Fact Practice

The goal of the math facts strand in Math Trailblazers is for students to learn the basic facts efficiently, gain fluency with their use, and retain that fluency over time. A large body of research supports an approach that is built on a foundation of work with strategies and concepts. This not only leads to more effective learning and better retention, but also leads to development of mental math skills. Therefore, the teaching of the basic facts in Math Trailblazers is characterized by the following elements:


Use of Strategies. Students first approach the basic facts as problems to be solved rather than as facts to be memorized. We encourage the use of strategies to find facts, so students become confident that they can find answers to fact problems that they do not immediately recall. In this way, students learn that math is more than memorizing facts and rules which “you either get or you don’t.”

Distributed Facts Practice. Students study small groups of facts that can be found using similar strategies. In fourth grade, the multiplication and division facts are divided into five groups. During the first semester students review the multiplication facts and develop strategies for the division facts, one group at a time. During the second semester, they review and practice the division facts in each group so that they can develop fluency with all of the facts by the end of the year. Practice of the five groups of facts is distributed throughout the curriculum and students are also given flash cards to practice groups of facts at home.


Practice in Context. Students learn the facts as they use them to solve problems in the labs, activities, and games.

Appropriate Assessment. Students are regularly assessed to determine whether they can find answers to fact problems quickly and accurately and whether they can retain this skill over time. A short quiz follows the study and review of each group of facts. Each student records his or her progress on Facts I Know charts and determines which facts he or she needs to study.

A Multiyear Approach. In Grades 1 and 2, the curriculum emphasizes the use of strategies that enable students to develop fluency with the addition and subtraction facts by the end of second grade. In Grade 3, they review the subtraction facts and begin strategy work with multiplication facts in order to achieve fluency by the end of the year. In Grade 4, the addition and subtraction facts are checked, the multiplication facts are reviewed, and fluency with the division facts is achieved. In Grade 5 all facts continue to be reviewed so as to retain fluency.

Facts Will Not Act as Gatekeepers. Use of strategies, calculators, and printed multiplication tables allows students to continue to work on interesting problems and experiments while they are learning the facts. Students are not prevented from learning more complex mathematics because they cannot perform well on facts tests.