15 Math Projects for Gifted Middle School Students

As a middle school student, an independent math project is an opportunity for you to apply what you have learned in the classroom to practical problems or dive deeper into a topic that sparks your curiosity. Whether it is discovering patterns, solving puzzles, or using math to create something new, a project in the field helps you develop problem-solving skills and boost your understanding of mathematical concepts. If you work on a project as early as middle school, you will have the time and room to tweak your ideas, test different methods, and make improvements in high school and beyond. Your long-term work on such projects will also give you an edge in high school!

What are projects for middle school students?

Projects are activities, tasks, campaigns, written work, or initiatives that go beyond regular homework or school work. The goals of these projects can range from solving real-world problems with math to creating a new math model. You could work on tasks such as figuring out the best design for a small business or analyzing data to make predictions. You can even explore advanced topics in algebra or geometry that are not covered in the middle school curriculum. The possibilities are endless, and you get to choose what excites you the most!

Why should I take on a project in middle school?

Starting a project in middle school helps you build important skills early on. You will learn how to organize your work, research ideas, learn mathematical concepts and methods, and communicate your findings to others. It also gives you a chance to discover new areas of math that you might not get to explore in regular classes.

To help you with your search for the right idea, here are a few math projects for gifted middle school students:

1. Sports stats visualization

Pick a sport you like and collect stats based on recent or past games. You can choose individual player statistics or general sport statistics. For example, you can find data such as points scored, shooting percentages, or win-loss records from publicly available sources. Observe the trends and changes in stats over time. Present your findings in a report, graph, or poster, highlighting interesting trends or surprises. This project can help you combine your passion for sports with math and develop an understanding of data analysis and probability.

Materials/investment required: Access to sports statistics (via websites, local papers, dedicated analysis platforms, etc), calculators, and spreadsheet software

Suitable for: Students who are interested in data and statistics, especially sports fans; those with basic programming skills can aim for a deeper analysis.

2. Geometry art gallery

You can transform geometry into art by creating drawings or sculptures that demonstrate geometric ideas, like symmetry, polygons, or Platonic solids. For each piece, include a short written explanation of the math concept it illustrates and why it’s interesting. Assemble your creations into a “gallery” to share with peers, family, and friends. This project can help you blend your artistic flair with math.

Materials/investment required: Paper, glue, scissors, modeling clay, and other relevant art supplies

Suitable for: Students with an understanding of geometry and interest in the physical/visual expression of math

3. Arithmetic sequence exercises

An arithmetic sequence is a sequence of numbers that follows a specific rule/logic to derive the next number. For example, (1,4,9,16...) is a sequence of the squares of all numbers starting from 1. You can find some examples of arithmetic sequence questions and solve them. Once you have explored a few types of sequences, start making your own! Trade questions with your classmates and solve each other’s incomplete sequences.

Materials/investment required: Pen and paper

Suitable for: Students with a basic understanding of arithmetic

4. Dice rolling experiment

A die is a great tool to illustrate probability. You can create a project where you take more than one die, roll them together, and track the probabilities of the sum of faces at each turn. You will be surprised at the patterns that will emerge from a project that sounds quite simple! Decide on a number of dice, roll the dice a few hundred times, and record the sum of all dice faces. Do all numbers have the same probability? Or are some numbers more likely to appear than others? Once you do this, you can try similar experiments with more complex objects like a deck of cards.

Materials/investment required: Dice, notebook, and pen

Suitable for: Students with proficiency in basic math and an interest in statistics

5. Prime number exploration

Prime numbers are those divisible only by the number 1 and themselves. Try finding prime numbers up to a certain point and then look for patterns. You can create a chart with all prime numbers, or you can try using the Sieve of Eratosthenes method to find all the primes up to a certain number. Prime numbers also have a place in encryption; find out how! You can also investigate some of the most famous unsolved problems in mathematics and explore the reasons for the lack of solutions.

Materials/investment required: Pen and paper, and a computer for calculations

Suitable for: Students with an understanding of basic arithmetic

6. Divisibility tests

A divisibility test is run on a number to find out if it’s divisible by another number. For example, if the sum of all the digits of a number is a multiple of 3, that number is always divisible by 3. Find out the divisibility tests of numbers from 2 to as high as you can go. Some tests will be easy, but some numbers (like 17) have much more complex tests! Present the divisibility tests to peers and try to explain why they work.

Materials/investment required: Calculator, pen, and paper

Suitable for: Students with an understanding of basic arithmetic

7. Graphing linear and quadratic equations

Equations in the form y=mx+n are called linear equations. Take a few examples of such equations and present them on graph paper. Find out how the y-axis correlates to the x-axis, and where the functions turn from a downward slope to an upward slope. If you get good at this, you can try your hand at graphing quadratic equations. Find out what changes once you introduce squares into equations.

Materials/investment required: Pencil, ruler, and graph paper

Suitable for: Students with an understanding of basic arithmetic

8. Working with pi (π)

Pi is a constant used in mathematics. It denotes the ratio of a circle’s circumference to its diameter. Take a few circular objects, ranging from coins to plates, and calculate the value of π. Study the origins of π and how π is used in shapes other than circles (such as spheres). You can also document circular elements in local buildings, bridges, and structures, and calculate how much material would be needed for their construction using π-based formulas. You can analyze dome structures, arches, or cylindrical columns and present your findings to demonstrate the application of π in construction! Find out what other uses this constant has in modern math and science.

Materials/investment required: Circular and spherical objects, measuring tape, calculator, pen, and paper

Suitable for: Students with an understanding of basic geometry

9. Fibonacci sequence exploration

In the Fibonacci sequence, the upcoming number is the sum of the previous two numbers (1,1,2,3,5,8,13 …). This sequence appears in many natural phenomena, and even in the stock market! Study the sequence, and make a list of everything under the sun that has this pattern. Create a chart or a scrapbook with your findings.

Materials/investment required: Internet access, pen, and paper

Suitable for: Students who have an understanding of basic arithmetic

10. Basic encryption exercises

In this project, you will explore basic encryption methods; i.e., methods to encode your text in a way that only the intended recipient can decode. You can start with basic ciphers such as Caesar’s cipher, and move on to substitution ciphers with more complex keys. Get together with a friend and create your own code! You can even leave letters/notes to your classmates in your code language, challenging them to decode it.

Materials/investment required: Pen and paper

Suitable for: Students with proficiency in basic algebra and pattern recognition

11. Stock market simulation

In this project, you can work with a virtual sum of money that can be invested in the stock market. Track your buy price and sell price, and calculate your returns. This is a good way to understand percentages, compounding, and data tracking. You can also get familiar with terms like IRR and ROI.

Materials/investment required: Pen and paper, access to companies’ real-time share prices and fluctuations

Suitable for: Students who have an understanding of basic arithmetic and an interest in the stock market

12. Class survey and data analysis

You can survey your class and seek answers for 8-10 questions. Later, you can analyze the data and see if any patterns emerge. What are the names that are common and likely to repeat? What is the average age of the class? What is the ratio of blonde to dark-haired students? Make your own data points and present them to the class.

Materials/investment required: Pen and paper/note-taking or recording tool

Suitable for: Students who have an understanding of data collection and statistics

13. Mathematical modeling of real problems 

Mathematical models are simplified representations of real situations using mathematical language, equations, and relationships. You can present real problems on graphs or through equations to make them easy to grasp. Collect data on a topic of interest, like overall home/school energy usage or local traffic patterns, and create mathematical models to predict trends or come up with solutions. This project combines data analysis, graphing, and algebraic thinking.

Materials/investment required: Graph paper, pen, writing app/notebook, Suitable for: Students with an interest in data analysis and graphing

14. Vacation budget

Budgeting is a math concept that is quite useful in real life. To gain experience in this area, choose a destination and a duration for your dream vacation and set a spending budget for the entire trip. Break the vacation down into small tasks, setting a spending limit for each component. Through this project, you will learn how to track and manage expenses.

Materials/investment required: Pen, paper/computer, and internet access to check prices and rates of things

Suitable for: Students with a basic understanding of arithmetic

15. Communication using Venn diagrams

Venn diagrams are a popular medium for presenting data, especially data that is better understood visually. You can start with a small example: “All cats have ears; some cats are grey; no dogs are grey; some dogs have ears.” Present this information using a Venn diagram. Keep adding complexity to situations.

Materials/investment required: Pen and paper.

Suitable for: Students with an interest and understanding of logic and data comparison

One more option—The Lumiere Junior Explorer Program

The Lumiere Junior Explorer Program is a program for middle school students to work one-on-one with a mentor to explore their academic interests and build a project they are passionate about. Our mentors are scholars from top research universities such as Harvard, MIT, Stanford, Yale, Duke, and LSE.

The program was founded by a Harvard & Oxford PhD who met as undergraduates at Harvard. The program is rigorous and fully virtual. We offer need-based financial aid for students who qualify. You can find the application in the brochure! To learn more, you can reach out to our Director, Dhruva, at dhruva.bhat@lumiere.education, or go to our website.

Multiple rolling deadlines for JEP cohorts across the year, you can apply using this application link! If you'd like to take a look at the upcoming cohorts + deadlines, you can refer to this page!

Stephen is one of the founders of Lumiere and a Harvard College graduate. He founded Lumiere as a Ph.D. student at Harvard Business School. Lumiere is a selective research program where students work 1-1 with a research mentor to develop an independent research paper.

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