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CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS

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Page 1: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

CHAPTER

1

1-1 V

ARIABLE

S AND

EXPRES

SIONS

Page 2: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONS

Objectives:

Translate between words and algebraic expressions

Evaluate algebraic expressions

Page 3: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONSVOCABULARY

variable: is a letter or symbol used to represent a value that can change.

Constant: is a value that does not change.

Numerical expression: may contain only constants and/or operations.

Algebraic expression: may contain variables, constants and/or operations.

Page 4: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONSVOCABULARY EXAMPLES

Give examples for the following:

Variables :

Constants:

Algebraic Expressions:

Page 5: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONSDIAGRAM

+ Plus, sum , increased by , more than

__ Minus, difference, less than

* Times, product ,equal group of, multiply by

Divided by, quotient

Use diagram to help translate algebraic expressions to words

Page 6: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONS TRANSLATE FROM ALGEBRAIC EXPRESSION TO WORDS

I. Give different ways to write each algebraic expression into words

Example 1:

A) x+5

• The sum of x and 5

• Five more than x

• X plus 5

• X increased by 5

Page 7: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

TRANSLATE FROM ALGEBRAIC EXPRESSIONS TO WORDSB) m-6

The difference of m and 6

6 less than m

m minus 6

C) 3*k

• The product of 3 and k

• 3 times k

Page 8: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

TRANSLATE FROM ALGEBRAIC EXPRESSIONS TO WORDS

D) g

g divided y 8

The quotient of g and 8

Page 9: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

TRANSLATE FROM ALGEBRAIC EXPRESSIONS TO WORDS

Student practice :

Check it out 1a to 1d

1a. 4-n 1c. 9+q

1b. 1d. 3(h)

Page 10: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONS DIAGRAM

Use to help you translate words into algebraic expressions

Add Put together, combine

Subtract Find how much more or less

Multiply Put together equal groups

divide Separate into equal group

Page 11: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

TRANSLATE WORDS INTO ALGEBRAIC EXPRESSIONS

Example 2:

A) Evelyn has 2 more years than her sister Adriana. Write and expression for Evelyn’s age.

* a+2

B) Sam is 3 years younger than sue, who is y years old. Write an expession for sam’s age.

* y-3

Page 12: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

TRANSLATE WORDS INTO ALGEBRAIC EXPRESSIONS

Words to look for that will help you with translation

addition sum , more

Subtraction Less, difference, minus

Multiplication Per, times, product

Division Quotient, ratio

Page 13: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

TRANSLATING WORDS INTO ALGEBRAIC EXPRESSIONS

C) Mario’s car is going 55 miles per hour. Write an expressions for how fast is Mario’s car going.

55 h

D) William runs a mile in 15 minutes. Write a an expression for the number of miles that william run in m minutes.

*

Student Practice : check it out 2a-2c

Page 14: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

EVALUATING ALGEBRAIC EXPRESSIONS

Evaluate: is to find its value.

Substitute: to replace

To evaluate an algebraic expression substitute the variables in the expression for numbers and then simplify as needed.

Hint: Usually they give the numbers you need to substitute the variables for.

Page 15: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

EVALUATING ALGEBRAIC EXPRESSIONS

Example 3:

Evaluate each expression for x=8 , y=2 and z=4

A) x+z

x+z= 8+4 * substitute x with 8 and z with 4

= 8+4= 12 simplify

Page 16: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

EVALUATING ALGEBRAIC EXPRESSIONS

B) xyz

xyz = 8*2*4 substitute x,y and z with 8,2 and 4

= 8*(2*4)=8*8 simplify

= 64

= substitute

== 4 simplify

Page 17: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

STUDENT PRACTICE

Evaluate the following expressions give x=3,y=-7 and z=5

A) xy

B) 2x+y

C) x-z-y

* Check it out 3a-5

Page 18: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

EVALUATING ALGEBRAIC EXPRESSIONS

• Example 4: Challenge

• Example 5:

Comparing cellphones plans

*Lets says company AC has a plan that consists of $35 plan fee for the first 600 minutes plus 10 cents per minute pass the 600 minutes.

• Company BC has a plan that consists of $25 plan fee for the first 600 minutes plus 25 cents per minute pass the 600 minutes.

• which plan is less expensive for 800 minutes?

Page 19: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

VARIABLES AND EXPRESSIONS

Homework for lesson 1-1

Do 2-16 evens from page 9

Page 20: CHAPTER 1 1-1 VARIABLES AND EXPRESSIONS. VARIABLES AND EXPRESSIONS Objectives: Translate between words and algebraic expressions Evaluate algebraic expressions

CLOSURE

Today we learned about what are variables, translating algebraic expressions into words and vice versa.

We also learned about evaluating algebraic expressions.

Tomorrow we are going to learn chapter 1-2 solving equations by adding or subtracting