HolcombMath

Wednesday, November 08, 2006

Geometry (Class 25)

Overview
§4.6 (p.236) Isosceles, Equilateral, and Right Triangles
We continue our work with equilateral and right triangles. If time permits we begin to develop our ability to use algebra to help us prove conjectures about triangles.

Key Ideas
Base angles of isosceles triangles are congruent.
If a triangle is equilateral, then it is also equiangular.

Vocabulary
No new vocabulary

Assignment
§4.6 (Txt. p.239) #10, 13-15, 18, 21, 23-25, 33

Chapter 3 Test (Txt. p.183) 10 most important problems-- you pick them!

Tuesday, November 07, 2006

Algebra 1 (Class 25)

Announcements
There will not be a quiz this week.

Overview
§5-3 (p.194) Monomial Factors of Polynomials
A Visual Approach to Functions: §5 and §6

We extend our work with factoring so that we can use it to divide polynomials by monomials. We see how dividing polynomials by monomials is actually an extension of the distributive property of multiplication over addition.

In the remaining time we continue our work with graphs and using coordinates to help interpret the information presented on the graph.

Key Ideas
(a+b)/c = a/b + b/c
To divide a polynomial by a monomial, divide each term of the polynomial by the monomial and add the results.
If the greatest common factor of the numerator and denominator of a fraction is 1 (if the numerator and denominator are relatively prime), then the fraction can not be simplified further.
Examples for this topic can be found at http://www.regentsprep.org/regents/math/algebra/AV4/Ldiv.htm
A tutorial on this topic can be found at http://www.ltcconline.net/greenl/courses/152a/polyExp/polydiv.htm

Vocabulary
monomial
polynomial
GCF
relatively prime
coordinates
independent variable
dependent variable

Assignment
§5-3 (Txt. p.196) #3k| k= 1 to 6 and 11 to 13
§5-2 (Txt. p.192)#3k-1| k=1 to 5
§4-7 (Txt. p.166) #3k| k = 7 to 9

Monday, November 06, 2006

Geometry (Class 24)

Announcements
Assignment has changed from the assignment sheet!
Students need construction tools for this lesson.

Overview
§4.6 (p.236) Isosceles, Equilateral, and Right Triangles
Isosceles, equilateral, and right triangles have special properties that help when trying to draw conclusions about figures. In today’s lesson we investigate these special properties and see how to make them work for us.

Key Ideas
Base angles of isosceles triangles are congruent.
If a triangle is equilateral, then it is also equiangular.

Vocabulary
isosceles triangle
base angle
vertex angle
leg
equilateral triangle
equiangular triangle
right triangle
corollary

Assignment
Proofs for Practice #12
§4.6 (Txt. p.239) #8, 9, 11, 12, 17, 20, 26*, 45, 48, 54

Chapter 3 Review (Txt. p.180) 5 most important problems-- you pick them!

Friday, November 03, 2006

Algebra 1 (Class 24)

Overview
§5-2 (p.189) Dividing Monomials
Quiz 5

Factoring and dividing are closely related skills. Today we explicitly link these skills in order to develop our ability for dividing monomials. We also discuss how to determine if two numbers are relatively prime and see how this connects to dividing monomials.

In the last 50 minutes of the class we take Quiz 5.

Key Ideas
You can simplify an algebraic fraction by simplifying each monomial.
You can find the GCF of two or more monomials by using a Venn Diagram.
To divide two monomials, rewrite the division so that you get a fraction (Ex: 4÷2 = 4/2) and then simplify (4/2 = 2 so 4÷2 = 2).

Vocabulary

Assignment
§5-2 (Txt. p.192)#3k| k=1 to 5
§5-1 (Txt. p.186) #3k-1| k=5 to 10
§4-10 (Txt. p.175) #4
§4-9 (Txt. p.173) #6

Thursday, November 02, 2006

Word Problems Causing You Grief?

If word problems are causing you grief, check out Ms. Lindquist! “She” is a computerized math tutor focused on helping students learn how to solve word problems. Let Mr. Holcomb know if it helped! There is a possibility for having your work count in your grade. Ask Mr. H for details.

Geometry (Class 23)

Overview
§4.5 (p.229) Using Congruent Triangles
Today we examine how to use what we have learned about proving triangles congruent to help us reach conclusions about congruent figures. Students will need their contruction tools during the lesson.

Key Ideas
If two triangles are congruent, then the corresponding parts of the triangles are congruent.
All figures can at least be approximated by “breaking them up” into triangles.
When using congruent triangles as a tool for proving other theorems, first prove the triangles are congruent using one of our congruence postulates (SSS, SAS, ASA, AAS), then use the fact the definition of congruence: “If two triangles are congruent, then the corresponding (matching) parts of the triangles are congruent”.

Vocabulary
No new vocabulary

Assignment
Proofs for Practice #11
§4.5 (Txt. p.232) #8, 9, 14, 15, 23, 25-27, 34-36

Chapter 2 Review (Txt. p.118) 5 most important problems-- you pick them!
Chapter 2 Test (Txt. p.118) 5 most important problems-- you pick them!

Wednesday, November 01, 2006

Algebra 1 (Class 23)

Overview
§5-1 (p.185) Factoring Integers
Today we review factoring integers. In particular we will express numbers as the product of primes, find the least common multiple of two numbers, and find the greatest common factor of two numbers. We will also see how a Venn diagram can help us to find the LCM and GCF of pairs of numbers.

Key Ideas
A “factor tree” is an efficient tool for finding the prime factorization of a number.
A Venn diagram and the prime factorization of two numbers can help you find the LCM or GCF of the the two numbers.

Vocabulary
factor
factor pair
factorization
prime number
prime factorization
factor tree
LCM
GCF
Venn diagram

Assignment
§5-1 (Txt. p.186) #3k| k=1 to 15
§4-10 (Txt. p.175) #3
§4-9 (Txt. p.173) #5
§4-7 (Txt. p.166) #3k-2| k = 4 to 6