HolcombMath

Tuesday, February 09, 2010

IB Math SL (Class 54)

Lesson Title
Lesson 16: What if the variable is an exponent? (2)

Overview
In today’s lesson students continue to explore how the derivative of a function which has a variable for an exponent may be found.
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
How can an equation for the derivative of a function be created?
How can the derivative of a function which has a variable as an exponent be found?

Key Knowledge
The inverse of a function undoes a function.

Key Skills
I can find the derivative of functions which have variables as exponents.

Turn-In (#-1)
PS 15

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.

Math 7 (Class 109)

Lesson Title
Investigation 2: Similar Figures

Overview
In today’s class students return to the problem for trying to figure out the number of different arrangements that are possible with the letters MIAMI. (We’ve gotten a bit side tracked by this problem.)
Textbook Sections
Problem 2.1 (Txt. p.15) Drawing Wumps

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
distance-time graph
speed-time graph
continuous
discrete
area
definite integral
point of intersection
parallel
coincident
profit
income
expenses
cost
slope
ratio
intersection of grid lines
easy points
equilateral
regular
triangle
square
pentagon
hexagon
octagon
typical
average
horizontal
slope
gradient
rate of change
coefficient
declare your variable

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?

Key Knowledge
Certain properties of a shape are maintained when a shape is enlarged or reduced.

Key Skills
I can plot points accurately.
I can calculate the locations of points using an algebraic formula.

Handouts
No Handouts Posted

Assignment
Finish “City Scramble 1”
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 54)

Lesson Title
Lesson 20: Related Rates (1)

Overview
In today’s class students begin to investigate how to use the rate of change of one variable with respect to another, and a relationship between variables, to calculate another rate.
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
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 109)

Lesson Title
Investigation 3: Polygons and Angles

Overview
In today’s class students continue to develop their understanding of angle measures by playing the game of Four in a Row on a circular (polar) graph.
Textbook Sections
Problem 3.4 (Txt. p.29) Playing Four in a Row

Vocabulary
tiling
regular polygon
polygon
pentagon
hexagon
octagon

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 thought of as the result of a turning motion, a wedge, or two sides coming together to form a common vertex.

Key Skills
I can sketch, and determine the angle measure, of an angle created by turning a fractional amount of a right angle turn.
I can sketch, and determine the angle measure, of an angle created by turning a fractional amount of a given angle.
I can determine the size of the angles of the vertices of shapes A, B, D, M, R, and V in the shape set.

Turn-In (#-1)
ACE p. 35 #19-22, 27-29

Handouts
No Handouts Posted

Assignment
ACE p.35 #23-26, 36
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.