Fact Family Houses Worksheet

The house

Each problem is a little house. The whole sits in the triangular roof, the two parts sit in windows on the ground floor, and four blank lines run underneath for the child to write the four related facts.

Two to eighteen houses a sheet. Numbers up to 144, answer key optional.

Why a house rather than a row of numbers

Because the picture encodes the relationship, and a row of numbers does not.

Roof on top. Parts below, holding it up. A child looking at the house can see that the two windows together make the roof, and that is the part-part-whole idea on which the whole of early number work quietly rests. Written as "4, 6, 10" it is three numbers. Drawn as a house it is a structure.

It also makes the four facts findable rather than memorable. The child reads them off the drawing instead of trying to recall which combinations are allowed.

Four facts, and why four

From 4, 6 and 10: two additions, 4 + 6 and 6 + 4, and two subtractions, 10 − 6 and 10 − 4.

That subtraction pair is the whole point of the exercise. A child who knows the addition and treats subtraction as a separate skill will count backwards on their fingers for years; a child who sees the house answers 10 − 6 by looking at the roof and one window.

The multiplication houses work identically

Product in the roof, factors in the windows. 3, 4 and 12 give two multiplications and two divisions.

This is the fastest route into division facts there is, and it is routinely skipped. Anyone who knows 7 × 8 = 56 already knows 56 ÷ 8, and the house makes that impossible to miss.

Watch for the doubles

When both parts are the same — 5, 5 and 10 — there are only two distinct facts rather than four, because 5 + 5 and 5 + 5 are the same statement.

Children find this confusing. Explain it rather than marking it wrong — they have noticed something real about the structure, which is exactly what the sheet was for.

Level and use

The addition houses suit roughly ages five to seven; the multiplication ones eight to ten. Keep the numbers small at first, because the point is the relationship and not the arithmetic.

Related: plain fact families without the drawing, and number bonds for the pairs themselves.