# Math and Science Scaling Equivalencies in the Table of Pythagorus

A Math Story

The Table of Pythagoras (Decanomial Square) is a beautiful manifestation of the power of Montessori’s math. It introduces the decanomial: the concept that all numbers are organized by decades (tens). Children are usually given the sensorial presentation of this material around the age of four or five in casa. When it re-emerges early in Elementary, it is used to situate and reinforce multiplication facts before charting a course into new understandings of the commutative law, squaring, and binomials. It lays the foundation for algebraic determination and eventually, for the cubing material that follows in upper elementary. Interestingly, this material is visually resolved to the pink tower they are first introduced to sensorially at the age of two and a half. We discovered that none of this is by accident.

Every step of the way, the materials pluck strings laid deep in the child’s absorbent mind years prior. Materials are auto-didactic, not just to correct errors made as they work with it but also to lead them to the next place of discovery. Midway through the year, some of our students deduced the great reveal hidden within the decanomial square. At its diagonal centre, sits a magnificent secret: the sum of the units of the bissected square divided as a right angled triangle are identical to the sum of the cubed material that takes the square into a third dimension. This is a cool math fact to be sure but the days the children spent solving it were breathtaking. They will remember what they “learned” because they experienced and discovered it, not because they memorized it for a test. They worked together to test different theories and approaches. They got a little frustrated and in the end, they came together and found a solution.

Moving on to the Math Curriculum at the Lyceum

The children are privately tutored in math by Amanda. Over the past year, our grade eight students have studied functions and relations, force and energy and quadratic equations. These in-class studies are augmented by real-world problem scenarios and case studies such as building massing, hydrolics and planetary orbits. Our grade six and seven students are learning fractions and decimals, graphing and linear equations by applying their lessons to real world problems such as nutritional analysis and budgeting. Our small class sizes allow for the flexibility and resources to work on individualized plans tailored to each student’s needs.