P2B · Number · NUM.MULT.MULTIDIGIT

Multi-digit multiplication

Intuition

Understand first, compress later.

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

Switch representations

Multiplication as area14 · 12 = 168

10 · 104 · 1010 · 24 · 2

The rectangle is 14 wide and 12 tall, drawn to scale: its area is the product 14 · 12. Split the two sides into 10 + 4 and 10 + 2 and 4 sub-rectangles appear; their areas add back up to 168. That is exactly what the written method computes: every partial product is a piece of area.

Formal view

You can multi-digit multiplication 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.