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6th Grade Variable, Expression, Evaluate, Simplify a · b = ab by Monica Yuskaitis, M.A. Ed. Copyright © 2013 by Monica Yuskaitis 1 Objectives • To be able to distinguish between a numerical expression and an algebraic expression. • To be able to simplify algebraic expressions. • To be able to evaluate algebraic expressions. Copyright © 2013 by Monica Yuskaitis 2 Essential Question • How can I evaluate and simplify algebraic expressions? • How can I identify if an expression is numerical or algebraic? 3 Copyright © 2013 by Monica Yuskaitis Vocabulary Sum - what you get when you add 1 +1 = 2 Difference - what you get when you subtract 2 -1 = 1 Product- the answer to a multiplication problem 2 x 1 = 1 Quotient – what you get when you divide 2÷1=2 Factor - a number multiplied to get another number 2 x1 =2 Copyright © 2013 by Monica Yuskaitis Variables Copyright © 2013 by Monica Yuskaitis 5 Vocabulary • Constant – is a quantity that stays the same. The opposite of a variable. • Inches in a foot. Copyright © 2013 by Monica Yuskaitis 6 Vocabulary • Variable – A is a quantity that can change. •8+n= In this problem n could be 1, 2, 3, 4 or whatever the author wants it to be. Note as n changes, so does the answer. Copyright © 2013 by Monica Yuskaitis 7 Vocabulary • Variable – A variable is a letter that represents a number (unknown quantity). • 8 + n = 12 Copyright © 2013 by Monica Yuskaitis 8 Vocabulary • A variable can use any letter of the alphabet. •n+5 •x–7 • w - 25 Copyright © 2013 by Monica Yuskaitis 9 Find the Variables ? n # f p % 7 v $ b Variables • Variables are great to use when you are doing a word problem and you don’t know a number. • A full box of crayons with 4 extra crayons. n+4 • A box of crayons missing 2 crayons. n-2 • 3 full boxes of crayons. 3n • A full box of crayons shared equally with 3 people. n/3 Multiplication in Algebra • Sometimes the x for multiplication gets confused with a variable. So we show multiplication in different ways in algebra. • • • • 4·5 4(5) ab 3b means 4 times 5 (not this 4.5) means 4 times 5 means a times b means 3 times b Check Up – What do these mean? • • • • • • • p·4 3q s/2 cd j+3 6(3) 9-e p times 4 3 times q s divided by 2 c times d j plus 3 6 times 3 9 minus e Placement Rule • Always write the variable after the number. b x 6 write 6b Copyright © 2013 by Monica Yuskaitis Using parentheses 4xb • 4 (b) • (4) b • (4b) Copyright © 2013 by Monica Yuskaitis Algebraic and Numerical Expressions Copyright © 2013 by Monica Yuskaitis 16 Vocabulary • Numerical expression – contains only numbers amd operations • 15 + 9 x 3 • 12 ÷ 3 - 3 Copyright © 2013 by Monica Yuskaitis 17 Vocabulary • Algebraic expression – may contain numbers, operations, and one or more variables. • 45 ÷ p - q • r–3 Copyright © 2013 by Monica Yuskaitis 18 Which ones are algebraic expressions? h-7 a+b+c p–6+1 y÷5 5+9 n+4 area vertex Which ones are numerical expressions? 7x2 24 ÷ 12 29 - 7 9 x 3-7 b+9 2+4 32 x 7a 7x4 + c The Anatomy of An Algebraic Expression 3b + 6 - b Coefficient – Like terms # multiplied Terms with by variable. Terms – parts the same separated by variable. + and -. Copyright © 2013 by Monica Yuskaitis 21 Simplifying Expressions Copyright © 2013 by Monica Yuskaitis 22 Vocabulary • Simplify – Combine like terms and complete all operations. Use parentheses around operations you are going to do first. m=2 m+8+m (2 x 2) + 8 2m+8 4 + 8 = 12 Copyright © 2013 by Monica Yuskaitis 23 Simplify these expressions 3s •s+s+s 2b + m •b+b+m • The quantity of c + c + 6 ÷ c when c = 2 (4 + 6) ÷ 2 (2c + 6) ÷ c 10 ÷ 2 = 5 Evaluating Expressions Copyright © 2013 by Monica Yuskaitis 25 Vocabulary • Evaluate an expression – To find the value of an expression by substituting numbers for variables. •m + 8 •r – 3 m = 2 2 + 8 = 10 r=5 5–3=2 Copyright © 2013 by Monica Yuskaitis 26 Evaluate each expression when x = 10 18 •x+8 59 • x + 49 20 •x+x 0 •x-x 3 •x-7 • 42 - x 32 Copyright © 2013 by Monica Yuskaitis 27 Complete This Table independent dependent n 5 10 21 32 n-3 2 7 18 29 Copyright © 2013 by Monica Yuskaitis 28 Complete This Table independent dependent x 5 10 21 32 x+6 11 16 27 38 Copyright © 2013 by Monica Yuskaitis 29 Stop Lesson 1.1 PPT Copyright © 2013 by Monica Yuskaitis 30 Writing Addition and Subtraction Expressions 1.2 Copyright © 2013 by Monica Yuskaitis 31 Words That Lead to Addition • • • • • • • • Sum More than Increased by Total of Plus Altogether Added to And Copyright © 2013 by Monica Yuskaitis 32 Words That Lead to Subtraction • • • • • • • • Decreased by Less than Difference of Minus How many more Subtract from Fewer than Take away Copyright © 2013 by Monica Yuskaitis 33 Now You Try! Copyright © 2013 by Monica Yuskaitis 34 Write the Expressions • Ten more than a number • A number decrease by 5 • 6 less than a number • A number increased by 8 • The sum of a number & 9 • 4 more than a number Copyright © 2013 by Monica Yuskaitis n + 10 w-5 x-6 n+8 n+9 y+4 35 Write the Expressions • A number s plus 2 • A number decrease by 1 • 31 less than a number • A number b increased by 7 • The sum of a number & 6 • 9 more than a number Copyright © 2013 by Monica Yuskaitis s+2 k-1 x - 31 b+7 n+6 z+9 36 Writing Multiplication and Division Expressions Copyright © 2013 by Monica Yuskaitis 37 Words That Lead to Multiplication • Times • Multiplied by • Product of • Groups of • Twice • Of Copyright © 2013 by Monica Yuskaitis 38 Words That Lead to Division • Divided by • Divided into • Quotient of Copyright © 2013 by Monica Yuskaitis 39 Now You Try! Copyright © 2013 by Monica Yuskaitis 40 Write the Algebraic Expression • The product of 5 and a number c 5 x c or 5 • c or 5c • Seven times a number t 7 x t or 7 • t or 7t • 6 multiplied by a number d 6 x d or 6 • d or 6d Copyright © 2013 by Monica Yuskaitis Write an algebraic expression • 24 multiplied by a number 24n • Product of 32 and a number 32n • 300 times a number 300n Copyright © 2013 by Monica Yuskaitis Now Write Expressions with All 4 Operations Copyright © 2013 by Monica Yuskaitis 43 Write the Algebraic Expressions • 6 times a number plus 2 • Product of a number and 3 • Number divided by 4 • Quotient of 8 divided by n • 4 divided into a number • 3 groups of x Copyright © 2013 by Monica Yuskaitis 6n + 2 3w b/4 8/n n/4 3x 44 Write an algebraic expression • 3 times the sum of 4 and 2 3 (4 + 2) • Product of 4 and the sum of 3 & 2 4 (3 + 2) • Multiply 3 times the sum of r & 5 3 (r + 5) Copyright © 2013 by Monica Yuskaitis Write an algebraic expression • Twice the sum of z and 3 2 ( z + 3) • Multiply z by the sum of 7 and s z (7 + s) • 4 times the difference of w and 5 4 (w – 5) Copyright © 2013 by Monica Yuskaitis Write an Algebraic Expression • Twice the sum of q and 5 2 ( q + 5) • Multiply t by the sum of 8 and p t (8 + p) • 6 times the difference of h and 3 6 (h – 3) Copyright © 2013 by Monica Yuskaitis Evaluate these Expressions • m ÷ 3 when m = 12 12 ÷ 3 = 4 • 3p when p = 8 3 · 8 = 24 • k - 5 when k = 18 18 - 5 = 13 • 9 + b when b = 7 9 + 7 = 16 • 18/v when v = 6 18 ÷ 6 = 3 Problem Solving Copyright © 2013 by Monica Yuskaitis 49 Problem Solving Steps What information do you need? What is the problem asking you to find out? Is the answer going to be larger or smaller? What strategies will you use? What operations will you use? How many steps are there and in what order must you do them? Analysis Representation How will you solve the problem? Did you check your answer? Does your answer make sense? Resolution Write an Algebraic Expression • Scott’s brother is 2 years younger than Scott. s-2 • The sum of two numbers is 12. v + c = 12 • The difference between two numbers is 5. m–n=5 Copyright © 2013 by Monica Yuskaitis 51 1.2 PPT Copyright © 2013 by Monica Yuskaitis 52