When learning how to compare fractions, students first learn that you can only compare fractions of the same sized whole. For example, we cannot compare half of a small package of skittles to half of a large package of skittles,
1. When comparing fractions with common denominators, you look to the numerator, and the fraction with the larger numerator is the larger fraction. This is because you have more equal sized parts. For example, 3/4 is greater than 2/4, because 3 pieces are more than 2 pieces.
2. When comparing fractions with common numerators, you look to the denominator. As the denominators get larger, the pieces get smaller, so the fraction with the smaller denominator is the larger fraction. This is because the pieces are larger. For example, 1/4 is larger than 1/6, because the fourths are larger pieces than the sixths, so one large piece is greater than one small piece.
1. Compare to a Benchmark of One-Half - Think about the fractions in terms of a half. If one fraction is less than a half and the other is greater than a half, then the fraction that is greater than a half is greater than the other fraction. For example, 1/4 is less than 4/6, and I can prove this because 1/4 is less than 2/4 and 4/6 is greater than 3/6. This strategy does not work when both fractions are less than or greater than a half.
2. Compare using a Model - Students can draw two rectangular models stacked on top of each other to compare fractions. You want to make sure the wholes drawn are the same size, and the parts are drawn equally within each whole. It is easiest for students to draw rectangles stacked on top of each other, rather than circles or rectangles / squares drawn side by side.
3. Find Common Denominators and Compare - Once students have learned how to find equivalent fractions, we teach them how to compare after finding common denominators.