topic 6: variables and expressions

Topic 6: Variables and Expressions

1

Can you form your own definition of a variable based on the following?

These are variables These are not

A = # , C = #, X = #,r = #, n = #

= # = #

A, C, n

3, 10, 75, 8, 12, 1, 0

2

Discuss and make a list of similarities and differences

(compare and contrast) These are variables These are not

A = # , C = #, X = #,r = #, n = #

= # = #

A, C, n

3, 10, 75, 8, 12, 1, 0

How they’re the same:

How they’re different:

Use interwrite board to fill in 3

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

4

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

5

Algebraic Expression • An algebraic expression is an expression

that contains one or more variables.

• Algebraic Expressions

7 + m3 (c + 8)2 a9 – 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. H + 6

• 1. answer: H plus 6

• 2. 9 – m

• 2. answer: 9 minus m

H + 69 – m

There are several ways to say these expressions…

+ - x

plus

sum

more than

increased by

total

in all

added to

minus

difference

less than

subtract

decreased by

Take awaySubtracted from

times

product

multiplied

each

of

divided

quotient

divided by

Other ways to show

multiplication : 5 x 6 5(6) 5 · 6

Other ways to showdivision:

12 ÷ 6 12/6

Reading and Writing Algebraic Expressions

Glue this in your notes and go over examples of how to read/write algebraic expressions9

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

•Stop here Monday

Guided practice page 146 HW – page 146 #8-20

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

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.

15

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

16

Now, try to translate, or write the following algebraic expressions into a

word phrase on your own.

1) n - 5

2) 9 + t

17

Now, try to translate, or write the following algebraic expressions into a

word phrase on your own.

1) n - 5

2) 9 + t

Answers will vary…

1)Take 5 away from a number

2)9 added to a number

18

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

• 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) 6m

• 2) 6 + m

• 3) 6 – m

• 4) 6/m

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.

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

1)a + 3

2)17 – a

26

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

1)a + 3

13 + 3

16

2) 17 – a

17 – 13

427

You try to evaluate the following when n = 4

1) 9n

*(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

28

You try to evaluate the following when n = 4

1) 9n

9 x 4

36

2) 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

31

Determine if the following are expressions or equations:

1)7x

2) (6-3) – 1 = 2

3)14 = 7(2)

4)X + 9 = 13

5)12 – 5

32

Determine if the following are expressions or equations:

1)7x

2) (6-3) – 1 = 2

3)14 = 7(2)

4)X + 9 = 13

5)12 – 5

• 1) expression

• 2) equation

• 3) equation

• 4) equation

• 5) expression

How could you tell the difference between the two?33

For Practice:

34

Mixed Reviewfor 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:

#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 expressionexpression 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 expressionexpression 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

#6) 7 + x _________

#7) x – 3 _________

Evaluate each expression when x = 9

#6) 7 + x _________

7 + 9 = 16

#7) x – 3 _________

9 – 3 = 6

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. 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 bExplain how you know: 33 + 5 = 38 38 = 38It 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