HolcombMath

Monday, April 30, 2007

Geometry (Class 72)

Announcements
Quiz Friday: Chapter 12.1 to 12.5, Chapter 11.1-11.2

CST Part 1, Monday May 14
CST Part 2, Wednesday May 16

Overview
In today’s class we continue our investigation concerning the relationship between the number of sides and the size of the angles of regular polygons and then use our results as a tool for finding the area of regular polygon when: 1) the number of sides and the length of the side are given, or 2) the size of an central, interior, or exterior angle and the length of a side are given.
Textbook Sections
§11.1 (Txt. p.661) Angle Measures in Polygons
§11.2 (Txt. p.669) Areas of Regular Polygons

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
An exterior angle of a regular polygon is equal to the measure of the corresponding central angle of the polygon.
The number of sides of a regular polygon is equal to 360 divided by the measure of a central angle.
The area of a regular polygon can be found using trigonometry.

Key Skills
Finding the area of a regular polygon when:
1) the number sides and the length of a side are given
2) the size of an central, interior, or exterior angle and the length of a side are given

Turn In
§11.1 (Txt. p.665) #6-8, 14, 15, 17, 18, 22, 23

Handouts
No Handouts Posted

Assignment
§11.1 (Txt. p.665) #10-12, 18, 20, 24, 33-36
§11.2 (Txt. p.672) #9, 16, 19
Chapter 11: Lesson 1- All
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.

Semester 2, Second Six Week Progress Reports

Grades are now posted for the progress reports for the second six-seeks of the second semester. There are only 6 weeks left! It is time to really turn up the effort and sprint for the finish.

Comments for the progress reports were calculated as follows:
If Content % ≤ 70, then a comment on the progress report will be “Low/failing test scores”.
If Learning Behavior % < Content % and Learning Behavior %<80, then a comment will be "Not working to ability".
If the number of missed assignments >4, then a comment will be “Fails to hand in work”.
If Content %≤70 or Overall %≤70 and Content % is not > 80, then a comment will be “Not moving to next level”.

Please contact me, by email is best, if you have comments or questions about your grade or the comments.

Friday, April 27, 2007

Algebra (Class 73)

Announcements
CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
In today’s class we extend our ability for linear graphing inequalities to graphing systems of linear inequalities.
Textbook Sections
§10-8 (Txt. p.495) Systems of Linear Inequalities

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Shading is used to show the region that contains the solutions to an inequality.
The region that contains shading for both inequalities represents solutions to both inequalities and is the solution to the system of inequalities.
We also write Quiz 11 which focuses on linear equations and solving systems of linear equations.

Key Skills
Graphing linear equations.
Graphing linear inequalities.

Key Skills
Graphing linear equations.
Graphing linear inequalities.

Turn In
Nothing to turn in.

Handouts
No Handouts Posted

Assignment
§10.7 (Txt. p.492) #1, 3, 13-15, 25-27
§10.8 (Txt. p.496) #9-12, 19, 20
Practice Worksheet p.129
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 26, 2007

Geometry (Class 71)

Announcements
CST Part 1, Monday May 14
CST Part 2, Wednesday May 16

Overview
In today’s class we investigate the relationship between the exterior angle of a polygon and the number of sides of the polygon. We also work to develop our ability to find the area of a regular polygon when we know the length of one of its sides.
Textbook Sections
§11.1 (Txt. p.661) Angle Measures in Polygons
§11.2 (Txt. p.669) Areas of Regular Polygons

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
If you know the the length of a side and the measure of an exterior angle of a regular polygon, you can find the area.

Key Skills
Finding the number of sides of a regular polygon given the measure of an exterior, or interior, angle.
Finding the measure of a missing angle of a polygon.
Finding the area of a regular polygon given the length of it side.

Turn In
Worksheet Practice 12.4A-12.6A

Handouts
Chapter 11-Lesson 1: Walking Around

Assignment
§11.1 (Txt. p.665) #6-8, 14, 15, 17, 18, 22, 23
Ch. 11-Lesson 1 #1-6
CST Practice #1-11
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 25, 2007

Algebra (Class 72)

Announcements
Quiz Friday focusing on writing equations for linear patterns and finding the point of intersection of two lines using graphing and algebra.

CST Part 1, Tuesday May 15
CST Part 2, Thursday May 17

Overview
In this lesson we extend our methods of graphing lines to include graphing linear inequalities.
Textbook Sections
§10-7 (Txt. p.490) Graphing Systems of Linear Inequalities

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
Shading can be used to represent an area on a graph that makes an inequality true.

Key Skills
Finding the point of intersection of two lines by: graphing, using substitution, using addition or subtraction of equations.
Finding regions of intersection using graphing

Key Skills
Finding the point of intersection of two lines by: graphing, using substitution, using addition or subtraction of equations.
Finding regions of intersection using graphing

Turn In
Class 71 Warm-Up and Notes

Handouts
No Handouts Posted

Assignment
§10-7 (Txt. p.492) #9-12, 28-29
Practice worksheet p.128
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 24, 2007

Geometry (Class 70)

Announcements
CST Part 1, Monday May 14
CST Part 2, Wednesday May 16

Overview
In today’s class we extend our study of solids to include finding the volumes of prisms, pyramids, cones, and spheres. We also learn how to find the surface area of a sphere.
Textbook Sections
§12.4 (Txt. p.743) Volume of Prisms and Cylinders
§12.5 (Txt. p.752) Volume of Pyramids and Cones
§12.6 (Txt. p.759) Surface Area and Volume of Spheres

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
The volume of a pyramid 1/3 of its surrounding prism.
The volume of a cone is 1/3 the volume of its surrounding cylinder.

Key Skills
Finding the volume of a pyramid, prism, cylinder, cone, or sphere by applying the appropriate formula.
Finding the surface area of a sphere by applying the formula S = 4πr^2

Key Skills
Finding the volume of a pyramid, prism, cylinder, cone, or sphere by applying the appropriate formula.
Finding the surface area of a sphere by applying the formula S = 4πr^2

Turn In
Worksheet Practice 12.2 A and 12.3 A

Handouts
No Handouts Posted

Assignment
Practice Worksheets 12.4A, 12.5A, 12.6A

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 23, 2007

Algebra (Class 71)

Announcements
Quiz Friday focusing on writing equations for linear patterns and finding the point of intersection of two lines using graphing and algebra.

Overview
In the last class we saw that we could find the point of intersection using three different methods: 1) by graphing, 2) by using substitution, 3) by adding or subtracting the two equations. In this class we practice all three methods as well as extend the third method so that it works in more cases. The key will be putting multiplication to work for us.
Textbook Sections
§9-5 (Txt. p.430) Multiplication with the Addition-or-Subtraction Method

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The solution to a system of equations is represented graphically by the point of intersection of two lines.
The coordinates of the point of intersection of two lines will be a shared solution to both equations.
Two equations will have a shared solution ONLY IF the two lines intersect.
The law of balance helps us solve systems of equations by allowing us to add equal expressions to both sides of an equation thereby eliminating a variable.

Key Skills
Finding the point of intersection of two lines by: graphing, using substitution, using addition or subtraction of equations.
Finding regions of intersection using graphing

Key Skills
Finding the point of intersection of two lines by: graphing, using substitution, using addition or subtraction of equations.
Finding regions of intersection using graphing

Turn In
Class 70 Notes
WS 13.13 and 13.14

Handouts
No Handouts Posted

Assignment
§9-5 (Txt. p.432) #10-15
§9-4 (Txt. p.427) #1-6, 19-21, 28
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 20, 2007

Geometry (Class 69)

Announcements
Quiz Friday, April 20 focusing on Chapter 10 Lessons 1-5

Overview
In this lesson we begin our study of how to compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres. Students will need to commit to memory the formulas for prisms, pyramids, and cylinders.

In addition, we take Quiz 11
Textbook Sections
§12.2 (Txt. p.728) Surface Area of Prisms and Cylinders
§12.3 (Txt. p.735) Surface Area of Pyramids and Cones

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
The surface area can be computed by finding the areas of each face of a solid.
The surface area of a cylinder is made up of two circles and a rectangle whose height is the height of the cylinder and whose width is the circumference of the cylinder.

Key Skills
Finding the surface are of a prism by applying formulas for the areas of polygons.
Finding the surface area of a cylinder using the formula S=2πr^2+2πh.
Finding the surface area of a pyramid by applying formulas for the areas of polygons.
Finding the surface area of a cone using the formula S = πr^2+πrL
Finding the surface area of a sphere by applying the formula S = 4πr^2

Vocabulary
Surface areas
Prism
Pyramid
Cone
Cylinder

Handouts
No Handouts Posted

Assignment
Worksheet 12.2 Practice A
Worksheet 12.3 Practice A
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 19, 2007

Algebra (Class 70)

Announcements
I am considering offering a bonus for students who score at a “Proficient” or “Advanced” level on the upcoming CST (STAR) tests. Here is one way it might work:
A student scores “Advanced”, the highest level, then I would raise that student’s second semester grade 2/3 of a letter grade. In other words, if that student had earned a B+ for the semester, then I would change the grade after I receive the CST scores in August to an A! If the student had a B, then his new grade would be an A-.
If a student scored “Proficient”, the second highest level, then I would raise the student’s second semester grade 1/3 of a letter grade. So a B would become a B+, or an B+ would become and A-.
For any other CST scores, Basic, Below Basic, of Far Below Basic, the student’s letter grade for the course would remain unchanged.
What do you think? Other suggestions? Share them with me either in class or via email.

Overview
In the last class we saw that two rules, linear equations, can share the same pair of values-- the pair of values where the lines intersect. In this class we will work towards mastering the algebra required to find this point of intersection.
Textbook Sections
§9-2 (Txt. p.417) The Substitution Method
§9-4 (Txt. p.426) The Addition-or-Subtraction Method

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The solution to a system of equations is represented graphically by the point of intersection of two lines.
The coordinates of the point of intersection of two lines will be a shared solution to both equations.
Two equations will have a shared solution ONLY IF the two lines intersect.

Key Skills
Finding the point of intersection of two lines by: graphing, using substitution, using addition or subtraction of equations.

Vocabulary
System of linear equations
point of intersection
substitution method
graphing method
intersect
intercept
solve a system of linear equations

Handouts
No Handouts Posted

Assignment
§§9-2 (Txt. p.419)#1-6
§9-4 (Txt. p.426) #1-6
Mixed Review p.425 #1-6
Practice Worksheet 13.14
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 18, 2007

Bonuses for CST Scores?

I am considering offering a bonus for students who score at a “Proficient” or “Advanced” level on the upcoming CST (STAR) tests. Here is one way it might work:
A student scores “Advanced”, the highest level, then I would raise that student’s second semester grade 2/3 of a letter grade. In other words, if that student had earned a B+ for the semester, then I would change the grade after I receive the CST scores in August to an A! If the student had a B, then his new grade would be an A-.
If a student scored “Proficient”, the second highest level, then I would raise the student’s second semester grade 1/3 of a letter grade. So a B would become a B+, or an B+ would become and A-.
For any other CST scores, Basic, Below Basic, of Far Below Basic, the student’s letter grade for the course would remain unchanged.
What do you think? Other suggestions? Share them with me either in class or via email.

Geometry Problems from Class 68

Problem 9 on Set 2 of the practice problems for Chapter 10 Lesson 5 is poorly labeled. It is unclear what exactly they want (236-15x) to be the measure of. Skip the problem. I apologize for not catching this earlier. If you do work it, and your result is justifiable, I will count it in as a bonus on the assignment. You might pass this along to other students in the class.

Geometry (Class 68)

Announcements
Quiz Friday, April 20 focusing on Chapter 10 Lessons 1-5

Overview
Today we review skills and concepts from Chapter 10.
Textbook Sections
§10.1 (Txt. p.595) Tangents to Circles
§10.2 (Txt. p.603) Arcs and Chords
§10.3 (Txt. p.613) Inscribed Angles
§10.4 (Txt. p.621) Other Angle Relationships in Circles
§10.5 (Txt. p.629) Segment Lengths in Circles)

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
Refer to key ideas from classes 63-67.

Key Skills
Refer to key skills from classes 63-67.

Handouts
No Handouts Posted

Assignment
Chapter 10 Lesson 5 Practice Set 2 #4-8 (#9 is poorly labeled)
Chapter 10 Review #1-26
Chapter 10 Test #1-17
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.

Tuesday, April 17, 2007

Algebra (Class 69)

Overview
The main question that we address today is: “Could two rules for linear functions ever have the same pairs of values? If yes, how can we find them? If no, why not?”
Textbook Sections
§9-2 Txt. (p.417) The Substitution Method

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
If lines intersect, then they will have a pair of values that are the same.
At a point of intersection, the x and y values for both rules are the same.

Key Skills
Drawing and labeling a coordinate graph.
Plotting points on a coordinate graph.
Determining the coordinates of points on a coordinate graph.
Finding the slope of a line given two points.
Finding the y-intercept using equations.
Operations with integers and positive or negative rational numbers.

Handouts
No Handouts Posted

Assignment
§9-2 (Txt. p.419)#1-6
Practice Work Sheet
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 16, 2007

Geometry (Class 67)

Announcements
Quiz Friday, April 20 focusing on Chapter 10 Lessons 1-5

Overview
In previous lessons we studied how to find the measures of angles and intercepted arcs when lines intersected on a circle. In this lesson we study how to find the measures of angles formed by lines which intersect either outside the circle or inside the circle.
Textbook Sections
§10.4 Other Angle Relationships in Circles

Key Attitudes
Mathematics is about looking for patterns.

Key Ideas
The angle between two secants is half the difference of the intercepted arcs.
The angle between a tangent and a chord drawn from the point of contact (tangency) is half of the intercepted arc.
The angle between a tangent and a secant is half of the difference of the intercepted arcs.
The angle between two chords is half the sum of the intercepted arcs.

Key Skills
Finding the measures of angles created by lines which intersect either inside or outside a circle.

Vocabulary
Factor
Rectangular Prism
Tangent Line
Radius (Radii)
Diameter
Center
Inscribed Angle
Remote interior angles of a triangle
Exterior angle of a triangle
Intercepted arc

Handouts
Chapter 10-Lesson 5: Inside or Outside- Measuring Angles

Assignment
Chapter 10-Lesson 5: Inside or Outside Practice Problems 1-13 on the second to last page.
§10.2 (Txt. p.607) #20-25
§10.3 (Txt. p.617) #11, 14, 17, 41-43
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.

Friday, April 06, 2007

Algebra (Class 68)

Overview
The main question remains-- How can we find an equation for a line, a rule, when we know the coordinates of two points on the line.

We also write Quiz 11 which focuses on graphing and finding the equations of lines.
Textbook Sections
§8-4 (Txt. p.366) The Slope-Intercept form of a Linear Equation

Key Attitudes
Mathematics is about generalizing and applying patterns.

Key Ideas
The slope of a line is the ratio of the change in y-values compared to the change in x-values.
The slope is represented in a linear equation by the coefficient of the x-value.
The y-intercept can be found by substituting a y-value, the corresponding x-value, the slope (coefficient of x) and then solving for the y-intercept.

Key Skills
Drawing and labeling a coordinate graph.
Plotting points on a coordinate graph.
Determining the coordinates of points on a coordinate graph.
Finding the slope of a line given two points.
Finding the y-intercept using equations.
Operations with integers and positive or negative rational numbers.

Handouts
No Handouts Posted

Assignment
Practice Worksheet
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.