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Fact Fluency
“Mathematical Fluency” can be defined as efficiency, accuracy, and flexibility. The GPS Math Curriculum emphasizes the development of flexible thinking with numbers. The learning activities we offer students build this fluidity through composition and decomposition of numbers, place value understanding, and the properties of operations. When referring to the “basic facts” it means automaticity with understanding. Automaticity is students’ ability to effortlessly recall a fact and use it in computation strategies and problem solving situation.
“Mathematical Fluency” can be defined as efficiency, accuracy, and flexibility. The GPS Math Curriculum emphasizes the development of flexible thinking with numbers. The learning activities we offer students build this fluidity through composition and decomposition of numbers, place value understanding, and the properties of operations. When referring to the “basic facts” it means automaticity with understanding. Automaticity is students’ ability to effortlessly recall a fact and use it in computation strategies and problem solving situation.
Being automatic with basic facts frees the brain to focus on other math processes. Committing basic math facts to memory speeds up math tasks. As math tasks increase in complexity, they often require multiple steps to find the solution. These tasks are time-consuming, and often stressful, for students who must stop to figure out each basic fact along the way. And stopping to determine each fact disrupts the flow of the math procedure.
Being automatic with basic facts frees the brain to focus on other math processes. Committing basic math facts to memory speeds up math tasks. As math tasks increase in complexity, they often require multiple steps to find the solution. These tasks are time-consuming, and often stressful, for students who must stop to figure out each basic fact along the way. And stopping to determine each fact disrupts the flow of the math procedure.
Students who have committed basic math facts to memory are able to perform critical mental math tasks. They estimate answers prior to solving problems so they are able to compare their estimates to the actual answers and determine the reasonableness of their solutions. Mastery of basic facts provides the foundation for everyday mental math tasks. The National Mathematics Advisory Panel (2008) urges that students develop automatic recall basic facts to be prepared for the study of algebra, in which solving multistep equations is a fundamental task.
The ability to recall items is enhanced when understanding is connected to the task. Memorizing a chain of nonsensical words (e.g., sat chair red girl a in little the) is more difficult than memorizing a sentence in which the words have meaning (e.g., A little girl sat in the red chair). Asking students to memorize dozens of number facts can be discouraging and confusing when students view them simply as pairs of numbers. Students who simply memorize math facts miss a prime opportunity to expand their understanding of equations. Problem solving is the central focus in today’s math classrooms. To be a successful problem solver, students must be able to accurately compute answers, but more than that, they must be able to figure out how to build equations that correspond to problem situations.
Basic fact instruction for fluency begins with conceptual understanding and many opportunities to develop strategic thinking. Understanding the relationship between operations,addition and subtraction, multiplication and division, is critical. A variety of practice methods builds automaticity and quick recall. Here in Glastonbury, instruction is based on key resources by Sue O'Connell and John SanGiovanni, Mastering the Basic Facts: Strategies, Activities and Interventions to Move Students Beyond Memorization as well as Graham Fletcher's Fact Fluency in Grades K and 1, and Reflex Math in Grades 2 - 5.
Common Core State Standards expectations for fact mastery:
Common Core State Standards expectations for fact mastery:
Kindergarten: Add and subtract within 5
Grade 1: Add and subtract within 10
Grade 2: Add and subtract within 20 and add and substract withing 100 with paper and pencil
Grade 3: Multiply through 10 x 10 (all single digit multiplication facts and 10x10) and add and subtract within 1,000,000
Grade 4: Multiply through 12x12; Divide through 10x10 facts
Grade 5: Fluently and efficiently compute all facts in all four operations
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