Rather than memorizing isolated number facts, students can be shown “families of facts” which easily allow for memorization of 4 related facts.

Any addition or multiplication fact can be “turned around” (e.g., 3 + 4 = 4 + 3; 7 x 2 = 2 x 7). This is a fact taught early to children, and is formally known as the “commutative principle” in mathematics: in general, a + b = b + a, and c * d = d * c.

Addition and multiplication facts can also be “inverted” to produce a pair of related subtraction or division facts. For example, since “5 + 2” equals 7, we can deduce that “7 – 5 = 2” and “7 – 2 = 5”.

This idea leads to a strategy of learning families of facts which all use the same three terms. For example, the following addition and subtraction facts each use the terms 4, 7 and 11: