Computational+Fluency

**Embedding Fluency in Conceptual Understanding**

 * The methods that a student uses to compute should be grounded in understanding (pp. 152-55).
 * Students can achieve computational fluency using a variety of methods and should, in fact, be comfortable with more than one approach (p. 155).
 * Students should have opportunities to invent strategies for computing using their knowledge of place value, properties of numbers, and the operations (pp. 35 and 220).
 * Students should investigate conventional algorithms for computing with whole numbers (pp. 35 and 155).

Goals of Fluency
//Based on an article by Susan Jo Russell, “Developing Computational Fluency with Whole Numbers” that appeared in Teaching Children Mathematics (November, 2000).//
 * Students should know the basic number combinations for addition and subtraction by the end of grade 2 and those for multiplication and division by the end of grade 4 (pp. 32, 84, and 153).
 * Students should be able to compute fluently with whole numbers by end of grade 5 (pp. 35, 152, and 155).
 * Students should be encouraged to use computational methods and tools that are appropriate for the context and purpose, including mental computation, estimations, calculators, and paper and pencil (pp. 36, 145, and 154).

Math Fact Fluency Expectations by Grade Level
The following goals for the math facts are consistent with the recommendations in the National Council of Teachers of Mathematics Principles and Standards for School Mathematics:
 * In **kindergarten**, students use manipulatives and invent their own strategies to solve addition and subtraction problems.
 * By the end of **first grade**, all students can solve all basic addition and subtraction problems using some strategy. Fluency is not emphasized; strategies are. Some work with beginning concepts of multiplication takes place. (Sums to 10)
 * In **second grade**,learning efficient strategies for addition and especially subtraction continue to be emphasized. Work with multiplication concepts continues. By the end of the year, students are expected to demonstrate fluency with all the addition and subtraction facts.
 * In **third grade**, students review the subtraction facts. They develop efficient strategies for learning the multiplication facts and demonstrate fluency with the multiplication facts.
 * In **fourth grade**,students review the multiplication facts and develop strategies for the division facts. By the end of the year, we expect fluency with all the division facts.
 * In **fifth grade**,students review the multiplication and division facts and are expected to maintain fluency with all the facts.