Variables, Algebraic Expressions, and Simple Equations

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 stands for an unknown number.

Examples: a , C, x, N, ,

Copy this down in your notes

Stop here on Monday

Go on to “Catch of the Day”4

Algebraic Expressions

• An expression consists of a combination of numbers, operation symbols, and grouping symbols such as parentheses ( ). An algebraic expression is an expression that contains one or more variables.

• Expressions: Algebraic Expressions 3 + 4 3 (c + 8)

6 – 2 2 a(6 + 3) -1 9 – x

Notice that you don’t see any equal signs

5

+ - x ÷

plussummore thanincreased bytotalin alladded to

minusdifferenceless thansubtractdecreased byTake awaySubtracted from

timesproductmultipliedeachof

dividedquotientdivided by

Other ways to showmultiplication : 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 expressions6

Using your notes that we just glued in, 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.

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.

8

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

9

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

word phrase on your own.1) n - 5

2) 9 + t

10

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

11

When we evaluate algebraic expressions, we are substituting a number in place of variable, then

solving for an answer

Evaluate each expression when a = 121) a + 3

2) 17 – a

12

When we evaluate algebraic expressions, we are substituting a number in place of variable, then

solving for an answer

Evaluate each expression when a = 121) a + 312 + 3

152) 17 – a 17 – 12

513

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

14

You try to evaluate the following when n = 4

1) 9n 9 x 4 36

2) 40 / n 40 / 4 10

15

If several students had trouble withthe algebraic expressions today, have them do WB 8 and save the partneractivity for Thursday.

Stop here for Tues.

Equations

http://www.learnalberta.ca/content/mesg/html/math6web/math6shell.html

(link to video)--- you will need to do the following:Skip intro, Click on Lessons, Click on the 11th video.

16

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

17

Determine if the following are expressions or equations:

1) 7x2) (6-3) – 1 = 23) 14 = 7(2)4) X + 9 = 135) 12 – 5

18

Determine if the following are expressions or equations:

1) 7x2) (6-3) – 1 = 23) 14 = 7(2)4) X + 9 = 135) 12 – 5

• 1) expression• 2) equation• 3) equation• 4) equation• 5) expression

How could you tell the difference between the two?19

For Practice:

• Do pg. 41 #17-20 together

• Then, with a partner, do #5-16 (using beans, buttons, etc..)

20

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 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

#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

• Evaluate means to substiture a value, then solve the problem.