HolcombMath

Tuesday, October 31, 2006

Geometry (Class 22)

Announcements
GEOMETRY MID-TERM Date Changed! Now on Friday November 17
Bring protractor and compass for next class!

Overview
Practice Proving Triangles Congruent
Today we spend time in class practicing our skill of proving triangles congruent. In addition we develop and explanation for why their is not an SSA congruence postulate.

Key Ideas
Identifying included and non-included sides and angles-- “included” can be thought of as meaning “between”
Determining if it is possible to prove two triangles congruent based on the given information. You always need at least three pairs of congruent angles or sides!
Identifying which congruence postulate is best for a given situation: SSS, SAS, ASA, AAS.
Proving two triangles congruent and writing congruence statements.
Points on the circumference of a circle are equidistant from the center of the circle.
How to use a Venn diagram to help identify similarities and differences when making a comparison.

Vocabulary
Compare
Venn Diagram

Assignment
Lesson 4.3 Practice B Handout (p.46) #12, 13
Lesson 4.4 Pracrtice B Handout (p.60) #10, 11

Chapter 1 Test (Txt. p.63) 5 most important problems-- you pick them! 

Monday, October 30, 2006

Geometry Midterm Date Changed

Friday Novemeber 10 is a Holiday (Yipee!). So we will have the Midterm the following Friday (11/17/2006).

Algebra 1 (Class 22)

Overview
§4-10 (p.175) Problems without Solution
A Visual Approach to Functions: §4 and §5

Not all problems have solutions! Some reasons for this are: 1) not enough information given, 2) the given facts lead to an unrealistic result (the result satisfies the equation used but not the conditions of the problem situation), 3) the given facts are contradictory (they cannot be used at the same time). Today we need to examine problems in order to determine if they are solvable. If they are, then we will solve them. If not, we will explain why.

Using a table to organize data, students create a graphs and write an equation for a distance versus time function.

Key Ideas
Not all problems have solutions.
Answers need to be reasonable based on the situation.
Sometimes there is not enough information given in order to answer a problem.
If there is no solution to a problem, you need to state “No solution is possible” and justify this statement. (Use the “Justify” card.)

Vocabulary
Independent Variable
Dependent Variable

Assignment
§4-10 (Txt. p.175) #1, 2
§4-9 (Txt. p.173) #3, 4
§4-8 (Txt. p.169) #12
§4-7 (Txt. p.166) #3k-1| k = 4 to 6

Sunday, October 29, 2006

Grades Updated

Grades have been updated.

Friday, October 27, 2006

Geometry Midterm Points

After looking over the number of points possible in the content category, it seems that the midterm should be worth 200 points rather than 400 points-- on from another perspective, the midterm should be equivallent to 2 quiz grades rather than 4. The final exam will most likely be worth more than this (roughly 10% of the semester grade). You will have the whole class period to work the midterm and the final exams.

Geometry (Class 21)

Overview
Practice Proving Triangles Congruent
Quiz 4: §3.5 to §4.4
We continue to develop our skills at proving triangles congruent spending the first part of the class working as many proofs for proving triangles congruent as possible (§4.4 Practice worksheets B and C)

We also take Quiz 4 which focuses on §3.5 to §4.4. Make sure to review older material as well!

Key Ideas
When proving triangles congruent, first identify the congruence postulate that fits the situation.
When writing the proof, write an “S” or and “A” to the left of the statement where you establish that two sides are congruent (S) or two angles are congruent (A).
The last step of proofs proving triangles congruent will always be a congruence statement and the reason will be one of the congruence postulates (SSS, SAS, AAS, ASA).
Be careful to identify if angles or sides are include or non-included!
When writing congruence statements, match the anlges!

Vocabulary

Assignment
Proofs for Practice #10
§4.4 (Txt. p.223) #31
Chapter 4 Quiz 2 (Txt. p.227) #1-7
Solving Systems of Equations Practice (Txt. p.796) #2, 8
Chapter 1 Review (Txt. p.60) 5 most important problems-- you pick them!

Thursday, October 26, 2006

Algebra 1 (Class 21)

Overview
§4-9 (p.172) Area Problems
A Visual Approach to Functions: §4 and §5
We turn our attention away from uniform motion problems and focus on another typical problem type: Area Problems. We develop our abilities of making clearly labeled diagrams as aides in solving these problems.

Using a table to organize data, students create a graphs and write an equation for a distance versus time function.

Key Ideas
Making a drawing is critical for solving these types of problems.
The area of a rectangle is equal to the length multiplied by the width.
To find the area of a “picutre frame” find the area of the “big rectangle” and subtract the area of the “small rectangle”

Vocabulary
Area

Assignment
Txt. p.173 #1, 2
Txt. p.169 #11
Txt. p.166 #3k| k = 4 to 6

Wednesday, October 25, 2006

Geometry Quiz 4

Geometry Quiz 4 is Friday! The focus of the quiz will be §3.5 to §4.4. You may use one side of an 8 1/2 x 11 sheet of paper for notes (hand written) containing ONLY definitions, postulates, and theorems.

Geometry (Class 20)

Overview
§4.4 (p.220) Proving Triangles Congruent using ASA and AAS.
We continue our work proving triangles congruent. We add two new congruence postulates to the one we have already developed. If time permits we also examine why SSA is not a congruence postulate.

Key Ideas
To prove triangles congruent you need three pieces of information.
When writing proofs for congruent triangles, first decide which congruence postulate you are going to use, then work your proof to establish congruence of each pair of angles or sides.
It is helpful to identify where in the proof you have established each of the pieces by writing “S”, or “A”, to the left of the statement.

Vocabulary
non-included side
non-included angle

Assignment
Proofs for Practice #9
§4.4 (Txt. p.223) #8-10, 19, 20
§4.3 (Txt. p.216) #23, 24
Solving Systems of Equations Practice (Txt. p.796) #3, 9

Tuesday, October 24, 2006

Algebra 1 (Class 20)

Overview
§4-8 (p.167) Uniform Motion Problems
A Visual Approach to Functions: §4 and §5
We continue our work with uniform motion problems, working in groups to practice and further develop our skills.

Our work with functions focuses on bringing together equations, graphs, and tables to understand and describe distance and time functions.

Key Ideas
Making a diagram helps you understand uniform motion problems.
A table helps you set-up an equation for uniform motion.

Graphs can have different sections.
Uniform motion is represented by a straight line.
The rate for a uniform motion graph can be determined from the coordinates of points on the line.
The points where the line crosses the axes for a uniform motion graph can tell you important information.

Vocabulary
x-intercept
y-intercept

Assignment
Txt. p.169 #4-10
Txt. p.166 #3k-2| k = 1 to 3
Txt. p.162 #3k| k=7 to 10

Monday, October 23, 2006

Geometry (Class 19)

Overview
§4.3 (p.212) Proving Triangles are Congruent using SSS and SAS.
Today we focus on the question “What information do we really need in order to know that two triangles are congruent?” In Investigation 4.3 (p.211) students explore the concept of SSS and SAS by using pencils to see if they can make two triangles NOT congruent when their sides are the same length or when two sides and the angle inbetween the sides are congruent. This work leads us to develop four fundamental approaches for proving triangles congruent.

Key Ideas
Two triangles can be inferred to be congruent using a minimum amount of information.

Vocabulary

Assignment
Proofs for Practice #8
§4.2 (Txt. p.206) #17, 18, 25-28, 35
§4.3 (Txt. p.216) #3-5, 13, 14, 16, 20, 22

Sunday, October 22, 2006

Math Grades Updated

Grades from the past week, including the quiz for Algebra, have been updated. Please let me know if you see any mistakes.

Friday, October 20, 2006

Algebra 1 (Class 19)

Overview
§4-8 (p.167) Uniform Motion

We turn our focus to solving problems related to uniform motion. We see that using the formula Distance = Rate x Time in conjunction with making a table to organize the given information can greatly aide in finding the solution.

We also take Quiz 4 today which focus on §3-1 to §4-7.

Key Ideas
Distance = Rate x Time
Using a table to organize and help solve uniform motion problems.
A key question to ask yourself when solving the problems is “How long has ___ been traveling”. Your answer will be the “time” for the problem.
Be careful of units! All units need to match in the table. If they give you miles/hour, then the time needs to be in hours (not minutes) and the distance needs to be in miles. Remember there are 60 minutes in an hour!
Uniform motion implies the rate is constant and that a graph of distance as a function of time would be a straight line.
Drawing a diagram, and labeling it with the information from the problem, is an important step in solving uniform motion problems.

Vocabulary
uniform motion
overtake

Assignment
Txt. p.169 #1-3
Txt. p.166 #3k-1| k = 1 to 3
Txt. p.162 #3k-2| k=3 to 6
Txt. p.159 #3k-2| k= 1 to 8

Thursday, October 19, 2006

Geometry (Class 18)

Overview
§4.1 (p.194) Triangles and Angles
§4.2 (p.202) Congruence and Triangles
Today we begin our study of triangles by reviewing how to classify triangles by length of sides or size of angles. We also learn what it means for two triangles to be congruent and how to write a congruence statement for two congruent triangles.

Key Ideas
Triangles can be classified by the length of their sides or by the size of their angles.
A triangles “full name” is created by stating its classification by angles and sides. For example, the full name of a triangle which has two equal sides and all angles less than 90˚ would be “isosceles acute triangle”.
A congruence statement for two triangles is written by matching the congruent angles of the triangles.
A congruent statement can be used to determine which angles are congruent and which sides are congruent.
Congruent triangles have reflexive, symmetric, and transitive properties.
Two triangles are congruent only if they are the same size and same shape. As a consequence we can say that two triangles are congruent if and only if each angle in one triangle is congruent to at least one angle in another triangle and each side of one triangle is congruent to at least one side of the other triangle.

Vocabulary
Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Acute Triangle
Equiangular Triangle
Right Triangle
Obtuse Triangle
Hypotenuse
Leg
Adjacent side
Opposite side
Congruence Statement

Assignment
§4.1 (Txt. p.198) #10-12, 16-18, 32, 34, 37, 41, 47, 56
§4.2 (Txt. p.206) #10-16, 24
Proof for Practice 7
Group Assignment 1

Wednesday, October 18, 2006

Geometry Mid-Term Date Set

The mid-term for Geometry, covering §1-1 to §4-7 of the textbook, will be given on Friday, November 10. Start to study now! A good place to begin is by reworking past quizzes. Then work problems from your assignments that you had trouble with (look for green pen). Then start working the Chapter Reviews and Chapter Tests in the book. With good planning, and follow-through, you should do well on the exam.