HolcombMath

Thursday, October 30, 2008

Geometry (Class 23)

Lesson Title
Missing Angles Puzzles (4)

Overview
The warm-up today continues the theme of fitting the proper units of measure to a story. We also continue with Model Drawing Problems -Distance and Midpoints 9. The lesson for the day works towards students developing the ability to see angle relationships in a drawing, to use these relationships to find missing angle measures, and then to sequence and record the steps they used to find the measure of a specific angle. All of this is background work intended to smooth the transition to the writing of formal two column proofs.
Textbook Sections
N/A

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect
deduce, deduction
counter example
congruent

Key Attitudes
Math is about thinking creatively.

Key Ideas
A proof is the sequence of reasons which, when put together, compels you to believe something.
Key Skills
I can deduce the measure of angles.
I can state the steps I use to come to a conclusion.
I can record the steps I used to come to a conclusion in written form.
I can use the concept of a counter example to show that something is not necessarily true.
Turn-In (#22)
Test Corrections
Txt. p. 796 #1-3
Txt. p.39 #28-30, 40-42, 47-49

Handouts
No Handouts Posted

Assignment
Txt. p. 796 #4,5
Txt. p.47 #8-10, 14-16, 20-24, 28-30
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.

Wednesday, October 29, 2008

Intro to Calculus (Class 23)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Transforming Functions

Overview
Today’s class is a minimum day. Students have the chance to work on Workshop 6 (due by the end of the period) and Workshop 7 in preparation for their test on Friday.
Textbook Sections
N/A

Vocabulary
stretch
shift
compress
flip
transform
transformation

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs of functions can be transformed by shifting, flipping, compressing, or combination of these.
How the graph of a function changes can be described using both words and algebra.
Key Skills
I can predict how the graph of a function will change as the result of changes to the equation that represents the function.
Turn-In (#22)
Workshop 6 #TBA

Handouts
Workshop 7

Assignment
Workshop 7 #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.

Tuesday, October 28, 2008

Geometry (Class 22)

Lesson Title
Missing Angles Puzzles (3)

Overview
The warm-up today is the first in a new series, “Fit the Units”, which asks students to complete a story using appropriate metric units. We also continue to work with Model Drawing Problems involving distance and midpoints.
The lesson for the day continues with finding the measures of missing angles and creating a flow chart to represent the steps we used.
Textbook Sections
N/A

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect
deduce, deduction
counter example
congruent

Key Attitudes
Math is about thinking creatively.

Key Ideas
A proof is the sequence of reasons which, when put together, compels you to believe something.
Key Skills
I can deduce the measure of angles.
I can state the steps I use to come to a conclusion.
I can record the steps I used to come to a conclusion in written form.
I can use the concept of a counter example to show that something is not necessarily true.
Turn-In (#21)
Chapter 1- Lesson 3: Angles and their Measures Worksheet #33-36, 43-46, 53, 54
Model Drawing Problem: Distance and Midpoints 7

Handouts
No Handouts Posted

Assignment
Txt. p. 796 #1-3
Txt. p.39 #28-30, 40-42, 47-49
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, October 27, 2008

Intro to Calculus (Class 22)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Transforming Functions

Overview
The warm-up for the day, Sketching Graphs from Pictures (4): Orbits, asks students to create a graph relating distance and time for a space craft orbiting a planet. Students are presented with different types of orbits (circular, elliptical) to use.
The remaining portion of the class will be used for working on Workshop 5. There is a test on Friday focusing on:
1) Inverse Functions
2) Transforming Functions

Textbook Sections
N/A

Vocabulary
stretch
shift
compress
flip
transform
transformation

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs of functions can be transformed by shifting, flipping, compressing, or combination of these.
How the graph of a function changes can be described using both words and algebra.
Key Skills
I can predict how the graph of a function will change as the result of changes to the equation that represents the function.
Turn-In (#21)
Workshop 5

Handouts
Workshop 7

Assignment
Workshop 6 #TBA
Workshop 7 #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.

Friday, October 24, 2008

Geometry (Class 21)

Lesson Title
Missing Angles Puzzles (2)

Overview
The warm-up for today is the last “Figure It Out!” problem for a while. These have been tough, but students have shown a lot of growth in identifying embedded shapes and determining the sum of their interior angles. The lesson for today will continue working with finding the missing angles in a figure using the theorems (rules) we have developed so far. Students also continue to work with recording the steps they followed to arrive at their conclusion through the use of flow charts. Finally, during the last 45 minutes of the class the students will be taking their fourth test for the year.
Textbook Sections
N/A

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect
deduce, deduction
counter example
congruent

Key Attitudes
Math is about thinking creatively.

Key Ideas
A proof is the sequence of reasons which, when put together, compels you to believe something.
Key Skills
I can deduce the measure of angles.
I can state the steps I use to come to a conclusion.
I can record the steps I used to come to a conclusion in written form.
I can use the concept of a counter example to show that something is not necessarily true.
Turn-In (#20)
Chapter 1- Lesson 3: Angles and their Measures Worksheet #7-10, 14, 15, 18-20, 25, 26, 30, 31, 39, 41, 42, 48, 51, 52

Handouts
No Handouts Posted

Assignment
Chapter 1- Lesson 3: Angles and their Measures Worksheet #33-36, 43-46, 53, 54
Model Drawing Problem: Distance and Midpoints 7
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, October 23, 2008

Intro to Calculus (Class 21)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Transforming Functions

Overview
The warm-up for the day examines a situation involving a Ferris Wheel. Students are asked to create two graphs representing the heights of two different cars as a function of time. The remaining part of the class is dedicated to working on Workshop 5 and Workshop 6.
Textbook Sections
N/A

Vocabulary
stretch
shift
compress
flip
transform
transformation

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs of functions can be transformed by shifting, flipping, compressing, or combination of these.
How the graph of a function changes can be described using both words and algebra.
Key Skills
I can predict how the graph of a function will change as the result of changes to the equation that represents the function.
Turn-In (#20)
Finish Workshop 5
Finish HW 8

Handouts
The Big Wheel
Workshop 6
Assignment
Workshop 5
Workshop 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.

Wednesday, October 22, 2008

Geometry (Class 20)

Lesson Title
Missing Angles Puzzles (2)

Overview
The warm-up today gives students another opportunity to work with the sum of the interior angles of polygons as well as improve their ability to see overlapping shapes in a figure (this is especially helpful for proofs we will be working with later in the year). The model drawing problem today involves distances, midpoints, equations of lines, and altitudes of triangles!
Also during class today students have the chance to review material concerning angle measures. And finally we will continue working with the new material concerning finding the measures of missing angles and recording the process we used to find a given measure.
Textbook Sections
N/A

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect
deduce, deduction
counter example
congruent

Key Attitudes
Math is about thinking creatively.

Key Ideas
A proof is the sequence of reasons which, when put together, compels you to believe something.
Key Skills
I can deduce the measure of angles.
I can state the steps I use to come to a conclusion.
I can record the steps I used to come to a conclusion in written form.
I can use the concept of a counter example to show that something is not necessarily true.
Turn-In (#19)
Chapter 1- Lesson 3
Txt. p.39 #17-20, 25-27, 37-39, 44-46

Handouts
Chapter 1- Lesson 3- Angles and their Measures Practice

Assignment
Chapter 1- Lesson 3: Angles and their Measures Worksheet #7-10, 14, 15, 18-20, 25, 26, 30, 31, 39, 41, 42, 48, 51, 52
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, October 21, 2008

Intro to Calculus (Class 20)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Transforming Functions

Overview
The warm-up for today continues with the race track theme. In this warm-up students need to evaluate different race tracks in order to determine which one matches a given graph relating speed to the distance along the track.
The lesson works towards developing the last type of transformation-- what happens to the graph of f(x) as the result of f(ax). Then students will have the rest of the class to work on homework 8 and Workshop 5
Textbook Sections
N/A

Vocabulary
stretch
shift
compress
flip
transform
transformation

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs of functions can be transformed by shifting, flipping, compressing, or combination of these.
How the graph of a function changes can be described using both words and algebra.
Key Skills
I can predict how the graph of a function will change as the result of changes to the equation that represents the function.
Turn-In (#19)
Homework 8 #1-5b
Finish Warm-Up

Handouts
No Handouts Posted

Assignment
Finish Workshop 5
Finish HW 8
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, October 20, 2008

Geometry (Class 19)

Lesson Title
Missing Angle Puzzles (1)

Overview
The warm-up for today, Figure It Out! (3), continues working with sum of the interior angles of polygons. Students also work another model drawing problem, Distance and Midpoints (5), concerning (Surprise!) distance and midpoints.
The lesson for the day moves us into the next chapter. This chapter will be primarily concerned with the logical structures that underlie formal mathematical proofs. In this first lesson students will be working on “Missing Angle Puzzles” as the context for developing the ability to explicitly state reasoning that compels them to draw a conclusion.
Textbook Sections
N/A

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect
deduce, deduction
counter example

Key Attitudes
Math is about thinking creatively.

Key Ideas
A proof is the sequence of reasons which, when put together, compels you to believe something.
Key Skills
I can deduce the measure of angles.
I can state the steps I use to come to a conclusion.
I can record the steps I used to come to a conclusion in written form.
I can use the concept of a counter example to show that something is not necessarily true.
Turn-In (#18)
Txt. p.29 #26-43
Txt. p.32 65-67, 77-79

Handouts
Chapter 2- Lesson 1: Missing Angle Puzzles

Assignment
Chapter 1- Lesson 3
Txt. p.39 #17-20, 25-27, 37-39, 44-46
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, October 17, 2008

Intro to Calculus (Class 19)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Transforming Functions

Overview
The warm-up today asks students to examine the layout of a motor racing course and to create a graph comparing the speed of the race car to the distance along the track. Students then create their own race tracks,make a similar graph, and then trade the graph with another student. They then try to recreate the race track from the graph.
The lesson for the day continues from last class, focusing on transforming graphs of functions by stretching, compressing, shifting, and reflecting and then developing the algebra to represent these transformations.
Textbook Sections
N/A

Vocabulary
stretch
shift
compress
flip
transform
transformation

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs of functions can be transformed by shifting, flipping, compressing, or combination of these.
How the graph of a function changes can be described using both words and algebra.
Key Skills
I can predict how the graph of a function will change as the result of changes to the equation that represents the function.
Turn-In (#18)
Workshop 5

Handouts
Intro to Calculus: Homework 8

Assignment
Homework 8 #1-5b
Finish Warm-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.

Thursday, October 16, 2008

Geometry (Class 18)

Lesson Title
Angles and their Measures

Overview
The warm-up today is another Figure It Out! problem where students need to work with the sum of the interior angles of polygons. They also work on another model drawing problem focusing on computing the distance between points in the plane. The lesson for the day continues to work with angles and their measures.
Textbook Sections
§1.4 (Txt. p.26) Angles and Their Measures
§1.5 (Txt. p.34) Segment and Angle Bisectos

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect

Key Attitudes
Math is about thinking creatively.

Key Ideas
An angle is created by two rays which have a common endpoint.
The measurement of an angle describes the amount the angle is “open” and can be measured in degrees.
Angles can be classified by their measure.
Key Skills
I can measure angles with a protractor.
I can identify and name angles using one letter, three letters, or numbers and can determine which approach is acceptable in a given situation.
I can classify an angle by its measure- acute, right, obtuse, straight.
I can write equations to represent relationships between angle measures and then solve these equations to determine the measure of an angle.
I can use the concept of “bisect” to find angle measures.
I can find the midpoint of a segment when given the coordinates of its endpoints.
Turn-In (#17)
Test Corrections
Txt. p.29 #17-25
Txt. p. 32 #61-64, 70-73, 74-76

Handouts
No Handouts Posted

Assignment
Txt. p.29 #26-43
Txt. p.32 65-67, 77-79
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, October 15, 2008

Intro to Calculus (Class 18)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Transforming Functions

Overview
The warm-up for today will ask students to think back over the work they have done so far with inverse functions and to do a quick 5 minute write of all that they know about this topic.
The lesson for the day starts our work with transforming functions. There is quite a lot of ideas to work through before we will be ready to tackle Homework 8-- at least two classes worth I think. So we will do some of this work today and then have a good chunk of time to work on Workshop 5.
Textbook Sections
N/A

Vocabulary
stretch
shift
compress
flip
transform
transformation

Key Attitudes
Math is about thinking creatively.

Key Ideas
Graphs of functions can be transformed by shifting, flipping, compressing, or combination of these.
How the graph of a function changes can be described using both words and algebra.
Key Skills
I can predict how the graph of a function will change as the result of changes to the equation that represents the function.
Turn-In (#17)
Finish Lesson for HW 7
Finish HW 7

Handouts
Lesson for Homework 8

Assignment
Workshop 5
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, October 14, 2008

Geometry (Class 17)

Lesson Title
Angles and their Measures

Overview
The warm-up today, “Figure It Out! (1)” introduces students to finding the sum of the interior angles of polygons. Students are asked to use clues related to the sum of the interior angles of polygons to make deductions about 3 figures. We also have a model drawing problem today which continues with finding the distance between points in the coordinate plane.
The lesson for the day continues to focus on measuring angles but shifts away from physically measuring them with a protractor to deducing measurements using algebra. Students also work more with finding the midpoint of a segment.
Textbook Sections
§1.4 (Txt. p.26) Angles and Their Measures
§1.5 (Txt. p.34) Segment and Angle Bisectos

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles
bisect

Key Attitudes
Math is about thinking creatively.

Key Ideas
An angle is created by two rays which have a common endpoint.
The measurement of an angle describes the amount the angle is “open” and can be measured in degrees.
Angles can be classified by their measure.
Key Skills
I can measure angles with a protractor.
I can identify and name angles using one letter, three letters, or numbers and can determine which approach is acceptable in a given situation.
I can classify an angle by its measure- acute, right, obtuse, straight.
I can write equations to represent relationships between angle measures and then solve these equations to determine the measure of an angle.
I can use the concept of “bisect” to find angle measures.
I can find the midpoint of a segment when given the coordinates of its endpoints.
Turn-In (#16)
Finish Chapter 1- Lesson 2 Practice Problems

Handouts
No Handouts Posted

Assignment
Test Corrections
Txt. p.29 #17-25
Txt. p. 32 #61-64, 70-73, 74-76
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, October 13, 2008

Intro to Calculus (Class 17)

Announcements
We will not be having a test this Friday. The next test will be on Friday, October 31.

Lesson Title
Inverse Functions

Overview
The warm-up for today asks students to create graphs to represent a situation described in words. We also review our work from our last class by creating a function flow diagram, then a function flow diagram for undoing the function, an equation for the undoing diagram, and finally we find the inverse of the original function algebraically.

Our lesson for the day continues to focus on inverse functions. In particular we answer the questions:
1) Do all functions have inverses?
2) How can you use algebra to determine if an inverse function exists?
3) How can you determine if an inverse function exists when given a graph of a function?

Finally, as time permits, students begin Workshop 5
Textbook Sections
N/A

Vocabulary
function
domain
inverse function

Key Attitudes
Math is about thinking creatively.

Key Ideas
Functions can undo other functions.
If you graph a function and the function which undoes it, then the graphs will be reflections of each other across the line y = x.
An equation for a function which undoes another function can be created by working to undo each step of the original function starting with the last step and working backwards.
Functions which undo each other are called “inverses”.
The notation for inverse functions can be tricky-- f^-1 would be the inverse of the function f. The “-1” symbol’s location is crucial and looks a lot like other uses.
Key Skills
I can create a “function flow diagram” to represent a function described in words or using algebra.
I can create a function flow diagram to represent undoing another function flow diagram.
I can write an English sentence to describe what happens to a value when it is used as the input to a function.
I can write an English sentence to describe what happens to an output value of a function in order to “work it backwards” through the function.
I can evaluate a function for specific values when given the graph of the function.
I can create the graph of the inverse of a function using values from the original function when given the graph of the original function.
I can create a graph of the inverse of a function using the fact that inverse functions are reflections across the line y = x.
I can create a rule for the inverse of a function and express this rule using function notation.
Turn-In (#16)
Notes for Lesson 7
HW 7

Handouts
Intro to Calculus: Workshop 5

Assignment
Finish Lesson for HW 7
Finish HW 7
Workshop 5 #1-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.

Friday, October 10, 2008

Geometry (Class 16)

Lesson Title
Using the Pythagorean Theorem

Overview
The warm-up for today continues the theme of using the Pythagorean theorem as a toll for finding the distance between two points. The lesson for the day marks the start of our working with angles. Also during the class students will be taking their third test.
Textbook Sections
§1.3 (Txt. p.17) Segments and their Measures

Vocabulary
acute angle
obtuse angle
right angle
straight angle
supplementary angles
complementary angles
adjacent angles

Key Attitudes
Math is about thinking creatively.

Key Ideas
The distance between points can be calculated.
The length of a line can be determined by thinking about it as a right triangle.
Key Skills
I can create a non-square rectangle, right triangle, or non-rectangular parallelogram on the coordinate plane when given the locations of two vertices of the shape.
I can determine the area of a figure drawn on dot paper.
I can create any of the possible squares whose vertices are on the dots of a 5 by 5 grid of dot paper.
I can determien the area of the square on the hypotenuse of a right triangle.
I can determine the length of the side of a square when I know the area of the square.
I can determine the length of a line segment using the locations of the endpoints of the segment.
Turn-In (#15)
Pythagorean Paths 5
Txt. p.124 #9, 10, 19-24, 44, 45

Handouts
Model Drawing Problem: Distance and Midpoints 2

Assignment
Finish Chapter 1- Lesson 2 Practice Problems
Pythagorean Paths 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.