HolcombMath

Thursday, December 21, 2006

Algebra (Class 39)

Overview
A Visual Approach to Functions
We continue our work with linear relationships and with our work on improving our ability to solve second degree trinomial equations using ZPP.

Key Attitudes
Mathematics is about reasoning.

Key Ideas
A person’s walking speed (rate) is represented by the slope of the line on a graph of distance compared to time.
A person’s walking rate can be calculated from data in a table of distance versus time.
A linear equation relating distance and time can be written once the persons rate and his starting distance (y-intercept) are known.

Key Skills
Plotting points on a graph.
Filling in a table of values using the rate.

Handouts
Algebra Semester 1 Final Exam Review

Assignment
Chapter Test (Txt. p.242) #3k| k = 1 to 12, and #38

Wednesday, December 20, 2006

Geometry (Class 38)

Overview

Today we conclude our work which focused on the question “How can you determine if it is possible to construct a triangle when you are given three segments?” We also begin working towards answering the question “How can we define ‘parallelogram’?”

Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.

Key Ideas
It is not always possible to construct a triangle from three segments.
In order for a triangle to be constructed from three segments, the sum of the lengths of any two sides must be greater than the length of the third side.
In a triangle, the smallest side is always opposite the smallest angle, and the largest sides is always opposite the largest angle.
A parallelogram can be defined in many ways.

Key Skills
Summarizing
Investigating
Working with a group to develop consensus
Drawing and measuring

Vocabulary
polygon
convex
concave
quadrilateral
parallelogram

Handouts
Properties of Parallelograms
Geometry Semester 1 Final Exam Review

Assignment
Final Exam Review (Due day of Final)
Mid-Segments of a Triangle

Tuesday, December 19, 2006

Algebra (Class 38)

Overview
A Visual Approach to Functions
We continue our work with linear relationships and with our work on improving our ability to solve second degree trinomial equations using ZPP.

Key Attitudes
Mathematics is about reasoning.

Key Ideas
A person’s walking speed (rate) is represented by the slope of the line on a graph of distance compared to time.
A person’s walking rate can be calculated from data in a table of distance versus time.
A linear equation relating distance and time can be written once the persons rate and his starting distance (y-intercept) are known.

Key Skills
Plotting points on a graph.
Filling in a table of values using the rate.

Assignment
Mixed Review (Txt. p.238) #1-9
§5-12 (Txt. p.232) #27-30
§5-11 (Txt. p.228) #19,20

Monday, December 18, 2006

Geometry (Class 37)

Overview
§5.4 (Txt. p.287) Midsegment Theorem
§5.5 (Txt. p.295) Inequalities in One Triangle
Today we focus on constructing triangles. The key question that we need to answer is: “How can you determine if it is possible to construct a triangle when you are given three segments?”
In addition, we examine an interesting property of the midpoints connecting adjacent sides of a trianlge.

Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.

Key Ideas
Determining if it is possible to construct a triangle when given three segments.
How are the angles and sides of a triangle related?

Key Skills
Constructing a triangle given three segments.
Identifying adjacent and opposite sides of a triangle.
Measuring angles using a protractor.
Measuring lengths using a ruler (cm).

Vocabulary
inequality

Assignment
Chapter 5 Review
Final Exam Review (Due day of Final)
The Triangle Inequality
Mid-Segments of a Triangle

Friday, December 15, 2006

Algebra (Class 37)

Overview
A Visual Approach to Functions
During this class we focus on connecting graphs of linear relationships (distance compared to time) to tables and equations. Quiz 7 will be given during the last 30 minutes of class.

Key Attitudes
Mathematics is about reasoning.

Key Ideas
Graphs, equations, and tables tell stories if you know how to read them.
If the rate is constant, then the graph will be a straight line.
If the graph is a straight line, then the equation will be linear.
When writing a linear equation to represent the distance as a function of time, y=mx + b, the “y” represents the distance, the “x” represents the time, the “m” represents the rate, and the “b” represents the y-intercept (or “starting distance”).

Key Skills
Plotting points on a graph.
Matching linear equations to graphs and tables.
Verifying that an equation matches a table and graph by substituting and evaluating expressions.
Creating a table of values from data on a graph.
Creating a graph from a table of values.

Assignment
§5-12 (Txt. p.232) #21-26
§5-11 (Txt. p.228) #16-18
§5-9 (Txt. p.222) #16,17

Thursday, December 14, 2006

Geometry (Class 36)

Overview
§5.3 Medians and Altitudes of a Triangle
In this class we continue our work with the altitudes of triangles using them to calculate area as well as examining the intersection of the altitudes of a triangle.

Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.

Key Ideas
The altitudes of a triangle are concurrent.
The point of concurency of the altitudes of a triangle is called the orthocenter.
Sometimes the orthocenter of a triangle is inside the triangle, sometimes it is on the triangle, and sometimes it is exterior to the triangle.

Key Skills
Constructing a perpendicular line passing through a point not on the line.
Constructing the orthocenter of a triangle.
Plotting points on a coordinate graph.

Vocabulary
Orthocenter

Assignment
Chapter 5 Review Page 2
Lesson 5.3 Practice B #1-10
Balance the Triangle Part 4

Wednesday, December 13, 2006

Algebra (Class 36)

Overview
§5-12 (p.231) Solving Equations by Factoring (Using the Zero Product Property)
A Visual Approach to Functions
Today we begin a more focused study of linear functions. We also continue to improve on our ability to solve polynomial equations by factoring.

Key Attitudes
Mathematics is about reasoning.

Key Ideas
The slope of a graph of distance compared to time can be used to infer the rate, in this case speed, of the object whose data is being graphed.

Key Skills
Labeling a graph properly with then names of the variables, the units in which the variables are being measured, the scale of the axes, and the title of the graph.
Factoring second degree trinomial equations.
Applying the Zero Product Property.
Clearly writing the steps for solving equations.

Assignment
§5-12 (Txt. p.232) #11-20
§5-11 (Txt. p.228) #11-15
§5-9 (Txt. p.222) #14,15

Tuesday, December 12, 2006

Geometry (Class 35)

Overview
§5.3 Medians and Altitudes of a Triangle
Today we learn how to construct the three altitudes of a triangle. We then use our constructions to calculate the areas of various triangles and discover (realize) something surprising.

Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Knowing what to measure and how to measure it makes a complicated world much less so.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.

Key Ideas
An altitude of a triangle is constructed by creating a perpendicular segment connecting a vertex to the side opposite the vertex.
Every triangle has three altitudes.
Sometimes altitudes are inside, sometimes they are outside, and sometimes they are on the triangle.

Key Skills
Constructing a perpendicular line passing through a point not on the line.
Constructing the orthocenter of a triangle.
Plotting points on a coordinate graph.

Vocabulary
altitude of a triangle
line that contains a side

Assignment
Balance a Triangle Part 4: Concurrency of the Medians of a Triangle (will be graded). Due Monday 12/18. This assignment is worth 200 points.  (Extra points if turned in at the start of class Thursday 12/14).
Chapter 5 Review: Part 1, page 1. The whole assignment (pages 1-4) will be worth 300 points.
Quiz 5 Corrections

Monday, December 11, 2006

Algebra 1 (Class 35)

Overview
§5-12 (p.231) Solving Equations by Factoring (Using the Zero Product Property)
In this lesson we begin our study of solving second degree trinomial equations by using factoring and the Zero Product Property (ZPP). As part of this process we define the Standard Form of a Polynomial Equation.

If time permits, we also continue our work with graphs.

Key Ideas
If the product of two numbers is zero, then at least one of the numbers must be zero (the Zero Product Property of ZPP).
Second degree trinomial equations frequently have two solutions.

Key Skills
Factoring second degree trinomial equations.
Applying the Zero Product Property.
Clearly writing the steps for solving equations.

Vocabulary

Assignment
§5-12 (Txt. p.232) #1-10
§5-11 (Txt. p.228) #7-10
§5-9 (Txt. p.222) #11-13

Friday, December 08, 2006

Geometry (Class 34)

Overview
§5.3 Medians and Altitudes of a Triangle
Today student finish and turn in their work relating to the balance point of a triangle. They also take Quiz 5, which focuses on §5.1 to §5.3 (medians only) of the text.

Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.

Key Ideas
The center of mass of an object is the location at which the object will balance.
For some triangles, the center of mass can be located by constructing the circumcenter of the triangle.
For some triangles, the center of mass can be located by constructing the incenter of the triangle.
A median of a triangle is created by connecting a vertex with the midpoint of the opposite side of the triangle.
The medians of a triangle are concurrent and the point of concurrency is called the “centroid”
The centroid of a triangle is the balance point, the center of mass, of the triangle.

Key Skills
Measuring lengths using a ruler (cm).
Drawing and constructing the medians of a triangle.
Drawing and constructing the centroid of a triangle.

Vocabulary

Assignment
Balance the Triangle Part 3 (It will be collected!)

Thursday, December 07, 2006

Algebra 1 (Class 34)

Overview
§5-11 (p.227) Using Several Methods of Factoring
Today we work on making decisions about what type of factoring we are going to perform as we factor many different types of second degree trinomial expressions.

We also continue our work analyzing, interpreting, and making predictions from graphical information.

Key Attitudes
When factoring, persistence is a key. “Try, try, again.”
Writing more often makes the problem easier.

Key Ideas
Anytime you see an equation, check to see if you can factor out common monomials from each term.
Try factoring by inspection (the “box”) first, but if you can not get an answer, then see if making a list of factors of the product of the fist and last terms helps. If the first term is not 1, then factoring by grouping my work.

Key Skills
Identifying the type of factoring to try.
Factoring common monomials from the terms of a polynomial expression.
Factoring second degree trinomial expressions by inspection.
Factoring second degree trinomial expressions by grouping.

Vocabulary

Assignment
§5-11 (Txt. p.228) #1-6
§5-9 (Txt. p.222) #6-10
§5-3 (p.198) #7

Wednesday, December 06, 2006

Geometry (Class 33)

Overview
§5.3 Medians and Altitudes of a Triangle
Today we will investigate the center of mass, the balance point, of a triangle and develop the geometry that can be used to locate the center of mass.

Key Attitudes
Mathematics can be a tool for investigating and uncovering facts.
Investigating requires creativity and persistence.
If you don’t first succeed, try, try again.

Key Ideas
The center of mass of an object is the location at which the object will balance.
For some triangles, the center of mass can be located by constructing the circumcenter of the triangle.
For some triangles, the center of mass can be located by constructing the incenter of the triangle.
A median of a triangle is created by connecting a vertex with the midpoint of the opposite side of the triangle.
The medians of a triangle are concurrent and the point of concurrency is called the “centroid”
The centroid of a triangle is the balance point, the center of mass, of the triangle.

Key Skills
Measuring lengths using a ruler (cm).
Drawing and constructing the medians of a triangle.
Drawing and constructing the centroid of a triangle.

Vocabulary
balance point
center of mass
median of a triangle
centroid

Assignment
Lesson 5.2 Practice C #3-8

Tuesday, December 05, 2006

Algebra 1 (Class 33)

Overview
§5-9 Factoring ax^2+bx+c where a>1
Today we apply our skills of factoring by grouping to factor second degree trinomials which have a coefficient of other than one for the second degree term (ax^2+bx+c where a≠1).

We also further our use of coordinates in the process of interpreting and making predictions about situations involving functions of distance and time.

Key Ideas
Factoring by grouping.
Interpreting coordinates
Writing equations to represent graphs of uniform motion

Key Skills
Factoring ax^2+bx+c where a≠1 into the product of two binomials by using factoring by grouping.

Vocabulary

Assignment
§5-9 (Txt. p.222) #1-5
§5-10 (Txt. p.225) #21-25
§5-3 (p.198) #6

Monday, December 04, 2006

Geometry (Class 32)

Announcements
Geometry Quiz 6 Friday! The quiz will focus on §4.7 to §5.3.

Overview
§5.2 (p.272) Bisectors of a Triangle
Using the concepts and skills that have been developed in the course, students will determine the location which will allow an architect to construct a circular house with the maximum area. We will then investigate the geometric properties of the location of the house and develop a method for its location based on previously learned concepts and skills.

Key Ideas
The angle bisectors of a triangle are concurrent.
A circle can be inscribed in a triangle by using the point of concurrency of the angle bisectors.
The circle with the maximum area that will fit inside a triangle can be constructed by using the point of concurrency of the angle bisectors.

Key Skills
Construct the angle bisectors of a triangle.
Construct the incenter of a triangle (the point equidistant from the sides of a triangle).
Construct the incircle (the circle that is tangent to the three sides) of a triangle.
Use the properties of the angle bisectors of the angles of a triangle to solve problems and write proofs.

Vocabulary
tangent
inscribe
incenter
incircle

Handouts
Building an Addition
Assignment
Practice 5.2 B #1-6, 9-13
Practice 5.2 C #1, 2, 5-7

Friday, December 01, 2006

Algebra 1 (Class 32)

Overview
§5-10 (p.224) Factoring by Grouping Continued

Quiz 6 (§4-6 to §5-10)
Today we continue to develop our skills at factoring by grouping as well as take Quiz 6 covering §4-7 to §5-8 as well as §5-10 (factoring by grouping).

Key Ideas
When factoring by grouping, first group terms so that they have common factors, then factor out the common factor from each of the terms. Next, factor again so that you are left with the product of two binomials.
When the “center term” is combined, multiply the coefficient of the second degree term and the constant, then write a list of factors of this product. Look for factors whose sum is equal to the “center term”. Then factor by grouping.
A “trick” that is sometimes helpful is that -(x-y) = (y-x). And of course (x+y) = (y+x). Switching terms around can sometimes make the factoring easier.

Key Skills
Listing the factors of numbers.
Grouping expressions so that they have common factors.
Identifying the greatest common factor of binomial expressions.
Factoring binomial expressions.
Factoring second degree trinomial expressions where the coefficient of the second degree term is not equal to 1.

Vocabulary

Assignment
Factoring by Grouping Practice Worksheet #1-5 and 11-15
§5-7 (p.215) #15-21