chapter 5 expressions. day….. 1.exponents 2.order of operations 3.numerical expressions...

Chapter 5

Expressions

Day…..

1. Exponents

2. Order of Operations

3. Numerical Expressions

4. Algebraic Properties

5. Distributive Property

Day 1

Vocabulary•

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A combination of variables, numbers, and at least one operation. Ex. 4x + 3

Expressions that have the same value. Ex. 5+9 = 20-6

Numerical Expression -

Algebraic Expressions -

Order of Operations-

Equivalent Expressions-

Evaluate-

Properties -

To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57

A combination of numbers and operations. Ex. 10 + 5 - 8

The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)

Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Variable -A letter or symbol used to represent an unknown number.

I Can….

Write and evaluate expressions involving

exponents

Exponent

Essential Understanding:• Exponents are a shorthand way to show how many

times a number, called the base, is multiplied times itself.

• A number with an exponent is said to be "raised to the power" of that exponent.

• The "Laws of Exponents” come from three ideas:1. The exponent says how many times to use the number in

a multiplication. 2. A negative exponent means divide, because the opposite

of multiplying is dividing3. A fractional exponent like 1/n means take the nth root

Laws of Exponents

Law: Examples:① x1 = x 61 = 6② x0 = 1 70 = 1③ x-1 = 1/x 4-1 = ¼④ xmxn = xm+n x2x3 = x2+3 = x5

⑤ xm/xn = xm-n x6/x2 = x6-2 = x4

⑥ (xm)n = xmn (x2)3 = x2×3 = x6

⑦ (xy)n = xnyn (xy)3 = x3y3

⑧ (x/y)n = xn/yn (x/y)2 = x2 / y2

⑨ x-n = 1/xn x-3 = 1/x3

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 2

Bell WorkComplete the provide page in your book.

Homework Check

Vocabulary•

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•

•

•

A combination of variables, numbers, and at least one operation. Ex. 4x + 3

Expressions that have the same value. Ex. 5+9 = 20-6

Numerical Expression -

Algebraic Expressions -

Order of Operations-

Equivalent Expressions-

Evaluate-

Properties -

To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57

A combination of numbers and operations. Ex. 10 + 5 - 8

The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)

Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Variable -A letter or symbol used to represent an unknown number.

I Can….

Solve expressions involving multiple

operations.

Order of OperationsEssential Understanding: Order of operation is the rule that states the order in which an expression or equation is solved. You can remember this order with simple mnemonic devices such as “Please Excuse My Dear Aunt Sally”. Where as:

P stands for parenthesis

E stands for Exponents

M stands for multiply

D stands for divide

A stands for addition

S stands for subtraction

Examples:

1) 4+6*8-6(12-9) =

2) 14-8+5*5+102=

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 3

Bell WorkDirections: Use your knowledge of the order of operations to simplify each expression.

I. 17 + 3 * 6 – 1 + 10II. 42 + 10 – 5III. 12 * 4 * 2 3 + 50 – 11IV. 6 + 21 * 5 – 3 * 7 + 9V. 1 + 2 + 3 * 4 * 5 6 + 7 – 8 * 9

Justify your response.

Homework Check

Vocabulary•

•

•

•

•

•

•

A combination of variables, numbers, and at least one operation. Ex. 4x + 3

Expressions that have the same value. Ex. 5+9 = 20-6

Numerical Expression -

Algebraic Expressions -

Order of Operations-

Equivalent Expressions-

Evaluate-

Properties -

To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57

A combination of numbers and operations. Ex. 10 + 5 - 8

The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)

Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Variable -A letter or symbol used to represent an unknown number.

I Can….

Solve expressions involving multiple

operations.

Order of Operations

Your Turn….

• Clear your desk of everything but a pencil.

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 4

Homework Check

Vocabulary•

•

•

•

•

•

•

A combination of variables, numbers, and at least one operation. Ex. 4x + 3

Expressions that have the same value. Ex. 5+9 = 20-6

Numerical Expression -

Algebraic Expressions -

Order of Operations-

Equivalent Expressions-

Evaluate-

Properties -

To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57

A combination of numbers and operations. Ex. 10 + 5 - 8

The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)

Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Variable -A letter or symbol used to represent an unknown number.

Properties• Commutative- states that the order in which numbers are added

or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7

• Associative- states that the way in which numbers are grouped does not change the sum or product.

Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will

be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4

• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.

Ex: 4(2 + 3) = 8 +12

I Can….

Apply the properties of operations to generate

equivalent expressions.

Algebraic PropertiesEssential Understanding:

Algebraic properties can be used to rewrite expressions or generate equivalent expressions. For instance, the expression 3+4+2 can be rewritten like this 4+3+2 using commutative property of addition to rearrange the numbers.

Examples of other algebraic properties:I. 1 x 4 x 3 = 4 x 3 x 1 -_____________________II. (6 + 3) +8 = (8 +3) + 6-____________________III. 9 x (3 x 2) = (9 x 3) x 2-____________________IV. 4(3 – 2)-______________________

Watch This• Associative property: http://

learnzillion.com/lessons/137-combine-parts-of-an-expression-using-the-associative-property ( 5 mins)

• Commutative property: http://learnzillion.com/lessons/2357-the-commutative-property (3 mins)

Group Work

Please take out your maker boards

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 5

pOp Quiz

• Take out a pencil and a calculator

• Clear everything else from your desk

Bell WorkDirections: Use your knowledge of associative and commutative properties to rewrite the following expressions.

I. 3 * 3 * 8

II. 5 + 7 + 9 + 6

III. 2 * (7 * 6)

IV. 5 + (4 + 3)

V. 4 + 5 + 6 – 2

VI. 15 3

Justify Your Methods

Homework Check

Vocabulary•

•

•

•

•

•

•

A combination of variables, numbers, and at least one operation. Ex. 4x + 3

Expressions that have the same value. Ex. 5+9 = 20-6

Numerical Expression -

Algebraic Expressions -

Order of Operations-

Equivalent Expressions-

Evaluate-

Properties -

To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57

A combination of numbers and operations. Ex. 10 + 5 - 8

The rules that tell which operation to preform first when more than one operation is used. (PEMDAS)

Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Variable -A letter or symbol used to represent an unknown number.

Properties• Commutative- states that the order in which numbers are added

or multiplied does not change the sum or product. Ex: 4+3=7 or 3+4=7

• Associative- states that the way in which numbers are grouped does not change the sum or product.

Ex: 1 + (2+3) = 6 or (1+2) +3= 6• Identity- states that any number added to 0 or multiplied by 1 will

be itself. Ex: 6 + 0 = 6 or 4 x 1 = 4

• Distributive- is used to simplify or rewrite expressions by multiplying a number outside the parenthesis by each number or term inside the parenthesis.

Ex: 4(2 + 3) = 8 +12

I Can….

Apply the properties of operations to simplify

expressions.

Distributive Property

Essential Understanding:Distributive property can be used to rewrite algebraic expressions by multiplying the number outside the parenthesis by each number, term, or variable inside. For instance the expression 3(p+2) can be rewritten as 3p + 6

Examples:I. 2(3+7)II. (6-3)3III. 5(3+6d)IV. (4-a)8V. (5b+6c)8VI. 9(ab + 4c)

Watch This• Distributive property: http://learnzillion.com/lessons/2338-create-an-equivalent-expression-using-the-standard-algorithm ( 5 mins)

Puzzle TimeBefore we begin…….1. Complete an exit ticket.2. Pack up everything except for your

pencil.3. Sit quietly unit everyone is ready.

Wrap it Up

• Review

• Questions

• Exit Tickets