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Math Facts Fluency. Meridian Joint School District No. 2 Spring 2009. What is a “3”?. The ability to compute efficiently and accurately with single-digit numbers (NCTM). Definition of fact “fluency”. How fast is fluent?. How fast is fluent? 7 (x + 6) = 35.
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Math Facts Fluency Meridian Joint School District No. 2 Spring 2009
The ability to compute efficiently and accurately with single-digit numbers (NCTM) Definition of fact “fluency”
Flash cards Practice worksheets Timed Tests Instructional Sequence x 1’s, x 2’s, x 3’s, x 4’s, etc. What does math fact instruction currently look like in our district?
Traditional Linear Instruction What does the research say about math fact instruction?
Cognitively Based Instruction Traditional Linear Instruction What does the research say about math fact instruction?
Three main approaches (Van de Walle): What does the research say about math fact instruction?
Three main approaches (Van de Walle): • Drill What does the research say about math fact instruction?
Three main approaches (Van de Walle): • Drill • Teach a collection of strategies or thought patterns What does the research say about math fact instruction?
Three main approaches (Van de Walle): Drill Teach a collection of strategies or thought patterns Focusing on number relationships and concepts What does the research say about math fact instruction?
Fluency Assessment Less than 3% of instructional time Timed Tests Fact Fluency Instructional Flow • Drill • 15 - 20% of instructional time, appropriate after a student demonstrates flexibility on related facts • Worksheet based fact practice or Flash Cards • Fact fluency related games • Fact Strategy Development30 - 40% of instructional time • Doubles, Near-Doubles • Fact Combinations to 10Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4) • Flexibility with Number Relationships & Concepts • 40 - 50% of instructional time • Contextualizing math fact problems • Creating arrays and drawing pictures • Decomposing or Using Known Facts • Using compensation strategies
Fluency Assessment Less than 3% of instructional time Timed Tests Fact Fluency Instructional Flow • Drill • 15 - 20% of instructional time, appropriate after a student demonstrates flexibility on related facts • Worksheet based fact practice or Flash Cards • Fact fluency related games • Fact Strategy Development30 - 40% of instructional time • Doubles, Near-Doubles • Fact Combinations to 10Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4) • Flexibility with Number Relationships & Concepts • 40 - 50% of instructional time • Contextualizing math fact problems • Creating arrays and drawing pictures • Decomposing or Using Known Facts • Using compensation strategies
Decomposing or Using Known Facts Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 17 8 + 8 + 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 17 8 + 8 + 1 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 17 8 + 8 + 1 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 20 – 3 = 17 17 8 + 8 + 1 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 20 – 3 = 17 17 8 + 8 + 1 = 17 (5 x 3) + 2 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 20 – 3 = 17 17 8 + 8 + 1 = 17 8 + 8 = 16 + 1 = 17 (5 x 3) + 2 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 20 – 3 = 17 17 8 + 8 + 1 = 17 8 + 8 = 16 + 1 = 17 (5 x 3) + 2 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 20 – 3 = 17 17 8 + 8 + 1 = 17 8 + 8 = 16 + 1 = 17 17 = 20 – 3 (5 x 3) + 2 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Decomposing or Using Known Facts 10 + 7 = 17 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1=17 20 – 3 = 17 17 8 + 8 + 1 = 17 8 + 8 = 16 + 1 = 17 17 = 20 – 3 (5 x 3) + 2 = 17 9 + 9 - 1 = 17 2+2+2+2+2+2+2+2+1=17 Flexibility with Number Relationships & Concepts
Contextualizing math fact problems Flexibility with Number Relationships & Concepts
Contextualizing math fact problems Creating arrays and drawing pictures Flexibility with Number Relationships & Concepts
Contextualizing math fact problems Creating arrays and drawing pictures Using compensation strategies Decomposing or using known facts Flexibility with Number Relationships & Concepts
Fluency Assessment Less than 3% of instructional time Timed Tests Fact Fluency Instructional Flow • Drill • 15 - 20% of instructional time, appropriate after a student demonstrates flexibility on related facts • Worksheet based fact practice or Flash Cards • Fact fluency related games • Fact Strategy Development30 - 40% of instructional time • Doubles, Near-Doubles • Fact Combinations to 10Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4) • Flexibility with Number Relationships & Concepts • 40 - 50% of instructional time • Contextualizing math fact problems • Creating arrays and drawing pictures • Decomposing or Using Known Facts • Using compensation strategies
Fact Strategy Development Please refer to your school’s fact fluency CD for detailed information on specific activities that can be used to develop these strategies.
Counting All Fact Strategy Development - Addition
Counting All • Counting On (+1 and +2) Fact Strategy Development - Addition
Fact Combinations of 10 0 + 10 1 + 9 2 + 8 3 + 7 4 + 6 5 + 5 and the reverse using the commutative property • Counting All • Counting On (+1 and +2) • Fact Combinations of 10 Fact Strategy Development - Addition
Doubles 0 + 0 1 + 1 2 + 2 3 + 3 4 + 4 5 + 5 6 + 6 7 + 7 8 + 8 9 + 9 • Counting All • Counting On (+1 and +2) • Fact Combinations of 10 • Doubles Fact Strategy Development - Addition
Counting All • Counting On (+1 and +2) • Fact Combinations of 10 • Doubles • Near Doubles Fact Strategy Development - Addition
Counting All • Counting On (+1 and +2) • Fact Combinations of 10 • Doubles • Near Doubles • Decomposing Facts • Make Ten • Compensation Make Ten 8 + 5 8 + 2 + 3 10 + 3 = 13 Compensation 9 + 7 10 + 6 = 16 Fact Strategy Development - Addition
x0, x1, x2 …does not allow for students to build understanding of fact relationships and does not help with retention. Fact Strategy Development - Multiplication
Doubles (x2) Fact Strategy Development - Multiplication
Doubles (x2) • Fives (x5) Fact Strategy Development - Multiplication
Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) Fact Strategy Development - Multiplication
Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) • Tens (x10) Fact Strategy Development - Multiplication
Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) • Tens (x10) • Nines (x9) Fact Strategy Development - Multiplication
Fours (x4) Example: 6 x 4 = 6 (doubled) or 6 x 2 = 12 12 (doubled) or 12 x 2 = 24 • Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) • Tens (x10) • Nines (x9) • Fours (x4) Fact Strategy Development - Multiplication