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

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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.
Dont 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. Its
just not enough to sit in class for 45 minutes
and then hope you have absorbed it all.
Study tips
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1-7 Logical Reasoning
1-9 Coordinate Plane
For tomorrows lesson you will need a colored
pencil and a ruler.
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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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.
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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.
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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 gt 27, then x gt 6.
hypothesis 4x 3 gt 27 conclusion x gt 6
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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.
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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.
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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.
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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 gt -6, then x
must be negative.
Counterexample ___________________________
When x is 10 the statement is true
and 10 is a positive number.
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Example 7 Find a counterexample to show that the
conditional statement is false.
Conditional statement Every four-sided figure
is a rectangle.
Counterexample
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1-9 Coordinate Plane
All coordinate plane graphs must be completed on
grid paper.
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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










I
II
The coordinate plane is divided into four regions
called quadrants.

x
IV
III
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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
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(3,4).
Graph the coordinate











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










x

y
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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
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Example 3 In which quadrant or on which axis
does each ordered pair lie?

• A.
• B.
• C.
• D.
• E.
• F.
• G.
• H.

IV
E

H
x-axis II IV y-axis origin III I


C
B


F
x

A
G


D
y
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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
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Homework

• 1-A12 Pages 4244 1524,2934,4749 and
• Page 57 1018.