HolcombMath

Tuesday, September 29, 2009

IB Math HL (Class 18)

Lesson Title
Lesson for PS 8— Derivatives and Transformations

Overview
Today’s class focuses on determining how transformations of functions effect the value of the derivative of the function.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
I can explain the four basic transformations of a function in terms of its graph or its equation.

Key Skills
I can predict how the derivatives of two functions will be related to each other based on the transformations needed to change one function into another.
Turn-In (#-1)
PS 7 (all of it) is due on Tuesday

Handouts
No Handouts Posted

Assignment
WS 3 #3 (Write English Sentences and draw number lines), 4
Begin work on IA 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 36)

Lesson Title
Multiplying and Dividing Integers

Overview
Students continue to investigate the multiplication of integers in context or changing temperature. As time permits, the investigation of the multiplication of integers will be extended to a geometric model.
Textbook Sections
Problem 4.1 (Txt. p. 53) Rising and Falling Temperatures

Vocabulary
Integer
temperature
opposites
chip board
model
inverse
rate

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

Key Ideas
How can I model the multiplication of integers?
What types of situations involve the multiplication of integers?
Key Skills
I can create a table of values to represent how the temperature over time changes.
I can write a multiplication sentence to represent a number line showing repeated addition.
I can create a situation about temperature which can be represented by the multiplication of negative and positive integers.
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Turn-In (#-1)
ACE p. 60 #1, 2

Handouts
No Handouts Posted

Assignment
Problem 4.1 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.

Math 6 (Class 36)

Lesson Title
Investigation 5: Factorizations

Overview
In today’s class student continue their investigation concerning strings of numbers whose product is equal to 840.
Textbook Sections
Problem 5.1 (Txt. p. 46) Searching for Factor Strings

Vocabulary
analyze
prime
composite
product
factor
divisor
conjecture

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

Key Ideas
Any integer greater than one can be written as the unique product of prime numbers.
Key Skills
I can create strings of numbers whose product is equal to a given value.
Turn-In (#-1)
ACE p. 52 #16, 17

Handouts
No Handouts Posted

Assignment
ACE p.52 #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.

Monday, September 28, 2009

Algebra 2 (Class 17)

Lesson Title
1.2.2 How can I investigate a function?

Overview
We will continue our work with investigating functions of the form y = 1/(x-h).
Textbook Sections
1.2.2 How can I investigate a function?

Vocabulary
input
output
relation
function
dependent variable
independent variable

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

Key Ideas
Graphs of functions have important parts that need to be included when making a graph.
When doing an investigation I am looking for generalizations I can make and ways in which I can support these generalizations.
Key Skills
I can create graphs of a family of functions using my graphing calculator so that all important parts of the graph are shown.
I can write a summary statement and provide justification for an investigation.
Turn-In (#-1)
1-80, 1-73, 1-74

Handouts
No Handouts Posted

Assignment
1-75 to 1-77, 1-83
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 35)

Lesson Title
Investigation 5: Factorizations

Overview
In today’s lesson students investigate strings of numbers whose product is equal to a specified value. Is it possible to get a longest string? If so, how do you do that? If not, why is it not possible?
Textbook Sections
Problem 5.1 (Txt. p. 46) Searching for Factor Strings

Vocabulary
analyze
prime
composite
product
factor
divisor
conjecture

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

Key Ideas
Any integer greater than one can be written as the unique product of prime numbers.
Key Skills
I can create strings of numbers whose product is equal to a given value.
Turn-In (#-1)
No Homework.

Handouts
No Handouts Posted

Assignment
ACe p. 52 #16, 17
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 35)

Lesson Title
Multiplying and Dividing Integers

Overview
In today’s lesson students investigate the operation of multiplication with integers by thinking about how temperatures can rise and fall at a given rate during the day. They are asked to construct tables of values to keep track of the change in temperature and then are asked to construct number-line models to represent the situation.
Textbook Sections
Problem 4.1 (Txt. p. 53) Rising and Falling Temperatures

Vocabulary
Integer
temperature
opposites
chip board
model
inverse
rate

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

Key Ideas

Explore the use of integers in applied settings.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
Numbers above zero are positive and below zero are negative.
A number line can be used to model the addition of integers.
A number line can be used to model the addition of integers.
A number line can be used to model the addition of integers.
Addition of integers can be modeled with a chip board.
Addition of integers can be modeled with a chip board.
Addition of integers can be modeled with a chip board.
Subtraction of integers can be modeled using a chip board.
Subtraction of integers can be modeled using a chip board.
Subtraction of integers can be modeled using a chip board.
Subtraction of integers can be modeled using a number line.
Subtraction of integers can be modeled using a number line.
Subtraction of integers can be modeled using a number line.

Patterns can help you make predictions.
Addition and subtraction are operations which undo each other, they are inverses of each other.
Addition and subtraction are operations which undo each other, they are inverses of each other.
Addition and subtraction are operations which undo each other, they are inverses of each other.
Addition and subtraction are operations which undo each other, they are inverses of each other.

Key Skills
I can create a table of values to represent how temperature changes from hour to hour when I know the rate at which it is changing.
I can construct a number-line model for the multiplication of integers.
Turn-In (#-1)
No Homework

Handouts
No Handouts Posted

Assignment
ACE p. 60 #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, September 25, 2009

IB Math HL (Class 17)

Lesson Title
Lesson for PS 5: Know Your Limits (4)

Overview
We will finish up our initial work with the limits of functions whose x-value is approaching some finite value and will turn our attention to dealing with limits of functions for x-values which are getting really, really big or really, really small.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
I can write an English sentence about the distance between points on a number line to represent equations and inequalities involving absolute value.
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
I can write an English sentence about the distance between points on a number line to represent equations and inequalities involving absolute value.
Turn-In (#-1)
PS 5 ##11, 12
Work on the Internal Assessment

Handouts
No Handouts Posted

Assignment
Finish Internal Assessment 1
Finish Lesson for Assignment 5- Know Your Limits.
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 17)

Lesson Title
Lesson for PS 7: The Derivative Function (1)

Overview
In today’s class students will get some extended time to work on Workshop 3. As time permits we will being our work related to the effect transforming a function has on the derivative of the function.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
I can explain the four basic transformations of a function in terms of its graph or its equation.

Key Skills
I can predict how the derivatives of two functions will be related to each other based on the transformations needed to change one function into another.
Turn-In (#-1)
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
PS 7 (all of it) is due on Tuesday
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 17)

Lesson Title
Lesson for PS 5: Know Your Limits (3)

Overview
We will finish up our initial work with the limits of functions whose x-value is approaching some finite value and will turn our attention to dealing with limits of functions for x-values which are getting really, really big or really, really small.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
A limit can be thought of as the value a function approaches.
Limits can be determined graphically, numerically, or algebraically.
When evaluating limits algebraically, first substitute the value and see what happens. If you get an indeterminate form, then you re-write it using algebra so that it is not an indeterminate form.
Key Skills
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
I can write an English sentence about the distance between points on a number line to represent equations and inequalities involving absolute value.
I can explain the meaning of a limit of a function.
I can determine the limit of a function using a graph, a table of values, or algebra.
I can write an English sentence about the distance between points on a number line to represent equations and inequalities involving absolute value.
Turn-In (#-1)
PS 5 ##11, 12
Work on the Internal Assessment

Handouts
No Handouts Posted

Assignment
PS 6 #TBA
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 34)

Lesson Title

Overview
As an opener we play a game designed focused on practice adding and subtracting integers. Students then write their 5th quiz for the course.
Textbook Sections

Vocabulary
Integer
temperature
opposites
chip board
model
inverse

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

Key Ideas
Addition and subtraction are operations which undo each other, they are inverses of each other.
Key Skills
I can write a subtraction sentence which undoes a given addition statement.
Turn-In (#-1)
ACE p.47 #25-32 (No calculators)

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 6 (Class 34)

Lesson Title
Investigation 4: Common Factors and Multiples

Overview
Students share their LCM and GCF problems today and the class works to solve them. Then students write the 5th quiz for the course.
Textbook Sections

Vocabulary
analyze
prime
composite
product
factor
divisor
conjecture

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

Key Ideas
Pairs of numbers have common factors.
Pairs of numbers have common multiples.
Key Skills
I can find the GCF of two numbers.
I can find the LCM of two numbers.
I can determine if a problem is calling for finding the GCF or LCM.
Turn-In (#-1)
Finish creating your word LCM or GCF word problem.

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.

IB Math HL (Class 16)

Lesson Title
Lesson for PS 7: The Derivative Function (1)

Overview
We continue developing the idea of a function whose values are the derivatives of another function.
Textbook Sections

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative

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

Key Ideas
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
Key Skills
I can explain what is meant by “derivative function”.
I can determine over what interval a function is differentiable given the graph of the function.
When given four graphs, I can determine if any two represent a function and its derivative function.
I can sketch the graph of the derivative function when given the graph of a function.
I can sketch the graph of a function without using a calculator and then create a graph of the derivative function.
Turn-In (#-1)
PS 6— Finish the Assignment

Handouts
No Handouts Posted

Assignment
PS 7 (all of it) is due on Tuesday
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, September 24, 2009

Math 7 (Class 33)

Lesson Title
Investigation 3: Subtracting Integers

Overview
We finish up our work with “undoing” with addition and subtraction today.
Textbook Sections
Problem 3.4 (Txt. p.44) “Undoing” with Addition and Subtraction

Vocabulary
Integer
temperature
opposites
chip board
model
inverse

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

Key Ideas
Addition and subtraction are operations which undo each other, they are inverses of each other.
Key Skills
I can write a subtraction sentence which undoes a given addition statement.
Turn-In (#-1)
Write the inverse of the following:
-3 + 5 = 2
9 + (-10) = -1
Using a chip board as well as writing a flow chart for the process both forwards and backwards.

Handouts
No Handouts Posted

Assignment
ACE p.47 #25-32 (No calculators)
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 33)

Lesson Title
Investigation 4: Common Factors and Multiples

Overview
In the last few classes we have been working with problems which require finding the LCM or GCF of two numbers for solution. As we have been working on these problems students have been asked to identify how they are deciding if they should use the LCM or GCF. In today’s class students are challenged to create their own LCM or GCF word problem. As an additional challenge, students are asked to construct their problem to disguise which of the approaches wil work.
Textbook Sections
Supplemental

Vocabulary
analyze
prime
composite
product
factor
divisor
conjecture

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

Key Ideas
Pairs of numbers have common factors.
Pairs of numbers have common multiples.
Key Skills
I can find the GCF of two numbers.
I can find the LCM of two numbers.
I can determine if a problem is calling for finding the GCF or LCM.
Turn-In (#-1)
PS 4.4 #3 and 4

Handouts
No Handouts Posted

Assignment
Finish creating your word LCM or GCF word problem.
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, September 23, 2009

Algebra 2 (Class 16)

Lesson Title
1.2.2 How can I investigate a function?

Overview
We will continue our work with investigating functions of the form y = 1/(x-h).
Textbook Sections
1.2.2 How can I investigate a function?

Vocabulary
input
output
relation
function
dependent variable
independent variable

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

Key Ideas
Graphs of functions have important parts that need to be included when making a graph.
When doing an investigation I am looking for generalizations I can make and ways in which I can support these generalizations.
Key Skills
I can create graphs of a family of functions using my graphing calculator so that all important parts of the graph are shown.
I can write a summary statement and provide justification for an investigation.
Turn-In (#-1)
1-69 to 1-72
Quiz Corrections

Handouts
No Handouts Posted

Assignment
1-80, 1-73, 1-74
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.