem Set 8- Finish it, but skip #3
Continue your work on the IA

Handouts
No Handouts Posted

Assignment
Finish Lesson 9
WS 6 #1
IA
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, October 28, 2009

Algebra 2 (Class 26)

Lesson Title
2.1.2 Rebound Ratios

Overview
In today’s class we examine how mathematics can be used to describe and predict the height a ball bounces.
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.

Key Ideas
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)
2-11 to 2-14

Handouts
No Handouts Posted

Assignment
2-15 to 2-17
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 52)

Lesson Title
Investigation 1: Organizing Your Data

Overview
In today’s class students begin to explore mathematical ways in which to identify and describe what is “typical”.
Textbook Sections
Problem 1.3 (Txt. p.9) Identifying the Mode and Range

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

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

Key Ideas
One way to describe what is typical, or average, about a set of data is to give the value that occurs most frequently.
The value that occurs most frequently is called the “mode”.
It is often helpful to talk about how data is spread out.
The “range” of a set of data is one way to describe how a set of data is spread out.
Key Skills
I can create a set of data to fit a specified range and have a given mode.
I can make a line plot to display data.
I can describe the shape of data using a line plot.
Turn-In (#-1)
ACE p.15 #3-5

Handouts
No Handouts Posted

Assignment
ACE p.15 #11, 12, 13
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 52)

Lesson Title
Investigation 1: Variables and Coordinate Graphs

Overview
In today’s class students will apply what they have learned from past units as well as this unit to solve problems involving tables of data and coordinate graphs.
Textbook Sections
Problem 1.1 (Txt. p.5): Preparing for a Bicycle Tour

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.

Key Ideas
A table of values can be used to organize and analyze data.
A table of values, or a coordinate graph, need to be setup properly in order to be understood.
Key Skills
I can setup a coordinate graph: numbers (scale), unit names, variable names, title
I can collect and organize data for an experiment.
I can organize the data I collect using a properly labeled table.
I can plot data I have collected on a coordinate graph.
Turn-In (#-1)
ACE p.14 #5

Handouts
No Handouts Posted

Assignment
ACE p.10 #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.

Tuesday, October 27, 2009

Math 6 (Class 51)

Lesson Title
Investigation 1: Organizing Your Data

Overview
In today’s class students continue exploring ways of representing data.
Textbook Sections
Problem 1.2 (Txt. p.7) Interpreting Graphs

Vocabulary
typical
variable
frequency
line plot
bar graph
axis
scale

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

Key Ideas
A line plot is one way to organize data.
Data can be used to make predictions.
The way that data is organized can help you make a better prediction.
Collecting and organizing data helps you make a better prediction.
Key Skills
I can write statements based on data organized in a line plot or in a bar graph.
I can make a prediction based on data.
I can state the similarities and differences of line graphs and bar graphs.
Turn-In (#-1)
ACE p.15 #1-- Using the list of student names, write two observations like we did in class today. Here is an example from our class work today: “The names in the class all have 10 letters”

Handouts
No Handouts Posted

Assignment
ACE p.15 #3-5
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.

Math 7 (Class 51)

Lesson Title
Investigation 1: Variables and Coordinate Graphs

Overview
In today’s class students will conduct an experiment to help them better understand how fatigue effects physical performance. They will be collecting and organizing the data using a table.
Textbook Sections
Problem 1.1 (Txt. p.5): Preparing for a Bicycle Tour

Vocabulary
Integer
temperature
opposites
chip board
model
inverse
rate
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.

Key Ideas
A table of values can be used to organize and analyze data.
A table of values, or a coordinate graph, need to be setup properly in order to be understood.
Key Skills
I can setup a coordinate graph: numbers (scale), unit names, variable names, title
I can collect and organize data for an experiment.
I can organize the data I collect using a properly labeled table.
I can plot data I have collected on a coordinate graph.
Turn-In (#-1)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
ACE p.14 #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.

IB Math SL (Class 25)

Lesson Title
Class Canceled

Overview
Class was canceled today due to all of the students being absent.
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.

Key Ideas
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
A function can be created using the derivatives (slopes) 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)
PS 7 #1-3
WS 6 #4

Handouts
No Handouts Posted

Assignment
No Assignment
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 25)

Lesson Title
Lesson for PS 8: Derivatives and Transformations (2)

Overview
Today we continue our work exploring how the derivative of a function is effected by transformations of the function.

Derivatives and Functions 4
Derivatives and Functions 5
Derivatives and Functions 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.

Key Ideas
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 explain the four basic transformations of a function in terms of its graph or its equation.
I can describe how the derivative of a function will be changed as the result of a transformation of the function.
Turn-In (#-1)
PS 8 #3-5

Handouts
No Handouts Posted

Assignment
PS 8.5
WS 5- 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.