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Chapter 5 Expressions Day….. 1. Parts of an Expression 2. Simplifying Expressions 3. Simplifying Expressions Continued… 4. Evaluating Expressions 5. Mid Unit Assessment Day 1 Bell Work Directions: Identify the property used to rewrite each expression. 1. 4x + 5x + 7y = 7y +5x +4x 2. (5 + 3) + 9 = 3 + (5 +9) 3. 4(x + y) = (4*x) + (4*y) 4. 1 * (2 * 3) = ( 1* 2) * 3 5. 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 Evaluate• with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 • 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• Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) 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 I Can…. identify parts of an expression using mathematical terms. 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 I. 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) II. Coefficients are numbers that are being multiplied by a variables. They are called coefficients because the prefix co- means together. III. Constants are numbers that stand alone. They are called constants because their value is consistent regardless of the variables. Your Turn Please clear your desk of everything except for a pencil and several highlighters. Wrap it Up • Review • Questions • Exit Tickets Day 2 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 1. 18x + 4y + 6y – 14x + 21ab 2. 3r – 7s + 21r – 14p 3. 15st + 42s + 51t – 9st Homework Check 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 Evaluate• with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 • 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• Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) 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 I Can…. combine like terms to simplify expressions. I Can…. combine like terms to simplify expressions. 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. 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. Example: • 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 Example: Your Turn…. Take out your marker boards. Wrap it Up • Review • Questions • Exit Tickets Day 3 Bell Work Directions: Simplify the following expression. 1. 3x + 6x + 8y +10x – 4y 2. 12a – 17c – 11b + 25c - 6c + 13b 3. 6x + y + 7y + 5x 4. 13x- 5xy + 20xy – 6x Justify Your Response Homework Check 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 Evaluate• with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 • 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• Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) 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 Combining Like Terms Essential Understandings: • Algebraic expression can be simplified by combining (adding or subtracting) like terms. Example: • Unlike terms can not be combined (added or subtracted), but they can be distributed (multiplied) to clear a set of parenthesis. Example: • Remember the order of operations states you must multiply before adding or subtracting. Thus you must distribute before combining like terms Example: Partner Work Clear your desk of everything except for a pencil and a calculator. Wrap it Up • Review • Questions • Exit Tickets Day 4 Bell Work Directions: simplify the following expressions. 1. 3x + 5x + 7y – 2x + 11y 2. 17t – 12v + 8tv + 5v + 3tv – 12t 3. 5(a + b) – 3a + 9b – 6a + 2a - 31b 4. 10fx + 5f(2x + 3x) – 13fx 5. 8(2d + 5c) - 6d + 19c + 4(5d – 3c) Homework Check 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 Evaluate• with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 • 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• Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) 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 I Can…. evaluate expressions using substitution. Evaluating Expressions Essential Understanding: To evaluate an expression using substitution, you simply replace the variable(s) with the defined quantity. 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 Write the Room Clear your desk of everything except for a pencil. Wrap it Up • Review • Questions • Exit Tickets Day 5 Bell Work Directions: simplify or evaluate the following expressions. 1. 3x + 4y + 7g – 2x + 11g 2. 4h – 2h when h=11 3. x(y – 7) + 15xy + 19y 4. 5p + 4r -3r when r=2 5. 3d + 4a +5b + 10a + 6d Homework Check 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 Evaluate• with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57 • 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• Each part of an algebraic expression or equation separated by a plus or minus sign. ( ex. 2x, -3, y, +10 ) 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 Mid-Unit Assessment Please clear your desk of everything except for a pencil and a calculator. Wrap it Up • Review • Questions • Exit Tickets