The Decanomial

Ember & Stella

One thing Montessori elementary classes are known for is work with timelines in history, which supply the framework for all the subjects. In our timeline of “Classical Civilizations”, the work of the ancient Greek Pythagoras is noted. Do you know who he was and what his contribution was?  He is credited with the invention of the multiplication table! Yes, in early 500 BC, the “Table of Pythagoras” was plotted.

In the Montessori class, we expand on this ancient table with manipulative bead work. You’ve seen the color-coded chains of beads that we use for math operations (addition, etc). We also have the student build up a Table of Pythagoras with chains of beads, giving a visual impression of the rectangular arrays, which are actually a representation of the multiplication table.

Thomas & Dusty

This is important, because all numbers have shape, and we teach more advanced multiplication based on the rectangular arrays that are formed. We can represent geo- metrical multiplication (what you probably learned as “long multiplication”) by constructing rectangular arrays. If you wish to see this in person, let me know, and I will gladly give you a demon- stration.

The next iteration of the Table of Pythagoras (the multiplication table) in the curricular progression is the Decanomial, a delightful puzzle of rectangular grids, color-coded to the concrete bead material. I made the set for Moon- flower with 1-cm graph paper to emphasize visually the “value” of each rectangle (i.e. 4×6).

Nevin & Leroy

Kindergartners would be able to build just the puzzle, but as they do so, they are laying the foundation for understanding the mathematical shape of the multiplication table.

For the upper elementary students, I will have them build the Decanomial Square in the opposite direction (just look at the Table of Pythagoras upside-down for this). Then, we can use it manipulatively to find squares of numbers. For example, the square of (6+5) would require the student to place the (5×5) square in the lower right-hand corner of his work space. On the diagonal to the upper left, he then places the (6×6) square.

Now, he fills in the empty rectangular spaces adjacent to these—a (5×6) and a (6×5). He adds the values of the four rectangles to find the square of those numbers together. Our fifth-grade student has already discovered that she can save time by multiplying each array rather than adding the individual squares.


You can imagine the great math concepts the children acquire, which will be theirs forever, as they are absorbing them both concretely and in the mind’s eye. This will make all mathematical operations easier to grasp in future situations, no matter what school your child attends.

Parent Meeting Scheduled

On Tues, Feb 6, at 6:00 pm, there will be a meeting at the school for parents. There will be presentations by the teachers of several of the mathematics lessons. You will also be given an ex- planation of what to expect on the written progress reports to be distributed at the end of February. Bring your questions!

Amended Snow Procedure

Due to the “snow” day ex- perienced last week—a Wednesday when there were only two teachers and two preschoolers present—the board will be making decisions about snow days that may include closing the school. Snow day decisions will be sent via email, as well as being announced on the television news.

Guest Musician

Susan Thomas brought her dobro this week:




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