Part part whole relationships (PPW) involve seeing numbers as being made of two or more parts. Many researchers have said this is the major conceptual achievement of the early years. A strong understanding of PPW has been shown to increase understanding of subsequent work with place value, number concepts, and word problems.
After students learn to count, they need to work on part part whole relationships before beginning addition and subtraction. The Hands On Math program follows this order.
As in the other number relationships, students use counting as a scaffold to form their ideas about PPW.
When students are exploring parts of a number, they need to work with one number in a variety of ways and with a variety of concrete materials. We also want to use a multisensory approach, which requires visualization and begins to move students away from relying on their counting skills.