Composing & Decomposing
Notions of equivalence must be maintained within each manipulation. The purpose of composing and decomposing is to simplify the mathematics.
It is an essential skill for making calculating easier because it is all about making and then using friendlier numbers. Learners will encounter all kinds of scenarios where they will need to join or separate, sometimes identifying the parts that make up a whole, and sometimes comparing the parts. Thinking flexibly about putting numbers together as well as taking them apart leads to a greater understanding of relationships not only between numbers and operations but in all strands of mathematics.