Mathematical Journeys

These three activities are taken from the Association of Teachers of Mathematics (ATM) publication ‘Mathematical Journeys’.

Arithmagons begins by exploring triangular arithmagons. Students are encouraged to produce a strategy for solving the arithmagons rather than rely upon trial and error. Students are also asked to explore whether the solution is unique, when fractions are required and when negative numbers are required. Extension work consists of exploring the same questions for square arithmagons, pentagonal arithmagons and hexagonal arithmagons.

Frogs is an investigation in which students find the minimum number of moves required for three white counters and three black counters to change places. Students are expected to work logically to investigate the minimum number of moves required for different numbers of counters. Students should be required to generalise their results.

Round and Round requires students to choose any four numbers and place them at the corners of a square. On the middle of each side of the square is written the difference between the two numbers at the corners of that side. Students explore what happens as this procedure is repeated.