by Monica Yuskaitis, M.A. Ed. 6th Grade Algebra I Variable, Expression, Evaluate, Simplify a · b = ab by Monica Yuskaitis, M.A. Ed. Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis 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

Copyright © 2013 by Monica Yuskaitis 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

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

Copyright © 2013 by Monica Yuskaitis Variables Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Vocabulary Constant – is a quantity that stays the same. The opposite of a variable. Inches in a foot. Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis 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. 7 Copyright © 2013 by Monica Yuskaitis 7

Copyright © 2013 by Monica Yuskaitis Vocabulary Variable – A variable is a letter that represents a number (unknown quantity). 8 + n = 12 8 Copyright © 2013 by Monica Yuskaitis 8

Copyright © 2013 by Monica Yuskaitis Vocabulary A variable can use any letter of the alphabet. n + 5 x – 7 w - 25 Copyright © 2013 by Monica Yuskaitis

Find the Variables ? n % 7 # f v $ b p

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. A box of crayons missing 2 crayons. 3 full boxes of crayons. A full box of crayons shared equally with 3 people. n + 4 n - 2 3n 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 means 4 times 5 (not this 4.5) 4(5) means 4 times 5 ab means a times b 3b means 3 times b

Check Up – What do these mean? 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

Copyright © 2013 by Monica Yuskaitis Placement Rule Always write the variable after the number. b x 6 write 6b Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Using parentheses 4 x b 4 (b) (4) b (4b) Copyright © 2013 by Monica Yuskaitis

Algebraic and Numerical Expressions 16 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Vocabulary Numerical expression – contains only numbers amd operations 15 + 9 x 3 12 ÷ 3 - 3 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Vocabulary Algebraic expression – may contain numbers, operations, and one or more variables. 45 ÷ p - q r – 3 Copyright © 2013 by Monica Yuskaitis

Which ones are algebraic expressions? y ÷ 5 5 + 9 a + b + c n + 4 n + 4 area vertex

Which ones are numerical expressions? 29 - 7 7 x 2 9 x 3-7 b + 9 24 ÷ 12 2 + 4 32 x 7a 7x4 + c

3b + 6 - b The Anatomy of An Algebraic Expression Terms – parts separated by + and -. Coefficient – # multiplied by variable. Like terms - Terms with the same variable. 21 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Simplifying Expressions 22 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis 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 m + 8 (2 x 2) + 8 4 + 8 = 12 Copyright © 2013 by Monica Yuskaitis

Simplify these expressions s + s + s b + b + m The quantity of c + c + 6 ÷ c when c = 2 3s 2b + m (4 + 6) ÷ 2 (2c + 6) ÷ c 10 ÷ 2 = 5

Copyright © 2013 by Monica Yuskaitis Evaluating Expressions 25 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Vocabulary Evaluate an expression – To find the value of an expression by substituting numbers for variables. m + 8 m = 2 2 + 8 = 10 r – 3 r = 5 5 – 3 = 2 Copyright © 2013 by Monica Yuskaitis

Evaluate each expression when x = 10 x + x x - x x - 7 42 - x 18 59 20 3 32 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Complete This Table independent dependent n n - 3 5 10 21 32 2 7 18 29 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Complete This Table independent dependent x x + 6 5 10 21 32 11 16 27 38 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Stop Lesson 1.1 PPT Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Writing Addition and Subtraction Expressions 1.2 31 Copyright © 2013 by Monica Yuskaitis

Words That Lead to Addition Sum More than Increased by Total of Plus Altogether Added to And Copyright © 2013 by Monica Yuskaitis

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

Copyright © 2013 by Monica Yuskaitis Now You Try! Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis 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 n + 10 w - 5 x - 6 n + 8 n + 9 y + 4 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Write the Expressions s + 2 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 k - 1 x - 31 b + 7 n + 6 z + 9 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Writing Multiplication and Division Expressions 37 Copyright © 2013 by Monica Yuskaitis

Words That Lead to Multiplication Times Multiplied by Product of Groups of Twice Of Copyright © 2013 by Monica Yuskaitis

Words That Lead to Division Divided by Divided into Quotient of Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Now You Try! Copyright © 2013 by Monica Yuskaitis

Write the Algebraic Expression The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 x c or 5 • c or 5c 7 x t or 7 • t or 7t 6 x d or 6 • d or 6d Copyright © 2013 by Monica Yuskaitis

Write an algebraic expression 24 multiplied by a number Product of 32 and a number 300 times a number 24n 32n 300n Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis Now Write Expressions with All 4 Operations 43 Copyright © 2013 by Monica Yuskaitis

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 6n + 2 3w b/4 8/n n/4 3x Copyright © 2013 by Monica Yuskaitis

Write an algebraic expression 3 times the sum of 4 and 2 Product of 4 and the sum of 3 & 2 Multiply 3 times the sum of r & 5 3 (4 + 2) 4 (3 + 2) 3 (r + 5) Copyright © 2013 by Monica Yuskaitis

Write an algebraic expression Twice the sum of z and 3 Multiply z by the sum of 7 and s 4 times the difference of w and 5 2 ( z + 3) z (7 + s) 4 (w – 5) Copyright © 2013 by Monica Yuskaitis

Write an Algebraic Expression Twice the sum of q and 5 Multiply t by the sum of 8 and p 6 times the difference of h and 3 2 ( q + 5) t (8 + p) 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

Copyright © 2013 by Monica Yuskaitis Problem Solving Copyright © 2013 by Monica Yuskaitis

Analysis Representation Resolution 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? Analysis Representation What strategies will you use? What operations will you use? How many steps are there and in what order must you do them? Resolution How will you solve the problem? Did you check your answer? Does your answer make sense?

Write an Algebraic Expression Scott’s brother is 2 years younger than Scott. The sum of two numbers is 12. The difference between two numbers is 5. s - 2 v + c = 12 m – n = 5 Copyright © 2013 by Monica Yuskaitis

Copyright © 2013 by Monica Yuskaitis 1.2 PPT Copyright © 2013 by Monica Yuskaitis