In the last unit of Math 251, we started fractions, decimals, and percentage. Personally, I think this will be the most helpful unit because partial numbers are always more difficult to think about than whole numbers, or even integers.
The big ideas in this unit are partitioning and unit iteration. We are very familiar with partitioning. For fractions, partitioning is again just splitting the whole unit into equivalent parts. (illustrated below) Partitioning is best used when you start with the whole unit.
Unit iteration is just as useful and common as partitioning, although it's not as obvious. Unit iteration is consistently repeating a unit to build a whole. (illustrated below) This method is best used when you only have part of the whole.
Lastly, the most efficient way to teach fraction names is to say it as: 3/4 = three 1/4 pieces. It's easy to confuse a child by saying fractions like "three out of four" because that is not always the case with all fractions!
