Slide 1 / 185 Slide 2 / 185 7th Grade Math Expressions 2015-11-17 www.njctl.org Slide 3 / 185 Table of Contents Mathematical Expressions Click on a topic to go to that section. Order of Operations The Distributive Property Like Terms Translating Words Into Expressions Evaluating Expressions Glossary & Standards
Slide 4 / 185 Mathematical Expressions Return to Table of Contents Slide 5 / 185 Expressions Algebra extends the tools of arithmetic, which were developed to work with numbers, so they can be used to solve real world problems. This requires first translating words from your everyday language (i.e. English, Spanish, French) into mathematical expressions. Then those expressions can be operated on with the tools originally developed for arithmetic. Slide 6 / 185 Expressions An Expression may contain: numbers, variables, mathematical operations Example: 4x + 2 is an algebraic expression.
Slide 7 / 185 What is a Term? Terms of an expression are the parts of the expression which are separated by addition or subtraction. Circle the terms of this expression. Example: 4x + 2 There are two terms: 4x; 2 Circle the terms and then click to check. Slide 8 / 185 What is a Constant? A constant is a fixed value, a number on its own, whose value does not change. A constant may either be positive or negative. Example: 4x + 2 In this expression 2 is the constant. Circle the constant and then click to check. Slide 9 / 185 What is a Variable? A variable is any letter or symbol that represents a changeable or unknown value. Example: 4x + 2 In this expression x is the variable. Circle the variable and then click to check.
Slide 10 / 185 What is a Coefficient? A coefficient is a number multiplied by a variable. It is located in front of the variable. Example: 4x + 2 In this expression 4 is the coefficient. Circle the coefficient and then click to check. Slide 11 / 185 Coefficient If a variable contains no visible coefficient, the coefficient is 1. Example 1: x + 7 is the same as (1)x + 7 Example 2: -x + 7 is the same as (-1)x + 7 Slide 12 / 185 1 In 2x - 12, the variable is "x". True False
Slide 13 / 185 2 In 6y + 20, the variable is "y". True False Slide 14 / 185 3 In 3x + 4, the coefficient is 3. True False Slide 15 / 185 4 In 9x + 2, the coefficient is 2. True False
Slide 16 / 185 5 What is the constant in 7x - 3? 7 A B x C 3 D - 3 Slide 17 / 185 6 What is the coefficient in - x + 3? A none B 1 C -1 D 3 Slide 18 / 185 7 x has a coefficient. True False
Slide 19 / 185 8 ) 19 has a coefficient. True False Slide 20 / 185 Order of Operations Return to Table of Contents Slide 21 / 185 Order of Operations Mathematics has its grammar, just like any language. Grammar provides the rules that allow us to write down ideas so that a reader can understand them. A critical set of those rules is called the order of operations.
Slide 22 / 185 Order of Operations The order of operations allows us to read an expression and interpret it as intended. It lets us understand what the author meant. For instance, the below expression could mean many different things without an agreed upon order of operations. How would you evaluate this expression? (5-8)(5)(3)-4 2 ÷2+8÷4+(3-2) Slide 23 / 185 Use Parentheses Parentheses will make your life much easier. Each time you do an operation, keep the result in parentheses until you use it for the next operation. You'll be able to read your own work, and avoid mistakes. When you're done, read each step you did and you should be able to check your work. Also, when you substitute a value into an expression, put it in parentheses first...that'll save you a lot of trouble. Slide 24 / 185 Order of Operations (5-8)(5)(3)-4 2 ÷2+8÷4+(3-2) Do all operations in parentheses first. (-3)(5)(3)-4 2 ÷2+8÷4+(1) Then, do all exponents and roots. (-3)(5)(3)-(16)÷2+8÷4+1 Then, do all multiplication and division. (-45)-(8)+(2)+1 Then, do all addition and subtraction. -50
Slide 25 / 185 Order of Operations One acronym used for the order of operations is PEMDAS which stands for: Parentheses Exponents/Roots Multiplication/Division Addition/Subtraction This order helps you read an expression...but it also helps you write expressions that others can read. Since parentheses are always done first, you can always eliminate confusion by putting parentheses around what you want to be done first. They may not be needed, but they don't ever hurt. Slide 26 / 185 Order of Operations Let's simplify this step by step... -7 + (-3)[5 - (-2)] What should you do first? 5 - (-2) = 5 + 2 = 7 click to reveal What should you do next? (-3)(7) = -21 click to reveal What is your last step? -7 + (-21) = -28 click to reveal Slide 27 / 185 Order of Operations Let's simplify this step by step... What should you do first? What should you do second? Click Click to to Reveal Reveal
Slide 28 / 185 Order of Operations Let's simplify this step by step... What should you do third? What should you do last? Click Click to to Reveal Reveal Slide 29 / 185 9 Simplify the expression. -12 ÷ 3(-4) Slide 30 / 185 10 Simplify the expression. [-1 - (-5)] + [7(3 - 8)]
Slide 31 / 185 11 Simplify the expression. 40 - (-5)(-9)(2) Slide 32 / 185 12 Simplify the expression. 5.8 - 6.3 + 2.5 Slide 33 / 185 13 Simplify the expression. -3(-4.7)(5-3.2)
Slide 34 / 185 14 Simplify the expression. Slide 35 / 185 15 Complete the first step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)] Slide 36 / 185 16 Complete the next step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)] click to reveal -12.4 - 6[4.1 - (-5.3)] step from previous slide
Slide 37 / 185 17 Complete the next step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)] click to reveal -12.4 - 6[4.1 - (-5.3)] steps from previous slides -12.4 - 6[9.4] Slide 38 / 185 18 Complete the next step of simplifying. What is your answer? [3.2 + (-15.6)] - 6[4.1 - (-5.3)] click to reveal -12.4 - 6[4.1 - (-5.3)] steps from previous slides -12.4 - 6[9.4] -12.4 - 56.4 Slide 39 / 185
Slide 40 / 185 20 Simplify the expression. Slide 41 / 185 21 Simplify the expression Slide 42 / 185 22 Simplify the expression
Slide 43 / 185 23 Simplify the expression (-4.75)(3) - (-8.3) Slide 44 / 185 Order of Operations Solve this one in your groups. Slide 45 / 185 Order of Operations How about this one?
Slide 46 / 185 24 Simplify the expression Slide 47 / 185 25 Simplify the expression [(-3.2)(2) + (-5)(4)][4.5 + (-1.2)] Slide 48 / 185 26 Simplify the expression
Slide 49 / 185 27 Simplify the expression Slide 50 / 185 28 Simplify the expression Slide 51 / 185 29 Evaluate the expression (9 - 13) 2 ÷ 2(3 - 1) + 9 ∙ 8 - (5 + 6)
Slide 52 / 185 30 Evaluate the expression 7 ∙ 9 − (7 − 4) 3 ÷ 9 + (10 − 12) Slide 53 / 185 31 Evaluate the expression (7 + 3) 2 ÷ 25 + 4 ∙ 2 - (7 + 8) Slide 54 / 185 Order of Operations and Fractions The simplest way to work with fraction is to imagine that the numerator and the denominator are each in their own set of parentheses. Before you divide the numerator by the denominator, you must have them both in simplest form. And, then you must be very careful about what you can do with them.
Slide 55 / 185 Order of Operations and Fractions For instance, a common error is shown below: x 1+x I CANNOT divide the top and the bottom by x to get: 1 1+1 Rather, I have to think of the denominator (1+x) as being in parentheses. x (1+x) Until I can simplify that further (which I can't) this is the simplest form. x 1+x Slide 56 / 185 Order of Operations and Fractions How would you evaluate this expression? (4)(3)-3 2 ÷5+6÷2+(5-8) 7-8 Slide 57 / 185 Order of Operations (4)(3)-3 2 ÷5+6÷2+(5-8) 7-8 First, recognize that terms in a denominator act like they are in parentheses. (4)(3)-3 2 ÷5+6÷2+(5-8) (7-8) Then, do all operations in parentheses first. (Keep all results in parentheses until the next operation.) (4)(3)-3 2 ÷5+6÷2+(-3) (-1) Then, do all exponents and roots. (4)(3)-(9)÷5+6÷2+(-3) (-1)
Slide 58 / 185 Order of Operations (4)(3)-9÷5+6÷2+(-3) (-1) Then, all multiplication and division (12)-(1.8)+(3)+(-3) (-1) Then, do all addition and subtraction. (10.2) (-1) Then, divide the numerator by the denominator. (-10.2) Slide 59 / 185 32 Simplify the expression. Slide 60 / 185 33 Evaluate the expression 3(5 − 3) 3 + 5(7 + 5) − 9 2 ∙ 5 + 5
Slide 61 / 185 34 Evaluate the expression 2(9 − 4) 2 + 8 ∙ 6 − 3 3 ∙ 4 2 + 2 Slide 62 / 185 35 Evaluate the expression −4(2 − 8) 2 + 7(−3) + 15 5(2 5 − 12) Slide 63 / 185 36 Select the correct number from each group of numbers to complete the equation. _____ _____ A 2 E 2 B -2 F -2 C 3/4 G 4/3 D -4/3 H -3/4 From PARCC EOY sample test non-calculator #6
Slide 64 / 185 Slide 65 / 185 The Distributive Property Return to Table of Contents Slide 66 / 185 Area Model Write an expression for the area of a rectangle whose width is 4 and whose length is x + 2 4 x 2
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