1.3 real numbers and the number line
TRANSCRIPT
1-3 Real Numbers and the Number Line
I Can:- classify, graph, and compare real
numbers .- find and estimate square roots.
1.OpenerSimplify each of these:
a)
b)
c)
d)
e) Evaluate: for x = 6
f) What number could you evaluate in (e) so that g) What appetizer is most requested with a last meal?
10 (32) ( 22)
( 1)( 1)(1)( 1)(1)( 1)( 1)( 1)( 1)(50)
( 2)(3)( 4)(5)
1 2 3 4 50
x 2 5x 6
x 2 5x 60
Focus Question• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?
Vocabulary to Know • Square Root
• A number a is a square root of a number b if a2 = b
• Example: 72 = 49, so 7 is the square root of 49.
Square Root• You can use the definition of square root to find the exact square roots of some
nonnegative numbers.
• You can approximate the square roots of other nonnegative numbers.
• The radical symbol indicates a nonnegative square root, that is also called the principal square root.
Vocabulary to Know• Radicand
• The expression under the radical symbol is called the radicand.
• x is the radicand in this case
Vocabulary to Know • Radical
• Together, the radical symbol and radicand form a radical.
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
• Numbers can be classified by their characteristics.
BIG Ideas• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
• The square roots of other nonnegative numbers can be approximated.
• Numbers can be classified by their characteristics.
• Some types of numbers can be represented on the number line.
Simplifying Square Root Expressions• What is the simplified form of each expression?
Simplifying Square Root Expressions• What is the simplified form of each expression?
Vocabulary to Know• Perfect Square
• The square of an integer
Vocabulary to Know• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.
Vocabulary to Know• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.
• Copy this list and study it. You will be quizzed.
12 = 1 72 = 49
22 = 4 82 = 64
32 = 9 92 = 81
42 = 16 102 = 100
52 = 25 112 = 121
62 = 36 122 = 144
Estimating a Square Root• Lobster eyes are made of tiny square regions. Under a microscope, the surface
of the eye looks like graph paper. A scientist measure the area of one of the squares to be 386 square microns. What is the approximate side length of the square of the nearest micron?
Estimating Square Root• What is the value of to the nearest integer?
Focus Question Answer• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?
Focus Question• Why is it helpful to classify, graph, and compare numbers?
2.Kinds of Numbers
0natural numbers
0whole numbers
0integers
2.Kinds of Numbers
4 5 6 7 8
51
3
11
2
5.75
rational numbers
3
2.Kinds of Numbers
4 5 6 7 8
irrational numbers
3
15
#1What kind of number is -5?
#1 #2
integer, rational
What kind of number is 42?
What kind of number is -5?
#3#2What kind of number is -4.5669?
What kind of number is 42?
natural, whole, integer, rational
#4#3
rational
Give an example of a positive integer.
What kind of number is -4.5669?
#5#4Give an example of a negative natural number.
Give an example of a positive integer.
#6#5Give an example of a negative natural number.
Give an example of a whole number that isn’t positive.
#7#6Give an example of a whole number that isn’t positive.
What kind of number is most useful to describe:
your shoe size
#8#7
rational
What kind of number is most useful to describe:
your shoe size
What kind of number is most useful to describe:
the temperature in a news report
#9#8
integers
What kind of number is most useful to describe:
the temperature in a news report
What kind of number is most useful to describe:
the number of siblings a person has
#10#9
whole
What kind of number is most useful to describe:
the number of siblings a person has
True or false:
Every rational number is also an integer.
If false, give a counterexample.
#11#10True or false:
Every rational number is also an integer.
If false, give a counterexample.
True or false:
Every whole number is also a natural number.
If false, give a counterexample.
false
#12#11True or false:
Every whole number is also a natural number.
If false, give a counterexample.
True or false:
Every natural number is also a rational number.
If false, give a counterexample.
false
#13#12True or false:
Every natural number is also a rational number.
If false, give a counterexample.
True or false:
Every negative number is also an integer.
If false, give a counterexample.
true
#13True or false:
Every negative number is also an integer.
If false, give a counterexample.true
2.Kinds of Numbers
0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9
8 -6>
2.Kinds of Numbers
0 1 2 3 4 5 6 7 8-8 -7 -6 -5 -4 -3 -2 -1-9
-7 7<
#14-7 10
<
#15#14-7 10 -5 + 10 10 - 5
<
#16#15-5 + 10 10 - 5 10 • 22 2 • 42
=
#1610 • 22 2 • 42
>
Graphing and Ordering Real Numbers• http://
www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-483s.html
Focus Question Answer• Why is it helpful to classify, graph, and compare real numbers?
Your Assignment• Pages 23-25
• 1-5
• 9-17 odd
• 18-34 even
• 35-47 odd
• 48
• 49-59 odd
• 60-64 even
• 66-79