Hover to see how Factors connect to Arithmetic Fact Retrieval. Then click connected Factors to explore strategies related to multiple Factors.

Arithmetic Fact Retrieval requires efficiently, accurately, and flexibly drawing basic number combinations from Long-term Memory to use in performing more complex calculations. Though arithmetic facts and number combinations are typically in place by the end of elementary school, fluent and flexible fact retrieval continues to scaffold math learning and outcomes through high school.

More recently, the term arithmetic or number **combinations** is often used in place of "fact retrieval" because basic arithmetic problems can be solved in a variety of ways and are not always retrieved as "facts."

There are three key components to Arithmetic Fact Retrieval:

**Efficiency:**Retrieval of arithmetic combinations should be fluent and use the most directly applicable strategy;**Accuracy:**Arithmetic combinations stored in Long-term Memory should be correct; and**Flexibility:**Combinations allow students to access and use their connected number networks for arithmetic problem solving.

Before students are able to use fact retrieval with efficiency, accuracy, and flexibility, they need to have experience working with number combinations using modeling and counting strategies. This experience provides opportunities for students to develop a network of connections that supports understanding. This network, in turn, allows students to use fact retrieval strategies that are less subject to interference and errors. For example, to figure 7 x 8, a student with a connected network of understanding might retrieve the fact 8 x 8 = 64 and relate it to 7 x 8 by subtracting 8: 7 x 8 = 8 x 8 - 8 or 64 - 8.