Topic 6: Variables and Expressions

Can you form your own definition of a variable based on the following? These are variables These are not A, C, n 3, 10, 75, 8, 12, 1, 0 A = # , C = #, X = #,r = #, n = # = #

Discuss and make a list of similarities and differences (compare and contrast) These are variables These are not How they’re the same: A = # , C = #, X = #,r = #, n = # = # A, C, n 3, 10, 75, 8, 12, 1, 0 How they’re different: Use interwrite board to fill in

See if your definition that you came up with matches the definition of a variable: Variable is…. A letter or symbol that represents an unknown number/amount. Examples: a , C, x, N, , Copy this down in your notes

Notice that you don’t see any equal signs Expressions An expression consists of a combination of numbers, operation symbols, and grouping symbols such as parentheses ( ).   Expressions: 3 + 4 6 – 2 (6 + 3) -1 Notice that you don’t see any equal signs

Again notice that you don’t see any equal signs Algebraic Expression An algebraic expression is an expression that contains one or more variables. Algebraic Expressions 7 + m 3 (c + 8) 2 a 9 – x Again notice that you don’t see any equal signs What is the difference between an expression and an Algebraic expression?

We are going to focus on… Algebraic expressions 506.3.2 Use variables appropriately to represent numbers whose values are not yet known.

What do you think… How do you think you should say these expressions? 1. answer: H plus 6 2. 9 – m 2. answer: 9 minus m H + 6 9 – m There are several ways to say these expressions…

+ - x ¸ plus sum more than increased by total in all added to minus Reading and Writing Algebraic Expressions + - x ¸ plus sum more than increased by total in all added to minus difference less than subtract decreased by Take away Subtracted from times product multiplied each of divided quotient divided by Other ways to show division: 12 ÷ 6 12/6 Other ways to show multiplication : 5 x 6 5(6) 5 · 6 Glue this in your notes and go over examples of how to read/write algebraic expressions

Let’s look at it step by step Watch video 06-01 https://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=toc&newServiceId =10363&product_isbn=0-328-52262-7

Catch of the Day Guided practice page 146 HW – page 146 #8-20 Stop here Monday

What are algebraic expressions? An algebraic expression is an expression that contains one or more variables.

Video 06-00 https://www.pearsonsuccessnet.com/snpapp/learn/navigateIDP.do?method=toc&newServiceId =10363&product_isbn=0-328-52262-7

4 increased by a number 25 less than a number Using your notes that we just glued in yesterday , try to figure out what operation (+,-,x,/) to use for the following: 4 increased by a number 25 less than a number Add Subtract The phrase “a number” or “some number” means that a variable is needed.

4 increased by a number 4 + c Now, that we know the components of this expression, let’s try to write an algebraic expression for each word phrase 4 increased by a number 4 + c *it does not matter what letter you use, just as long as you include a variable. 25 less than a number n – 25 *just because we see 25 first in the word phrase, doesn’t mean that 25 is written first in the expression.

Try to write these on your own: Add 3 to a number 3 + n or n + 3 Some number multiplied by 16 16 x b or b x 16

Now, try to translate, or write the following algebraic expressions into a word phrase on your own.

Now, try to translate, or write the following algebraic expressions into a word phrase on your own. Answers will vary… Take 5 away from a number 9 added to a number n - 5 9 + t

5 less than a number n – 5 This is the correct answer because it is 5 less. If it is 5 less, then you are taking 5 away. You are taking 5 away from a number.

Example n - 6 What is 5 less than 30? 25 What is 5 less than 20? 15 NOW Write the expression for: 6 less than a number n - 6

Write the following in word form 1) 6 multiplied by m OR? 2) added to m or m added to 6 OR? 3) 6 minus m or m taken away from 6 OR? 4) 6 divided by m

Write the following as an algebraic expression 1) a number added to 7 2) a number taken away from 7 3) a number divided by 7 4) a number times by 7 7 + n or n +7 7 - n n/7 or n ÷ 7 7 x n or 7n

textbook page 148 & 149 Guided practice at top of 149 With a partner or whole group page 149 #5-19 HW- WB 100

Evaluating algebraic expressions 0505.3.1 Evaluate an expression by substituting a number for the variable or variables in the problem.

Evaluate means to substitute a value, then solve the problem.

Evaluate each expression when a = 13 When we evaluate algebraic expressions, we are substituting a number in place of variable, then solving for an answer Evaluate each expression when a = 13 a + 3 17 – a

Evaluate each expression when a = 13 When we evaluate algebraic expressions, we are substituting a number in place of variable, then solving for an answer Evaluate each expression when a = 13 a + 3 13 + 3 16 2) 17 – a 17 – 13 4

You try to evaluate the following when n = 4 *(what operation does this mean when a number is right beside a variable? Look at your notes if you don’t know) 2) 40 / n

You try to evaluate the following when n = 4 9 x 4 36 40 / n 40 / 4 10

Brainpop-Equations http://www.brainpop.com/math/algebra/equationswithvariables/

An Equation is a complete sentence that is either true or false = shows that each side has the same value examples: x + 7 = 14 47 = 50 – 3 7 + 7 = 14 y – 6 = 13 14 = 14

Determine if the following are expressions or equations: (6-3) – 1 = 2 14 = 7(2) X + 9 = 13 12 – 5

Determine if the following are expressions or equations: (6-3) – 1 = 2 14 = 7(2) X + 9 = 13 12 – 5 1) expression 2) equation 3) equation 4) equation 5) expression How could you tell the difference between the two?

For Practice:

Mixed Review for Quiz Each student needs a sheet of paper

Directions: The following questions are similar to the types of questions that you will see on tomorrow’s quiz. Every student needs to answer or attempt to answer each question. If you find that you get several answers wrong, please talk to the teacher at the end of class or during content mastery for additional help 

#1 - In your own words, tell me what a variable is? #2 - Write down at least 2 examples of variables:

#2 - Write down at least 2 examples of variables: C, x, n, #1 - In your own words, tell me what a variable is? A variable is a letter or symbol that represents an unknown # #2 - Write down at least 2 examples of variables: C, x, n, Answers may vary

Write an algebraic expression for each word phrase: #3) take 14 from a number #4) 15 is decreased by a number #5) add 8 to a number

Write an algebraic expression for each word phrase: #3) take 14 from a number n – 14 #4) 15 is decreased by a number 15 – n #5) add 8 to a number n + 8 or 8 + n

Evaluate each expression when x = 9

Evaluate each expression when x = 9 7 + 9 = 16 #7) x – 3 _________ 9 – 3 = 6

Use mental math to solve the equations Use mental math to solve the equations. Rewrite the equation showing that both sides are equal. #8) 75 + t = 80 t = ____ ___________ #9) b – 52 = 17 b= ____ __________

Use mental math to solve the equations Use mental math to solve the equations. Rewrite the equation showing that both sides are equal. #8) 75 + t = 80 t = 5 75 + 5 = 80 80 = 80 #9) b – 52 = 17 b= _69_ 69 – 52 = 17 17 = 17

Which number sentence is true if x= 5 #10) a) 38 – x = 30 b) 33 + x = 38 c) 38 = x + 30 d) x – 38 = 33 The correct answer is ____ Explain how you know:

Which number sentence is true if x= 5 #10) a) 38 – x = 30 b) 33 + x = 38 c) 38 = x + 30 d) x – 38 = 33 The correct answer is b Explain how you know: 33 + 5 = 38 38 = 38 It was the only equation that was “true”

You decide what the following equation represents. $50.00 – x = $45.00 11) Write a word problem to fit the equation. Then solve your problem.

You decide what the following equation represents. $50.00 – x = $45.00 11) Write a word problem to fit the equation. (example: ) My grandparents gave me fifty dollars for my birthday. I spent some of my money on a toy, and now I have $45 left. How much was the toy that I bought? Then solve your problem. $50 – $5 = $45 x = $5

Quiz Tomorrow CW/HW – Sink that Basket