HolcombMath

Wednesday, October 18, 2006

Algebra 1 (Class 18)

Overview
§4-7 (p.165) Transforming Formulas
A Visual Approach to Functions: §4
Formulas are key for using math in many different applications, from cooking to chemistry. It is often useful to be able to transform formulas so that they are more helpful in answering the question asked. We focus on learning how to make these transformations and to see that this all rests on our ideas of balance.

Our work with functions resumes today as we write stories to match graphs of distance related to time functions as well as create graphs to match stories.

Key Ideas
A formula is a standard procedure for solving a class of mathematical problems.
Transforming a formula means to use the rule of balance to change the formula into an equivalent form.
The rule of balance can be used to move expressions from one side of an equation to another.
Dividing by zero is never permitted. A formula needs to be “restricted” so that division by zero does not happen.

Graphs can have different sections representing different events.
Labeling the axes of a graph helps communicate what the graph is showing.

Vocabulary
Formula
Transform
Solve for a given variable
Scale
Units
Variable Name
Rate

Assignment
Txt. p.166 #3k| k = 1 to 3
Txt. p.162 #3k-1| k=3 to 6
Txt. p.159 #3k-1| k= 1 to 8
Txt. p.157 #3k-1| k=1 to 3
Txt. p.122 #8

Tuesday, October 17, 2006

Geometry (Class 17)

Overview
§3.6 (p.165) Parallel Lines in the Coordinate Plane
§3.7 (p.172) Perpendicular Lines in the Coordinate Plane
Students review their knowledge of the equations for lines and link this knowledge to the geometry of parallel lines and perpendicular lines. More specifically students:  1) find the slopes of lines and use slope to determine if lines are parallel or perpendicular. 2) write equations of lines which are parallel or perpendicular to a given line. The material in this lesson should largely be review from Algebra 1.

Key Ideas
Parallel lines have equal slopes.
Perpendicular lines have slopes that are opposite reciprocals of each other.
Parallel lines have equal slopes.
Perpendicular lines have slopes that are opposite reciprocals of each other.

Review from Algebra 1:
1) Writing the equation of a line:
a) given the coordinates of two points,
b) given the coordinates of one point and the slope of the line,
c) parallel to a given line through a given point,
d) perpendicular to a given line through a given point.
2) Transforming equations of lines:
a) Writing the equation of a line in standard form when given an equation in slope-y-intercept form
b) Writing the equation of a line in slope-y-intercept form when given an equation in standard form.

Vocabulary
reciprocal
opposite
∆x
∆y
b
y-intercept
slope
standard form
slope, y-intercept form

Assignment
Proofs for Practice #6
§3.4 (Txt. p.153) #30, 33
§3.6 (Txt. p.168) #13, 18, 27, 33, 36, 42
§3.7 (Txt. p.175) #7, 8, 13, 14, 22, 25, 34, 38, 42

Monday, October 16, 2006

Algebra 1 (Class 17)

Overview
§4-4 (p.155) Powers of Monomials
§4-5 (p.158) Multiplying Polynomials by Binomials
§4-6 (p.161) Multiplying Polynomials
We take a break from our work with functions today and spend the additional time focusing on the multiplication of monomials and polynomials. We develop the rules for working with exponents and multiplication and see how multiplication of binomials can be represented by the use of an area model.

Key Ideas
It helps to see expressions in “chunks”—to see x^5 as the same as (2x)^5.
When the bases are the same and you are multiplying, you add the exponents.
Multiplying polynomials can be done by thinking about the areas of rectangles.

Vocabulary
polynomial
monomial
binomial
trinomial

Assignment
Txt. p.162 #3k| k=3 to 6
Txt. p.159 #3k | k= 1 to 8
Txt. p.157 #3k| k=1 to 3
Txt. p.148 #3k-1| k = 5 to 10
Txt. p.127 #8

Sunday, October 15, 2006

Practice for Writing Proofs

Here is a site (Proofs to Practice) that has some nice practice for writing proofs. Give them a try. These are not nearly as nice as what is offered at aleks.com, but it is free.

Saturday, October 14, 2006

Grades Updated

Math grades have been updated to reflect last week’s work. Let Mr. Holcomb know if you see any mistakes.

Friday, October 13, 2006

Geometry (Class 16)

Overview
§3.5 (p.157) Using Properties of Parallel Lines
Quiz 3: §2.6 to 3.2

In §3.4 students construct parallel lines by applying their knowledge of angle relationships and construction skills. In the second part of the class students will show what they know by working Quiz 3. For this quiz they should have one side of an 8 1/2 x 11 sheet of paper with all of the important definitions, postulates, and theorems (hand written only).

Key Ideas
Construct parallel lines using a straightedge and compass.

Vocabulary
No new vocabulary

Assignment
§3.3 (Txt. p.149) #1–5, 8
Proofs for Practice #5
§3.4 (Txt. p.153) #10, 11, 13, 16, 17, 20, 23, 26, 28
§3.5 (Txt. p.160) #8-10, 13, 16, 18, 21, 22, 27

Thursday, October 12, 2006

Algbera 1 (Class 16)

Overview
§4-1 (p.141) Exponents
§4-2 (p.146) Adding and Subtracting Polynomials
A Visual Approach to Functions: §3 and §4
Our work with algebraic symbols focuses on reviewing the meaning of exponents and learning how to add and subtract polynomial expressions.

In our work with functions we continue looking at distance versus time graphs using the coordinates of graphs to help answer questions.

Key Ideas
“If you add them, they’ve got to be the same!”
For terms to be like terms they have to have the same variables raised to the same powers.
An exponent tells you how many times you are multiplying something.
The degree of a monomial is the sum of the powers of its variable.
The degree of a polynomial is equal to the greatest degree of its terms.

Vocabulary
Exponent (Power)
Monomial
Binomial
Trinomial
Polynomial
Terms

Assignment
Txt. p.148 #3k| k = 1 to 10
Txt. p.127 #7
Txt. p.122 #7
Txt. p.118 #9

Wednesday, October 11, 2006

Geometry Quiz Friday

The third quiz for Geometry will be this Friday. The focus for this quiz is writing proofs for statements about segments and angles. Make sure you bring your completed 8 1/2 x 11 sheet of paper with the definitions, postulates, and theorems you think will be useful. See the back of your book (p. 827 - p.829) for a nice list! You might want to include drawings to help you remember.

Geometry (Class 15)

Overview
§3.4 (p.150) Proving Lines Parallel
The central question for today is “How can you prove that two lines are parallel”? A point of confusion for students is to discern between the theorems that we proved in the last class and the converses to those theorems which we will prove during this class. The importance of the hypothesis and conclusion of an conditional statement take on increased importance as we work on making this distinction.

Key Ideas
Using the converses of the parallel lines postulates and theorems to determine if two lines are parallel.

Vocabulary
No new vocabulary.

Assignment
§3.1 (p.132) #40
Proofs for Practice #4
Write Postulates, Definitions, and Theorems for use on Quiz-- one side of 8.5 x 11 paper hand written
§3.2 (p.138) #19, 26, 35, 36
§3.3 (Txt. p.146) #14, 17, 18, 19, 21, 22, 27
§3.4 (Txt. p.153) #14, 15, 28

Tuesday, October 10, 2006

Algebra 1 (Class 15)

Overview
Today we extend our work interpreting graphs that represent situations involving distance and time. In particular we work on Lesson 3: Comparing and Describing Motion from “A Visual Approach to Functions”.

Vocabulary
Axis (pl: Axes)
Origin
Intersect

Key Ideas
Writing descriptions of a situation represented by a graph
Using graphs to infer speed, direction of travel
Developing a deeper understanding of what can not be inferred from a distance and time graph (like the actual location of each person).

Assignment
Txt. p.127 #5, 6
Txt. p.118 Written Exercises #3k-1| k = 6 to 10;
Txt. p.28 #10