P2B · Number · NUM.ORDER.OPERATIONS

Order of operations

Intuition

Understand first, compress later.

Connect symbolic calculation to magnitude, estimation and a visual representation.

Switch representations

Expression tree3·(x + 4) − 5

operator (internal node)operand (leaf)

The tree shows the order the work happens in: the leaves are numbers and variables, each internal node is one operation. It is evaluated from the bottom up — the root is the operation performed last, here the subtraction. Brackets have disappeared; their effect is now the shape of the tree.

Formal view

You can order of operations when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.