Variables and Expressions Week of September 9mathmotthall.wikispaces.com/file/view/Variables...

Variables and Expressions Week of September 9

AIM: Understanding Variables and Expressions

Do Now:

1) Define what a variable is and give an example

2) Ms. Harris has $5 less than Ms. Harriott. Ms. Harriott has a $20 in her wallet. How much money does Ms. Harris have?

Did you add or subtract?

In what order?

PowerAlgebra

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Algebraic Expression

- An algebraic expression is a mathematical phrase that includes a variable but NO equal/inequality sign.

Ex: 3x + 558 - n

Identify the variables in the examples above.

Check yourself:

Is 3x + 5 > 8 an expression? Why or why not?


Group ActivityWith the person sitting to your right, work on "Words into Math"

-Using the words in the word bank, place them under their correct math word/symbol.


Level 1

Write the algebraic expression for the word phrase

32 more than a number

8 times a number

the quotient of a number n and 5

Level 298 less than a number

the sum of 15 and x, plus 7

Level 3

4 less than three sevenths of y

Solutions:n + 32

8n

n/5 or n ÷ 5

n - 98

(15 + x) + 7

(3/7)y - 4


Write a word phrase for each algebraic expression

q + 5

12x

9n + 1

2(5 - n)

Answers my vary:

1. the sum of an number and 5 or 5 more than a number2. 12 times a number3. the sum of 9 times a number and 1 or 9 times a number plus 15. 2 times the difference of 5 and a number or twice the quantity n less than 5...multiple answers

(if you finish early check with your table partner)


THINK FIRST

How can you represent the diagram below as an algebraic expression?

CHALLENGEYou and some friends are going to a museum. Each ticket cost $4.50

a) If n is the number of tickets purchased, write an expression that gives the total cost of buying n tickets.

b) Suppose the total cost of n tickets is $36. What is the total cost if one more ticket is purchased?

Answers:a) 4.50nb) $36 + $4.50 = $40.50


Reasoning

With a partner, discuss the following problem. Justify your answer

- You write (5 - 2) ÷ n to represent the phrase 2 less than 5 divided by a number n. Your friend writes (5 ÷ n) - 2. Are these both reasonable interpretations? Explain


Practice with Variables and Expressions

Work in group of 2(no more than 3)

-Algebraic Expressions 1- Algebraic Expressions 2


EXIT SLIP

1) Give an example of an algebraic expression

2) What word phrases represent the expressions 2 + 3x and 3x +2. Are the two expressions the same? Explain

3) Today I didn't understand _________________


AIM: How to use Order of Operations to evaluate Expressions

Do Now:(work with a partner)

PowerAlgebra

A.SSE.1.a

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Do you REMEMBER......

Write "eight less than the product of five and a number" as an algebraic expression

5n - 8

Sally had 21 marbles. Her friend gave her some more. She then had 35 marbles. Write an expression that shows how many marbles she had.

21 + x = 35


Need to Know...

Power has two parts, the BASE and the EXPONENT. The exponent tells you how many times to write out the base number.

25base

exponent


Simplify the following

Level 1

34

Level 2

(2/3)3

Level 3

(0.5)3

81

8/27

.125


Essential Understanding: When simplifying an expression, you need to perform operations in the correct order.


Can you find the error on the one on the left?


Let's TRY

What is the simplified form of the expression?

(6 - 2)3 ÷ 2

= (4)3 ÷ 2

= 64 ÷ 2

= 32

in your calculator4 *4 *4 or 4^3


TRY #2

5 ⋅ 7 - 42 ÷ 2

= 5 · 7 - 16 ÷ 2= 35 - 16 ÷ 2= 35 - 8= 27

If you got this wrong, where was your mistake??


YOUR TURN

4 + 34

7 - 2

Hint: Think of a fraction line as separating the top and bottom like a set of parenthesis

= 4 + 815

= 85/5 = 17


EVALUATE an algebraic expression by replacing(plug in) each variable with a given number

What is the value of the expression for x = 5 and y = 2

x2 + x - 12 ÷ y2

Step 1: Plug in the given values for x and y.

52 + 5 - 12 ÷ 22

Step 2: Use order of operations to simplify.

25 + 5 - 12 ÷ 425 + 5 - 330 - 327


TRY #1

Evaluate the expression for s = 4 and t = 8

3st2 ÷ (st) + 6**careful - if two variables are next to each other, avoid mistakes by using parenthesis!**

Step 1: Substitute

Step 2: use order of operations to solve

3(4)(8)2 ÷ (4)(8) + 6

3(4)(64) ÷ (4)(8) + 6= 768 ÷ 32 - 6= 24 - 6 = 18


TRY #2

Evaluate for x = 3 and y = 4

x2 + 2(x + y)

Step 1: Substitute

Step 2: Simplify using the order of operations

32 + 2(3 + 4)

= 32 + 2(7)= 9 + 14 = 23


FACEBOOK CHALLENGEIf you choose

a) Come to the front of the roomb) Go to the back of the roomc) Go to the right of the roomd) Go to the left of the room


FIND THE ERROR

23 - 8 ⋅ 2 + 32 = 23 - 8 ⋅ 2 + 915 ⋅ 2 + 930 + 939 ×

Find the error and simplify the expression correctlyDON'T FORGET TO CHECK YOUR PARTNER!!


Challenge #1

Simplify the expression 3[(4 - 2)5 - 20]

Challenge #2

A student wrote the expressions shown and claimed they were equal for all values of x and y

a) Evaluate each expression for x = 1 and y = 0b) Evaluate each expression for x = 1 and y = 2c) Choose another pair of values for x and y. Evaluate each

expression for those values.d) Is the student's claim correct? Justify your answer

(x + y)2

x2 + y2


PARTNER WORK


EXIT SLIP

1) Write a word phrase you can use to represent the algebraic expression n ÷ 8

2) Evaluate for x = 1 and y = 1

( y + x) ÷ 2+ x



AIM: To Identify and Use the Properties of Real Numbers

Do Now:

Try- Write an algebraic equation to represent the following, challenge yourself to solve it

1)

-Half of a number is 16

2) 16 - 3(8 - 3)2 ÷ 5

3) 4A2 + B(C - A)

Evaluate for A= 3, B= 5 and C = -2** **

A.RE.1


1) 2 + 3 = 3 · 2 =

3 + 2 = 2 · 3 =

does order matter? how do you know?

2) 2 - 3 = 3 ÷ 2 =3 - 2 = 2 ÷ 3 =

does order matter? how do you know?

Discovering the Commutative Property

so order does NOT matter for which two operations?

ThinkPairShare


Commutative Properties of Addition/Multiplication

Think about commuting. You haveto come to school and go backhome.

2 + 3 = 3 + 2

2 ⋅ 3 = 3 ⋅ 2


Discovering the Associative Property

1) (2 + 3) + 4 =

2 + (3+ 4) =

Does it matter where the numbers are grouped together (in parenthesis) ?

2) (2 - 3) - 4 =

2 - (3 - 4) =

Does it matter where the numbers are grouped together (in parenthesis) ?

So grouping does NOT matter for which operation? Can you guess the second operation it does NOT matter for?

ThinkPairShare


Associative Property of Addition/Multiplication

a + (b + c) = (a + b) + c

a(b ⋅ c) = (a ⋅ b)c

** Realize that what's inside the parenthesis is DIFFERENT **

Put in your notes!!


Distributive Property

1 (2 + 3) = (1 ⋅ 2) + (1 ⋅ 3)


Discovering your IDENTITIES!! ThinkPairShare

Talk it out (20 seconds):

What number can I ADD to anything and always get back what I started with??

What number can I MULTIPLY anything by and always get back what I started with??


Additive Identity Property ( 0 )

Remember: NO MATTER WHAT I DO TO YOU IN MATH, your identity never changes

a + 0 = a

5 + 0 = 5


Multiplicative Identity Property ( 1 )

Remember: NO MATTER WHAT I DO TO YOU IN MATH, your identity never changes

a ⋅ 1 = a

5 ⋅ 1 = 5


Discovering the Inverse Properties! ThinkPairShare

Talk it out (20 seconds):

What can I add to 3 to make 0 ?

What can I add to - 4 to make 0?

What can I multiply 3 by to get 1?

What can I multiply 1/4 by to get 1?


Additive Inverse

Remember: ALL YOU DO IS CHANGE THE SIGN IN FRONT

3 + (-3) = 0

a + (-a) = 0


Multiplicative Inverse

Remember: THIS IS WHEN YOU FLIP

3 ⋅ 1/3 = 1

a ⋅ 1/a = 1


Evaluate the expression

2xy

x = -3 y = -4

Step 1: Substitute

Step 2: Simplify

2(-3)(4)

= 2(-3)(4)= (-6)(4)= -24


Which equation represents the situation below?Explain your answer


Identify the Property

commutative

distributive

multiplicative identity

associative


Working in Groups...

Spiral Worksheet- Your chance to ask your group members questions on topics you don't really understand.

If NO ONE in the group understands a problem, that's the ONLY time you can consult the teacher.

USE YOUR RESOURCES!!!


DAILY EXIT

1) 7n + 2n = (7 + 2)n

2) Find the additive and multiplicative inverse of

a) -11 b) 0.4 16


Variables and Expressions Week of September 9mathmotthall.wikispaces.com/file/view/Variables...

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