Do not use a calculator to complete homework. Students who are calculator dependent tend to make more calculating errors on tests. 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. 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. Study tips 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.

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

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

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

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

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

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

A counterexample is a triangle with perimeter of 3 and sides of 0.9, 0.9, and 1.2. 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. It takes only one counterexample to show that a statement is false.

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

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

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

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. The coordinate plane is divided into four regions called quadrants. I II III IV x y

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

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

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

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). x y A B C D E F

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

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

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