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Expressions
Objective: EE.01
I can write and evaluate numerical
expressions involving whole number
exponents.
Key Vocabulary:
Fraction: Part of a whole. It has a numerator and
denominator. Example: ¾ means 3 out of 4 parts
Decimal: Part of a whole. It has a decimal point. Place
value is located to the right of the whole number.
Example: 3.45 means 3 and 45 hundredths.
Exponent: tells the number, (base), how many times to
multiply itself. Example: 3³ = 3 x 3 x 3 = 27
Exponents are called powers.
Mathematical Practices:
• MP 2: Reason abstractly and quantitatively.
What does this mean?
I can think about numbers in many ways.
I can take numbers and put them in a realworld context. I can work with numbers
mathematically.
Essential Questions:
• 1. What is an exponent? An exponent tells
a base how many times to multiply itself.
• 2. How do you calculate a value containing
an exponent? You multiply the base the
number of times the power indicates.
Exponent Review: Whiteboards
•
•
•
•
•
Write in expanded form:
3 -²
4 -³
½ ³
50
Bell work Review: Square
• Remember: Area = Length x Width.
• The area for a square is x 2 .
• Find the area of each square:
• A square has a side length of 6 cm.
• A square has a side length of 3 cm.
• A square has a side length of 10 cm.
New Learning!!
• Let’s explore different exponents.
• Since we learned that 2 0 equals 1, what do you
think 2 -1 will represent? Discuss in your
group.
Table: Let’s create a table to learn about
negative exponents.
Positive and Negative Exponents
Exponential
Expanded
Value
24
2· 2 · 2 · 2
16
23
2·2·2
8
22
2·2
4
21
2
2
20
1
1
2 -1
½1
½
½
2 -2
½2
½·½
¼
2 -3
½3
½·½·½
1/8
2 -4
½4
½·½·½·½
1/16
Rule
÷2
x2
Note Taking: Exponent Rules
• Any whole number, fraction, or decimal to
the power of zero equals 1.
• Any whole number, fraction, or decimal to
the power of 1 equal itself.
• Any whole number, fraction, or decimal to
the 2nd power makes a square.
Exponent Practice:
• Write the following expressions in exponent
form:
• 7·7·7
• 10 x 10 x 10 x 10 x 10
• 2·2·2·2·2
• 3/5 · 3/5 · 3/5
Review!
•
•
•
•
20
21
22
23
= ____
1
2
= ____
4
= ____
= ____
8
Exponent Practice:
• Write correctly using exponents:
• (3 + 4) · (3 + 4) +( 4 - 2) · (4 - 2) · (4 - 2)
• (7 + 3) · (7 + 3) - (5 + 1) · (5 + 1)
• (10 – 1) · (10 – 1) ÷ ( 2 + 1) · (2 + 1)
More Exponent Practice:
• Solve the following exponential equation
for x:
• X = 3² + 5²
• X = 4³ - 3³
• X = 10² - 7²
• 3. What is a variable? A variable is a letter that
represents a number.
• 4. What is Order of Operations? What do the letter
PEMDAS represent?
• Order of Operations is a set of rules for solving
problems.
• P – Parenthesis
• E- Exponents
• M/D – Multiply or Divide – left to right
• A/S – Add or Subtract – left to right
True or False
4m = m 4
4m = m + m + m + m or 4 (m)
m4
=m·m·m·m
Explain your thinking.
Solve: If m = 3
Group Discussion:
• Look at the following equation:
• 7y = y²
Round Robin: Decide if the equation above is
a true or false equation. Explain and defend
your group answer.
Key Vocabulary:
• Variable – A variable is a letter
or symbol that represents a
number (unknown quantity).
• 8 + n = 12
Examples:
• A variable can use any letter of
the alphabet.
•n+5
•x–7
• w - 25
Properties of and Multiplication
• Get your math book out and turn to page 46.
• Note taking: Properties of Multiplication.
Group Discussion:
• Decide if the following equation is true or
false:
• h³ = 3h
• Round Robin: Explain and defend your
answer.
Key Vocabulary:
• Algebraic expression – a group of
numbers, symbols, and variables
that express an operation or a
series of operations.
• m+8
• r–3
Examples:
• Evaluate an algebraic expression –
To find the value of an algebraic
expression by substituting numbers
for variables.
• m+8
• r–3
m=2
r=5
2 + 8 = 10
5–3=2
Key Vocabulary:
• Simplify – Combine like terms
and complete all operations
m=2
•m+8+m
2m+8
• (2 x 2) + 8
4 + 8 = 12
Words That Lead to Addition
• Sum
• More than
• Increased
• Plus
• Altogether
Words That Lead to Subtraction
• Decreased
• Less
• Difference
• Minus
• How many more
Let’s Practice: Write Algebraic Expressions
for These Word Phrases
• Ten more than a number
• A number decrease by 5
• 6 less than a number
• A number increased by 8
• The sum of a number & 9
• 4 more than a number
n + 10
w-5
x-6
n+8
n+9
y+4
Let’s Practice: Write Algebraic Expressions
for These Word Phrases
• A number s plus 2
• A number decrease by 1
• 31 less than a number
• A number b increased by 7
• The sum of a number & 6
• 9 more than a number
s+2
k-1
x - 31
b+7
n+6
z+9
Evaluate each algebraic expression when
x = 10
•x+8
• x + 49
•x+x
•x-x
•x-7
• 42 - x
18
59
20
0
3
32
Complete This Table
n
5
10
21
32
n-3
2
7
18
29
Complete This Table
x
5
10
21
32
x+6
11
16
27
38
Let’s Practice: Write an Algebraic Expression for
These Situations
• Scott’s brother is 2 years younger than
Scott
s-2
• The sum of two numbers is 12
v + c = 12
• The difference between two numbers is 5
m–n=5
Review:
http://www.mathsisfun.com/exponent.html
http://www.mathsisfun.com/algebra/index.ht
ml
Variables and Expressions
Variable – a symbol used to represent a quantity that can
change.
Coefficient – the number that is multiplied by the variable in
an algebraic expression.
Numerical expression – an expression that contains only
numbers and operations.
Algebraic expression – an expression that contains numbers,
operations and at least one variable.
Constant – a value that does not change.
Evaluate – To find the value of a numerical or algebraic
expression.
Simplify – perform all possible operations including
combining like terms.