# Learning Trajectories

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- Number Word Sayer: Foundations
- Chanter
- Reciter
- Reciter (10)
- Corresponder
- Counter (Small Numbers)
- Counter (10)
- Producer (Small Numbers)
- Counter and Producer (10+)
- Counter Backward from 10
- Counter from N (N + 1, N - 1)
- Skip Counter by 10s to 100
- Counter to 100
- Counter On Using Patterns
- Skip Counter
- Counter On Keeping Track
- Counter of Quantitative Units/Place Value
- Counter Beyond 100
- Number Conserver
- Counter Forward and Back (10s and 1s)

- Number Senser: Foundations
- Very Small Number Recognizer
- Maker of Small Collections
- Small Collection Namer
- Perceptual Subitizer to 4
- Perceptual Subitizer to 5
- Conceptual Subitizer to 5
- Conceptual Subitizer to 7
- Conceptual Subitizer to 10
- Conceptual Subitizer to 20
- Conceptual Subitizer with Place Value
- Conceptual Subitizer with Place Value and Multiplicative Thinking

- Comparison Senser: Foundations
- Early Comparison Corresponder
- Perceptual Comparer
- First-Second Ordinal Counter
- Early Comparer of Similar Items
- Early Comparer of Dissimilar Items
- Matching Comparer
- Counting Comparer (Same Size)
- Spatial Extent Estimator—Small/Big
- Counting Comparer (5)
- Mental Number Line to 5
- Serial Orderer to 5 (Comparing Number)
- Ordinal Counter
- Counting Comparer (10)
- Mental Number Line to 10
- Serial Orderer to 6+ (Comparing Number)
- Spatial Extent Estimator
- Place Value Comparer
- Mental Number Line to 100
- Scanning with Intuitive Quantification Estimator
- Mental Number Line to 1000
- Benchmarks Estimator
- Composition Estimator

- "Same Thing" Comparer: Foundations
- Shape Matcher—Identical Orientations & Sizes
- Shape Recognizer—Typical
- Shape Matcher—More Shapes; Sizes & Orientations; Combinations
- Shape Recognizer—Circles, Squares, and Triangles
- Constructor of Shapes from Parts—Looks Like
- Shape Recognizer—All Rectangles
- Side Recognizer
- Most Attributes Comparer
- Corner (Angle) Recognizer
- Shape Recognizer—More Shapes
- Shape Identifier
- Angle Recognizer—More Contexts
- Parts of Shapes Identifier
- Congruence Superposer
- Constructor of Shapes from Parts-Exact
- Angle Representer
- Congruence Representer
- Shape Class Identifier
- Shape Property Identifier
- Property Class Identifier
- Angle Synthesizer

- Length Senser: Foundations
- Length Quantity Recognizer
- Length Direct Comparer
- Length Indirect Comparer
- Serial Orderer to 5 (Length)
- End-to-End Length Measurer
- Serial Orderer to 6+ (Length)
- Length Unit Relater and Repeater
- Length Measurer
- Conceptual Ruler Measurer
- Integrated Conceptual Path Measurer
- Abstract Length Measurer

## Special Thanks To

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.