If you are a teacher who likes to sing, here are two songs. One is simply to help students remember the 6 multiplication tables. The other is to help students remember the Fibonacci numbers and the golden ratio. Fibonacci numbers are the series of numbers in which each number is obtained by adding the two previous numbers. The ratio of a Fibonacci number to the preceding Fibonacci number approaches the golden ratio value 1.618034...., growing ever closer as the Fibonacci numbers get larger.
 

 Mathematics as Problem Solving:
Students use problem-solving approaches to investigate and understand mathematical context.

 Mathematical Connections:
Students use mathematics in other curriculum areas.
Students use mathematics in their daily lives.

 Patterns and Functions:
Students can describe, extend, analyze, and create a wide variety of patterns.

 The Mathematical World, Symbolic Relationships:
Similar patterns may show up in many places in nature and in the things people make.

 The Nature of Mathematics, Patterns and Relationships:
Students learn that mathematics is the study of any patterns of relationships, where as natural science is concerned only with those patterns that are relevant to the observable world.
Although mathematics began long ago in practical problems, it soon focused on abstractions from the material world, and then on even more abstract relationships among those abstractions.