Topics
4. Operations with Integers
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United States of AmericaVirginia
Grade 6

4.04 Real-world problems with integers

Lesson
Practice

Real-world problems with integers

We can use our knowledge of addition and subtraction on the number line to describe how the real world quantities change.

A number line showing one tick labeled as 1 unit and an arrow going right labeled as positive direction.

We can also talk about changes in the quantity we are representing using integer operations. Given a starting temperature and some change in a certain direction, what is the final temperature? Given a starting balance and an ending balance of money in an account, what has been the amount and sign of the change?

When using integers to represent real-world situations, it is important to correctly identify any positive and negative integers as well as the correct operations.

Table of common key words to look for:

TermKey Words:
Positiveexcess, profit, above zero temperature
Negativedebt, owes, below sea level
Additionplus, more than, total, sum, combined
Subtractionminus, difference, less than, decreased by
Multiplicationtimes, product of, double/triple
Divisionquotient, per, split, ratio, into

Estimation can be a good strategy for solving real-world problems if the context doesn't require an exact solution.

Examples

Example 1

Tara is waiting for the next flight to Los Angeles, which was scheduled to be in 64 minutes, but there is a 34-minute delay. She takes a nap and wakes up 23 minutes later. How much longer does Tara have to wait before the plane departs?

Worked Solution
Create a strategy

Add the delay and subtract her sleep time from her wait time.

Apply the idea
\displaystyle \text{Waiting time}\displaystyle =\displaystyle 64 + 34 - 23Set up the equation
\displaystyle \text{ }\displaystyle =\displaystyle 98 - 23Perform 64 + 34
\displaystyle \text{ }\displaystyle =\displaystyle 75 \text{ minutes}Evaluate

Example 2

A science club has a budget of \$600 for a new project. The club members decide to spend \$450 on laboratory equipment and the rest on protective gear. If each set of protective gear costs \$25, how many sets of protective gear can the club buy with the remaining budget?

Worked Solution
Create a strategy

Our goal here is to figure out how many sets of protective gear the science club can buy after spending part of their budget on laboratory equipment.

We will subtract the amount of money spent on lab equipment from the total budget. This will let us know how much they have left to spend on protective gear. We will divide this amount by the cost of protective gear to find how many they can purchase.

Apply the idea

The total budget for the project is \$600. The club decided to spend \$450 of that budget on laboratory equipment. We can find how much money is left by subtracting the amount spent on equipment from the total budget.

\displaystyle \text{Money leftover}\displaystyle =\displaystyle 600 - 450Set up the equation
\displaystyle \text{ }\displaystyle =\displaystyle 150 \text{ dollars}Subtract

We have now figured out that we have \$150 left in the club's budget. We know that each set of protective gear costs \$25, so to find how many sets of protective gear we can purchase we will divide our remaining money, \$150, by the cost of each set of protective gear, \$25

\displaystyle \text{Number of sets of gear}\displaystyle =\displaystyle 150 \div 25Set up the equation
\displaystyle \text{ }\displaystyle =\displaystyle 6 \text{ sets of gear}Divide

The science club can purchase 6 sets of protective gear with the remaining budget.

Idea summary

Answers that are integers can be positive or negative. When solving a problem, the sign of the integer determines the location of a thing or person, or whether we have a profit or loss, or savings or debt.

TermKey Words:
Positiveexcess, profit, above zero temperature
Negativedebt, owes, below sea level
Additionplus, more than, total, sum, combined
Subtractionminus, difference, less than, decreased by
Multiplicationtimes, product of, double/triple
Divisionquotient, per, split, ratio, into

Outcomes

6.CE.2

The student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context.

6.CE.2d

Estimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, multiplication, and division with integers.

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