Writing Inequality Statements for Real World Scenarios

1

Warm Up

Agenda2

Write each inequality statements #1-4 in your notebook. Then write the letter and phrase on the right that it represents.

1. C < 122. C ≤ 123. C > 124. C ≥ 12

a. No more than 12 cars.b. At least 12 candies.c. Fewer than 12 cats.d. More than 12 coins.

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.”

Agenda3

You are going to have some total number of guests, n, attending your party, skating and eating.

It costs $13 per person to skate and eat pizza.

Launch

What is the equation for calculating the cost?

The cake costs $50.

3 students will be randomly selected to share their equations.

Agenda4

It costs $13 per person to skate and eat pizza.

Launch

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.

The cake costs $50.

C = $13n + $50

Agenda5

It costs $13 per person to skate and eat pizza.

Launch

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.

The cake costs $50.

C = $13n + $50

Agenda6

Your mom tells you that the cost of the skating and the cake cannot be more than $200.

$13n + $50 = $200Does this equation represent the situation described?

Mini-Lesson: Writing Inequalities

Think, Write, Pair, Share: Write a quick answer. Take turns answering the question (1 min).

It costs $13 each to skate and eat. The cake costs $50.

Agenda7

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.

$13n + $50 = $200

Mini-Lesson: Writing Inequalities

But the situation says it “cannot be more than” $200.

Does this symbolrepresent the idea “cannot

be more than?

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.

Agenda8

This statement can be represented as an inequality.$13n + $50 ≤ $200

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.

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.

Agenda9

The inequality symbols you can use are:

Let’s practice selecting the appropriate symbol to represent different situations at the party.

Less than

< ≤ > ≥Greater than

Less than or equal to Greater than or equal to

Mini-Lesson: Writing Inequalities

Inequalities

Guided Practice

10

Agenda

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 ≥ 10d. n ≥ 10

The number of guests, n, must be more than 10 or at least 10 (equal to 10).

Guided Practice

11

Agenda

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 only bring a present that costs under $15.

a. C < $15 b. C ≤ $15 c. C > $15 d. C ≥ $15a. C < $15

How could you rewrite this question so that the answer is B?

Ex. 2) You don’t want your friends to spend a lot of money on presents so you tell them to bring a present that costs no more than $15.

“no more than” includes $15

b. C ≤ $15

Guided Practice

12

Agenda

Which inequality statement best represents this situation?

Ex. 3) You want a DJ to play at your birthday party for 2 or more hours.

a. t < 2 b. t ≤ 2 c. t > 2 d. t ≥ 2d. t ≥ 2

How could you rewrite this question so that the answer is c?

Ex. 3) You want a DJ to play at your birthday party for more than 2 hours.

“more than” does not include 2 hours.

c. t > 2

Independent Practice

13

Agenda

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.

Review

14

Agenda

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

≥ ≤

≤ <

Review

15

Agenda

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.

OR

• Multiply $18 by the number of students to get the total cost of all the lunches and the museum admissions.

Why are both answers correct?

Review

16

Agenda

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.

Review

17

Agenda

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

Assessment: Exit Ticket

18

Agenda

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