Last week, I introduced Dora to the knobless cylinders. Though she has expressed absolutely no interest in working with the knobbed cylinders, she loved working with the knobless cylinders. They are the perfect tool for teaching about variations in height and width, as well as the accompanying descriptive labels, such as “wide”, “thin”, “tall”, “short”, “large”, “small”, etc. We also did a lot of what Montessorians call “extensions”. The use of the word “extension” in regards to the Montessori Method seems to refer simply to using materials for anything other than their original intended purpose (please someone correct me if I am wrong, I could not find a definition anywhere). At our house, we call this “playing with blocks” and it is something that we excel at. We combined the cylinders in various fashions, created patterns with them, and made designs with them. I even had fun creating “math problems” for myself while Dora was doing her own thing, but refusing to let me go anywhere else. Here are some photos of the work we did:
Here are my “math problems”. I decided to create various numbers of stacks of the blue cylinders while having as few blocks left over as possible. After finally deciding to assign each block a value (the shortest block equaling 1, the next shortest block 2, and so on), it was much easier to do. I found that the total number represented by all ten blocks is 55. Therefore, there would be one block left when I created 2, 3, or 4 stacks, but none leftover if I created 5 stacks, thereby using knobless cylinders to illustrate the concept of factorization. Now that I have amazed and stunned you with my incredible math prowess, here are the photos of the towers that I built to support my hypothesis.