Transcript Lesson 1

Lesson 3-1
Writing Equations
5-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
4. (36d – 18) / (-9)
3. 8(-2c + 5) + 9c
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.
Standardized Test Practice:
Which of the following is a true
statement
A
8/4 < 4/8
B
-4/8 < -8/4
C
-4/8 > -8/4
D
-4/8 > 4/8
5-Minute Check on Chapter 2
1. Evaluate 42 - |x - 7| if x = -3
2. Find 4.1  (-0.5)
Transparency 3-1
32
-8.2
Simplify each expression
3. 8(-2c + 5) + 9c
-7c + 40
4. (36d – 18) / (-9)
-4d + 2
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?
62.5% = 5/8
6.
Standardized Test Practice:
Which of the following is a true
statement
A
8/4 < 4/8
B
-4/8 < -8/4
C
-4/8 > -8/4
D
-4/8 > 4/8
Objectives
• Translate verbal sentences into equations
• Translate equations into verbal sentences
Vocabulary
• Four-step problem solving plan – “Key Concept”
–
–
–
–
Step 1:
Step 2:
Step 3:
Step 4:
Explore the problem
Plan the solution
Solve the problem
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
six less than c.
is equal to
Answer: The equation is
.
Example 2
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?
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.
Plan
Write an equation to represent the situation. Let h
represent the number of hours needed to produce the
jellybeans.
1,250,000
1,2500,000
times
hours
h
equals
10,000,000.
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.
1,250,000
1,2500,000
times
hours
h
equals
10,000,000.
10,000,000
Solve
Find h mentally by asking, “What number times 125 equals 1000?”
h=8
Answer:
It will take 8 hours to produce 10,000,000 jellybeans.
Example 3
Translate the sentence into a formula.
The perimeter of a square equals four times the length of
the side.
Words
Perimeter equals four times the length of the side.
Variables
Let P = perimeter and s = length of a side.
Perimeter
equals
P
Answer: The formula is
four times the length
of a side.
4s
.
Example 4
Translate this equation into a verbal sentence.
a2
3b
a squared
Answer:
plus three times b equals
c divided by six.
a squared plus three times b equals c divided by six.
Example 5
Translate each equation into a verbal sentence.
1.
Answer: Twelve divided by b minus four equals negative
one.
2.
Answer: Five times a equals b squared plus one.
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