Multiplication and Division Fact Families

Four houses fill this Grade 3 page, and the trios on their roofs are not addition families. Each roof carries a factor, a factor and their product — 6, 7 and 42, say — and underneath it the four related facts are printed with an empty box at the end of each: 6 × 7, 7 × 6, 42 ÷ 6 and 42 ÷ 7. Sixteen boxes, four families, factors between 2 and 9, and never the same factor twice in one house.

The house is familiar from first grade, and reusing it here is precisely the point: multiplication and division undo one another exactly as addition and subtraction do. What makes this version powerful is what it does to division. A child who reads 42 ÷ 6 as how many sixes fit inside forty-two is counting groups; a child who sees the house behind it thinks six times what makes forty-two, and simply recalls a fact they already own. That unknown-factor view is the single most useful idea in third-grade division, and it is worth far more than any division algorithm taught early.

The page prints free as a PDF and makes an excellent follow-up to table work, once the facts themselves are reasonably secure. The times table of 5 and the times table of 3 supply the raw recall these houses depend on, and fact families to 10 is where the same structure first appeared with plus and minus.