Spinning Straw into Gold since 2001

Math in a Hat

We introduce numbers to children organically (they grow up with some understanding of them), but don’t really discuss the origins of number systems, or the fact that number systems can be created. i.e. they are not just there for no particular reason.  I developed this lecture for my son’s school (The New School in Syracuse, NY) for two reasons: to demonstrate that 1) how a number system can be generated, essentially an origin for the numbers we use, and 2) complex systems can be generated from a simple set of rules and concepts.  Both of these ideas are important.  The latter is especially important, as it is a concept that is repeated often in natural systems.  I will give an outline of the talk and then expand on it in dialogue format.

Introduce basic numbers

  • 0: Start out wearing a heat, remove the hat and ask the children what is in the hat: “Nothing”
  • 1: Contrast the concept of nothing with the concept of something, which is represented by 1
  • talk about the idea of
    • sets with examples
    • binomial set with examples

Introduce operators starting with +

  • How do we get from 0 to 1 ? : +

Create the natural numbers using +

Introduce infinity.

  • Show that there is no maximum and introduce the idea of infinity.
  • Discuss infinity and infinity concepts

Introduce the subtraction operator

Introduce negative numbers

Introduce the set of Integers

Introduce the multiplication operator, x, by showing how tedious multiple addition can be

Introduce the division operator (moving backwards quickly)

Introduce the set of Rational Numbers

Introduce Irrational Numbers using a Proof.

Sum it all up!




In this way all basic number systems and operators can be introduced.  The children will clearly see that the number systems were generated from a few simple ideas.



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