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Published byBruno Mathews Modified over 8 years ago
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Part One: Vocabulary Review
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What is a Constant? A constant is a fixed value, a number on its own, whose value does not change. What is the constant in the expressions below? Example: 4x + 2 In this expression 2 is a constant. click to reveal Example: 11m - 7 In this expression -7 is a constant. click to reveal
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What is a Variable? A variable is any letter or symbol that represents a changeable or unknown value. What is the variable? Example: 4x + 2 In this expression x is a variable. click to reveal
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What is a Coefficient? A coefficient is the number multiplied by the variable. It is located in front of the variable. What is the coefficient in the expression below? Example: 4x + 2 In this expression 4 is a coefficient. click to reveal
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Example 1: x + 4 is the same as 1x + 4 - x + 4 is the same as -1x + 4 Example 2: If a variable contains no visible coefficient, the coefficient is 1.
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Identifying Algebraic Expressions and Equations
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What does an algebraic expression contain? An expressions consists of 3 items ·numbers ·variables ·operations Click to reveal
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Each term in an algebraic expression is separated by a plus (+) or minus ( - ) sign. 15w is an algebraic expression with one term. 7m - 12 is an algebraic expression with two terms. -4x + 3y - 20 is an algebraic expression with three terms.
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Let's take a look and decide if the examples are expressions or not. 5 + n What is the constant?______________ What is the variable?______________ What is the coefficient?______________ Is it an algebraic expression?______________ If yes, how many terms does it have?______________ Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!
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Let's take a look and decide if the examples are expressions or not. 5 + n What is the constant?5 What is the variable?n What is the coefficient?1 Is it an algebraic expression?Yes! If yes, how many terms does it have?2
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3b - 4c -7 What is/are the constants?______________ What is/are the variables?______________ What is/are the coefficients?______________ Is it an algebraic expression?______________ If yes, how many terms does it have?______________ Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!
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3b - 4c -7 What is/are the constants?-7 What is/are the variables?b and c What is/are the coefficients?3 and 4 Is it an algebraic expression?YES! If yes, how many terms does it have?three
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p What is the constant?______________ What is the variable?______________ What is the coefficient?______________ Is it an algebraic expression?______________ If yes, how many terms does it have?______________ Let's try a challenge. Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!
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p What is the constant?none What is the variable?p What is the coefficient?1 Is it an algebraic expression?YES! If yes, how many terms does it have?one Let's try a challenge.
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Translating Between Words and Expressions
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With a partner – or on a white board – brainstorm all of the words you can think of that mean addition
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With a partner – or on a white board – brainstorm all of the words you can think of that mean subtraction
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Sort each as either an addition word or subtraction word. Check with a classmate or the teacher if you are unsure. Addition Subtraction plus sum addend greater than minus difference less than how much more how much less take away
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Sort each as either a multiplication word or division word. Check with a classmate or the teacher if you are unsure! Multiplication Division product factor quotient times of divisor share dividend divide
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Be aware of the phrase "less than". For example: “3 more than eight times a number” can be written as: either 8n + 3 or 3 + 8n (both are correct) BUT… “three less than eight times a number” Can ONLY be written as 8n - 3 It is NOT the same as 3 – 8n Confused? Think about it this way: Mr. Baxter has $25. Ms. Foley has $6 less than Mr. Baxter. She has $25 - $6 = $19. This is NOT the same as $6 - $25
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As a rule of thumb, if you see the words "than" or "from" it means you have to reverse the order of the two items on either side of the word. Examples: 8 less than b means b – 8 3 more than x means x + 3 (although 3 + x is okay) x less than 2 means 2 – x click to reveal
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Three times j Eight divided by j j less than 7 5 more than j 4 less than j TRANSLATE THE WORDS INTO AN ALGEBRAIC EXPRESSION Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!
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Three times j3j Eight divided by j8/j j less than 77 – j 5 more than jj + 5 4 less than jj - 4 TRANSLATE THE WORDS INTO AN ALGEBRAIC EXPRESSION
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Seventy-one plus c Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide! Twenty-four less than d The sum of twenty-three and m Four times the difference of eight and j The product of seven and w, divided by 12 The square of the sum of six and p
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71+cSeventy-one plus c Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide! Twenty-four less than dd - 24 The sum of twenty-three and m23 + m Four times the difference of eight and j 4(8-j) The product of seven and w, divided by 12 7w 12 The square of the sum of six and p(6+p) 2
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Evaluating Expressions
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Steps for Evaluating an Expression: 1. Write the expression 2.Substitute the values given for the variables (use parentheses!) 3. Simplify the Expression Remember Order of Operations! Write - Substitute - Simplify click to reveal
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1.Solve in your journal. 2.Show all steps. (Write. Substitute. Simplify.) 3.Check your work on the next slide! What is the value of 4n + 6 2 when n = 3 ?
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How you show your work is just as important as the answer What is the value of 4n + 6 2 when n = 3 ? 4n + 6 2 Write! = 4(3) + 6 2 Substitute. = 4(3) + 36Simplify. = 12 + 36 = 48
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1.Solve in your journal. 2.Show all steps. (Write. Substitute. Simplify.) 3.Check your work on the next slide! Evaluate (4n + 6) 2 for n = 1
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(4n + 6) 2 = (4(1) + 6) 2 = (4 + 6) 2 = (10) 2 = 100
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4x + 2x 3 1.Solve in your journal. 2.Show all steps. (Write. Substitute. Simplify.) 3.Check your work on the next slide! What is the value of the expression below when x = 2 ?
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4x + 2x 3 = 4(2) + 2(2) 3 = 4(2) + 2(8) = 8 + 16 = 24 What is the value of the expression below when x = 2 ?
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