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:

1. Carrots: 5 + 1 = 6
2. Lettuce: 5 + 3 = 8
3. 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.

Sample answers for the Challenge questions:

• 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:

1. 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.
2. 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.
3. 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.

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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.