Embed Size (px)
DESCRIPTION
Addition and Subtraction - Arithmetical Strategies. Conceptual Construct. Brief Description. Construct 0 Emergent Counting. - PowerPoint PPT Presentation
Citation preview
Addition and Subtraction - Arithmetical Strategies
The student uses a range of non-count-by-one strategies. For example, in additive and subtractive situations, the student uses strategies such as compensation, using a known result, adding to ten, commutativity, subtraction as the inverse of addition, and awareness of the “ten” in a teen number.
Construct 5Facile Number Sequence
The student counts-down-to to solve missing subtrahend tasks (e.g., 17 - 14 as 16, 15, 14; the answer is 14!”). The student can choose the more efficient of count-down-from and count-down-to strategies.
Construct 4Intermediate Number Sequence
The student counts-on rather than counting from “one”, to solve addition or missing addend tasks. The student uses a count-down-from strategy to solve removed items tasks (e.g., 17 - 3 as “16, 15, 14; the answer is 14!”).
Construct 3Initial Number Sequence
Can count concealed items using a re-presentation, but counting typically includes what adults might regard as redundant activity. For example, when presented with two screened collections, told how many in each and asked to find the total, the student will count from “one” instead of counting on.
Construct 2Figurative Counting
Can count perceived items but not those in concealed collections. This may involve seeing, hearing or feeling items.
Construct 1Perceptual Counting
Cannot count visible items. The student either does not know the number words or cannot coordinate the number words with items or cannot use a cardinal number to quantify the collection.
Construct 0Emergent Counting
Brief DescriptionConceptual Construct
Unit
ary
Com
posi
te
Development of Forward Number Word Sequences (FNWS)
Level Brief Description
Level 0Emergent FNWS
The student cannot produce the FNWS from "ten" to "one".
Level 1Initial FNWS
to “ten”
The student can produce the FNWS from "ten" to "one". The student cannot produce the number word just after a given number word in the range "ten" to "one". Note: Students at Levels 1, 2, and 3 may be able to produce FNWS beyond “ten”.
Level 2Intermediate FNWS to “ten”
The student can produce the FNWS from "ten" to "one". The student can produce the number word just after a given number word in the range "ten" to "one", but drops back to generate a running count when doing so.
Level 3Facile with FNWS to “ten”
The student can produce the FNWS from "ten" to "one". The student can produce the number word just after a given number word in the range "ten" to "one", but drops back to generate a running count when doing so.
Level 4Facile with FNWS to “thirty”
The student can produce the FNWS from “one” to “thirty”. The student can produce the number word just after a given number word in the range “one” to “thirty” without dropping back. Note: Students at this level may be able to produce FNWS beyond “thirty”.
Level 5Facile with FNWS to “one hundred”
The student can produce FNWS in the range “one” to “one hundred”. The student can produce the number word just after a given number word in the range “one” to “one hundred” without dropping back. Note: Students at this level may be able to produce FNWS beyond “one hundred”.
Development of Backwards Number Word Sequences (BNWS)
Level Brief Description
Level 0Emergent BNWS
The student cannot produce the FNWS from “ten” to “one”.
Level 1Initial BNWS
to “ten”
The student can produce the BNWS from “ten” to “one”. The student cannot produce the number word just before a given number word in the range “ten” to “one”. Note: Students at Levels 1, 2, and 3 may be able to produce BNWS beyond “ten”.
Level 2Intermediate FNWS to “ten”
The student can produce the BNWS from "ten" to "one". The student can produce the number word just before a given number word in the range "ten" to "one", but drops back to generate a running count when doing so.
Level 3Facile with FNWS to “ten”
The student can produce the BNWS from "ten" to "one". The student can produce the number word just before a given number word in the range "ten" to "one", but drops back to generate a running count when doing so.
Level 4Facile with FNWS to “thirty”
The student can produce the BNWS from “one” to “thirty”. The student can produce the number word just before a given number word in the range “one” to “thirty” without dropping back. Note: Students at this level may be able to produce FNWS beyond “thirty”.
Level 5Facile with FNWS to “one hundred”
The student can produce BNWS in the range “one” to “one hundred”. The student can produce the number word just before a given number word in the range “one” to “one hundred” without dropping back. Note: Students at this level may be able to produce FNWS beyond “one hundred”.
Development of Numeral Identification
Level Brief Description
Level 0Emergent
The student cannot produce the FNWS from “ten” to “one”.
Level 1Numerals
to “10”
The student can produce the BNWS from “ten” to “one”. The student cannot produce the number word just before a given number word in the range “ten” to “one”. Note: Students at Levels 1, 2, and 3 may be able to produce BNWS beyond “ten”.
Level 2Numerals
to “20”
The student can produce the BNWS from "ten" to "one". The student can produce the number word just before a given number word in the range "ten" to "one", but drops back to generate a running count when doing so.
Level 3Numerals to “100”
The student can produce the BNWS from "ten" to "one". The student can produce the number word just before a given number word in the range "ten" to "one", but drops back to generate a running count when doing so.
Level 4Facile with FNWS to “thirty”
The student can produce the BNWS from “one” to “thirty”. The student can produce the number word just before a given number word in the range “one” to “thirty” without dropping back. Note: Students at this level may be able to produce FNWS beyond “thirty”.
Level 5Facile with FNWS to “one hundred”
The student can produce BNWS in the range “one” to “one hundred”. The student can produce the number word just before a given number word in the range “one” to “one hundred” without dropping back. Note: Students at this level may be able to produce FNWS beyond “one hundred”.
Development of Backwards Number Word Sequences (BNWS)
Level Brief Description
Level 0Emergent
The student can subitize only small quantities (ip to 3) and relies on counting to quantify larger groups. The student builds finger patterns by raising fingers sequentially.
Level 1Facile Structures to 5
The student can subitize regular spatial patterns to 6 and irregular spatial patterns to 5. The student can create finger patterns in the range of 1 to 5 by raising fingers simultaneously. The student is able to combine and partition numbers in the range of 1 to 5 without counting.
Level 2Intermediate Structures to 10
The student can recognize spatial patterns and create simultaneous finger patterns in the range of 6 to 10 using both five-wise (5-plus) and pair-wisw (doubles) structures. The student may be unable to give other combinations and partitions in this range.
Level 3Facile Structures to 10
The student is able to use the sub-base of 5 and other structures to combine and partition numbers in the range of 1 to 10 without counting.
Level 4Intermediate Structures to 20
The student is able to combine 10 and a number in the range of 1 to 10, without counting. The student is able to give partitions involving 10 for numbers in the range of 11 to 20. The student may be unable to give other combinations and partitions in this range.
Level 5Facile Structures to 20
The student is able to use a base of 10, the sub-base of 5, and other structures to combine and partition numbers in the range of 1 to 20 without counting.
Number Words Numerals Addition and Subtraction
Structuring Numbers
Place Value Multiplication and Division
Chapter 3 Chapter 3 Chapters 4 & 6 Chapters 5 & 7 Chapters 18 & 9 Chapter 10
Forward/Backward Number Word Sequences to 10
Forward/Backward Number Word Sequences to 30
Forward/Backward Number Word Sequences to 100
Forward/Backward Number Word Sequences for Composite Units
Number Word Sequences to 1000 and Beyond
Numerals to 5
Numerals to 10
Numerals to 20
Numerals to 100
Numerals to 1000 and beyond
Emergent Counting
Perceptual Counting
Figurative Counting
Initial Number Sequence (Counting-on and Counting-back)
Facile Number Sequence
Early Spatial Patterns and Finger Patterns
Facile Structures to 5
Intermediate Structures to 10
Facile Structures to 10
Intermediate Structures to 20
Facile Structures to 20
Tens or Ones
Tens and Ones with Materials (Jump &/or Split)
Tens and Ones with/out Materials (Jump &/or Split)
Mental computation involving addition and subtraction with 2- and 3- digit numbers
Initial Grouping
Perceptual Counting in Multiples
Figurative Composite counting
Repeated Abstract Composite Grouping
Multiplication and Division as Operations
Classroom Instructional Framework for Early Number (CIFEN)
