The appropriate project for a math class depends on the grade level of the pupils. However, there are basic experiments in geometry, such as using juice boxes, and statistics, such as using the birthday paradox, that can give students a deeper understanding of mathematical concepts.
Juice boxes can be a great tool to perform basic experiments in geometry. Students can calculate the volume of the box by taking measurements of the sides of a box and multiplying the height by the width and depth. Then, the liquid volume of the contents can be measured by pouring the juice into a beaker that measures fluid quantities. More advanced students can convert the amounts to different measurement systems and look into how consistent the liquid volumes are and which brands of juice boxes contain the most accurate amounts.
Statistics is another field of math that may be explored by a simple math project. For example, the birthday paradox describes the phenomenon where, even though there are 365 days in a year, in any given group of 23 people there is a 50 percent chance that two of them share a birthday. Students can calculate what the odds of this happening are according to statistics, and carry out the experiment using the birthdays of everyone in the classroom.