Students demonstrate mastery of facts when they can produce an answer with speed and accuracy (in about 3 seconds) without resorting to inefficient means such as counting up, using fingers, etc.
Often students have difficulty mastering basic facts because they have not developed efficient methods of producing a fact answer based on number relationships and reasoning.
In other words, memorization is not enough; students must understand how numbers work together
in order to make the learning more meaningful.
Think of basic facts in terms of understanding the relationships between the numbers rather than just memorizing a set list.
BASD is moving towards introducing facts that are connected rather than isolated lists. As the year progresses and students continue to build their understanding of the patterns and relationships between numbers, some facts appear to be "left off" when compared to more traditional lists. The elimination of facts is purposeful and allows students to give attention to the “new” facts.
For example, with the understandings and connections we are building, a student that knows 4 X 2 = 8 should know 2 x 4 = 8 without the need to memorize it as an isolated fact. In this way, by the time students are introduced to the more difficult facts (x6, x7, x8), they are only a few “new” facts that need to be introduced. The division facts are included so that students see the connection between the two operations.
Common Core State Standards:
Kindergarten: Fluently add and subtract within 5. (K.OA.A.5 )
Grade 1: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). (1.OA.C.6)
Grade 2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. (2.OA.B.2 )
Grade 3: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. (3.OA.C.7 )
What is fluency? What is from memory?