Lesson 3-1

Writing Equations

5-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 2 Transparency 3-1

1. Evaluate 42 - |x - 7| if x = -3

2. Find 4.1 (-0.5)

Simplify each expression

3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9)

5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green?

6. Which of the following is a true statementStandardized Test Practice:

A CB D8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8

5-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 2 Transparency 3-1

1. Evaluate 42 - |x - 7| if x = -3

2. Find 4.1 (-0.5)

Simplify each expression

3. 8(-2c + 5) + 9c 4. (36d – 18) / (-9)

5. A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green?

6. Which of the following is a true statementStandardized Test Practice:

A CB D8/4 < 4/8 -4/8 < -8/4 -4/8 > -8/4 -4/8 > 4/8

32

-8.2

-7c + 40 -4d + 2

62.5% = 5/8

C

Objectives

• Translate verbal sentences into equations

• Translate equations into verbal sentences

Vocabulary

• Four-step problem solving plan – “Key Concept”– Step 1: Explore the problem– Step 2: Plan the solution– Step 3: Solve the problem– Step 4: Examine the solution

• Defining a variable – letting a variable represent one of the unspecified numbers in the problem

• Formula – is an equation that states a rule for the relationship between certain quantities

Language of Math: Equations

English expressions that suggest “=“• is• equals• is equal to• is the same as• is as much as• is identical to

Four-Step Problem Solving Plan

• Step 1: Explore the Problem

– Identify what information is given (the facts)

– Identify what you are asked to find (the question)

• Step 2: Plan the Solution

– Find an equation the represents the problem

– Let a variable represent what you are looking for

• Step 3: Solve the Problem

– Plug into your equation and solve for the variable

• Step 4: Examine the Solution

– Does your answer make sense?

– Does it fit the facts in the problem?

Example 1

Translate this sentence into an equation.

A number b divided by three is equal to six less than c.

b divided by three is equal to six less than c.

Answer: The equation is .

Example 2

Explore You know that 1,250,000 jellybeans are produced each hour. You want to know how many hours it will take to produce 10,000,000 jellybeans.

Jellybeans A popular jellybean manufacturer produces 1,250,000 jellybeans per hour. How many hours does it take them to produce 10,000,000 jellybeans?

Plan Write an equation to represent the situation. Let h represent the number of hours needed to produce the jellybeans.

1,2500,000 h 10,000,000

1,250,000 times hours equals 10,000,000.

Example 2 cont

Plan Write an equation to represent the situation. Let h represent the number of hours needed to produce the jellybeans.

1,2500,000 h 10,000,000

SolveFind h mentally by asking, “What number times 125 equals 1000?”

Answer: It will take 8 hours to produce 10,000,000 jellybeans.

1,250,000 times hours equals 10,000,000.

h = 8

Example 3

Answer: The formula is .

Translate the sentence into a formula.

Words Perimeter equals four times the length of the side.

Variables Let P = perimeter and s = length of a side.

The perimeter of a square equals four times the length of the side.

Perimeter equals four times the length of a side.

P 4s

Example 4

Translate this equation into a verbal sentence.

Answer: a squared plus three times b equals c divided by six.

a squared plus three times b equals c divided by six.

a2 3b

Example 5

Translate each equation into a verbal sentence.

Answer: Twelve divided by b minus four equals negative one.

Answer: Five times a equals b squared plus one.

1.

2.

Summary & Homework

• Summary:– Equations are the language of Math– Variables are used to represent unknowns when

writing equations– Formulas given in sentence form need to be

rewritten as algebraic equations

• Homework: – pg 124: 14-38 even