Download Algebra in Action! Verbal Expression

[Algebra 1 (X)]
1.1: Variables and Expressions HCPS III: 
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Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations. Benchmark MA.AI.10.2: Translate between verbal mathematical situations and algebraic expressions and equations. Objectives: 
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Translate verbal expressions into algebraic expressions. Translate algebraic expressions into verbal expressions. Algebra in Action! Situation I had an unknown amount of color pencils, and Ken took eleven. Verbal Expression An (unknown) number minus eleven Algebraic Expression 11 Verbal Expression A verbal expression is a simplified version of a situation using mathematical words. It identifies the relationships and actions that occur to quantities. Example: The sum of five times a number, x, and one. Algebraic (Mathematical) Expression An algebraic expression is a quick representation of a situation by using one or more numbers, variables, and operations. Number: a specific value, quantity or measurement Variable: a symbol used to represent an unknown number or value. The English and Greek alphabets are commonly used. Operation: Addition (+), subtraction (‐), multiplication (x), and division (÷) Example: 5
1 Keywords for Each Operation Addition (+) Plus Increased by Add More than Total * Sum * Subtraction (‐) Minus Decreased by Subtract Less Less than Difference * Multiplication (x)
Times Multiplied by Of Product * Division (÷) Divided by Over Quotient * * Words that indicate the use of “grouping” • Parentheses ( ) • Brackets [ ] • Braces { } Addition (+) How can I say “20
” as a verbal expression? Twenty plus a number x. Twenty increased by a number x. Twenty more than a number x. The sum of twenty and a number x. The total of twenty and a number x. Subtraction ( ‐) How can I say “5 – ” ? Five minus n Five decreased by n Five less n The difference of five and n Note: Multiplication (x) How can I say “2 ”? Two times the number a. Two multiplied by a. Twice the number a. The product of two and a Division ( ) How can I say “
6” ? z divided by 6 z over six The quotient of z and 6 One‐sixth the number z Quantity Quantity is a versatile “Grouping” term. The quantity #/variable plus #/variable. minus times divided by Example 1: Translation from Verbal to Algebraic Expression Translate each verbal expression into an algebraic expression. a.) Eight more than a number n b.) Seven less the product of four and a number x c.) One‐third of the size of the original area a d.) The two times the quantity eight minus k Power (Exponentiation) A power is an expression that involves exponentiation. Exponentiation is an operation that utilizes repeated multiplication of a base depending on its exponent. Example: Symbols 30 Words Meaning 3 to the zeroth power 1 31 3 to the first power 3 32 3 to the second power; 3 squared; the square of 3 3 • 3 = 9 33 3 to the third power; 3 cubed; the cube of 3 3 • 3 • 3 = 27 34 3 to the fourth power 3 • 3 • 3 • 3 = 81 2 times to the fifth power 2 •
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Example 2: Algebraic Expressions with Powers Translate each verbal expression into an algebraic expression. a.) The product of 7 and to the fifth power b.) The difference of 4 and squared Example 3: Evaluating Powers Evaluate each power.
a.) 2 b.) 4 Example 4: Translation from Algebraic to Verbal Expression Translate each algebraic expression into a verbal expression. a.) 4
b.) c.) 5 21 Extra Practice Translate each verbal expression into an algebraic expression. a.) The sum of three and seven times a number b.) One‐eighth the cube of c.) 8 decreased by 9 times a number d.) One‐third the difference of eight times a number and two