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Real-Life Math Problems with Solutions

How can you save money? How should a building be designed? How do you train for a competition? In the real world, math problems involve many disciplines, are complicated, and don’t have an answer key. In a math classroom, the problems usually need to be smaller scale and more focused. These problems still mimic and provide insight into the real world and can serve as a “diving board” into the sorts of math problems students encounter outside of math class.

Below are three open-ended math problems for Grades K, 2, and 4, which encourage students to explore math in real-life contexts. They get students thinking about how math can be used to solve problems in gardening, biology, and music.

Real-World Math Problems with Answers

These problems, which can all be found in HMH Into Math , do have clear solutions. Even though in all three cases many answers are possible, you can assess students’ understanding based on how they respond.

Kindergarten: 5-and-More Garden

• Key Standard: Represent addition within 10 with drawings and objects.
• Key Standard: Model with mathematics.

“ 5-and-More Garden ” asks students to create a visual representation of a garden bed by spinning a wheel and then “planting” different quantities of lettuce and carrots.

In this activity, students will make groups to show 5 and the number on the spinner. Answers can be represented in a variety of ways: drawn on the provided garden teacher resource, created using paper and counters, or possibly built out of clay and other materials. If students use the spinner provided, there should be between 5–10 carrots and 5–10 lettuce plants. If there are only 5 of both, make sure the student did in fact spin 0 on the spinner both times! The image on the first page of the activity shows a possible model if students build a garden using clay.

Sample answers for the Challenge questions:

• Carrots: 5 + 1 = 6
• Lettuce: 5 + 3 = 8
• If I pick 3 carrots, then 3 carrots will be left.

Grade 2: By the Sea

• Key Standard: Understand that the three digits of a three-digit number represent the amounts of hundreds, tens, and ones.
• Key Standard: Reason quantitatively.

“ By the Sea ” challenges students to imagine various quantities of plants and animals that they might observe by the sea and demonstrates the efficiency of using place value to denote three-digit numbers. They make a math storybook about the wildlife, choosing a number for each organism, writing the number two ways, and drawing to show the number using hundreds, tens, and ones.

In this activity, students should choose a number between 100 and 999 for snails, pieces of seaweed, starfish, and clams. They should record each value accurately, matching the models they make with manipulatives. Drawings should match the values chosen. For example, if they chose 583 starfish, then for starfish, they should note there are 5 hundreds, 8 tens, and 3 ones and draw 5 large starfish, 8 medium starfish, and 3 small starfish.

• Each page is made up of two types of plants and animals. On page 2, there are 583 starfish and 215 clams, so there are 798 animals total.
• There are four types of plants or animals in the whole journal. On page 1, there are 296 snails and 317 pieces of seaweed. On page 2, there are 583 starfish and 215 clams. So, there are 1,411 plants and animals total. That is 14 hundreds, 1 ten, and 1 one.

Grade 4: Concert Calculations

• Key Standard: Fluently add and subtract numbers through 1,000,000.
• Key Standard: Make sense of problems and persevere in solving them.

“ Concert Calculations ” gives students a budget of $300,000 to spend on a tour for their band; students must use their critical thinking and decision-making skills to weigh cities with the appropriate stadium capacity against tour costs. Their goal is to reach a million attendees.

In this activity, students select different cities around the U.S. They will need to keep track of costs (stadium + hotel + food for each city) and capacities (add the capacities for each city). If they find a successful answer for the activity, check the totals. The total cost should be under $300,000, and the total capacities should be over 1 million.

Sample answers for the Reflection Questions :

• The numbers being added included 2-, 3-, and 5-digit numbers. I had to ensure I was adding ones, tens, hundreds, thousands, and ten thousands, paying attention to which digit was contained in which place value.
• I decided to visit Atlanta because the stadiums had a high capacity (138,258) but low cost ($15,678). Evidence that this was a good decision is that I succeeded in having a total capacity of over 1,000,000 but did not go over $300,000.
• Authors do not need stadiums like popular musicians do. I would plan a book tour similar to the concert tour, but I would look at the capacity for different bookstores in each city and go to as many as possible to make the total amount of people who can meet the author as high as possible.

HMH Into Math is a core mathematics curriculum for Grades K­­–8 that inspires students to see the value and purpose of math in their daily lives through rewarding, real-life activities and lessons.

To learn more about the indicators of a powerful math task and strategies to promote math talk in the classroom, watch our webinar The Power of a Great Math Task.

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Using Math in the Real World

There’s a popular math meme that says, “Math: The only place where people buy 60 watermelons and no one wonders why.”

After a chuckle, you might realize there’s some truth to this joke. Sometimes, it may seem like math has nothing to do with the real world. In fact, it’s likely your students have asked you, “Why do I need to know this? When will I ever use this in real life?”

Of course, as a teacher, you know that math matters. Making math relevant to your students can be challenging, however.

You can talk about the importance of learning addition, subtraction, statistics, geometry, algebra, and more , but your students might not see the real-world applications. The truth is, we all need math. Math teaches us how to solve problems , a skill that’s useful in all career fields and just for navigating everyday life.

So, how can you make math relevant to your students? Try these examples of math in the real world.

Cooking and baking are great ways to show your students how math applies to life outside of the classroom . Lead your students in reading recipes, discuss fractions, and talk about how to double a recipe or cut one in half. Then, reward their hard work with a hands-on lesson. Try this classic recipe that will let them get sticky while they learn!

• Checks and Balances

Create a checkbook system in your classroom, where students can learn how to balance a bank account—a real-world skill we all need! Make your own “classroom dollars” and give them opportunities to spend and save throughout the year, from renting their desks monthly to earning cash for good behavior. They’ll practice basic math in the process, and, if you end the unit with the opportunity to purchase items with their hard-earned money, you’ll teach them the value of saving and budgeting.

• Buying Power

After your class has earned classroom dollars throughout the year, hold a yard sale or class auction. Have students donate items and let them spend their money however they’d like. Add to the challenge by announcing discounts—“everything’s 30 percent off for the next 10 minutes”—and let them do the real-world math to see what the new price would be.

• Measure for Measure

Many jobs, from construction workers to architects, require accurate measuring skills. Measuring and math go hand-in-hand, and you can up the fun factor in math by setting your students free throughout the classroom—or even the school. How tall is the principal? How long is the hallway? What’s the square footage of the gym? The possibilities are endless.

• Map a Course

With GPS as a regular part of our daily lives, many students have lost the art of reading a map . Map reading uses math skills, too, requiring an understanding of scale, coordinates, distances, fractions, and more. Chances are, your students have never really had to use a map to get anywhere. Go on a virtual field trip by following a map to your favorite destination, and practice math in the process.

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Ideas, Inspiration, and Giveaways for Teachers

We Are Teachers

26 Snappy Answers to the Question “When Are We Ever Going to Use This Math in Real Life?”

Next time they ask, you’ll be ready.

As a math teacher, how many times have you heard frustrated students ask, “When are we ever going to use this math in real life!?” We know, it’s maddening! Especially for those of us who love math so much we’ve devoted our lives to sharing it with others.

It may very well be true that students won’t use some of the more abstract mathematical concepts they learn in school unless they choose to work in specific fields. But the underlying skills they develop in math class—like taking risks, thinking logically and solving problems—will last a lifetime and help them solve work-related and real-world problems.

Here are 26 images and accompanying comebacks to share with your students to get them thinking about all the different and unexpected ways they might use math in their futures!

1. If you go bungee jumping, you might want to know a thing or two about trajectories.

Source: GIPHY

2. When you invest your money, you’ll do better if you understand concepts such as interest rates, risk vs. reward, and probability.

3. once you’re a driver, you’ll need to be able to calculate things like reaction time and stopping distance., 4. in case of a zombie apocalypse, you’re going to want to explore geometric progressions, interpret data and make predictions in order to stay human..

Trigger an outbreak of learning and infectious fun in your classroom with this Zombie Apocalypse activity from TI’s STEM Behind Hollywood series.

5. Before you tackle that home wallpaper project, you’ll need to calculate just how much wall paper glue you need per square foot.

6. when you buy your first house and apply for a 30-year mortgage, you may be shocked by the reality of what interest compounded over 30 years looks like., 7. to be a responsible pet owner, you’ll need to calculate how much hamster food to have on hand., 8. even if you’re just an armchair athlete, you can’t believe the math involved in kicking field goals.

Check out this Field Goal for the Win activity that encourages students to model, explore and explain the dynamics of kicking a football through the uprights.

9. When you double a recipe, you’re going to need to understand ratios so your dinner guests don’t look like this.

10. before you take that family road trip , you’re going to want to calculate time and distance., 11. before you go candy shopping, you’re going to have to figure out x trick or treaters times x pieces of candy equals…, 12. if  you grow up to be an ice cream scientist, you’re going to have to understand the effect of temperature and pressure at the molecular level..

Explore states of matter and the processes that change cow milk into a cone of delicious decadence with this Ice Cream, Cool Science activity .

13. Once you have little ones, you’ll need to know how many diapers to buy for the month.

14. because what if it’s your turn to organize the annual ping pong tournament, and there are 7 players at a club with 4 tables, where each player plays against each other player, 15. when dressing for the day, you might want to consider the percent likelihood of rain., 16. if you go into medical research, you’re going to have to know how to solve equations..

Learn more about inspiring careers that improve lives with STEM Behind Health , a series of free activities from TI.

17. Understanding percentages will help you get the best deal at the mall. For example, how much will something cost with 40% off? What about once the 8% tax is added? What if it’s advertised as half-off?

18. budgeting for vacation will require figuring out how many hours at your pay rate you’ll have to work to afford the trip you want., 19. when you volunteer to host the company holiday party, you’ll need to figure out how much food to get., 20. if you grow up to be a super villain, you’re going to need to use math to determine the most effective way to slow down the superhero and keep him from saving the day..

Put your students in the role of an arch-villain’s minions with Science Friction, a STEM Behind Hollywood activity .

21. You’ll definitely want to understand how to budget your money so you don’t look like this at the grocery checkout.

22. if you don’t work the numbers out in advance, you might at some point regret choosing that expensive out-of-state college., 23. before taking on a building project, remember the old saying—measure twice, cut once., 24. if have aspirations of being a fashion designer, you’ll have to understand geometry in order to make the perfect twirling skirt.

Geometry and fashion design intersect in this STEM Behind Cool Careers activity .

25. Everyone loves a good bargain! Figuring out the best deal is not only fun, it’s smart!

26. if you can’t manage calculations, running the numbers at the car dealership might leave you feeling like this:.

Elizabeth Mulvahill is a Contributing Editor with WeAreTeachers. She has taught elementary, literacy and small group intervention. She currently resides outside of Boulder, Colorado and loves learning new things, hearing people's stories and traveling the globe.

Nicely done! But – it doesn’t work for Algebra. Speaking as an A1 teacher, probably more than 80% of what they learn they won’t use. (Polynomials?!)

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