HolcombMath

Friday, September 28, 2007

Algebra (Class 11)

Overview
In today’s class we practice with solving equations by drawing balances and recording our solution process using algebraic notation. In addition we continue our work with input/output tables, graphs, equations, and situations where these ideas arise. In the last part of the block we take Test 2 which focuses on the material from our second unit.
Textbook Sections
§3-5 (Txt. p.116) Equations with the Variable on Both Sides

Vocabulary
capacity
conversion statement
direct variation
length
temperature
time
volume
explicit rule
linear function
variable

Key Attitudes
Math is about investigating and confirming

Key Ideas
A balance can be used to represent and solve algebraic equations.
Groups of objects can be represented on the balance and in equations.
Un-grouping by using the distributive property to expand an equation is a necessary step in solving equations using algebraic notation.
Input/Output tables can be used to represent situations and can be turned into coordinate graphs.

Key Skills
Solving a balance problem involving grouping symbols using both pictures and algebraic notation. (Week 11-SP10-SP12)
Creating Input/Output tables when given a rule.(Week 12: SP3-SP10)
Writing an equation for the Input/Output rule using algebraic notation.(Week 12: SP3-SP10)
Creating graphs from Input/Output tables. (Week 12: SP3-SP10)

Turn-In (#10)
§3-5 (Txt. p.118) #1-24

Handouts
No Handouts Posted

Assignment
§3-3 (Txt. p.110) #25-45
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, September 27, 2007

Geometry (Class 11)

Overview
In today’s class we finish our work with logic puzzles and move on to connect the skills and concepts we learned in the previous two lessons (Missing Angle Puzzles and Logic Puzzles) in order to begin writing two column proofs.
Textbook Sections
§2.6 (Txt. p.109) Proving Statements about Angles

Vocabulary
premise
implication
hypothesis
conclusion
transversal
syllogism
interior angle
exterior angle
alternate interior angles
alternate exterior angles
same side interior angles
consecutive angles

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A proof is a syllogism which uses mathematical facts.
Two columns are used to organize the statements we make and the reasons for why the statements are true.
We can use facts that we have previously established, often written as implications, as reasons in our proofs.
Proofs are final products-- you have to mess about first before you write them.
The more comfortable you are with the geometric facts we have established, the easier writing proofs will be.

Key Skills
Writing two column fill in the blank proofs.

Turn-In (#10)
Txt. p.55 #9-14
Txt. p.101 #35-37, 41-44, 48-50
Txt. p.124 #5, 6, 17, 18, 28, 29

Handouts
Chapter 2-Lesson 3: The Game of Proof

Assignment
Txt. p.93 #30-35, 45-50, 52-54
Txt. p.133 #6-9, 21-26, 41,42
Missing Angle Puzzle 7
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, September 26, 2007

Algebra (Class 10)

Overview
In today’s class we continue to work with solving equations-- drawing and using balances when given equations written in algebraic notation as well as writing equations using algebraic notation when given a drawing of a balance. In both cases we, given a balance or given an equation in algebraic notation, we record our solution process using algebraic notation. A key stumbling block for students is understanding notation for grouping. In addition to this review material, we continue to work with new ideas involving graphs of linear functions.
Textbook Sections
§3-5 (Txt. p.116) Equations with the Variable on Both Sides

Vocabulary
Input/Output rule
Input/Output table
Input/Output graph

Key Attitudes
Math is about investigating and confirming

Key Ideas
A balance can be used to represent and solve algebraic equations.
Groups of objects can be represented on the balance and in equations.
Un-grouping by using the distributive property to expand an equation is a necessary step in solving equations using algebraic notation.
Input/Output tables can be used to represent situations and can be turned into coordinate graphs.

Key Skills
Solving a balance problem involving grouping symbols using both pictures and algebraic notation. (Week 11-SP10-SP12)
Creating Input/Output tables when given a rule.
Writing an equation for the Input/Output rule using algebraic notation.
Creating graphs from Input/Output tables.

Turn-In (#9)
§3-3 (Txt. p.109) #1-24
§3-4 (Txt. p113) #1-3

Handouts
No Handouts Posted

Assignment
§3-5 (Txt. p.118) #1-24
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, September 25, 2007

Geometry (Class 10)

Overview
In today’s class we develop our ability to solve logic puzzles by using symbols that clarify the underlying structure of the problem. Specifically we use symbols for representing implications, and then link those implications to create syllogisms resulting in a clear conclusion to a puzzle.
Textbook Sections
§2.3 (txt. p.87) Deductive Reasoning

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
A syllogism is a method for linking together implications

Key Skills
Solving missing angle puzzles.
Writing steps to represent the solution path for solving the missing angle puzzle.

Turn-In (#9)
Txt. p.47 #8-32, 45, 46, 49, 50, 53, 54, 56-58.

Handouts
Chapter 2- Lesson 2: Logic Puzzles and Syllogisms

Assignment
Missing angle puzzle #6
Txt. p.55 #9-14
Txt. p.101 #35-37, 41-44, 48-50
Txt. p.124 #5, 6, 17, 18, 28, 29
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, September 24, 2007

Algebra (Class 9)

&tOverview
In today’s class we practice writing and solving equations involving grouping symbols. We focus on understanding what the grouping symbols represent and how an equivalent expression can be written without the grouping symbols.
Textbook Sections
§3-3 (Txt. p.107) Using Several Transformations

Key Attitudes
Math is about investigating and confirming

Key Ideas
A number in front of grouping symbols tells you how many of the group you have.
An expression with grouping symbols should be written as an equivalent expression without grouping symbols in order to solve the equation.

Key Skills
Solving a balance problem involving grouping symbols using both pictures and algebraic notation. (Week 11-SP10-SP12)

Turn-In (#8)
Packet-- Unit 3: Week 11 AND Txt. p.97 #25-36
Txt. p.98 “Problems” #4-6

Handouts
No Handouts Posted

Assignment
§3-3 (Txt. p.109) #1-24
§3-4 (Txt. p113) #1-3
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, September 21, 2007

Geometry (Class 9)

Overview
In today’s class we continue our work with missing angle puzzles, working towards writing steps for the solution process as well as justifying the steps with reasons. In addition, we take our first test which covers the materials from the first 8 classes (Chapter 1).
Textbook Sections
§1.6 (Txt. p.44) Angle Pair Relationships

Vocabulary
linear pair
vertical pair (vertical angles)
interior angles of a triangle
congruent angles
parallelogram
trapezoid
polygon
opposite angles

Key Attitudes
Math is about reasoning and justifying.

Key Ideas
You can use “If, then” reasoning to build up a solution to math problems.

Key Skills
Solving missing angle puzzles.
Writing steps to represent the solution path for solving the missing angle puzzle.

Turn-In (#8)
Chapter Test- Txt. p.63 #1-20

Handouts
No Handouts Posted

Assignment
Finish as many Missing Angle Puzzles as possible (eventually you will have to do them all).
Txt. p.47 #8-32, 45, 46, 49, 50, 53, 54, 56-58
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, September 20, 2007

Algebra (Class 8)

Overview
In today’s class we continue the development of our ability for writing and solving equations. We continue to represent the solution process with both balance scales and algebraic notation. A key element is working with groups of expressions in an equation. For example, 2(x-3)=4(2x+1).
Textbook Sections
§3-1 (Txt. p.95) transforming Equations: Addition and Subtraction
§3-2 (Txt. p.102) Transforming Equations: Multiplication and Division

Vocabulary
grouping symbols
distributive property

Key Attitudes
Math is about investigating and confirming

Key Ideas
Reading and using grouping symbols

Key Skills
Solving a balance problem involving grouping symbols using both pictures and algebraic notation. (Week 11-SP10-SP12)

Turn-In (#7)
Txt. p.97 #16-24
Txt. p98 “Problems” #1-3
Skill Builder 1A, 1B
Test Corrections

Handouts
No Handouts Posted

Assignment
Skill Builder 2, 3
Txt. p.97 #25-36
Txt. p.98 “Problems” #4-6
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, September 19, 2007

Back to School Night

Please use the links below to view the materials that were presented during Back to School Night.
Class Information and Frequently Asked Questions
Assignment Scoring Guide

Wish List-- if you can donate, we need
Kleenex
AAA batteries
Boxes of copy paper
Pencils
Your time-- if you are math inclined come tutor in the afternoons.

Geometry (Class 8)

Overview
In today’s class we finish our work with Chapter 1 and being moving towards writing proof. In order to build up our skills before we have to write proofs we by solving puzzles involving missing angles. In addition we practice the four constructions (copy a segment, perpendicular bisector of a segment, bisect an angle, copy an angle) which we learned in the last class. REMINDER-- test for Chapter 1 next class (Friday).
Textbook Sections
§1.6 (Txt. p.44) Angle Pair Relationships

Vocabulary
linear pair
vertical pair (vertical angles)

Key Attitudes
Math is about investigating.

Key Ideas
You can find a solution to problems step by step.

Key Skills
Solving missing angle puzzles.
Writing steps to represent the solution path for solving the missing angle puzzle.

Turn-In (#7)
Chapter 1- Lesson 3

Handouts
Chapter 2- Lesson 1: Missing Angle Puzzles

Assignment
Chapter 2- Lesson 1 Puzzle 4 & Puzzle 5
Chapter Test- Txt. p.63 #1-20
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, September 18, 2007

Algebra (Class 7)

Overview
In today’s class we continue building our skills at solving equations by working with diagrams of balances as well as writing the algebraic steps and written descriptions of the solution process.
Textbook Sections
§3-1 (Txt. p.95) transforming Equations: Addition and Subtraction
§3-2 (Txt. p.102) Transforming Equations: Multiplication and Division

Key Attitudes
Math is about investigating and confirming

Key Ideas
An equation is a balance.
Process used to solve a balance problem can be represented using algebraic symbols.

Key Skills
Solving a balance problem while using algebra to record the process. (Week 11-SP6-SP8)

Turn-In (#6)
§3-1 (Txt. p.97) #1-3 with pictures and algebra, #4-15 with just algebra
§3-2 (Txt. p.104) #1-4 with pictures and algebra (use “balloons” for negatives), #5-12 with just algebra

Handouts
No Handouts Posted

Assignment
Txt. p.97 #16-24
Txt. p98 “Problems” #1-3
Skill Builder 1A, 1B
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, September 17, 2007

Geometry (Class 7)

Overview
In today’s class we wrap-up Chapter 1- Lesson 3 with the development of a way to find the coordinates of the midpoint of a segment when given the coordinates of the endpoints of the segment. We also get to learn how to use a straight edge and compass to copy a segment, create a perpendicular bisector of a segment, bisect an angle, copy an angle, and divide a line segment into as many equal pieces as needed.
Check out the Math Open Reference for animated lessons on constructions with straight edge and compass.
Textbook Sections
§1.5 (Txt. p.34) Segment and Angle Bisectors

Key Attitudes
Math is about investigating.

Key Ideas
The coordinates of the midpoint of a segment can be found by averaging the change in x and the change in y of the coordinates of its endpoints.
A straightedge and compass can be used to solve geometric problems.

Key Skills
Find the midpoint of segment given the coordinates of the endpoints of the segment.
Use a straight edge and compass to:
copy a segment
create a perpendicular bisector of a segment
bisect an angle
copy an angle
create n equal divisions of a segment

Turn-In (#6)
Chapter 1- Lesson 3 through #12
Txt. p.29 #17-41, 61, 64, 67, 70-75

Handouts
No Handouts Posted

Assignment
Txt. p.38 #17-20, 25, 26, 31, 32, 37-39
Finish construction worksheets.
Txt. p124 #1-4, 13-16
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, September 14, 2007

Algebra (Class 6)

Overview
In today’s class we continue learning how to solve equations by thinking about balances. In particular we develop our skills for using algebraic symbols to represent the solution process for solving balance puzzles.

A great resource for thinking about solving equations as a balance can be found at http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html?open=instructions
Textbook Sections
§3-1 (Txt. p.95) transforming Equations: Addition and Subtraction
§3-2 (Txt. p.102) Transforming Equations: Multiplication and Division

Key Attitudes
Math is about investigating and confirming

Key Ideas
Process used to solve a balance problem can be represented using algebraic symbols.

Key Skills
Solving a balance problem while using algebra to record the process. (Week 11-SP6-SP8)

Turn-In (#5)
§1-4 (Txt. p.16) #1-28
§1-3 (Txt. p.8) #31, 32

Handouts
No Handouts Posted

Assignment
§3-1 (Txt. p.97) #1-3 with pictures and algebra, #4-15 with just algebra
§3-2 (Txt. p.104) #1-4 with pictures and algebra (use “balloons” for negatives), #5-12 with just algebra
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, September 13, 2007

Geometry (Class 6)

Overview
In today’s class we will review how to simplify a square root as well as begin a new section which focuses on the measurement of angles. We also learn how we can use the coordinates of a line segment to find the midpoint of the segment.
Textbook Sections
§1.4 (Txt. p.26) Angles and their Measures
§1.5 (Txt. p.34) Segment and Angle Bisectors

Vocabulary
vertex
acute angle
obtuse angle
right angle
straight angle
adjacent angles
complementary angles
supplementary angles
interior of an angle
exterior of an angle
midpoint of a segment

Key Attitudes
Math is about investigating.

Key Ideas
Angles can be classified by their measure

Key Skills
Name an angle using both three letter and one letter notation.
Classify an angle by its measure.
Draw angles given specification.
Writing and solving equations related to angle measures.

Turn-In (#5)
Chapter 1- Lesson 2 Packet with Text pages

Handouts
Chapter 1- Lesson 3: Angles and their Measures
Simplify Square Roots

Assignment
Chapter 1- Lesson 3 through #12
Txt. p.29 #17-41, 61, 64, 67, 70-75
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, September 12, 2007

Algebra (Class 5)

&tOverview
In today’s class we check to see how students doing on the material we have studied so far. In addition we begin our next section of material which focuses on the solving of equations-- first degree single-variable.

There is a nice interactive version of solving equations as a balance at http://nlvm.usu.edu/en/nav/frames_asid_324_g_3_t_2.html?open=instructions
Textbook Sections
§1-4 (Txt. p.14) Translating Words into Symbols
§3-1 (Txt. p.95) Transforming Equations: Addition and Subtraction

Vocabulary
balance scale
beam balance
equal sign
equation
expression
simplify an expression
solve an equation
distributive property
zero pairs

Key Attitudes
Math is about investigating and confirming

Key Ideas;/b>
The meaning of an equal sign.
An equation can be represented by a balance scale.
The law of balance-- in order to keep a balance, what you do to one side of the balance, you have to do to the other side of the balance