P2A · Number · NUM.MULT.CONCEPT

Multiplication as groups and arrays

Intuition

Understand first, compress later.

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

Switch representations

Array model4 × 6 = 24

rowscolumns

4 rows of 6 and 6 columns of 4 count the very same 24 dots. One arrangement, read two ways — that is why the two multiplication facts agree.

Formal view

You can multiplication as groups and arrays 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.