ABSTRACT
Visual models, both concrete and representational, play a key role in the teaching and learning of number, base ten, addition, and subtraction. Visual models can be used as an instructional bridge to help move students from concrete counting strategies to more abstract number, addition, and strategies based on conceptual understanding. In this way, visual models, when used strategically to support important mathematical ideas, can increase access to additive reasoning for all students. It is important for students to have opportunities to use a variety of visual models, sketch their own models, and develop understanding of the relationships between the models. Number lines are an important model throughout a student’s mathematical learning; the understanding of number lines can be introduced concretely in the earliest grades and progressively connected to more abstract ideas of distance, measurement, and magnitude and with various types of numbers for years to come.
