Friday, March 19, 2010
Math 6 (Class 131)
Lesson Title
Investigation 6: Turtle Tracks
Overview
In today’s class students continue to investigate how computer programing and geometry go together.
Textbook Sections
Problem 6.1 (Txt. p.66) Drawing with Logo
Vocabulary
tiling
regular polygon
polygon
pentagon
hexagon
octagon
angle ruler
precisely
vertex
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 transformations be described mathematically?
Key Knowledge
Basic commands for Web Turtle.
Key Skills
I can write a set of commands to draw a given design.
Turn-In (#-1)
Use Web Turtle to draw a square and a regular pentagon.
http://sonic.net/~nbs/webturtle/
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.
Posted by Mr. Holcomb on 03/19 at 07:46 AM
Permalink
Thursday, March 18, 2010
Math 7 (Class 131)
Lesson Title
Investigation 3: Patterns of Similar Figures
Overview
In today’s class students continue investigating subdividing shapes into similar shapes.
Textbook Sections
Problem 3.3 (Txt. p.31) Subdividing to Find Rep-tiles
Vocabulary
similar
corresponding sides
corresponding angles
segment
ratio
perimeter
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 transformations be described mathematically?
How do different shapes compare to each other?
What is required for two shapes to be similar?
Key Knowledge
Certain properties of a shape are maintained when a shape is enlarged or reduced.
Key Skills
I can visually determine if two shapes are similar.
Turn-In (#-1)
ACE p.33 #8-11
Handouts
No Handouts Posted
Assignment
ACE p.33 #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.
Posted by Mr. Holcomb on 03/18 at 07:19 AM
Permalink
IB Math Sl (Class 65)
Lesson Title
Lesson 19: Optimization (4)
Overview
In today’s class students work many optimization problems.
Textbook Sections
Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
difference quotient
derivative from first principals
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 has to be true about the value of a derivative in order to have a maximum or minimum value?
If the derivative of a function is zero, does this always represent a maximum or minimum?
What information does the first derivative give me about the original function?
What information does the second derivative give me about the original function?
Key Knowledge
The derivative of a function can be used to find the optimal solution to a problem.
If the derivative of a function changes sign around a critical point, the function is said to have a local (relative) extremum at that point.
If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point.
If the second derivative is positive at a point, the graph is concave up. If the second derivative is positive at a critical point, then the critical point is a local minimum.
If the second derivative is negative at a point, the graph is concave down. If the second derivative is negative at a critical point, then the critical point is a local maximum.
An inflection point marks the transition from concave up and concave down. The second derivative will be zero at an inflection point.
The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here. If, however, the function has a critical point for which f′(x) = 0 and the second derivative is negative at this point, then f has local maximum here. This technique is called Second Derivative Test for Local Extrema.
Key Skills
I can make and label a diagram to represent a situation.
I can identify the key variables in a situation.
I can mentally model what is going on in a situation.
I can create equations relating the key variables in a situation.
I can create an equation between the two main variables in a situation.
I can find and use a derivative to determine an optimal solution for a situation.
I can use multiple representations to determine if a function has a relative maximum or a relative minimum on a given interval.
I can use multiple representations to determine if a function is concave up or concave down on a given interval.
I can use multiple representations to determine if a function has an inflection point on a given interval.
Turn-In (#-1)
PS 19 and or Past Paper
Handouts
No Handouts Posted
Assignment
PS 19
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.
Posted by Mr. Holcomb on 03/18 at 07:19 AM
Permalink
Math HL (Class 65)
Lesson Title
Lesson 22: A Return to Limits (2)
Overview
In today’s class students continue developing their ability to find the limits of functions. As time permits students begin to investigate undoing differentiation.
Textbook Sections
Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
explicit equation
implicit equation
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 the fact that differentiable functions are locally linear help us find limits of functions which have an indeterminate form when evaluated at the limiting value?
Key Knowledge
Local linearization.
Finding the limits of functions using multiple representations.
Key Skills
I can determine if a limit has an indeterminate form.
I can find the limit of functions which are in the form 0/0 or infinity/infinity
I can transform functions which are in other indeterminate forms into 0/0 form.
Turn-In (#-1)
PS 21, PS 22
Handouts
No Handouts Posted
Assignment
PS 21, PS 22
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.
Posted by Mr. Holcomb on 03/18 at 07:19 AM
Permalink
Math 6 (Class 131)
Lesson Title
Investigation 6: Turtle Tracks
Overview
In today’s class students begin to investigate Geometry using Web Turtle http://sonic.net/~nbs/webturtle/
Textbook Sections
Problem 6.1 (Txt. p.66) Drawing with Logo
Vocabulary
tiling
regular polygon
polygon
pentagon
hexagon
octagon
angle ruler
precisely
vertex
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 transformations be described mathematically?
Key Knowledge
Basic commands for Web Turtle.
Key Skills
I can write a set of commands to draw a given design.
Turn-In (#-1)
ACE p.57 #13, 14, 17
Handouts
No Handouts Posted
Assignment
Use Web Turtle to draw a parallelogram
http://sonic.net/~nbs/webturtle/
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.
Posted by Mr. Holcomb on 03/18 at 07:18 AM
Permalink
Tuesday, March 16, 2010
SL (Class 64)
Lesson Title
Lesson 19: Optimization (3)
Overview
In today’s class students continue to work on developing their ability to set up and solve optimization problems.
Textbook Sections
Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
difference quotient
derivative from first principals
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 has to be true about the value of a derivative in order to have a maximum or minimum value?
If the derivative of a function is zero, does this always represent a maximum or minimum?
What information does the first derivative give me about the original function?
What information does the second derivative give me about the original function?
Key Knowledge
The derivative of a function can be used to find the optimal solution to a problem.
If the derivative of a function changes sign around a critical point, the function is said to have a local (relative) extremum at that point.
If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point.
If the second derivative is positive at a point, the graph is concave up. If the second derivative is positive at a critical point, then the critical point is a local minimum.
If the second derivative is negative at a point, the graph is concave down. If the second derivative is negative at a critical point, then the critical point is a local maximum.
An inflection point marks the transition from concave up and concave down. The second derivative will be zero at an inflection point.
The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here. If, however, the function has a critical point for which f′(x) = 0 and the second derivative is negative at this point, then f has local maximum here. This technique is called Second Derivative Test for Local Extrema.
Key Skills
I can make and label a diagram to represent a situation.
I can identify the key variables in a situation.
I can mentally model what is going on in a situation.
I can create equations relating the key variables in a situation.
I can create an equation between the two main variables in a situation.
I can find and use a derivative to determine an optimal solution for a situation.
I can use multiple representations to determine if a function has a relative maximum or a relative minimum on a given interval.
I can use multiple representations to determine if a function is concave up or concave down on a given interval.
I can use multiple representations to determine if a function has an inflection point on a given interval.
Turn-In (#-1)
PS 19
Handouts
No Handouts Posted
Assignment
PS 19 and or Past Paper
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.
Posted by Mr. Holcomb on 03/16 at 07:18 AM
Permalink
HL (Class 64)
Lesson Title
Lesson 22: A Return to Limits
Overview
In today’s class students see how the concept of local linearization can help us determine the limits of certain types of functions.
Textbook Sections
Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
explicit equation
implicit equation
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 the fact that differentiable functions are locally linear help us find limits of functions which have an indeterminate form when evaluated at the limiting value?
Key Knowledge
Local linearization.
Finding the limits of functions using multiple representations.
Key Skills
I can determine if a limit has an indeterminate form.
I can find the limit of functions which are in the form 0/0 or infinity/infinity
I can transform functions which are in other indeterminate forms into 0/0 form.
Turn-In (#-1)
PS 21 and any other previous work.
Handouts
No Handouts Posted
Assignment
PS 21, PS 22
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.
Posted by Mr. Holcomb on 03/16 at 07:18 AM
Permalink
Math 6 (Class 128)
Lesson Title
Investigation 5: Side-Angle-Shape Connections
Overview
In today’s class students finish up their work with flipping and turning shapes.
Textbook Sections
Problem 5.2 (txt. p.54) Flipping and Turning Quadrilaterals
Vocabulary
tiling
regular polygon
polygon
pentagon
hexagon
octagon
angle ruler
precisely
vertex
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 transformations be described mathematically?
Key Knowledge
Basic commands for Web Turtle.
Key Skills
I can write a set of commands to draw a given design.
Turn-In (#-1)
ACE p.57 #2, 8, 12
Handouts
No Handouts Posted
Assignment
ACE p.57 #13, 14, 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.
Posted by Mr. Holcomb on 03/16 at 07:17 AM
Permalink
Math 7 (Class 128)
Lesson Title
Investigation 3: Patterns of Similar Figures
Overview
In today’s class students continue working with multiplication of fractions during the opener and then return to working with subdividing shapes.
Textbook Sections
Problem 3.3 (Txt. p.31) Subdividing to Find Rep-tiles
Vocabulary
similar
corresponding sides
corresponding angles
segment
ratio
perimeter
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 transformations be described mathematically?
How do different shapes compare to each other?
What is required for two shapes to be similar?
Key Knowledge
Certain properties of a shape are maintained when a shape is enlarged or reduced.
Key Skills
I can visually determine if two shapes are similar.
Turn-In (#-1)
ACE p.33 #16, 17
Handouts
No Handouts Posted
Assignment
ACE p.33 #8-11
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.
Posted by Mr. Holcomb on 03/16 at 07:17 AM
Permalink
Monday, March 15, 2010
Algebra 2 (Class 63)
Lesson Title
3.2.2 How can I find the equation?
Overview
In this lesson students continue their work from the previous lesson to develop a new method to find linear and exponential equations given two points.
Textbook Sections
3.2.2 (Txt. p.147) How can I find the equation?
Vocabulary
interest
simple interest
compound interest
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 does it grow?
How is the rate written as a percent? As a decimal?
How is it the same or different?
How can I find an equation for an exponential situation?
Key Knowledge
Exponential growth is caused by a constant multiplication.
Key Skills
I can find an equation for an exponential function when given a graph, a table, or a situation.
Turn-In (#-1)
3-84, 3-85, 3-95 to 3-99
Quiz Corrections
Handouts
No Handouts Posted
Assignment
3-100, 3-101, 3-103, 3-104, 3-109
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.
Posted by Mr. Holcomb on 03/15 at 08:34 AM
Permalink
Math 6 (Class 127)
Lesson Title
Investigation 5: Side-Angle-Shape Connections
Overview
In today’s class students test out what they learned about flipping and turning while working on the last problem.
Textbook Sections
Problem 5.2 (txt. p.54) Flipping and Turning Quadrilaterals
Vocabulary
tiling
regular polygon
polygon
pentagon
hexagon
octagon
angle ruler
precisely
vertex
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 transformations be described mathematically?
Key Knowledge
Flipping means to turn a shape over.
Turning means to rotate a shape around a given point.
Key Skills
I can determine the number of ways a shape can be turned and or flipped in order to fit into a missing hole in a pattern.
Turn-In (#-1)
No Homework
Handouts
No Handouts Posted
Assignment
ACE p.57 #2, 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.
Posted by Mr. Holcomb on 03/15 at 08:34 AM
Permalink
Math 7 (Class 127)
Lesson Title
Investigation 3: Patterns of Similar Figures
Overview
The openers for this week help students review and deepen their understanding of multiplying with fractions and whole numbers. In the lesson today students continue exploring rep-tiles and how the scale factor for the area is related to the scale factor for the sides.
Textbook Sections
Problem 3.2 (Txt. p.29) Building with Rep-tiles
Vocabulary
similar
corresponding sides
corresponding angles
segment
ratio
perimeter
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 transformations be described mathematically?
How do different shapes compare to each other?
What is required for two shapes to be similar?
Key Knowledge
Certain properties of a shape are maintained when a shape is enlarged or reduced.
Key Skills
I can visually determine if two shapes are similar.
Turn-In (#-1)
No Homework
Handouts
No Handouts Posted
Assignment
ACE p.33 #16, 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.
Posted by Mr. Holcomb on 03/15 at 08:34 AM
Permalink
Friday, March 12, 2010
HL (Class 63)
Lesson Title
Lesson 21: Looking Closely (1)
Overview
Today students continue to examine functions from a very close perspective. They see that when viewed closely enough, all smooth continuous functions become essentially linear.
Textbook Sections
Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
explicit equation
implicit equation
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 does a function look like when viewed very closely? Do all functions behave like this?
How can an equation for the line which approximates a function at a given point be created?
Key Knowledge
How to zoom using a GDC.
Finding the limit of a function graphically, numerically, and algebraically.
Key Skills
I can explain what it means for a function to be locally linear.
I can determine if a function will have a local linearization.
I can find the local linearization of a function, if it exists.
Turn-In (#-1)
§ (Txt. p.)
Handouts
No Handouts Posted
Assignment
PS 21 and any other previous work.
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.
Posted by Mr. Holcomb on 03/12 at 08:05 AM
Permalink
Math 7 (Class 126)
Lesson Title
Investigation 3: Patterns of Similar Figures
Overview
In today’s class students continue to work with Rep-tile.
Textbook Sections
Problem 3.2 (Txt. p.29) Building with Rep-tiles
Vocabulary
similar
corresponding sides
corresponding angles
segment
ratio
perimeter
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 transformations be described mathematically?
How do different shapes compare to each other?
What is required for two shapes to be similar?
Key Knowledge
Certain properties of a shape are maintained when a shape is enlarged or reduced.
Key Skills
I can visually determine if two shapes are similar.
Turn-In (#-1)
No Homework
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.
Posted by Mr. Holcomb on 03/12 at 08:04 AM
Permalink
Sl (Class 63)
Lesson Title
Lesson 19: Optimization (2)
Overview
In today’s class students continue to develop their ability to use calculus to determine the optimal solution to a variety of applied problems.
Textbook Sections
Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
difference quotient
derivative from first principals
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 has to be true about the value of a derivative in order to have a maximum or minimum value?
If the derivative of a function is zero, does this always represent a maximum or minimum?
What information does the first derivative give me about the original function?
What information does the second derivative give me about the original function?
Key Knowledge
The derivative of a function can be used to find the optimal solution to a problem.
If the derivative of a function changes sign around a critical point, the function is said to have a local (relative) extremum at that point.
If the derivative changes from positive (increasing function) to negative (decreasing function), the function has a local (relative) maximum at the critical point.
If the second derivative is positive at a point, the graph is concave up. If the second derivative is positive at a critical point, then the critical point is a local minimum.
If the second derivative is negative at a point, the graph is concave down. If the second derivative is negative at a critical point, then the critical point is a local maximum.
An inflection point marks the transition from concave up and concave down. The second derivative will be zero at an inflection point.
The second derivative may be used to determine local extrema of a function under certain conditions. If a function has a critical point for which f′(x) = 0 and the second derivative is positive at this point, then f has a local minimum here. If, however, the function has a critical point for which f′(x) = 0 and the second derivative is negative at this point, then f has local maximum here. This technique is called Second Derivative Test for Local Extrema.
Key Skills
I can make and label a diagram to represent a situation.
I can identify the key variables in a situation.
I can mentally model what is going on in a situation.
I can create equations relating the key variables in a situation.
I can create an equation between the two main variables in a situation.
I can find and use a derivative to determine an optimal solution for a situation.
I can use multiple representations to determine if a function has a relative maximum or a relative minimum on a given interval.
I can use multiple representations to determine if a function is concave up or concave down on a given interval.
I can use multiple representations to determine if a function has an inflection point on a given interval.
Turn-In (#-1)
PS 18
Handouts
No Handouts Posted
Assignment
PS 19 and or Past Paper
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.
Posted by Mr. Holcomb on 03/12 at 08:04 AM
Permalink