21st Century Lessons
Writing Inequality Statements
for Real World Scenarios
1
Warm Up
OBJECTIVE: SWBAT write inequalities for real-world problem scenarios.
LANGUAGE OBJECTIVE: SWBAT translate and use the language of
inequalities including phrases such as “no more than” and “at least.”
Write each inequality statements #1-4 in your notebook. Then
write the letter and phrase on the right that it represents.
1. C < 12
2. C ≤ 12
3. C > 12
4. C ≥ 12
a.
b.
c.
d.
No more than 12 cars.
At least 12 candies.
Fewer than 12 cats.
More than 12 coins.
Agenda
2
Agenda:
OBJECTIVE: SWBAT write inequalities for real-world problem scenarios.
LANGUAGE OBJECTIVE: SWBAT translate and use the language of
inequalities including phrases such as “no more than” and “at least.”
1) Warm Up – inequality statements and symbols - YOU
2) Launch – review how to write an equation - US
3) Mini-Lesson – writing and solving inequalities – ME/US
4) Guided Practice – practice writing and solving inequalities - YOU
5) Independent Practice – write inequalities – YOU
6) Review – correct the class work – ME/US
7) Assessment – Exit Ticket - YOU
3
Launch
In a previous lesson we wrote equations
for calculating the cost of a birthday party
held at the local roller rink.
It costs $13 per person to
skate and eat pizza.
The cake costs
$50.
Agenda
4
Launch
It costs $13 per person to
skate and eat pizza.
The cake costs
$50.
You are going to have some total number of guests,
n, attending your party, skating and eating.
What is the equation for calculating the cost?
3 students will be randomly selected to share their equations.
Agenda
5
Launch
It costs $13 per person to
skate and eat pizza.
The cake costs
$50.
C = $13n + $50
Think, Pair, Share:
Lefty: Tell Righty how to calculate the cost for 1 guest.
Righty: Tell Lefty how to calculate the cost for 2 guests.
Agenda
6
Launch
It costs $13 per person to
skate and eat pizza.
The cake costs
$50.
C = $13n + $50
How does this equation work?
• I multiply the number of people times $13 to get the
cost to skate and eat.
• I add $50 to that cost to get the total cost.
Agenda
7
Mini-Lesson: Writing Inequalities
It costs $13 each to skate and eat. The cake costs $50.
Your mom tells you that the cost of the skating and the
cake cannot be more than $200.
$13n + $50 = $200
Does this equation represent the situation described?
Think, Write, Pair, Share:
Write a quick answer.
Take turns answering the question (1 min).
Agenda
8
Mini-Lesson: Writing Inequalities
It costs $13 each to skate and eat. The cake costs $50.
Your mom tells you that the cost of the skating and the
cake cannot be more than $200.
Does this symbol
$13n + $50 = $200
represent the
idea “cannot
be more than?
This equation says that if you multiply the number of
guests times $13 and add the $50 for the cake it will
equal exactly $200.
But the situation says it “cannot be more than” $200.
Agenda
9
Mini-Lesson: Writing Inequalities
It costs $13 each to skate and eat. The cake costs $50.
Your mom tells you that the cost of the skating and the
cake cannot be more than $200.
$8n + $50 ≤ $200
This statement can be represented as an inequality.
An inequality is used because the cost does not have to
be exactly $200. But the cost must be less than or
equal to $200.
Keep in mind that n can be any of several different
numbers and the statement is still true.
Agenda
10
Mini-Lesson: Writing Inequalities
Inequalities
The inequality symbols you can use are:
<
≤
Less than
Less than or equal to
>
≥
Greater than
Greater than or equal to
Let’s practice selecting the appropriate symbol to
represent different situations at the party.
Agenda
11
Guided Practice
Pick the correct symbol for each statement to best
represent the situation.
Ex 1.) You tell your mother that the party won’t be fun
unless there are at least 10 friends attending.
a. n < 10
b. n ≤ 10
c. n > 10
d. n ≥ 10
The number of guests, n, must be more than 10 or
at least 10 (equal to 10).
Agenda
12
Guided Practice
Pick the correct symbol for each statement to best
represent the situation.
Ex. 2) You don’t want your friends to spend a lot of
money on presents so you tell them to bring
only bring
a a
present that costs no
under
more
$15.
than $15.
a. C < $15
b. C ≤ $15
c. C > $15
d. C ≥ $15
“no more
How
couldthan”
you rewrite
includes
this
$15
question so that the
answer is B?
Agenda
13
Guided Practice
Which inequality statement best represents this
situation?
Ex. 3) You want a DJ to play at your birthday party for 2
more
than
2 hours.
or more
hours.
a. t < 2
b. t ≤ 2
c. t > 2
d. t ≥ 2
“more
How
could
than”
you
does
rewrite
not include
this question
2 hours.
so that the
answer is c?
Agenda
14
Independent Practice
You will use what you have learned here to write and
solve more equations and inequalities on your own.
You will have 15 minutes to work on the class work
problems. Then we will review the work.
Agenda
15
Review
Students will be selected at random to share their
answers. Use the symbol names below.
≥
≤
≤
<
> Greater than
≥ Greater than or equal to
< Less than
≤ Less than or equal to
Agenda
16
Review
Some of the students from East Boston Academy are taking a
trip to a museum. The cost for lunch is $6 each and admission to
the museum is $12 per student.
How would you calculate the cost of the trip for n number of
students. Explain each step. Why are both answers correct?
• Multiply the $6 by the number
of students to get the total cost
of all the lunches.
• Multiply $12 by the number of
students to get the total cost of
all the museum admissions.
• Add them together.
OR
• Multiply $18 by the
number of students
to get the total cost
of all the lunches
and the museum
admissions.
Agenda
17
Review
Some of the students from East Boston Academy are
taking a trip to a museum. The cost for lunch is $6 each
and admission to the museum is $12 per student.
How would you calculate the cost of the trip for n
number of students. Explain each step.
• Multiply the $6 by the number of students to
get the total cost of all the lunches.
• Multiply $12 by the number of students to get
the total cost of all the museum admissions.
• Add them together.
Agenda
18
Review
Some of the students from East Boston Academy are
taking a trip to a museum. The cost for lunch is $6 each
and admission to the museum is $12 per student.
3. Write an equation for the total cost C of the museum
trip for n number of students.
C = $6s + $12s OR C = $18s
4. The East Boston Academy has a budget of $500 for
each field trip.
$6s + $12s ≤ $500 OR $18s ≤ $500
Agenda
19
Assessment: Exit Ticket
You have a budget of $600 to pay for a health club membership.
The YMCA costs $35 a month but also has a one-time only joining
fee of $100. Which inequality statement shows this relationship?
A. $35m + $100m < $600
B. $35m + $100 ≤ $600
C. $135m > $600
D. $35m + $100 ≥ $600m
Agenda
20