Part One: Vocabulary Review

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 click to reveal In this expression 2 is a constant. Example: 11m - 7 click to reveal In this expression -7 is a constant.

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 click to reveal In this expression x is a variable.

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 click to reveal In this expression 4 is a coefficient.

Example 1: x + 4 is the same as 1x + 4 - x + 4 is the same as -1x + 4 If a variable contains no visible coefficient, the coefficient is 1. Example 1: x + 4 is the same as 1x + 4 - x + 4 is the same as -1x + 4 Example 2:

Algebraic Expressions and Identifying Algebraic Expressions and Equations

What does an algebraic expression contain? Click to reveal An expressions consists of 3 items ·numbers ·variables ·operations

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.

Let's take a look and decide if the examples are expressions or not. 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? ______________ Answer: Yes, 2 terms Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

Let's take a look and decide if the examples are expressions or not. 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 Answer: Yes, 2 terms

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? ______________ Answer: Yes, 2 terms Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

What is/are the constants? -7 What is/are the variables? b and c 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 Answer: Yes, 2 terms

Let's try a challenge. 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? ______________ Answer: Yes, 1 term Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

What is the constant? none What is the variable? p Let's try a challenge. 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 Answer: Yes, 1 term

Translating Between Words and Expressions

Sort each as either an addition word or subtraction word. Check with a classmate or the teacher if you are unsure. plus minus how much less greater than addend difference take away sum how much more less than Addition Subtraction

Sort each as either an addition word or subtraction word. Check with a classmate or the teacher if you are unsure. Addition Subtraction minus plus addend how much less sum difference how much more take away greater than less than

Sort each as either a multiplication word or division word. Check with a classmate or the teacher if you are unsure! product dividend times quotient of divide factor share divisor Multiplication Division

Sort each as either a multiplication word or division word. Check with a classmate or the teacher if you are unsure! Multiplication Division quotient product dividend times of divide share divisor factor

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 

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

TRANSLATE THE WORDS INTO AN ALGEBRAIC EXPRESSION Three times j Eight divided by j j less than 7 5 more than j 4 less than j Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide!

TRANSLATE THE WORDS INTO AN ALGEBRAIC EXPRESSION Three times j 3j Eight divided by j 8/j j less than 7 7 – j 5 more than j j + 5 4 less than j j - 4

Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide! Seventy-one plus c 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

Write your answers on a white board or in your notebook BEFORE checking your answers on the next slide! Seventy-one plus c 71+c Twenty-four less than d d - 24 The sum of twenty-three and m 23 + m Four times the difference of eight and j 4(8-j) 7w 12 The product of seven and w, divided by 12 The square of the sum of six and p (6+p)2

Evaluating Expressions

Steps for Evaluating an Expression: 1. Write the expression Substitute the values given for the variables (use parentheses!) 3. Simplify the Expression Remember Order of Operations! click to reveal Write - Substitute - Simplify

What is the value of 4n + 62 when n = 3 ? Solve in your journal. Show all steps. (Write. Substitute. Simplify.) Check your work on the next slide! What is the value of 4n + 62 when n = 3 ?

What is the value of 4n + 62 when n = 3 ? How you show your work is just as important as the answer  What is the value of 4n + 62 when n = 3 ? 4n + 62 Write! = 4(3) + 62 Substitute. = 4(3) + 36 Simplify. = 12 + 36 = 48

Solve in your journal. Show all steps. (Write. Substitute. Simplify.) Check your work on the next slide! Evaluate (4n + 6)2 for n = 1

Evaluate (4n + 6)2 for n = 1 (4n + 6)2 = (4(1) + 6)2 = (4 + 6)2 = (10)2 = 100

What is the value of the expression below when x = 2 ? Solve in your journal. Show all steps. (Write. Substitute. Simplify.) Check your work on the next slide! What is the value of the expression below when x = 2 ? 4x + 2x3

What is the value of the expression below when x = 2 ? 4x + 2x3 = 4(2) + 2(2)3 = 4(2) + 2(8) = 8 + 16 = 24