Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.
The materials demonstrate strong vertical coherence across concepts and grade bands, specifically connecting patterns, big ideas, and relationships from kindergarten through grade 6. This is evident through the consistent progression and extension of key mathematical models and concepts. For example, ten frames are initially introduced for counting in kindergarten and then strategically extended for addition and subtraction in grade 1, illustrating a foundational pattern for number sense.Additionally,students in kindergarten use cube trains for counting, addition, and subtraction. In grade 1, they continue using cube trains for these operations. By grades 1–2, the same manipulative is further applied to measuring length, showing how one tool cansupport evolving mathematical ideas. Number lines serve as a consistent model through grades 1–6 for ordering, modeling, and operations. Their use gradually extends from whole numbers to fractions, decimals, and integers, culminating in their application on the coordinate planeto demonstratea clear progression of relationships.In grade 6, percents are modeled with strips and area models, directly connecting to and building upon the representations of fractions and decimals introduced in earlier grades, highlighting the relationship between these related concepts.Area is introduced and connected to multiplication in grade 3, and subsequently, area models are consistently used throughout grades 4–6 to model multiplication and division with whole numbers, fractions, decimals, and variable expressions, showcasing a coherent development of a big idea across multiple grade levels and increasing complexity.