Algebra Foundations Series- 1.1 Variables and Expressions
1.3 Real Numbers and the Number Line
1. 1-3 Real Numbers and
the Number Line
I Can:
- classify, graph, and compare real
numbers .
- find and estimate square roots.
2. 1. Opener
Simplify each of these:
a) ( 1 1 1 1 1 1 1)( 1)( 1
)( )( )( )( )( )( )(50)
b) ( 2)(3)( 4)(5)
c) 10 ( 32) ( 22)
d)
1 2 3 4 50
e) x 2 5x 6
Evaluate: for x = 6
f) What number could you evaluate in (e) so that x2 5x 6 0
g) What appetizer is most requested with a last meal?
3. Focus Question
• What is the difference between finding the square root of a perfect square and
the square root of a nonperfect square?
4. 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.
5. 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.
6. Vocabulary to Know
• Radicand
• The expression under the radical symbol is called the radicand.
• x is the radicand in this case
7. Vocabulary to Know
• Radical
• Together, the radical symbol and radicand form a radical.
8. BIG Ideas
• The definition of a square root can be used to find the exact square roots of
some nonnegative numbers.
9. 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.
10. 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.
11. 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.
15. Vocabulary to Know
• Perfect Square
• The square of an integer
• For this class, you are required to memorize all perfect squares from 1-144.
16. 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
17. 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?
25. #1
What kind of number is -
#2
What kind of number is
5? 42?
integer, rational
26. #2
What kind of number is
#3
What kind of number is -
42? 4.5669?
natural, whole, integer,
rational
27. #3
What kind of number is -
#4
Give an example of a
4.5669? positive integer.
rational
28. #4
Give an example of a
#5
Give an example of a
positive integer. negative natural
number.
29. #5
Give an example of a
#6
Give an example of a
negative natural whole number that isn’t
number. positive.
30. #6
Give an example of a
#7
What kind of number is
whole number that isn’t most useful to describe:
positive.
your shoe size
31. #7
What kind of number is
#8
What kind of number is
most useful to describe: most useful to describe:
your shoe size the temperature in a
news report
rational
32. #8
What kind of number is
#9
What kind of number is
most useful to describe: most useful to describe:
the temperature in a the number of siblings a
news report person has
integers
33. #9
What kind of number is
#10
True or false:
most useful to describe:
Every rational number is
the number of siblings a also an integer.
person has
If false, give a
counterexample.
whole
34. #10
True or false:
#11
True or false:
Every rational number is Every whole number is
also an integer. also a natural number.
If false, give a If false, give a
counterexample. counterexample.
false
35. #11
True or false:
#12
True or false:
Every whole number is Every natural number is
also a natural number. also a rational number.
If false, give a If false, give a
counterexample. counterexample.
false
36. #12
True or false:
#13
True or false:
Every natural number is Every negative number
also a rational number. is also an integer.
If false, give a If false, give a
counterexample. counterexample.
true
37. #13
True or false:
Every negative number
is also an integer.
If false, give a
counterexample.
true
