Origami Fractions or paper folding is a great hands on way to introduce fractions and fraction operations. The paper folding techniques introduce the single digit primes (2, 3, 5, and 7) as the first four fundamental numbers of equal sections in which a piece of paper can be folded. See the folding fractions lesson example. These four primes can then lead students into the exploration of the Sieve of Erasthenes and the primes included within the numbers 1 to 100. 
See Origami Fraction to learn how the fraction operations and numerical rules can be derived from paper folding. I recommend students become familiar with fraction operations by folding paper before using the Pythabacus, so that first the area concept of multiplication and the comparison of areas to define fractions are well understood. See the multiplying fractions lesson example. Equivalent fractions are also easily produced and defined using paper folding techniques. See lesson example.
The four fraction operations, equivalent fractions, reducing (see my reducing page) and the introduction to primes can constitute a first year or fourth grade introduction to fractions. Working out the answers to fractions on the Pythabacus is a great way for students to demonstrate and hone the understanding of fractions and fraction operations through the the area concept of multiplication and the comparison of areas. 
Finding the GCD and LCM, as well as prime factoring, decimals and percents might constitute second year or fifth grade fraction related math lessons. See the addition and formulas lesson examples.