1. 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 5 Facile 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 4 Intermediate 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 3 Initial 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 2 Figurative Counting Can count perceived items but not those in concealed collections. This may involve seeing, hearing or feeling items. Construct 1 Perceptual 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 0 Emergent Counting Brief DescriptionConceptual Construct Unitary Composite

2. Development of Forward Number Word Sequences (FNWS) LevelBrief Description Level 0 Emergent FNWS The student cannot produce the FNWS from "ten" to "one". Level 1 Initial 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 2 Intermediate 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 3 Facile 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 4 Facile 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 5 Facile 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”.

3. Development of Backwards Number Word Sequences (BNWS) LevelBrief Description Level 0 Emergent BNWS The student cannot produce the FNWS from “ten” to “one”. Level 1 Initial 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 2 Intermediate 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 3 Facile 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 4 Facile 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 5 Facile 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”.

4. Development of Numeral Identification LevelBrief Description Level 0 Emergent The student cannot produce the FNWS from “ten” to “one”. Level 1 Numerals 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 2 Numerals 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 3 Numerals 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 4 Facile 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 5 Facile 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”.

5. Development of Backwards Number Word Sequences (BNWS) LevelBrief Description Level 0 Emergent 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 1 Facile 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 2 Intermediate 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 3 Facile 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 4 Intermediate 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 5 Facile 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.

6. Number WordsNumeralsAddition and Subtraction Structuring Numbers Place ValueMultiplication and Division Chapter 3 Chapters 4 & 6Chapters 5 & 7Chapters 18 & 9Chapter 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)