1. Do not use a calculator to complete homework
Do not use a calculator to complete homework. Students who are calculator dependent tend to make more calculating errors on tests.
After you finish an odd homework problem check the answer in the back of the book. If the answer is incorrect, investigate why it is wrong. When students find their errors right away it is more effective.
Don’t skip steps. Write out the support work so your eyes can see what your brain needs to calculate. “I did it in my head” often leads to errors.
Take notes in class, read the related lesson in the text, and then review, review, review. It’s just not enough to sit in class for 45 minutes and then hope you have absorbed it all.
Study tips

2. 1-7 Logical Reasoning 1-9 Coordinate Plane
For tomorrow’s lesson you will need a colored pencil and a ruler.
Algebra Glencoe McGraw-Hill Linda Stamper

3. Logical Reasoning includes conditional statements, deductive reasoning, and counterexamples.
A conditional statement has a hypothesis and a conclusion and is often written in if-then form.
Deductive reasoning is a process that uses facts and rules to reach a valid conclusion.
A counterexample is a specific example that can be used to show that a statement is false.

4. Example of a conditional statement:
If the popcorn burns, then the heat was too high.
The part of the statement immediately following if is called the hypothesis.
The part of the statement immediately following then is called the conclusion.
Identify the hypothesis and conclusion of the statement.
If it is Friday, then the Smiths are going out to dinner.
hypothesis: it is Friday
conclusion: the Smiths are going out to dinner
Note that “then” is not part of the conclusion.
Note that “if” is not part of the hypotheses.

5. Identify the hypothesis and conclusion of each statement.
Example 1 If it is raining, then the party will be indoors.
hypothesis: it is raining
conclusion: the party will be indoors
Example 2 If 4x + 3 > 27, then x > 6.
hypothesis: 4x + 3 > 27
conclusion: x > 6

6. Deductive reasoning is the process of using facts, rules, definitions, or properties to reach a valid conclusion.
You can use deductive reasoning to determine whether a valid conclusion follows from a conditional statement.
Determine a valid conclusion that follows from the conditional statement below. Explain your answer.
Conditional statement: If two numbers are odd, then their sum is even.
Given condition:
The two numbers are 7 and 3.
7 and 3 are odd so the hypotheses is true.
The sum of 7 and 3 is even so the conclusion is valid.

7. Example 3 Determine a valid conclusion that follows from the conditional statement below.
Conditional statement: There will be a quiz every Wednesday.
Given condition: It is Wednesday.
Valid conclusion: _______________________
There will be a quiz.
Example 4 Determine a valid conclusion that follows from the conditional statement below.
Conditional statement: If your test score is in the 90th percentile, then your grade is an A.
Given condition: score is 95%
Valid conclusion: ________________________
Your grade is an A.

8. To show that a condition is false, we can use a counterexample
To show that a condition is false, we can use a counterexample. A counterexample is a specific case in which the hypotheses is true and the conclusion is false.
Conditional statement: If a triangle has a perimeter of 3 inches, then each side measure is 1 inch.
A counterexample is a triangle with perimeter of 3 and sides of 0.9, 0.9, and 1.2.
It takes only one counterexample to show that a statement is false.

9. Example 5 Find a counterexample to show that the conditional statement is false.
Conditional statement: If you graduate from Colina, then you go to Westlake High.
Counterexample: _______________________
A graduate attends TOHS.
Example 6 Find a counterexample to show that the conditional statement is false.
Conditional statement: If x + 3 > -6, then x must be negative.
Counterexample: ___________________________
When x is 10 the statement is true
and 10 is a positive number.

10. Example 7 Find a counterexample to show that the conditional statement is false.
Conditional statement: Every four-sided figure is a rectangle.
Counterexample:

11. 1-9 Coordinate Plane
All coordinate plane graphs must be completed on grid paper.

12. A coordinate plane is formed by two real number lines that intersect at a right angle at the origin. The horizontal axis is the x-axis and the vertical axis is the y-axis. y II I
The coordinate plane is divided into four regions called quadrants. • x
III IV

13. Each point in a coordinate plane corresponds to an ordered pair of real numbers.
(–2,3) •
The first number identifies the x-coordinate and the second number identifies the y-coordinate. x y

14. • Graph the coordinate (3,4).
The first number identifies the x-coordinate and the second number identifies the y-coordinate. x y

15. • Example 1 Graph the coordinate (4,–2).
The first number identifies the x-coordinate and the second number identifies the y-coordinate. x • y

16. Example 2 Graph and label the coordinates in the same coordinate plane:
A (3,–1), B (–4,0), C (–5,2), D (2,–4), E (0,3), F (0,0). E • C • B • • x F • A • D y

17. Example 3 In which quadrant or on which axis does each ordered pair lie?B. C. D. E. F. G. H. IV E •
x-axis II IV
y-axis
origin
III I H C • • B • F • x • A G • • D y

18. Coordinates are written as ordered pairs. You must use parentheses!
Example 4 Write the coordinates of each point. D •
A. B. C. D. E. F. G.
Coordinates are written as ordered pairs. You must use parentheses!
(3,–2) G •
(–4,0) (–5,–2) (2,4) (0,–3) (0,0) (–4,3) B • F • x C • • A • E y

19. Homework
1-A12 Pages 42–44 #15–24,29–34,47–49 and
Page 57 #10–18.