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 = 27Exponents 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 real-world 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

• 5 0

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 Rule

2 4 2· 2 · 2 · 2 16 ÷2

2 3 2 · 2 · 2 8

2 2 2 · 2 4

2 1 2 2

2 0 1 1 x2

2 -1 ½ 1 ½ ½

2 -2 ½ 2 ½ · ½ ¼

2 -3 ½ 3 ½ · ½ · ½ 1/8

2 -4 ½ 4 ½ · ½ · ½ · ½

1/16

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!

• 2 0 = ____

• 2 1 = ____

• 2 2 = ____

• 2 3 = ____

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

Explain your thinking.

Solve: If m = 3

4m = m + m + m + m or 4 (m)

m4 = m · m · m · m

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 m = 2 2 + 8 = 10• r – 3 r = 5 5 – 3 = 2

Key Vocabulary:

• Simplify – Combine like terms and complete all operations

m = 2

• m + 8 + m 2 m + 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 Expressionsfor 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 + 8n + 9

y + 4

Let’s Practice: Write Algebraic Expressionsfor 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 + 7n + 6

z + 9

Evaluate each algebraic expression when x = 10

• x + 8

• x + 49

• x + x

• x - x

• x - 7

• 42 - x

1859

20

03

32

Complete This Table

n n - 35

102132

27

1829

Complete This Table

x x + 65

102132

11162738

Let’s Practice: Write an Algebraic Expression for These Situations

• Scott’s brother is 2 years younger than Scott

• The sum of two numbers is 12

• The difference between two numbers is 5

s - 2

v + c = 12

m – n = 5

Review:

http://www.mathsisfun.com/exponent.html

http://www.mathsisfun.com/algebra/index.html

Variables and ExpressionsVariable – 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.