Stomp rockets are a fun project to explore STEM design at home. About $15 will buy all the materials you'll need to create this project (a few feet of plastic pipe, some pipe fittings and a bit of card stock will get you started).
There are lots of things to consider when you design your rocket. How long with it be? How many and what size/shape of fins will it have to provide stability? Why does it even need fins (while most model rockets have fins, modern space launch rockets don't). What type of nose cone will it have (flat, round, cone, etc)? Will you add a small weight to the front of the rocket (such as a ball of cotton or bit of clay) to move the centre of mass forward?
My favourite part of this project is the iterative design process. You experiment with all sorts of different design features and building techniques and then immediately test them out. My son and I have been building and testing rockets all summer. We've been trying out different rocket lengths as well as fin shapes and size.
You can be inspired by real life rockets or other objects you might see. The fins on the rocket below were inspired by the plastic fletching on arrows my son and I saw at a local store. Would arrow fins be a better source of inspiration than model rocket fins for paper stomp rockets?
Where's the Math?
Over the summer, my son and I made a number of different rockets and tested them out. We were trying to launch are rockets as far as possible. We even bought a 100 ft open reel tape measure to help us measure distances. Our current house record is 158 ft (with a 2L bottle as the launch "engine").
Rocket Aerodynamics - https://www.sciencelearn.org.nz/resources/392-rocket-aerodynamics
Rocket and Launcher Instructions - https://www.instructables.com/id/Paper-Stomp-Rockets-Easy-and-Fun/
Designing Your Own Model Rocket by D. Mark Ponder - https://ohio4h.org/sites/ohio4h/files/imce/Designing%20Your%20Own%20Model%20Rocket.pdf (this document has some great information about different nose cone and fin designs)
Mathematics Essentials 12 - 1.6 Identify, use, and convert among and between SI units and Imperial units to measure and solve measurement problems
Mathematics 10 - M01 Students will be expected to solve problems that involve linear measurement, using SI and imperial units of measure, estimation strategies, and measurement strategies.
Mathematic at Work 10 - M03 Students will be expected to solve and verify problems that involve SI and imperial linear measurements, including decimal and fractional measurements.
Mathematics Essentials 10 - D3 estimate distances in metric units and in imperial units by applying personal referents.