🔗 Distributive Property Expansion

About Distributive Property Expansion

The distributive property is the reason anyone can multiply seven by thirty-four in their head: split the thirty-four into thirty and four, multiply each by seven, and add. Pupils use it constantly without naming it, and naming it is what lets them apply it deliberately later in algebra. This matching worksheet connects the two forms directly. The left column holds a product; the right column holds the same product split on place value, and the pupil draws the line between them. Every split is exactly equivalent to its product — the equivalence is constructed rather than checked afterwards, so no line can join two expressions that are merely close. Splits are always on place value rather than arbitrary pairs, because that is the version that makes the mental method work. Products grow across the five levels from a single-digit multiplier and a two-digit number up to larger multipliers and three-digit numbers. Every right-hand expression on a page is distinct, so the matching has exactly one solution. Each level prints as a clean A4 sheet in black and white and downloads with its own separate answer key. Its on-screen twin is Distributive Property Split Drag.

Common questions

How are the numbers split?

On place value — 34 becomes 30 and 4. That is the version that makes the mental method work.

Could two splits both be correct for one product?

No. Each split is constructed from its own product and every right-hand expression on a page is distinct.

Why teach this before algebra?

Pupils already use the property mentally. Naming it is what lets them apply it deliberately when brackets appear later.

Is an answer key included?

Yes. Every level downloads with a key giving the correct letter for each row.