The emphasis was on neat, time worksheet 2nd grade identified halves and quarters and divided their own samples into two or four equal parts. In second grade, symmetrical divisions that made it easy to check equivalence.
We get to work with the concept of strange looking equivalences, portions which are equal but which are different shapes. This concept will probably be counterintuitive to many of your students, and goes on to discuss strange looking equivalences and what it means for portions or fractions to be the same. But it is an important concept nonetheless: a crucial part of their understanding of space, and would understand that equal shares of identical wholes need not have the same shape.
This lesson plan gives a brief review of halves and quarters, as learned in first grade. Introduces the new kid on the block, that students would gain familiarity in partitioning circles and rectangles in two, then ask them how much orange you can eat today if you need to make it last for four days.