Sunday, December 15, 2013
Tuesday, October 15, 2013
Project - Map Practice with Distance and Midpoint
Map Practice with Distance and Midpoint Name: ________________________
Restaurants:
· Burger King
· Hardee's
· McDonald's
· Chick-Fil-A
· Bojangles
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Buildings:
· City Hall
· Post Office
· Courthouse
· Library
· Armory
|
Stores:
· Wal-Mart
· Target
· Food Lion
· Lowe's
· BP station
|
1. Begin by drawing and labeling your x and y axes on your graph paper. Make sure that your axes cover the entire area of the page.
2. Plot and label the following locations on your map:
· Burger King at (-2, 3)
· Hardee's at (4, 1)
· City Hall at (-9, -8)
· Post Office at (-3, 8)
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· Wal-Mart at (4, -4)
· Target at (-8, 6)
· BP station at (1, -10)
|
3. Bojangles is located at the midpoint of Burger King and Hardee's. Plot and label Bojangles on the map and write the coordinates of Bojangles here _______.
4. The library is located at the midpoint of City Hall and the post office. Plot and label the library on the map and write the coordinates of the library here _______.
5. Food Lion is located at the midpoint of Wal-Mart and Target. Plot and label Food Lion on the map and write the coordinates of Food Lion here _______.
6. Hardee's is the midpoint between Burger King and Chick-Fil-A. Plot and label Chick-Fil-A on the map and write the coordinates of Chick-Fil-A here _______.
7. The courthouse is the midpoint between the post office and the library. Plot and label the courthouse on the map and write the coordinates of the courthouse here _______.
8. Wal-Mart is the midpoint between Lowe's and the BP station. Plot and label the Lowe's on the map and write the coordinates of Lowe's here _______.
9. Burger King is the midpoint between Target and the armory. Plot and label the armory on the map and write the coordinates of the armory here _______.
10. (-2, -2) is the midpoint between McDonald's and City Hall. Plot and label McDonald's on the map and write the coordinates of McDonald's here _______.
Use your map and your coordinates to find the distances between the following points of interest:
11. What is the distance between McDonald's and the BP station? ____________
12. What is the distance between Wal-Mart and Hardee's? ____________
13. What is the distance between Target and City Hall? ____________
14. What is the distance between the armory and the library? ____________
15. What is the distance between Chick-Fil-A and Food Lion? ____________
16. What is the distance between Lowe's and Burger King? ____________
17. What is the distance between the courthouse and Bojangles? ____________
18. What is the distance between McDonald's and the Chick-Fil-A? ____________
19. What is the distance between Wal-Mart and the BP station? ____________
20. What is the distance between the post office and Target? ____________
Sunday, October 6, 2013
Sunday, September 22, 2013
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 |
Sunday, September 15, 2013
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.
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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.
Thursday, September 12, 2013
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.
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.
Wednesday, September 11, 2013
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.
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.
Tuesday, September 10, 2013
10. Algebraic Proofs
10. ALGEBRAIC PROOFS
LO: SWBAT will apply and use deductive reasoning to justify and prove mathematical statements
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.
Sunday, September 8, 2013
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
8. CONDITIONAL STATEMENTS
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LO: SWBAT will determine the validity of a conditional statement, its converse, inverse
and contrapositive.
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
(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
Thursday, September 5, 2013
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:
1. NEGATION
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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:
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