Engineers design, make and test things to see how they can be improved and made fit for purpose. Try some of these ideas, and see how maths can help.
A simple robot to make, plus robots in everyday life to investigate.
Design and test a paper helicopter. What is the best design?
What shape and size of drinks mat is best for flipping and catching?
Build a scaffold out of drinking-straws to support a cup of water
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.