In this example, a 3 by 5 rectangle stands for the number 1. That choice makes it easy to represent the fractions we are adding. By examining the figure, we see that the sum is 13/15. Doing this once, of course, would not be very helpful, but discussing the dimensions of useful rectangles, leads to a powerful strategy which can be applied to comparing, adding, or subtracting fractions.
Have students make things. In some cases, a constructionist approach can yield much learning. Constructionism is a theory of learning espoused by the Logo movement in the 1980’s, and it is still going strong with Logo descendants such as Scratch and Snap, or with the current popularity of maker spaces and STEM. To enhance math education, what students make needs to have a curricular payoff. It can be a turtle geometry computer program, a GeoGebra construction, a tiling of the plane, etc.
For an example of the latter, using a plastic template and a pencil (or a computer), students can create tessellations using triangle or quadrilateral tiles. Here is one based on a scalene triangle: