Solve real-world and mathematical problems involving the four operations with rational numbers.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Once students can add, subtract, multiply and divide signed numbers, the real test is choosing which operations a situation calls for. A bank account that is overdrawn, a submarine changing depth, a stock price rising and falling over a week, or a temperature dropping at a steady rate per hour all involve rational numbers that can be negative, fractional or both.
Here students translate a situation into a calculation, carry it out with the correct signs and order of operations, and interpret the answer back in the context. A result of -11 means 11 degrees below zero, and a negative change in a balance means money left the account. Good problem solvers also check whether an answer is reasonable, for example noticing that a submarine rising toward the surface should end at a depth closer to zero. Many problems mix forms, so converting between fractions, decimals and integers along the way is part of the skill.
Students sometimes report a depth or a debt as a positive number because 'you cannot have negative feet'. Ask what the sign tells the reader before deciding how to phrase the answer.
In (-2/3) × 18 + 5, the product must be found first. Adding 18 + 5 first gives a very different result, so underlining the multiplication step helps.
Words like 'drops' do not always mean subtract. A temperature that drops 2.5 degrees per hour for 6 hours needs multiplication first, then the change is added to the start.
Sam's account balance is -$35.50. He deposits three checks of $42.25 each and is then charged a $12 fee. What is the new balance?
Answer: The new balance is $79.25.
Ask students to write the whole calculation as one expression before computing anything. That habit exposes sign and order errors early, and it mirrors the multistep items found on state tests. Encourage a one-line estimate as a final check.
Rich contexts include golf scores relative to par, elevation above and below sea level, budgets and weekly changes in a stock or a savings jar. Having students write their own problem for a given expression, such as -4 × 2.5, deepens understanding of what each operation means.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: -11 (also accepted: -11°F, -11 degrees)
The total drop is 2.5 × 6 = 15 degrees. 4 - 15 = -11, so the temperature is -11°F.
Answer: B) 10
It must rise from -240 to -90, a change of 150 ft. 150 ÷ 15 = 10 minutes.
Answer: -3 (also accepted: -3.00)
-1.25 + 0.75 = -0.5, then -0.5 - 2.5 = -3. The stock lost $3 in total.
Answer: D) -13.5
A debt is negative: -54 ÷ 4 = -13.5. Each friend's balance goes down by $13.50.
Answer: -7
Multiply first: (-2/3) × 18 = -12. Then -12 + 5 = -7.
Answer: B) (-4 + 7 - 9 + 2) ÷ 4
The mean is the sum of the values, keeping their signs, divided by how many there are. The sum is -4 and the mean is -1.
A full lesson with slides, activities and an exit ticket on real-world problems with rational numbers, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.NS.A.3 with an answer key, ready in about a minute.
Make a worksheet →Turn real-world problems with rational numbers into a quiz students answer online that marks itself, with a class summary for you.
Build a test →7.NS.A.1 and 7.NS.A.2 teach the operations. 7.NS.A.3 asks students to use all four of them together to solve real and mathematical problems.
Yes. Rational numbers include integers, fractions and decimals, positive and negative, and problems often mix these forms.