Unit 1 Test

Student	Tests
3001655	0
2098663	30
2609284	34
2145922	42
2047789	0
2145033	24
2129962	37
2059830	0
2148735	30
2104570	8
4110529	68
2147135	0
3020608	0
2062743	62
2634044	49
2098479	76
2080104	5
2098755	60
2107638	77
2109400	24
2099908	54
2097446	32
2048692	14
2062723	0
2147925	42

2949017	80
2131265	30
2097335	17
3088191	69
2161658	52
2152568	0
2125061	66
2099881	60
2100711	30
2099369	54
2119410	0
2079774	6
2639060	0
4112163	13
2145140	6
2148999	45
2097798	36
2099492	0
2603422	0
2060166	69
2145861	77
2123998	44
3054945	76
3023119	0
2200900	28

2079769	86
2166873	8
2124951	36
2107664	16
2079767	44
4004840	24
2102778	36
2162292	66
2087668	0
2095139	44
2146488	64
4003388	0
2003760	25
2148990	80
2101968	0
2118585	6
2092574	6
2037381	0
2950298	0
2099623	0
2195439	20

2053580	65
4025819	--
3028771	33
2601020	7
2147660	36
4028617	12
2144625	--
2653152	27
2080975	12
2097538	68
2095858	30
2148948	42
2125902	36
2247087	6
2136531	30
2112601	6
2129609	12

13. Unit 1 Review

13.  UNIT 1 REVIEW
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LO:  I will review the concepts I learned about conjectures, angle relationships, logic and conditional statements.
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Handout is as follows:

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DOL:
I will have completed at least two problems from each category.

11. Informal Proofs

For 9/12 Class:

11.  INFORMAL PROOFS
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LO:  SWBAT will apply and use deductive reasoning, postulates and properties to prove mathematical statements.
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We will mostly work on the handout which we will add to your notebook.

12. Formal Proofs

For 9/12/13 class day:

12.  FORMAL PROOF
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LO:  SWBAT apply and use deductive reasoning, postulates and properties to prove geometrical statements using formal proofs
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Today is about proofs using geometric concepts.  We will be looking at several examples and then it's your turn. 

 Here are two examples:

Now it's your turn.  Try to fill in the blanks in these two proofs.
If  you do not finish in class, this becomes homework.

10. Algebraic Proofs

10.  ALGEBRAIC PROOFS

LO:  SWBAT will apply and use deductive reasoning to justify and prove mathematical statements

 Today is all about proving algebraic equations.

 

9. Law of Detachment and Syllogism

9.  Law of Detachment and Syllogism

LO:  SWBAT use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false

Venn Diagram

Can be used to represent a conditional statement

 

 

 

  

No Homework.

 

8. Conditional Statements

For September 9th class

8.  CONDITIONAL STATEMENTS
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LO:  SWBAT will determine the validity of a conditional statement, its converse, inverse
and contrapositive.
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(Textbook Chapter 2-3, starting from page 91)


1. Conditional Statements
To change a statement to an If-Then statement is to make a conditional statement.  

Let's look at the statement:  "Rain means it's cloudy."
Changing this to a conditional means identifying the hypothesis and conclusion then adding the if-then words to it like this:
 

The "if" is always followed by the hypothesis and the "then" is always followed by the conclusion.

Now you try.  Rewrite these advertisements into If-Then forms:

2.  Converse, Inverse, and Contrapositive
Other statements based on the conditional statements are Converse, Inverse and Contrapositive.  They are formed by exchanging and negating the hypothesis and conclusion of the conditional statements in various ways.

Notice that the symbols for the Conditional Statement reads as "p to q".

Now you try: using the same conditionals from the advertisements from section 1 above, write each one's converse, inverse and contrapositive.

3.  Counterexample
A Counterexample is a true example to prove a statement false.

For example:
Statement:  "If it has four right angles, then it's a square"
This is a false statement.  We then give the counterexample:  A rectangle.

The counterexample proves that the statement was false.

Now you try:  for each false statement from #2 above, provide a counterexample.

4.  Biconditional Statements

A conjunction of two statements where both the conditional and its converse are true is called biconditional. 

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Homework
Page 94, questions 1-10

7. Logical Reasoning

7. LOGICAL REASONING
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LO:  SWBAT use logical reasoning to prove statements are true and find counterexamples to disprove statements that are false.
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Before we start, let's look at the format we will be using:

• Lower case letters will be used to name a statement.

 1. NEGATION

Negation is changing the truth value of a statement to its opposite value.  We designate the negated value with the symbol "~".

Example Statement:

p:  Austin is the capital city of Texas.    The truth value of this statement is True.  

~p:  Austin is NOT the capital city of Texas.  The truth value is now False.

Again, the ~p statement is the negated statement.

2. CONJUNCTION

A conjunction is a compound statement formed by joining two or more statements with the word and.  We then use the statements to write a compound statement.  (Compound just means mixing two things together in one). 

p:  Parallel lines have the same slopes

q:  Vertical angles are congruent

r:  The expression -5x + 11x simplifies to -6x

To write the compound statement, we use the symbol ∧.

So now we write our compound statements:

• p∧q (read as "p and q"):  Parallel lines have the same slope and vertical angles are congruent.
• ~p ∧ ~q (read as "not p and not q"):  Parallel lines DOES NOT have the same slope and vertical lines are NOT congruent.
• ~q ∧ r (read as "not q and r"):  Vertical angles are NOT congruent and the expression -5x + 11x simplifies to -6x.

3. DISJUNCTION

A disjunction is a compound statement formed by joining two or more statements with the word or.  We then use the the statements to write a compound statement.

Let's use the same statements from above

p:  Parallel lines have the same slopes

q:  Vertical angles are congruent

r:  The expression -5x + 11x simplifies to -6x

To write the compound statement, we use the symbol ∧.

So now we write our compound statements:

So now we write our compound statements:

• p∧q (read as "p and q"):  Parallel lines have the same slope or vertical angles are congruent.
• ~p ∧ ~q (read as "not p and not q"):  Parallel lines DOES NOT have the same slope or vertical lines are NOT congruent.
• ~q ∧ r (read as "not q and r"):  Vertical angles are NOT congruent or the expression -5x + 11x simplifies to -6x.

Note that the statements are identical except they are now joined by the word "OR" instead of "AND".

4.  TRUTH TABLES

We will fill in this table in class and discuss it.

5.  VENN Diagrams

We will examine the Venn Diagram and interpret data from it.

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Class Activity:

Handouts will be provided in class. 

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Homework:

P.87, questions 1 to 9.  The book is as below:

6. Homework

6. Construction Explorations

6.  CONSTRUCTION EXPLORATIONS
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LO:  SWBAT explore the attributes of segments, perpendiculars, angles and bisectors.
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These are the relationships we will use today to explore the attributes of our constructions.

Acute Angle

Right Angle

Obtuse Angle

Reflex Angle

Supplementary Angles

Complementary Angles

Linear Pairs

Midpoint

Congruent angles

Vertical angles

Adjacent angles

Perpendicular lines

Segment Addition Postulate

Angle Addition Postulate





Homework:
Page 28, question 50
Page 36, questions 9 to 36, every 3rd question  (9, 12, 15, 18, 21, 24, 27, 30, 33, 36)

5. Constructing angles and angle bisectors

Hello Class!  Please make sure you put down the following notes for class on 9/4/13.  Again, note that these go on the right side of your notebook.


5.  CONSTRUCTING ANGLES AND ANGLE BISECTORS
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LO:  SWBAT use constructions to explore the attributes of angles and angle bisectors.
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1. Constructing a copy of an angle
Please watch the following:  www.youtube.com/watch?v=cQ6v9muH2G8

Please write, in your own words, the steps to do this.


2.  Constructing an angle bisector
Please watch the following video:  www.youtube.com/watch?v=xFx6uHj16jE
Here is another version:  www.teachertube.com/viewVideo.php?video_id=228878

Write, in your own words, the steps to do this.

4. Constructing Perpendiculars Through a Point

For Tuesday, 9/3/13, our topic is more on construction.

Lesson Objective (LO):  

SWBAT use constructions to explore attributes of perpendicular bisectors.

The two construction models we are doing are the following:  (Do these on the right side of your notebook)

1.  Constructing a perpendicular through a point on a line.

http://www.youtube.com/watch?v=0wxrjoHDGAM

Your job is to draw your own and write, in your own words, the steps needed to make this construction.

(Hint:  the first step is to draw a segment and put a point on it somewhere)

2.  Constructing a perpendicular through a point not on a line

(I haven't been able to find a youtube video of this yet.  I will update this post as soon as I find it.)

Your job is to again draw your own and write, in your own words, the steps needed to make this construction.  (Hint:  the first step is to draw a segment and put a point somewhere above it.)

The final drawing for each of the above two tasks is going to look like this: