HolcombMath

Friday, March 26, 2010

Math 6 (Class 136)

Lesson Title
Investigation 6: Turtle Tracks

Overview
In today’s class students continue to make drawings for Web Turtle programs.
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.69 #3, 4, 7

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 7 (Class 136)

Lesson Title
Investigation 4: Using Similarity

Overview
Students then will apply what they have learned about scaling to determine if it is possible to enlarge an advertisement to fit a given space.
Textbook Sections
Problem 4.2 (Txt. p.43) Scaling Up

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 do different shapes compare to each other?
What is required for two shapes to be similar?

Key Knowledge
If shapes are similar, then scale factor between corresponding sides is constant.

Key Skills
I can determine if it is possible to enlarge an advertisement to fit a given set of dimensions.

Turn-In (#-1)
Fraction Practice 1
Make your own add.

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.

SL (Class 68)

Announcements
Quiz Friday on Optimization

Lesson Title
Lesson 23: Antiderivatives (2)

Overview
In today’s class we continue working on finding the anti-derivatives of functions.
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 is an antiderivative?
How do I find an antiderivative from a graph?
How do I find an antiderivative from an equation?

Key Knowledge
If the function g(x) is the derivative of some function f(x), then f(x) is the antiderivative of g(x).
There are an infinitely many antiderivatives of a given function.

Key Skills
I can determine if a given graph represents the antiderivative of a function.
I can sketch the graph of an antiderivative of a function when given the graph of the function.
I can determine if a given graph represents the antiderivative of a function.
I can sketch the graph of an antiderivative of a function when given the graph of the function.

Turn-In (#-1)
PS 19, PS 23

Handouts
No Handouts Posted

Assignment
PS 19, PS 23
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, March 24, 2010

Algebra 2 (Class 67)

Lesson Title
4.1.1 How can an equation help me predict?

Overview
Today students work towards bringing closure to this chapter by conducting: 1) a team brainstorming session, 2) Making a concept map which shows the connections between the key ideas, 3) Answering questions related to the key concepts, 4) Summarizing their own understanding, 5) Cleaning up their learning log, 6) Solving problems representing the main ideas and skills for this chapter.
Textbook Sections
4.1.1 (Txt. p.165) How can an equation help me predict?

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.
I can use what I have learned about exponential functions to conduct an investigation into the depreciation of cars.

Turn-In (#-1)
3-124 to 3-127

Handouts
No Handouts Posted

Assignment
3-128 to 3-130, 3-131, 3-132
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 134)

Lesson Title
Investigation 6: Turtle Tracks

Overview
In today’s class students continue to work with Web Turtle and Geometry.
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)
Web Turtle

Handouts
No Handouts Posted

Assignment
Web Turtle-- Use the repeat command to make a regular pentagon.
Circle Sums 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 134)

Lesson Title
Investigation 4: Using Similarity

Overview
In the last class students worked to figure out how a person’s height could be determined using a surveillance camera photograph. In today’s class they will verify their findings.
Textbook Sections
Problem 4.1 (Txt. p.41) Using Similarity to Solve a Mystery

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 do different shapes compare to each other?
What is required for two shapes to be similar?

Key Knowledge
If shapes are similar, then scale factor between corresponding sides is constant.

Key Skills
I can determine if it is possible to enlarge an advertisement to fit a given set of dimensions.

Turn-In (#-1)
ACE p.47 #1, 2, 6

Handouts
No Handouts Posted

Assignment
Finish Problem 4.1 Follow-Up: Determine the height of the door and be ready to share your method.
Fraction Review 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.

Tuesday, March 23, 2010

HL (Class 66)

Lesson Title
Lesson 22: A Return to Limits (3)

Overview
In today’s class students finish up working with L’Hospital’s Rule by seeing how different indeterminate forms can be transformed into ones for which L’Hospital’s Rule can be used.

As time permits students begin to investigate how to reverse the process of 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 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.

SL (Class 66)

Lesson Title
Lesson 19: Optimization (5)

Overview
In today’s class students work another problem reviewing vectors. Then they continue to develop their ability to setup and solve optimization problems. As time permits they will begin to investigate how the process of differentiation can be reversed.
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
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 133)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class, which is brief due to morning meeting, students will continue to develop their ability to multiply with whole numbers and fractions.
Textbook Sections
Problem 4.1 (Txt. p.41) Using Similarity to Solve a Mystery

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 do different shapes compare to each other?
What is required for two shapes to be similar?

Key Knowledge
If shapes are similar, then scale factor between corresponding sides is constant.

Key Skills
I can determine if it is possible to enlarge an advertisement to fit a given set of dimensions.

Turn-In (#-1)
No Homework

Handouts
No Handouts Posted

Assignment
ACE p.47 #1, 2, 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 133)

Lesson Title
Investigation 6: Turtle Tracks

Overview
In today’s class students continue to work with Web Turtle and Geometry.
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)
Web Turtle

Handouts
No Handouts Posted

Assignment
Web Turtle-- Use the repeat command to make a regular pentagon.
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, March 22, 2010

Math 7 (Class 132)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students explore how similarity can be used to solve a mystery! Students are first given a photograph and using a known size of an object in the photograph the are asked to deduce the size of another object.
Textbook Sections
Problem 4.1 (Txt. p.41) Using Similarity to Solve a Mystery

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 do different shapes compare to each other?
What is required for two shapes to be similar?

Key Knowledge
If shapes are similar, then scale factor between corresponding sides is constant.

Key Skills
I can determine the size of an object in a photograph using similarity.

Turn-In (#-1)
ACE p.33 #12, 13

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.

Algebra 2 (Class 66)

Lesson Title
Chapter 3 Closure

Overview
In today’s class students write a quiz focusing on the homework problems from the last two weeks.
Textbook Sections
Chapter 3 Closure (Txt. p.155)

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.
I can use what I have learned about exponential functions to conduct an investigation into the depreciation of cars.

Turn-In (#-1)
3-102, 3-110 to 3-112

Handouts
No Handouts Posted

Assignment
3-124 to 3-127
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 132)

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)
No Homework

Handouts
No Handouts Posted

Assignment
Web Turtle
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.

Friday, March 19, 2010

Algebra 2 (Class 65)

Lesson Title
Chapter 3 Closure

Overview
In today’s class students work to integrate their understanding of different methods for writing equations for exponential equations.
Textbook Sections
Chapter 3 Closure (Txt. p.155)

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.
I can use what I have learned about exponential functions to conduct an investigation into the depreciation of cars.

Turn-In (#-1)
3-102, 3-110 to 3-112

Handouts
No Handouts Posted

Assignment
3-113, 3-115, 3-116, 3-121 to 3-123
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 131)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students continue to review multiplication of fractions and whole numbers.
Textbook Sections
Problem 4.1 (Txt. p.41) Using Similarity to Solve a Mystery

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 do different shapes compare to each other?
What is required for two shapes to be similar?

Key Knowledge
If shapes are similar, then scale factor between corresponding sides is constant.

Key Skills
I can determine the size of an object in a photograph using similarity.

Turn-In (#-1)
ACE p.33 #12, 13

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.