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Math Facts Fluency

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

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  1. Math Facts Fluency Meridian Joint School District No. 2 Spring 2009

  2. What is a “3”?

  3. The ability to compute efficiently and accurately with single-digit numbers (NCTM) Definition of fact “fluency”

  4. How fast is fluent?

  5. How fast is fluent?7 (x + 6) = 35

  6. Joint School District No. 2Math Facts Data

  7. 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?

  8. What does the research say about math fact instruction?

  9. Traditional Linear Instruction What does the research say about math fact instruction?

  10. Cognitively Based Instruction Traditional Linear Instruction What does the research say about math fact instruction?

  11. Three main approaches (Van de Walle): What does the research say about math fact instruction?

  12. Three main approaches (Van de Walle): • Drill What does the research say about math fact instruction?

  13. Three main approaches (Van de Walle): • Drill • Teach a collection of strategies or thought patterns What does the research say about math fact instruction?

  14. 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?

  15. 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

  16. 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

  17. Flexibility with Number Relationships & Concepts

  18. Decomposing or Using Known Facts Flexibility with Number Relationships & Concepts

  19. Decomposing or Using Known Facts 17 Flexibility with Number Relationships & Concepts

  20. 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

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. Contextualizing math fact problems Flexibility with Number Relationships & Concepts

  32. Contextualizing math fact problems Creating arrays and drawing pictures Flexibility with Number Relationships & Concepts

  33. Contextualizing math fact problems Creating arrays and drawing pictures Using compensation strategies Decomposing or using known facts Flexibility with Number Relationships & Concepts

  34. 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

  35. 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.

  36. Counting All Fact Strategy Development - Addition

  37. Counting All • Counting On (+1 and +2) Fact Strategy Development - Addition

  38. 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

  39. 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

  40. Counting All • Counting On (+1 and +2) • Fact Combinations of 10 • Doubles • Near Doubles Fact Strategy Development - Addition

  41. 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

  42. x0, x1, x2 …does not allow for students to build understanding of fact relationships and does not help with retention. Fact Strategy Development - Multiplication

  43. Doubles (x2) Fact Strategy Development - Multiplication

  44. Doubles (x2) • Fives (x5) Fact Strategy Development - Multiplication

  45. Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) Fact Strategy Development - Multiplication

  46. Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) • Tens (x10) Fact Strategy Development - Multiplication

  47. Doubles (x2) • Fives (x5) • Zeros and Ones (x0 & x1) • Tens (x10) • Nines (x9) Fact Strategy Development - Multiplication

  48. 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

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