Middle School, Pure Mathematics Projects, Lessons, Activities (Page 2)

Gigantic, Invisible Triangles: Measuring Height (or Altitude) with an Inclinometer

Science Fair Project Idea

Scientific Method

If you've ever wondered how tall that bridge is, or how high your kite was, then this could be a good project for you. You'll learn how you can use the mathematics of right triangles to measure the height of an object with two measurements that you can make on the ground. Read more

Money Problems

Science Fair Project Idea

Scientific Method

Math can make you money! If you understand some basic math, you can make good decisions about how to keep, spend, and use your hard earned dollars. Try an experiment comparing the same balance in different types of bank accounts. How much better is a savings account than a checking account? What difference does the interest rate make? Which is better, an account that earns compound or simple interest? Can you compare the short and long term costs of borrowing money compared to saving the cash… Read more

Playing Games

Science Fair Project Idea

Scientific Method

Almost all of the games we play are based on math in some way or another. Card games, board games, and computer games are designed using statistics, probabilities, and algorithms. Begin by reading about games and game theory. Then you can choose your favorite game and investigate the mathematical principles behind how it works. Can combinatorial game theory help you to win two-player games of perfect knowledge such as go, chess, or checkers? (Weisstein, 2006; Watkins, 2004) In a multi-player… Read more

Playing Music

Science Fair Project Idea

Scientific Method

Music has many mathematical elements in it: rhythm, pitch, scale, frequency, interval, and ratio. There are many ways to turn these elements into a science fair project. You can investigate how the scale is based upon a special type of number sequence called a Harmonic Series. Another scale used by Bach, called the "Well-Tempered-Scale" or the "Equal-Tempered-Scale", is based upon a series. How are these mathematical series and ratios related to notes, chords, intervals, and octaves? You can… Read more

Around the World: The Geometry of Shooting Baskets

Science Fair Project Idea

Scientific Method

Take shots at a set distance from the basket, but systematically vary the angle to the backboard. For a basic project: How do you think your success rate will vary with angle? Draw a conclusion from your experimental results. A bar graph showing success rate at different angles can help to illustrate your conclusion. For a more advanced project: Use your knowledge of geometry and basketball to come up with a mathematical expression to predict your success rate as a function of angle… Read more

Design Your Own 3D Optical Illusions

Lesson Plan Grade: 8th-12th

In this lesson your students will design their own 3D objects that exhibit "anomalous mirror symmetry"—that is, their reflections appear flipped left to right when you put them in front of a mirror. Students will start by defining the outline of a 2D shape using functions. They will then use MATLAB or Python code to convert the 2D shape into a 3D curve that replicates the outline of the 2D shape when viewed from a certain angle. Finally, they will convert the 3D curve into a solid 3D… Read more

Divide and Conquer: Proving Pick's Theorem for Lattice Polygons

Science Fair Project Idea

Scientific Method

If you like to play Tetris, then you might like this project. You will learn something interesting about the mathematics of complex shapes as you try to prove Pick's Theorem. The strange shape below is an example of a lattice polygon, which is a polygon whose vertices lie on points in the plane that have integer coordinates. As you can see, it is a complex shape, but there is an easy way to calculate its area, by simply counting lattice points! If you count the number of lattice points on… Read more

Draw a Spirograph with a Raspberry Pi

Science Fair Project Idea

Scientific Method

Have you ever used a toy like a Spirograph® to draw precise, repeatable patterns on a piece of paper? What if you could use a computer to automatically draw the patterns for you? This project will show you how to do just that using a Raspberry Pi. Check out the video to see what this simple, but fun, project looks like. IMPORTANT: The instructions for this project were originally written using Scratch 2 on a Raspberry Pi 3B+. If you are using a newer Raspberry Pi running Scratch 3, you… Read more

Frequency Histograms

Science Fair Project Idea

Scientific Method

Can you remember what the weather was like last week? Last year? Here's a project that looks at what the weather was like for over a hundred years. You'll use historical climate data to look at moisture conditions in regions across the continental U.S. You'll use a spreadsheet program to calculate the frequency of different moisture conditions for each region and make graphs for comparison. Which part of the country has the most frequent droughts? The most frequent periods of prolonged… Read more

Frequency of Outcomes in a Small Number of Trials

Science Fair Project Idea

Scientific Method

People often draw conclusions from a small number of observations, and use those conclusions to evaluate the likelihood that an event will take place. But how easy is it to draw the wrong conclusion based on those observations? Will your predictions be accurate if an experiment is only performed a few times? The objective of this project is to determine what happens when a test with two equally-likely outcomes is performed only a small number of times. You can test this by flipping a coin. A… Read more

Middle School, Pure Mathematics Projects, Lessons, Activities (28 results)

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