Transcript Unit 1 Integers, Exponents, Scientific Notation

Unit 1
Integers, Exponents, Scientific
Notation
Lessons 1-6
Unit 1
Pre-Test
Today we will take the pre-test for this unit. Pretests are used to see what you know before we
begin. Don’t get discouraged if you don’t know all
or any of the answers. This is just a way to see
what you already know!
Lesson 1
Exponential Notation
• OBJECTIVE:
– Students will understand what it means to raise a
number to a power and represent with repeated
multiplication.
– Students will explain reason for some bases
requiring parentheses.
Lesson 1
Let’s try these together!
1. 5 x 5 x 5 x 5 x 5 x 5=
2. .
3. .
4. (-2)
5. 3.8
Think about this…
– Quick write:
• Why did we use the parentheses on examples
2, 3, and 4?
• In cases where the base is either a fraction or
a negative number, it prevents ambiguity
about which portion of the expression is going
to be multiplied repeatedly.
• For example:
Try exercises 1-10 on your own!
Check your answers!
1. 4
2. 47 times
3. (-11.63)
4. 15 times
5. (-5)
6. ( )
7. (-13)
8. ()
9. .
10. n times
Exercise 11-12
11.
Part 1:This product will be positive, why?
Part 2: This product will be negative, why?
12.
Odd number of negative factors yield a
_________ product.
Even number of negative factors yield a
_________ product.
Exercises 13-14
13.
If n is a postive even number, then (-55) is
______________.
If n is a positive odd number, then (-72.4) is
______________.
14.
Is Josie correct? Why or why not?
Closing!
• Why bother with exponential notation? Why
don’t we just write out all the multiplication?
• Suppose a colony of bacteria doubles in size
every 8 hours for a few days under tight
laboratory conditions. If the initial size is B,
what is the size of the colony after 2 days?
– Answer: In 2 days there are six- 8 hours periods,
so the size will be 2 B
Lesson 2
Multiplication of Numbers in
Exponential Form
• OBJECTIVE:
– Students will use exponential notation.
– Students will simplify exponential expressions
– Students will write equivalent expressions using
first law of exponents.
How do I multiply different powers of the
same number x; if m and n are positive
integers, what is
?
Let’s try these together!
1.
2. (-
) X (-
)
Try exercises 1-8 on your own!
Exercises 1-8
Check your answers!
Notes
• Expressions can ONLY be simplified when the
bases are the SAME.
• If the bases are not the same, you can rewrite
them.
• For example:
– What factors do 2 and 8 have in common?
– Using the base 2, what exponent needs to be used
to equal 8?
• Quick write:
– Can the following example be simplified using the
rule of adding exponents?
– Why or why not?
What if there were more terms with
the same base?
• Tell whether the following examples can be
simplified or not. Why or why not?
Can the following be simplified?
Exercises 11-16
Check your answers!
Exercises 17-20
Check your answers!
Notes
• We have now learned how to multiply 2
different positive integer powers of the same
base.
– Same base add the exponents
• How do you think we divide powers with the
same base?
– If m, n are positive integers, what is
?
Example
• What is
?
• Expanded form:
•
=
• What pattern do you see?
Examples
Exercises 21-24
Try these on your own!
Check your answers!
If x is a non-zero number, what is it?
Simplify
Can the following be simplified?
Exercise 31
Hint: What is the denominator of the expression in parentheses?
Exercise 32
Fluency Activity
• When I call a number out, tell me the square
of that number.
– For example: 1 x 1= 1, so 1 = 1.
Closing!
• Summarize the lesson.
• What did you learn today?
– How do you multiply exponential expressions with
the same bases?
– How do you divide exponential expressions with
the same bases?
• Exit Ticket: Complete and turn in for your
classwork grade!
• Homework: Complete for homework
– Pick expressions from # 3
– Complete # 5