Our Unifying Thread
The thread that underlies our approach to teaching all of arithmetic is that people talk about numbers but what they see are quantities. For example, we have seen 3 fingers, 3 apples, 3 tally marks, 3 people, etc.; but we have never seen “threeness'' itself.

In a phrase such as “3 apples”, 3 is an adjective that modifies the noun“apples”. We refer to such a phrase as a quantity. More formally:


A quantity is a phrase that consists of an adjective (in the form of a number) that modifies a noun (usually referred to as a unit).

People in science talk about quantities, not numbers. That is, they will talk about 3 ounces, 3 grams, 3 pounds, etc., but never just about 3.


In the quantity “3 apples”, the adjective is 3 and the noun (unit) it modifies is “apples”.



Our Underlying Contention:

People tend to see numbers as quantities. And if we allow students to visualize numbers as being quantities, all of arithmetic becomes much easier to internalize and understand.


Our website is dedicated to helping you understand how we implement our goal and what you can do to help students attain greater success in internalizing the basics of mathematics. What is important to keep in mind is that we are not asking you to abandon anything that you prefer to do in class. Instead we are supplying you with an additional tool; a tool that has worked very well for us.

The resources on this site are dedicated to teachers. We invite you to send ideas, comments and suggestions. Email us at or add an idea or comment to our guestbook.

We wish to acknowledge the support of Corning Enterprises and in particular Director Chris Sharkey as well as Corning Community College and in particular Dr. Katherine Douglas, President.  Without them, the successful workshop held for the Corning-Painted Post region would never have occurred.  Please visit our Corning-Painted Post Workshop page to learn more about this endeavor.  There is a lot more to come! 

Our page devoted to mapping resources (PowerPoint presentations and Classroom Activiites) to new Common Core Standards is now available.  Go to the NEW Common Core Standards Resources page and have a look!  Download any item and please feel free to send suggestions.  


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