HolcombMath

Wednesday, February 03, 2010

Math 7 (Class 104)

Lesson Title
No Classes Today-- Languages Project

Overview
In today’s class students work on estimating the measures of angles.
Textbook Sections
Problem 3.2 (Txt. p.25) Estimating Angle Measures

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.

Turn-In (#-1)
Problem 3.1
Find an example of a non-rectangle parallelogram
Quiz Corrections

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 02/03 at 07:19 AM
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Math 6 (Class 104)

Lesson Title
Investigation 1: Enlarging Figures

Overview
In today’s class students begin the next unit of study, “Stretching and Shrinking”. In this unit students explore the concepts related to the enlargement or reduction of shapes, scale factors, area growth, and indirect measure. They learn how ratios, fractions, and percents as well as equations, graphs, and tables can help them understand and make predictions in such situations.
Textbook Sections
Problem 1.1 (Txt. p. 5) Stretching a Figure

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 use a rubber band stretcher to enlarge a figure.
I can make a detailed list of what is the same and what is different about two shapes.

Turn-In (#-1)
TBA

Handouts
No Handouts Posted

Assignment
ACE p.9 #1, 2
Concept Map Rough Draft (for those of you who did not do it!)
Weekly Summary
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 02/03 at 07:19 AM
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Algebra 2 (Class 52)

Lesson Title
3.1.1 What do exponential graphs look like?

Overview
In today’s class students continue to work on the group quiz they started on Friday. In addition, they will also continue their work exploring what exponential graphs look like.
Textbook Sections
3.1.1 (Txt. p.115) What do exponential graphs look like?

Vocabulary
input
output
relation
function
dependent variable
independent variable
parameters
linear relationship
subscript
exponential relationship
discrete
continuous
sequence
initial value
term
arithmetic sequence
geometric sequence
common difference
common ratio
slope
rise/run
rate

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 we make an expression or equation simpller?
How can we be sure that we are correct?

Key Knowledge
The factors of an equation can be determined by using an area model.
If the product of two numbers is zero, then at least one of the two numbers must be zero.

Key Skills
I can use an area model to find equivalent expressions.
I can rewrite an equation in a form which is easier to solve.

Turn-In (#-1)
§ (Txt. p.)

Handouts
No Handouts Posted

Assignment
3-26 to 3-30
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 02/03 at 07:19 AM
Permalink

Tuesday, February 02, 2010

IB Math SL (Class 51)

Lesson Title
Lesson 15- Y-Not! (2)

Overview
In today’s class we continue to explore how to calculate the derivatives of implicit 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
How can I find the derivative of a composite function?

Key Knowledge
Functions can be defined both explicitly or implictly.

Key Skills
I can determine if an equation is defined explicitly or implicitly.
I can use implicit differentiation to find the derivative of a function.

Turn-In (#-1)
WS 9, PS 15

Handouts
No Handouts Posted

Assignment
PS 15
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 02/02 at 08:01 AM
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Math 6 (Class 103)

Lesson Title
Investigation 3: Polygons and Angles

Overview
In today’s class students begin to investigate the angles relationships inherent in different polygons.
Textbook Sections
Problem 3.1 (Txt. p.22) Polygon’s and Angles

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 identify angles which are the result of a turning motion, a wedge, or two sides with a common vertex.

Turn-In (#-1)
TBA

Handouts
No Handouts Posted

Assignment
Problem 3.1
Find an example of a non-rectangle parallelogram
Quiz Corrections
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 02/02 at 08:00 AM
Permalink

Math 7 (Class 103)

Lesson Title
Unit Closure

Overview
In today’s class students continue to work on brining closure to the unit.
Textbook Sections
Problem 1.1 (Txt. p. 5) Stretching a Figure

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 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?
How are the ideas of rate of change, ratio, and slope related to each other?
How can I use a graphing calculator to make graphs?

Key Knowledge
A graphing calculator (GDC) can be used to quickly and accurately make a graph of an equation.
In order to make a graph on a graphing calculator (GDC) the equation must first be in “y=” form.

Key Skills
I can enter an equation properly in a GDC.
I can adjust the window on a GDC in order to view specific areas of a graph.
I can use GDC to explore equationss.
I can determine a y-value when given an x-value when I know the equation relating x and y.
I can create a table of x and y values when given an equation.
I can identify similarities and differences between two tables of values and can explain how these differences are related to the equations for these tables.
I can write an equation for a table of values which has a constant rate of change.

Turn-In (#-1)
TBA

Handouts
No Handouts Posted

Assignment
Rough Draft of Concept Map
Quiz Corrections
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 02/02 at 08:00 AM
Permalink

IB Math HL (Class 103)

Lesson Title
Lesson 19: Optimization (1)

Overview
In today’s class we begin our work with using calculus to find optimal solutions to various problems.

http://holcombmath.com/sketches/I2C_geogebra_sketches/Triangle_Function_1.html

http://holcombmath.com/sketches/I2C_geogebra_sketches/Triangle_Function_2.html

http://holcombmath.com/sketches/I2C_geogebra_sketches/Triangle_Function_3.html
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 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
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 02/02 at 01:57 AM
Permalink

Monday, February 01, 2010

Algebra 2 (Class 102)