HolcombMath

Thursday, April 29, 2010

HL (Class 77)

Lesson Title
Lesson 32: How do I remove a hole?

Overview
In today’s lesson students explore solids of revolution where using disks would be impossible since the solid has a hole!
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
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
How can you find the volume of a solid?
What’s a “solid of revolution” and why is that distinction important?
How can you use integration to find the volume of a solid of revolution?

Key Knowledge
In some cases it is helpful to use washers to find the volume of a solid.
The volume of a washer can be determined by finding the volume of the disk and then subtracting the volume of the whole.
The volume of a disk is calculated in the same manner as the volume of a cylinder.

Key Skills
I can determine when it is appropriate to use washers to find the volume of a solid of revolution.
I can determine the volume of a solid of revolution by using washers.

Turn-In (#-1)
Finish Lesson Summary, ODE 2, PS 31 and any previous problems you have not finished.

Handouts
No Handouts Posted

Assignment
PS 32 and any previous unfinished 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.

SL (Class 77)

Lesson Title
Lesson 32: How do I remove a hole? (2)

Overview
In today’s class we continue working with solids of revolution first finishing up dealing with solids which have a hole, and then working with revolutions about lines other than the axes.
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
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
How can you find the volume of a solid?
What’s a “solid of revolution” and why is that distinction important?
How can you use integration to find the volume of a solid of revolution?

Key Knowledge
In some cases it is helpful to use washers to find the volume of a solid.
The volume of a washer can be determined by finding the volume of the disk and then subtracting the volume of the whole.
The volume of a disk is calculated in the same manner as the volume of a cylinder.

Key Skills
I can determine when it is appropriate to use washers to find the volume of a solid of revolution.
I can determine the volume of a solid of revolution by using washers.

Turn-In (#-1)
§ (Txt. p.)

Handouts
No Handouts Posted

Assignment
PS 32 and previous problem sets
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 154)

Lesson Title
Investigation 1: Using Percents

Overview
In today’s lesson students work towards solidifying their understanding of fractions.
Textbook Sections
Problem 1.3 (Txt. p.9) Finding Bargains

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
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
What makes an estimate reasonable?
What makes an answer exact?
What makes a strategy both effective and efficient?

Key Knowledge
A sale price can be expressed as a percent discount.

Key Skills
I can compute a final price of an item including a discount and sales tax.
I can use my calculating skills to compare different “bargains”.

Turn-In (#-1)
ACE p.12 #31, 32, 33

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 154)

Lesson Title
Investigation 1: Using Percents

Overview
In today’s lesson students work towards solidifying their understanding of fractions.
Textbook Sections
Problem 1.3 (Txt. p.9) Finding Bargains

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
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
What makes an estimate reasonable?
What makes an answer exact?
What makes a strategy both effective and efficient?

Key Knowledge
A sale price can be expressed as a percent discount.

Key Skills
I can compute a final price of an item including a discount and sales tax.
I can use my calculating skills to compare different “bargains”.

Turn-In (#-1)
ACE p.12 #31, 32, 33

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.

Wednesday, April 28, 2010

Algebra 2 (Calss 76)

Lesson Title
4.1.4 How can I model the data?

Overview
In the past few lessons students have determined how to move graphs of parabolas around on a set of axes. in this lesson they will put these new skills to work as they use parabolas and their equations to model situations.
Textbook Sections
4.1.4 (Txt. p.179) How can I model the data?

Vocabulary
interest
simple interest
compound interest

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
What changes can we make to a parabola’s graph?
What changes can we make to the equation y=x^2?
How do changes in the equation relate to changes in the graph?

Key Knowledge
An equation for a parabola can be written in the form y = a(x-h)^2+k
Each parameter for a parabola in the form y = a(x-h)^2+k controls a certain aspect of the graph of the parabola.

Key Skills
I can explain how each parameter in equations of the form y = a(x-h)^2+k effects the graph of the function.
In can construct an equation of a parabola to model a situation.

Turn-In (#-1)
4-30 to 4-32, 4-39, 4-40

Handouts
No Handouts Posted

Assignment
4-40 to 4-43
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 153)

Lesson Title
Investigation 1: Using Percents

Overview
In the last few classes students have developed their ability to find percentages of numbers using benchmarks of 10%, 5%, and 1%. They applied those skills to developing ways to compute the tip on a meal. In today’s class we stretch out this understanding to examine some alternative ways to compute tips.
Textbook Sections
Problem 1.2 (Txt. p.7) Computing Tips

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
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
What makes an estimate reasonable?
What makes an answer exact?
What makes a strategy both effective and efficient?

Key Knowledge
A sale price can be expressed as a percent discount.

Key Skills
I can compute a final price of an item including a discount and sales tax.
I can use my calculating skills to compare different “bargains”.

Turn-In (#-1)
ACE p.12 #31, 32, 33

Handouts
No Handouts Posted

Assignment
Working with Fractions Review #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.

Monday, April 26, 2010

Algebra 2

Lesson Title
4.1.3 How can I graph it quickly?

Overview
In today’s class students reflect on the work they did in the last class and come up with a way to find change (some) equations which are in the form y = ax^2+bx+c into graphing form. As time permits they will begin to put what they have learned in the last few classes to work by creating models of situations.
Textbook Sections
4.1.3 (Txt. p. 175) How can I graph it quickly?

Vocabulary
interest
simple interest
compound interest

Key Attitudes
Willingness to work as a group to help meet individual and group goals.

Enduring Understandings
Changes in various parameters have specific effects on graphs of parent functions in the coordinate plane.

Essential Question
What changes can we make to a parabola’s graph?
What changes can we make to the equation y=x^2?
How do changes in the equation relate to changes in the graph?

Key Knowledge
An equation for a parabola can be written in the form y = a(x-h)^2+k
Each parameter for a parabola in the form y = a(x-h)^2+k controls a certain aspect of the graph of the parabola.

Key Skills
I can explain how each parameter in equations of the form y = a(x-h)^2+k effects the graph of the function.

Turn-In (#-1)
4-26 to 4-29

Handouts
No Handouts Posted

Assignment
4-30 to 4-32, 4-39 and 4-38c
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 151)

Lesson Title
Investigation 1: Using Percents

Overview
In today’s class students continue to explore how to use percents to figure appropriate tips. The concept of a “Benchmark” is introduced as a tool for making calculations.
Textbook Sections
Problem 1.2 (Txt. p.7) Computing Tips

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
Numbers can be represented in multiple ways.
Knowing the reasonableness of an answer comes from using good number sense and estimation strategies.

Essential Question
What makes an estimate reasonable?
What makes an answer exact?
What makes a strategy both effective and efficient?

Key Knowledge
A tip can be computed in various ways.

Key Skills
I can determine the cost of the tax on a bill.
I can determine the appropriate tip to leave on a bill.
I can determine how much money each person should pay in order to share the costs fairly.
I can quickly determine 10% or 5% of a number mentally.

Turn-In (#-1)
ACE p.12 #3

Handouts
No Handouts Posted

Assignment
ACE p.12 #18, 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.

Monday, April 19, 2010

Math 6 (Class 146)

Lesson Title
Investigation 1: Using Percents

Overview
In today’s class students work on using a one-hundred grid to convert between fractions, decimals and percents.
Textbook Sections
Problem 1.1 (Txt. p.5) Taxing Tapes

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
What makes an estimate reasonable?
What makes an answer exact?
What makes a strategy both effective and efficient?

Key Knowledge
Percents are special fractions which have a denominators of 100.

Key Skills
I can use a hundreds grid to help solve percent problems.
I can determine the tax owed on an item when I know the cost of the item and the tax rate.
I can convert between fractions, decimals, and percents.

Turn-In (#-1)
ACE p. 12 #5, 10

Handouts
No Handouts Posted

Assignment
Problem 1.1 Follow-Up #1, 2
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 146)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students share their answers regarding using the map of the state of Utah.
Textbook Sections
Problem 4.4 (Txt. p.45) Using Map Scales

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?
Why do we use multiplication to find fractions of fractions?

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
Revise your answers from problem 4.4 and do the follow-up.
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 73)

Lesson Title
4.1.2 How can I shift a parabola?

Overview
In today’s class students continue to explore how the equation y = x^2 can be changed, and how these changes effect its graph.
Textbook Sections
4.1.2 (Txt. p.168) How can I shift a parabola?

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
What changes can we make to a parabola’s graph?
What changes can we make to the equation y=x^2?
How do changes in the equation relate to changes in the graph?

Key Knowledge
The shape of a parabola can be modified by changing its parameters.

Key Skills
I can describe the types of changes that can be made to a parabola’s graph.
I can use appropriate terminology in discussing key aspects of the graph of a parabola.
I can create an equation for a parabola that opens downward or opens upward.
I can create equations of different parabolas which all touch the x-axis at one specific point.

Turn-In (#-1)
No Homework

Handouts
No Handouts Posted

Assignment
4-21 to 4-25
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, April 16, 2010

Math 6 (Class 145)

Lesson Title
Investigation 1: Using Percents

Overview
In today’s class students begin their next unit of study focusing on using rational numbers: fractions, decimals, and percents.
Textbook Sections
Problem 1.1 (Txt. p.5) Taxing Tapes

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
What makes an estimate reasonable?
What makes an answer exact?
What makes a strategy both effective and efficient?

Key Knowledge
Percents are special fractions which have a denominators of 100.

Key Skills
I can use a hundreds grid to help solve percent problems.
I can determine the tax owed on an item when I know the cost of the item and the tax rate.

Turn-In (#-1)
ACE p. 12 #5, 10

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.

Algerba 2 (Class 72)

Lesson Title
Investigation 4: Using Similarity

Overview
How do you use a map? How does similarity help you understand what is going on? In today’s class students explore these questions.
Textbook Sections
Problem 4.4 (Txt. p.45) Using Map Scales

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?
Why do we use multiplication to find fractions of fractions?

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 Review 2 Practice 1 #6-10. Please do your work on separate paper since there is not enough work on the handout for doing this adequately.

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.

Thursday, April 15, 2010

SL (Class 72)

Lesson Title
Lesson 26: How do the limits of integration work?

Overview
In today’s lesson students explore the properties of integration.
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 are the properties of integration?

Key Knowledge
Properties of integration are implied from the properties of differentiation.

Key Skills
I can use graphs to derive and explain the properties of integration.
I can recognize and use the properties of integration.

Turn-In (#-1)
§ (Txt. p.)

Handouts
No Handouts Posted

Assignment
PS 26
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.

HL (Class 72)

Lesson Title
Lesson 25: What’s Under There?

Overview
In today’s class students explore how to calculate the definite integral based on their understanding of the relationship between time, distance, and speed.
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 you recognize a situation which involves integration?
How can you calculate the definite integral?
What’s the difference between a definite integral, an indefinite integral, and an integral?
How are anti-derivatives and definite integrals related?
What does “Numerical integration” mean and how can you use them?
What are “Riemann sums” and why are they helpful?
How can you set up a definte integral for a given situation?

Key Knowledge
The definite integral can be calculated of a function can be calculated using the anti-derivative of a function.

Key Skills
I can recognize a problem whose solution requires a definite integral.
I can set-up a definite integral for a given situation.
I can solve a problem which requires the use of a definite integral.
I can describe how to evaluate a definite integral using anti-differentiation.

Turn-In (#-1)
PS 24, PS 25

Handouts
No Handouts Posted

Assignment
,PS 25
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.