The ability to compute efficiently and accurately with single-digit numbers (NCTM)
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Transcript of The ability to compute efficiently and accurately with single-digit numbers (NCTM)
![Page 1: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/1.jpg)
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The ability to compute efficiently and accurately with single-digit numbers (NCTM)
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Flash cards Practice worksheets Timed Tests Instructional Sequence
◦x 1’s, x 2’s, x 3’s, x 4’s, etc.
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Three main approaches Three main approaches (Van de Walle)(Van de Walle)::
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Three main approaches Three main approaches (Van de Walle)(Van de Walle)::
Drill
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Three main approaches Three main approaches (Van de Walle)(Van de Walle)::
Drill
Teach a collection of strategies or thought patterns
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Three main approaches Three main approaches (Van de Walle)(Van de Walle)::
Drill
Teach a collection of strategies or thought patterns
Focusing on number relationships and concepts
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Fact Fact FluencyFluency
InstructioInstructional Flownal Flow
Fluency AssessmentFluency AssessmentLess than 3% of instructional time
Timed Tests
Fact Strategy DevelopmentFact Strategy Development30 - 40% of instructional time
Doubles, Near-DoublesFact Combinations to 10
Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4)
Drill 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
Flexibility with Number Relationships Flexibility with Number Relationships & Concepts& Concepts
40 - 50% of instructional time Contextualizing math fact problems
Creating arrays and drawing pictures Decomposing or Using Known Facts
Using compensation strategies
![Page 18: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/18.jpg)
Fact Fact FluencyFluency
InstructioInstructional Flownal Flow
Fluency AssessmentFluency AssessmentLess than 3% of instructional time
Timed Tests
Fact Strategy DevelopmentFact Strategy Development30 - 40% of instructional time
Doubles, Near-DoublesFact Combinations to 10
Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4)
Drill 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
Flexibility with Number Relationships Flexibility with Number Relationships & Concepts& Concepts
40 - 50% of instructional time40 - 50% of instructional time Contextualizing math fact problemsContextualizing math fact problems
Creating arrays and drawing picturesCreating arrays and drawing pictures Decomposing or Using Known FactsDecomposing or Using Known Facts
Using compensation strategiesUsing compensation strategies
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Decomposing or Using Known FactsDecomposing or Using Known Facts
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Contextualizing math fact problems
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Contextualizing math fact problems
Creating arrays and drawing
pictures
![Page 35: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/35.jpg)
Contextualizing math fact problems
Creating arrays and drawing
pictures
Using compensation strategies
Decomposing or using known facts
![Page 36: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/36.jpg)
Fact Fact FluencyFluency
InstructioInstructional Flownal Flow
Fluency AssessmentFluency AssessmentLess than 3% of instructional time
Timed Tests
Fact Strategy DevelopmentFact Strategy Development30 - 40% of instructional time30 - 40% of instructional time
Doubles, Near-DoublesDoubles, Near-DoublesFact Combinations to 10Fact Combinations to 10
Change Instructional Sequence Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4)(x2, x5, x1, x0, x10, x9, x4)
Drill 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
Flexibility with Number Relationships Flexibility with Number Relationships & Concepts& Concepts
40 - 50% of instructional time Contextualizing math fact problems
Creating arrays and drawing pictures Decomposing or Using Known Facts
Using compensation strategies
![Page 37: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/37.jpg)
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Counting All
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Counting All
Counting On (+1 and +2)
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Counting All
Counting On (+1 and +2)
Fact Combinations of 10
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Counting All
Counting On (+1 and +2)
Fact Combinations of 10
Doubles
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Counting All
Counting On (+1 and +2)
Fact Combinations of 10
Doubles
Near Doubles
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Counting All
Counting On (+1 and +2)
Fact Combinations of 10
Doubles
Near Doubles
Decomposing Facts◦ Make Ten◦ Compensation
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……does not allow for students to build does not allow for students to build understanding of fact relationships and understanding of fact relationships and
does not help with retention.does not help with retention.
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Doubles Doubles (x2)
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Doubles Doubles (x2)
Fives Fives (x5)
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Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
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Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
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Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
Nines Nines (x9)
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Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
Nines Nines (x9)
Fours Fours (x4)
![Page 51: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/51.jpg)
Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
Nines Nines (x9)
Fours Fours (x4)
Square Numbers Square Numbers (3x3, 4x4, 5x5, etc.)
![Page 52: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/52.jpg)
Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
Nines Nines (x9)
Fours Fours (x4)
Square Numbers Square Numbers (3x3, 4x4, 5x5, etc.)
Remaining FactsRemaining Facts
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Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
Nines Nines (x9)
Fours Fours (x4)
Square Numbers Square Numbers (3x3, 4x4, 5x5, etc.)
Remaining FactsRemaining Facts
![Page 54: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/54.jpg)
Doubles Doubles (x2)
Fives Fives (x5)
Zeros and Ones Zeros and Ones (x0 & x1)
Tens Tens (x10)
Nines Nines (x9)
Fours Fours (x4)
Square Numbers Square Numbers (3x3, 4x4, 5x5, etc.)
Remaining FactsRemaining Facts
![Page 55: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/55.jpg)
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8 + 2 = 108 + 2 = 10
7 – 2 = 57 – 2 = 5
10 + 5 = 1510 + 5 = 15
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8 + 2 = 108 + 2 = 10
7 – 2 = 57 – 2 = 5
10 + 5 = 1510 + 5 = 15
8 + 2 + 58 + 2 + 5
10 + 5 = 1510 + 5 = 15
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8 + 2 = 108 + 2 = 10
7 – 2 = 57 – 2 = 5
10 + 5 = 1510 + 5 = 15
8 + 2 + 5 = 8 + 2 + 5 = 1515
10 + 5 = 1510 + 5 = 15
1 + 7 + 7 = 1 + 7 + 7 = 1515
1 + 14 = 151 + 14 = 15
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District created resources:District created resources:
Fact Fluency Newsletter Practice worksheets organized around
strategy development Textbook alignment to specific
strategies for SFAW and Investigations for additional information & resources
Informational sheets with strategy examples and practice ideas
![Page 61: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/61.jpg)
Fact Fact FluencyFluency
InstructioInstructional Flownal Flow
Fluency AssessmentFluency AssessmentLess than 3% of instructional time
Timed Tests
Fact Strategy DevelopmentFact Strategy Development30 - 40% of instructional time
Doubles, Near-DoublesFact Combinations to 10
Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4)
Flexibility with Number Relationships Flexibility with Number Relationships & Concepts& Concepts
40 - 50% of instructional time Contextualizing math fact problems
Creating arrays and drawing pictures Decomposing or Using Known Facts
Using compensation strategies
Drill Drill 15 - 20% of instructional time15 - 20% of instructional time, , appropriate appropriate after after a a
student demonstrates flexibility on related factsstudent demonstrates flexibility on related facts Worksheet based fact practice or Flash CardsWorksheet based fact practice or Flash Cards
Fact fluency related gamesFact fluency related games
![Page 62: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/62.jpg)
Fact Fact FluencyFluency
InstructioInstructional Flownal Flow
Fact Strategy DevelopmentFact Strategy Development30 - 40% of instructional time
Doubles, Near-DoublesFact Combinations to 10
Change Instructional Sequence (x2, x5, x1, x0, x10, x9, x4)
Drill 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
Flexibility with Number Relationships Flexibility with Number Relationships & Concepts& Concepts
40 - 50% of instructional time Contextualizing math fact problems
Creating arrays and drawing pictures Decomposing or Using Known Facts
Using compensation strategies
Fluency AssessmentFluency AssessmentLess than 3% of instructional timeLess than 3% of instructional time
Timed TestsTimed Tests
![Page 63: The ability to compute efficiently and accurately with single-digit numbers (NCTM)](https://reader035.fdocuments.in/reader035/viewer/2022062717/56649e4e5503460f94b453ee/html5/thumbnails/63.jpg)
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