HolcombMath

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.

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.

Math 6 (Class 144)

Lesson Title
Investigation 1: What do you know about fractions?

Overview
In today’s class students continue to explore their understanding of fractions by coming up with clever ways to determine which is larger 7/15 + 9/17 or 1 whole. In addition, students also get their book for the next unit of study-- how to use rational numbers.
Textbook Sections
Problem 1.1 (Txt. p.5) Using Percents

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)
Explain why the multiplication table method demonstrated in class can be used to show that two fractions, like 2/5 and 6/15, are equivalent.

Handouts
No Handouts Posted

Assignment
1/9 + 1/9 > 1/8 ? Explain why. See if you can do this in a clever way-- maybe using a number line-- in addition to calculating the answer.
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 144)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students continue working with multiplication of fractions as well as continue with applying their understanding of similar shapes.
Textbook Sections
Problem 4.3 (Txt. p.44) Making Copies

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 #1-5. 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
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.
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 14, 2010

Math 6 (Class 143)

Lesson Title
Investigation 0: What do you know about fractions?

Overview
In today’s class students investigate further how equivalent fractions can be determined thorough the use of a multiplication table.
Textbook Sections
N/A

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
Fractions can be compared using different approaches.

Key Skills
I can compare the size of fractions.
I can explain, without any mubo jumbo, which of two fractions are larger.

Turn-In (#-1)
Explain why you can fractions will be equivalent if you multiply the numerator and denominator by the same values. In other words, explain why 2/5 x 3/3 =6/15

Handouts
No Handouts Posted

Assignment
Explain why the multiplication table method demonstrated in class can be used to show that two fractions, like 2/5 and 6/15, are equivalent.
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 143)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students continue working with multiplication of fractions.
Textbook Sections
Problem 4.3 (Txt. p.44) Making Copies

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 2-6

Handouts
No Handouts Posted

Assignment
Fraction Review 2 Practice 1 #1-5. Please do your work on separate paper since there is not enough work on the handout for doing this adequately.
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.

Algbera 2 (Class 71)

Lesson Title
4.1.2 How can I shift a parabola?

Overview
In Algebra 1 students learned about slope and y-intercept, ideas that allowed them to write equations and sketch graphs of any line. In this lesson students will work on developing similar tools for parabolas.
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)
4-5 to 4-10

Handouts
No Handouts Posted

Assignment
4-11, 4-12, 4-18, 4-20
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.

Tuesday, April 13, 2010

HL (Class 71)

Lesson Title
Lesson 24: Up, or Down, the Slope (3)

Overview
In today’s class student wrap up their initial exploration of differential equations.
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 is an antiderivative?
How do I find an antiderivative from a graph?
How do I find an antiderivative from an equation?
What is meant by the terms “implicit” and “explicit” in general and in terms of equations?

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.
Finding the antiderivative of a 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.
I can explain what a differential equation is.
I can solve separable differential equations.
I can solve an initial value problem.

Turn-In (#-1)
PS 24

Handouts
No Handouts Posted

Assignment
PS 24
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 142)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students continue to develop their understanding and skills related to multiplication of fractions with other fractions.
Textbook Sections
Problem 4.3 (Txt. p.44) Making Copies

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)
ACE p.47 #3, 4

Handouts
No Handouts Posted

Assignment
Fraction Review 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.

SL (Class 71)

Lesson Title
Lesson 24: Up, or Down, the Slope (3)

Overview
In today’s class student wrap up their initial exploration of differential equations.
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 is an antiderivative?
How do I find an antiderivative from a graph?
How do I find an antiderivative from an equation?
What is meant by the terms “implicit” and “explicit” in general and in terms of equations?

Key Knowledge
Fractions can be compared using different approaches.
If shapes are similar, then scale factor between corresponding sides is constant.

If the function g(x) is the derivative of some function f(x), then f(x) is the antiderivative of g(x).

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.
I can explain what a differential equation is.
I can solve separable differential equations.
I can solve an initial value problem.

Turn-In (#-1)
PS 24

Handouts
No Handouts Posted

Assignment
PS 24
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 142)

Lesson Title
Investigation 0: What do you know about fractions?

Overview
In today’s class students continue exploring the comparison of fractions
Textbook Sections
N/A

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
Fractions can be compared using different approaches.

Key Skills
I can compare the size of fractions.
I can explain, without any mubo jumbo, which of two fractions are larger.

Turn-In (#-1)
True or False: 3/13 > 6/27? Include and explanation based on ideas you can justify (No “Because my fifth grade teacher told me”)

Handouts
No Handouts Posted

Assignment
Explain why you can fractions will be equivalent if you multiply the numerator and denominator by the same values. In other words, explain why 2/5 x 3/3 =6/15
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.

Monday, April 12, 2010

Algebra 2 (Class 70)

Lesson Title
Investigation 4: Using Similarity

Overview
In today’s class students continue to work on exploring how to use their knowledge of scale factors to determine how to use a photocopier to enlarge or reduce.
Textbook Sections
Problem 4.3 (Txt. p.44) Making Copies

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)
ACE p.47 #3, 4

Handouts
No Handouts Posted

Assignment
ACE p.47 #3, 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.