HolcombMath

Tuesday, February 16, 2010

Math 6 (Class 113)

Lesson Title
Investigation 4: Polygon Properties and Tiling

Overview
In today’s class students continue to investigate how the number of sides is related to the measure of the angles of a polygon.
Textbook Sections
Problem 4.1 (Txt. p.42) Relating Sides to Angles

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
Why do we compare contrast and classify objects?
How do decomposing and recomposing shapes help us build our understand of mathematics?

Key Knowledge
An angle can be measured with an angle ruler.

Key Skills
I can measure an angle with an angle ruler.
I can determine with shapes in the shape set can be used to make a tiling.

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

Handouts
No Handouts Posted

Assignment
ACE p.35 #42
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 113)

Lesson Title
Investigation 2: Similar Figures

Overview
In today’s class students investigate probabilities and revisit the “ATLANTA” problem to see how a letter which is repeated three times effects the number of different possible combinations.
Textbook Sections
Problem 2.2 (Txt. p.18) Nosing Around

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 collect data and organize data.
I can use data to make predictions and generalizations.
I can confirm or refute generalizations using data.

Turn-In (#-1)
No Homework

Handouts
No Handouts Posted

Assignment
Justification of your answer to “ATLANTA”
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 56)

Lesson Title
Lesson 20: Related Rates (3)

Overview
In today’s class we wrap up our work with related rates and take a brief look at mathematical modeling.
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 rate of change be used to find other rates of change?

Key Knowledge
The derivative of a function can be found implicitly.

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 find a related rate.
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 20
IA
Review Matrices and Vectors (emailed to you).
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 56)

Lesson Title
Lesson 18: Inferences from Derivatives (1)

Overview
In today’s lesson, students finish up the work on developing techniques for finding the derivative of inverse trigonometric functions. They then begin turn their attention to furthering their understanding regarding information the derivative of a function can provide.

http://holcombmath.com/sketches/I2C_geogebra_sketches/Inferences_from_Derivatives_1.html

http://holcombmath.com/sketches/I2C_geogebra_sketches/Inferences_from_Derivatives_2.html

http://holcombmath.com/sketches/I2C_geogebra_sketches/Inferences_from_Derivatives_3.html

http://holcombmath.com/sketches/I2C_geogebra_sketches/Inferences_from_Derivatives_4.html
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 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
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 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 16

Handouts
No Handouts Posted

Assignment
PS 16
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.