MCC6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. five to the fourth power = eight squared = twelve cubed =

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1 MCC6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. WORD DEFINITION EXAMPLE Exponent Base The number of times a number or expression (called base) is used as a factor of repeated multiplication. Also called the power. The number or expression used as a factor for repeated multiplication Exponential Form A number written with an exponent. For example, 6,3 is called an exponential. five to the fourth power = eight squared = twelve cubed = Standard Form Whole number solution three cubed= = 7 2 = = Square Number A number times itself Evaluate each of the following: = squared = ( ) = = = = 1 UNIT 3

2 MCC6.EE.1 Write and evaluate numerical expressions involving whole-number exponents. WORD DEFINITION EXAMPLE Order of Operations The rules to be followed when simplifying expressions. When you are simplifying expressions, operations should be performed in the following order to ensure accuracy: 1. Parentheses (and other grouping symbols) 2. Exponents 3. Multiplication and Division (in order from left to right) 4. Addition and Subtraction (in order from left to right) You can use the expression Please Excuse My Dear Aunt Sally to help you remember the order of operations or PE(MD)(AS)! 1) = 2) 7 + 9(3 + 8) = 3) 5 3-2(12 3) = 4) 3( ) = 5) = 6) 5 + (3 + 2) 2 6 = MCC6.EE.2c Evaluate expressions at specific values for their variables. Include expressions that arise from formulas in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particuar order (Order of Operations). WORD DEFINITION EXAMPLE Variable A letter or symbol that stands for a number. expression 2 UNIT 3 Expression Includes variables, letters, operations

3 To evaluate an expression: 1) Plug in the value given for the variable any time you see that letter. 2) Use the order of operations to evaluate the expression until you are left with the answer. 3 UNIT 3

4 MCC6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. When writing expressions, the most important thing is to look for KEY WORDS that tell you how to write the expression. ADDITION SUBTRACTION MULTIPLICATION DIVISION Sum, add, increased by, together, more, and, plus, combined Subtract, difference, decreased by, minus, take away Product, times, OF, multiple, twice, triple, area, Quotient, shared, per, ratio, divided by, average, x/y Parenthesis Words ( ) Times the difference of Twice the sum of Plus the difference of are IS were will be gives totals THAN (less than) (more than) FROM Some expressions have more than one operation. For these, look for two key parts: the word and or a comma. 1. Underline commas and the word and. Write the operation over the word and. 2. Put parentheses around each section that is separated by the word and or a comma. Write an expression for each of the following: The difference of a number and five, divided by ten The quotient of 12 and the sum of a number and 4 The product of a number and eight more than that number Eight less than the product of a number and three The product of three squared and seven more than a number The sum of 8 and a number squared 4 UNIT 3

5 MCC6.EE.3 Apply the properties of operations to generate equivalent expressions. WORD DEFINITION ALGEBRAICALLY MATHEMATICALLY Associative Property of Addition Sum of a set of numbers is the same no matter how the numbers are grouped. (a + b) + c = (4 + 3) + 2 = Associative Property of Multiplication Product of a set of numbers is the same no matter how the numbers are grouped. (ab)c = (5 x 7) x 3 = Commutative Property of Addition Sum of a group of numbers is the same regardless of the order in which the numbers are arranged. a + b = = Commutative Property of Multiplication The product of a group of numbers is the same regardless of the order in which the numbers are arranged. ab = 4 x 7 = Distributive Property Sum of two addends multiplied by number is the sum of the product of each addend and a number. a(b + c) = 3 x (1 + 4) = Identity Property of Multiplication Identity Property of Addition product of 1 and any number or variable is the number or variable itself. a 1 = the sum of zero and any number or variable is the number or variable itself. a + 0 = 24 x 1 = = Zero Property The product of zero and any number is zero a 0 = 14 x 0 = Identify the property of each example. 1) 4(15-12)= ) = ) 4.2 x 23 = 23 x 4.2 3) ( ) = ( ) ) (12 x 60) x 0.2 = 12 x (60 x 0.2) 5 UNIT 3 6) 8(1 + 3)=

6 MCC6.EE.2b 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. MCC6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them. WORD DEFINITION EXAMPLE Term A number, variable, or product of a number and a variable. Like Terms Terms in an algebraic expression that have the same variable raised to the same power. Only coefficients of like terms are different. Any term that can be combined together. x, 2x, 3x Coefficient A number multiplied by a variable in an algebraic expression. coefficient 2y variable Label the graphic organizer below: 4n + 2n + 9 x 2 + 4x x +3 Using the expression above, identify each of the following: A. List all of the terms: B. List like terms in groups: C. List all coefficients: 6 UNIT 3

7 To multiply a sum by a number, multiply each addend by the number on the outside of the parentheses. If the term has a coefficient, multiply the coefficient and keep the variable. 2(7 + 4) = = a(b + c) = Use the Distributive Property to rewrite 2(3x + 9). 2(3x + 9) = 2(3x) + 2(9) = 6x + 18 Use the Distributive Property to rewrite 8(x + 3) = Use the Distributive Property to rewrite 2(x y)= Use the Distributive Property to rewrite each algebraic expression. 5(x + 8) 4(2x + 7) 3(5x + 4) 2(x + 3y) x(x + 5) 7 UNIT 3

8 To simplify an algebraic expression, use properties to write an equivalent expression that has no like terms and no parentheses. Identify which properties you use as you simplify. Step 1: Use distributive property if present. Step 2:Identify all like terms using highlighting, chop it up and block it up, or putting shapes around it. Step 3: Group the problem with your like terms together. Step 4: Add or subtract the coefficients of like terms. Step 5: Simplify numeric operations. To combine like terms, add or subtract the 7x x 8y + 4x - 6y x x - 12 You can change the order of the terms if it is ALL addition or ALL multiplication. 3x x 2 x 7 2x You can move the parentheses around like terms if the statement is ALL addition or ALL multiplication. (14y + x) + 22y 4(6x) x (x 5) 8 UNIT 3

9 Simplify each expression by distributing and combining like terms; OR Plug in the same value for the variables and check for equivalence. 1. Is 2(3d + 18) + 3d equivalent to 9(d + 2)? Yes No Show how you know. 2) Is 3g + (7h - g) equivalent to 7h + 3? Yes No Show how you know. 3) Is 2(x + 5) + 4(x + 7) equivalent to 2x x + 7? Yes No Show how you know. 1 4) Is 2 (6x + 8) equivalent to 3x + 4? Yes No Show how you know. Factor out the greatest common factor of the terms. Rewrite each term using the greatest common factor. Factor the expressions UNIT 3

10 1) Write a ladder around the expression. 2) Find a factor that goes into every term. 3) Write the factor to the left of the ladder. 4) Divide each term by the factor and write the quotient below the ladder. 5) Repeat steps 2 through 4 until you have no common factors. 6) What you have left is your factored expression. 14x p y 3. 56r h + h x y 14x - 7x 2 10 UNIT 3