Algebraic Expressions (Part 2)

Day….. Distributive Property Parts of an Expression Combining Like Terms Simplifying Expressions Mid-Unit Assessment

Day 1

Bell Work Directions: Identify the property used to rewrite each expression. 4x + 5x + 7y = 7y +5x +4x (5 + 3) + 9 = 3 + (5 +9) 4(x + y) = (4*x) + (4*y) 1 * (2 * 3) = ( 1* 2) * 3 5w – 2w = w (5 – 2)

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Ex. 4x + 3 Equivalent Expressions- Expressions that have the same value. Ex. 5+9 = 20-6 To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 Evaluate- Numerical Expression - A combination of numbers and operations. Ex. 10 + 5 - 8 Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Vocabulary Term- Variable- Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) Variable- A letter or symbol used to represent an unknown number. Coefficient- The numerical part of a term followed by a variable. Constant- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable ( ex. +5 or -10 )

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

Apply the properties of operations to generate equivalent expressions. Today’s Standard Apply the properties of operations to generate equivalent 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: 2(3+7) (6-3)3 5(3+6d) (4-a)8 (5b+6c)8 9(ab + 4c)

9 Square Please clear your desk of everything except for a pencil and a blank piece of paper.

Wrap it Up Review Questions Exit Tickets

Day 2

Homework Critique

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Ex. 4x + 3 Equivalent Expressions- Expressions that have the same value. Ex. 5+9 = 20-6 To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 Evaluate- Numerical Expression - A combination of numbers and operations. Ex. 10 + 5 - 8 Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Vocabulary Term- Variable- Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) Variable- A letter or symbol used to represent an unknown number. Coefficient- The numerical part of a term followed by a variable. Constant- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable ( ex. +5 or -10 )

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

Today’s Standard Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

Parts of an Expression Essential Understanding: Expressions can be simplified by combining like terms. Terms are parts of an expression separated by a positive or negative sign. Example: There are three parts of an expression that make up terms; variables, coefficients, and constants Variables are lower case letters or shapes used to represent an unknown quantity. They are called variables because, until they are defined, their value could vary from one end of the spectrum to the other. (in other words it could be any number imaginable) Coefficients are numbers that are being multiplied by a variables. They are called coefficients because the prefix co- means together. Constants are numbers that stand alone. They are called constants because their value is consistent regardless of the variables.

Please take out a pencil and any highlighters you may have. Your Turn…. Please take out a pencil and any highlighters you may have.

Wrap it Up Review Questions Exit Tickets

Day 3

Bell Work Directions: Use your highlighters and the key below to identify the parts of the following expressions. Key: Green – Variables Orange- Coefficients Pink – Constants Terms – Boxed with a pencil 18x + 4y + 6y – 14x + 21ab 3r – 7s + 21r – 14p 15st + 42s + 51t – 9st

Homework Critique

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Ex. 4x + 3 Equivalent Expressions- Expressions that have the same value. Ex. 5+9 = 20-6 To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 Evaluate- Numerical Expression - A combination of numbers and operations. Ex. 10 + 5 - 8 Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Vocabulary Term- Variable- Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) Variable- A letter or symbol used to represent an unknown number. Coefficient- The numerical part of a term followed by a variable. Constant- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable ( ex. +5 or -10 )

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

Today’s Standard Write, read, and evaluate expressions in which letters stand for numbers.

Combining Like Terms Essential Understandings: Expressions that can not be solved , can often be simplified by combining like terms. 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 expression before combining the like terms. Be sure to keep the sign with the term. After you have coded the terms, you can rearrange them using your knowledge of commutative property. This will make combing the like terms easier. Once you have rearranged the terms, you can simply combine 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

Please Pack up all of your belongings. Monster Math Please Pack up all of your belongings. Yes, even your pencil!!! 

Wrap it Up Review Questions Exit Tickets

Day 4

Bell Work Directions: simplify the following expressions. 3x + 5x + 7y – 2x + 11y 17t – 12v + 8tv + 5v + 3tv – 12t 5(a + b) – 3a + 9b – 6a + 2a - 31b 10fx + 5f(2x + 3x) – 13fx 8(2d + 5c) - 6d + 19c + 4(5d – 3c)

Homework Critique

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Ex. 4x + 3 Equivalent Expressions- Expressions that have the same value. Ex. 5+9 = 20-6 To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 Evaluate- Numerical Expression - A combination of numbers and operations. Ex. 10 + 5 - 8 Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Vocabulary Term- Variable- Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) Variable- A letter or symbol used to represent an unknown number. Coefficient- The numerical part of a term followed by a variable. Constant- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable ( ex. +5 or -10 )

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

Today’s Standard Write, read, and evaluate expressions in which letters stand for numbers.

Simplifying Algebraic Expressions Essential Understandings: An algebraic term represents a multiplicative relationship between a number(the coefficient) and a variable (a letter of symbol). Example: 3a = 3 *a Algebraic expression can be simplified by combining like terms. Proof: But, unlike terms can not be combined (added/subtracted), because the variables do not represent the same unknown quantity. Thus, they can not be put together until the value is known. Unlike terms can, however, be distributed (multiplied), because algebraic terms are multiplication. This is how you must clear a set of parenthesis, containing unlike terms. Example: Because the order of operations states you must multiply/ divide before adding/subtracting, sometimes you have to use distributive property to multiply/get rid of the parenthesis before you can combine any like terms

Wrap it Up Review Questions Exit Tickets

Day 5

Bell Work Silent Study

Mid-Unit Assessment Please Clear Your Desk.

Homework Critique

Vocabulary Algebraic Expressions - A combination of variables, numbers, and at least one operation. Ex. 4x + 3 Equivalent Expressions- Expressions that have the same value. Ex. 5+9 = 20-6 To find the value of an algebraic expression by replacing variables with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 Evaluate- Numerical Expression - A combination of numbers and operations. Ex. 10 + 5 - 8 Order of Operations- The rules that tell which operation to preform first when more than one operation is used. (PEMDAS) Properties - Mathematical statements that are true of any number belonging to the set of numbers for which the properties are defined.

Vocabulary Term- Variable- Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) Variable- A letter or symbol used to represent an unknown number. Coefficient- The numerical part of a term followed by a variable. Constant- Part of an algebraic expression that is unchanged by a variable. A numerical term without a variable ( ex. +5 or -10 )

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