# Expressions Objective: EE.01 I can write and evaluate numerical expressions involving whole number exponents.

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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 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 ExponentialExpandedValueRule 2 4 2· 2 · 2 · 216÷2 2 3 2 · 2 · 28 2 2 · 24 2 1 22 2 0 11x2 2 -1 ½ 1 ½ ½ 2 -2 ½ 2 ½ · ½¼ 2 -3 ½ 3 ½ · ½ · ½1/8 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 2 nd 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) m 4 = 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 + 8m = 22 + 8 = 10 r – 3r = 55 – 3 = 2

Key Vocabulary: Simplify – Combine like terms and complete all operations m = 2 m + 8 + m 2 m + 8 (2 x 2) + 84 + 8 = 12

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 nn - 3 5 10 21 32 2 7 18 29

Complete This Table xx + 6 5 10 21 32 11 16 27 38

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.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.

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