I use a constructivist approach to introducing the many forms of fractions. Basing the opening activity on prior knowledge of money (decimals and fractions) and grades (percentages and fractions), I have my fourth and fifth graders work out decimal equivalents for halves, thirds, fourths, fifths, sixths, etc. through twentieths (we skip thirteenths and a few others that are not common). Then students use the decimal fractions to find fractions which are equivalent and look for and "discover" that the numerator/denominator relationship is constant for a given group of equivalent fractions--a pattern! Finally, students extend the pattern they have found to generate more equivalents to the lists already started (more that equal 1/2, etc.) and use new ratios to generate new lists 1:50, 1:100 etc.
How can we get from 1/2 to ,50? We think: Money...one dollar (1.00) divided by 2 is .50. So, could 1/2 be another way of writing 1 divided by 2? It is! ...another algorithm is "discovered"!
Next, students develop a chart showing relationships between:
fraction, division problem, decimal fraction, per cent, and ratio 1/2 = 1 divided by 2 = .50 = 50% = 1:2
We write word problems that show these connections. often ending up with three forms in the same problem and play with diagrams, circle graphs and manipulatives to develop number sense in this area. Then we USE this all year! Students receive fraction grades (21/24) and are responsible for figuring decimal then percentage equivalents...what fraction of the class is in band?...If only 17 students are getting hot lunches and 6 of them are getting milk in addition to the 4 brown baggers getting milk, what is the ratio of milk drinkers to non-milk drinkers today--is the percentage of milk drinkers going up since our nutrition study?.........
Yes, we do use calculators to find decimal fraction equivalents to fractions. At that point I want students to get excited about the division/fraction/decimal relationship...excitement with kids means go fast! Later, many equivalents are memorized (really, internalized) and we may work the division with paper/pencil or use calculator depending on time and objectives. Tonna Kershul 8-11 mixed age class