chapter 5 expressions. day….. 1.combining like terms (with exponents) 2.field trip 3.combining...

Chapter 5

Expressions

Day…..1. Combining Like Terms (with

Exponents)

2. Field Trip

3. Combining Like Terms (with Distributive

Property)

4. Evaluating Algebraic Expressions

5. Translating Verbal Expressions

Day 1

Bell Work1. What is the value of the expression 32 + 33?

2. Choose all the expressions equivalent to 4(9+3).

a. 4(12)b. 36+3c. 36+12d. 4+(9+3)e. (9+3) + (9+3) + (9+3) + (9+3)

3. What is the value of 1500/ (62 + 43 ) * 37 ?

Homework CheckPlease turn in your Facing Math projects.

Vocabulary•

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A combination of variables, numbers, and at least one operation.

Algebraic Expressions -

Coefficient-

Constant-

Equivalent Expressions-

Evaluate-

The numerical part of a term followed by a variable.

Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable.

Expressions that have the same value.

To find the value of a mathematical statement. To solve or find a solution.

Numerical Expression - A combination of numbers and operations.

Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base.

Vocabulary•

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Order of Operations-

Properties -

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.

Substitution-

Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ).

Translate-

Simplify- To make smaller or easier.

To replace one thing with another.

To change from one form or place to another.

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….

combine like terms to simplify algebraic

expressions.

Combining Like TermsEssential Understandings: Expressions that can not be solved , can often be simplified by combining the terms that are alike. •To simplify like terms, you must begin by identifying the types of terms you have. Terms are defined by their variables or lack of one. They must have the exact same variable with exact same exponent to be considered like terms. Example:

•To give your self a visual, you can use shapes to code expressions before attempting to combine the like terms. Remember the sign belongs to the term that follows.Example:

•After you have coded the terms, you can rearrange them using your knowledge of commutative property. This will make combing the like terms easier in the next step.Example:

•Once you have rearranged the terms, you can simply combine (add) the like terms. You should have the same number of terms in your final answer as the number of shapes you used to code the expression.Example:

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 2

Homework Check

Vocabulary•

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•

•

•

•

•

A combination of variables, numbers, and at least one operation.

Algebraic Expressions -

Coefficient-

Constant-

Equivalent Expressions-

Evaluate-

The numerical part of a term followed by a variable.

Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable.

Expressions that have the same value.

To find the value of a mathematical statement. To solve or find a solution.

Numerical Expression - A combination of numbers and operations.

Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base.

Vocabulary•

•

•

•

•

•

•

Order of Operations-

Properties -

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.

Substitution-

Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ).

Translate-

Simplify- To make smaller or easier.

To replace one thing with another.

To change from one form or place to another.

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

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 3

Bell Work1. Write a numerical expression that is equal to 10,

using at least four different numbers, parentheses, exponents, division, multiplication, and addition.

1. Factor 6x – 9a. 2(3x-9)b. 3(2x-3)c. 3(3x-2)d. 6(x-9)

Homework Check

Vocabulary•

•

•

•

•

•

•

A combination of variables, numbers, and at least one operation.

Algebraic Expressions -

Coefficient-

Constant-

Equivalent Expressions-

Evaluate-

The numerical part of a term followed by a variable.

Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable.

Expressions that have the same value.

To find the value of a mathematical statement. To solve or find a solution.

Numerical Expression - A combination of numbers and operations.

Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base.

Vocabulary•

•

•

•

•

•

•

Order of Operations-

Properties -

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.

Substitution-

Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ).

Translate-

Simplify- To make smaller or easier.

To replace one thing with another.

To change from one form or place to another.

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….

combine like terms to simplify algebraic

expressions.

Combining Like TermsEssential Understanding:•You can simplify an expression by combining like terms.Example:

•Only like terms can be combined (added). To be considered alike they must have the exact same variable with the exact same exponent. Terms without variable are called constants, and can be combined with other constants.Example:

•Terms can be coded and rearranged using commutative property to make simplifying easier. Remember to make a key.Examples:

•When simplifying an expression you must follow the order of operations. PEMDASExamples:

•Unlike like terms cannot be combined, but they can be multiplied by other unlike terms. Often this appears in the form of distributive property.Example:

Distributive Property

Essential Understanding:Distributive property can be used to rewrite algebraic expressions. This is done by multiplying the term on the outside of the parenthesis by Every term on the 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)

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 4

Bell Work1. What is the value of 6(x + 15) – 12 when x=12 ?

2. Does n=3 make the following equations true? Yes or Noa. 8n=512b. 0.5n = 1.25c. 2n = 6d. 4n – 30 = 34

3. At a bake sale, plates of cookies , p, are sold for $5 each. The amount of money from the sale of cookies is expressed as dollars, d. Which equation represents the earnings of the bake sale?

a. P =5db. d = p+5c. d= p/5d. d=5p

Homework Check

Vocabulary•

•

•

•

•

•

•

A combination of variables, numbers, and at least one operation.

Algebraic Expressions -

Coefficient-

Constant-

Equivalent Expressions-

Evaluate-

The numerical part of a term followed by a variable.

Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable.

Expressions that have the same value.

To find the value of a mathematical statement. To solve or find a solution.

Numerical Expression - A combination of numbers and operations.

Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base.

Vocabulary•

•

•

•

•

•

•

Order of Operations-

Properties -

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.

Substitution-

Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ).

Translate-

Simplify- To make smaller or easier.

To replace one thing with another.

To change from one form or place to another.

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….

evaluate algebraic expressions involving

substitution.

Evaluating ExpressionsEssential Understanding: Substitution is used to evaluate an algebraic expression, when the value of the variables is given.

•To do this, you simply replace the variable(s) with the given value. Example:

•Then simply evaluate the expressions following the standard procedure. PEMDASExample:

Additional Examples:1.3x + 5 when x=2

2.4w +5w when w=8

3.2abc when a=3, b=4, and c=5

4.7y – 3p when y=7 and p =2

Wrap it Up

• Review

• Questions

• Exit Tickets

Day 5

Bell Work1. Solve the expression if y=8. ((y3 – 212) *2) + (12 + 22 + 32)2

2. Which numerical expression is equivalent to add seven and seven, then multiply by seven, then divide by seven?

a. (7*7)+7/ 7b. 7*7+(7 / 7)c. ( 7*7*7)/ 7d. 7*(7+7)/ 7

Homework Check

Vocabulary•

•

•

•

•

•

•

A combination of variables, numbers, and at least one operation.

Algebraic Expressions -

Coefficient-

Constant-

Equivalent Expressions-

Evaluate-

The numerical part of a term followed by a variable.

Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable.

Expressions that have the same value.

To find the value of a mathematical statement. To solve or find a solution.

Numerical Expression - A combination of numbers and operations.

Exponent- A small number written to the right and above a base. Shorthand way to express repeated multiplication of the base.

Vocabulary•

•

•

•

•

•

•

Order of Operations-

Properties -

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.

Substitution-

Term- Each part of an algebraic expression or equation separated by a positive ( +) or negative sign ( - ).

Translate-

Simplify- To make smaller or easier.

To replace one thing with another.

To change from one form or place to another.

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….

Identify key terms for addition, subtraction,

multiplication, division, etc...

Key Terms for Addition

• Increased +

• Added +

• Combine +

• Plus +

• And +

• Climbed +

• Rose +

• Together +

• Sum ( + )

• Average ( + ) then ÷

Key Terms for Subtraction

• Subtracted -

• Decreased –

• Reduced -

• Minus -

• Less -

• Lower -

• Dropped -

• Difference ( - )

Key Terms for Multiplication

• Times x

• Each x

• Of x

• Multiply x

• Half x½

• Double x2

• Twice x2

• Triple x3

• Product ( x )

Key Terms for Division

Key Terms for Exponents

Key Terms for Order

• Than switch

• Sum ( + )

• Difference ( - )

• Product ( x )

• Quotient ( ÷ )

• First

• Then

• Next

• Last

Key Terms for Equations

• Is =

• Equals =

• Equivalent =

Key Terms for Inequalities

•Greater than ≥•Less than ≤•Is not equal to ≠

I Can….

Translate expressions from written/verbal form

to numerical form.

Translating verbal/written expressions

Essential Understanding: Translating expressions is the process of changing expressions and equations from one form to another.

•This is made simpler by breaking apart the phrase/problem.• Try to think about the meaning of each individual word. •Then code the problem/expression to make translating quick and precise.

Examples:

•The twenty six increased ten.

•Eighteen minus four.

•The product of nine and six.

•The quotient of four and two.

•Eight times the sum of four and x.

•Three more than eleven.

Let’s PracticeDirections: Translate the following expressions to numerical form.

1.Four more that the difference of six and two.

2.Fifteen less than the product of nine and a number.

3.Eleven added to the quotient of thirty six and six.

4.A number reduced by seven.

5.The product of nine and number divided by two less than the

product ten and number.

Wrap it Up

• Review

• Questions

• Exit Tickets