Students need to be fluent with all basic number facts, including all multiplication facts to 10×10 or 12×12, and associated division facts.
The so-called “times tables” are one of the best-known foundations of school mathematics, for good reason. Working efficiently with later mathematics in geometry, algebra, probability, trigonometry, and so on, will be achievable only if students have a solid recall of all the basic facts in the four operations.
Don’t be fooled by anyone who says that memorizing number facts is old-fashioned; don’t confuse number fact recall (a very good thing) with rote learning of facts (a very bad idea). We recommend the use of targeted strategies to help students to develop understanding of the facts they are learning, to give them a grounding on which to build the recall of the facts.
Basic multiplication and division facts can be extended by multiplying the terms by powers of ten. For example, starting with the “double double” fact “7 x 4”, we can extend it in ways such as these: