Materials: paper, pens
Time: 1-2 hrs
Complexity: easy to mid-level
This set of four pieces is called Hoopers Paradox. The top rectangle has an of area of 30 (10×3) and can be rearranged into the bottom shape, which is made up of two rectangles. Strangely these two rectangles have a combined area of 32 (2×6 + 4×5 ). When the magician performs this trick he exclaims how he has gained 2 more pieces for free.
Watch this video with your students to see Hoopers Paradox being performed by a professional magician, then ask them to make cardboard versions of Hoopers Paradox and investigate how it works!
Links to maths magic websites
Murderous Maths – website of longtime Maths Week presenter Kjartan Poskitt, featuring prime number tricks, predictor cards, the Five Card trick, Calendar trick and many more!
Stunning Friends with Math Magic – collection of 22 card tricks, number guessing games, paper and glue magic, and other maths magic tricks – all tricks are explained.
Maths & Magic has a range of interesting maths magic tricks.
Hidden Answers Mathematical Magic – 15 interesting mathematical tricks of varying difficulty.
YouTube has a seemingly infinite supply of videos on maths magic! Watching a short maths magic video with your class is a great place to start the lesson.
Books on mathematical magic
Mathematics, Magic and Mystery by Martin Gardner; magic tricks that may be played with cards, common objects, special equipment, drawings, and pure numbers. This is one of the great maths magic books.
Creative Magic by Steve Humble and Martin Duffy; children and adults will improve their mathematical skills in a fun way. This book shows you how to perform magic and how to create your own versions of classic magic tricks. The creativity comes from the chapters ideas on how to develop the tricks to make them your own.
Magic for Kids by Andrew Jeffrey; includes a huge range of mathematical tricks which both teach and entertain.
Murderous Maths books by Kjartan Poskitt; all books in this series contain some maths magic tricks.