Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

Core Components with a brief description of specific adult actions (The teacher will…)

• Student Decisions: Select tasks that allow students to decide which representations to use in making sense of the problems.
• Connecting Representations: Allocate substantial instructional time for students to use, discuss, and make connections among representations.
• Connections to Student Thinking: Introduce forms of representations that can be useful to students.
• Use of Visual Representations to Explain and Justify: Ask students to make math drawings or use other visual supports to explain and justify their reasoning.
• Mathematical Structure: Focus students’ attention on the structure or essential features of mathematical ideas that appear, regardless of the representation.
• Monitor Use of Representations: Design ways to elicit and assess students’ abilities to use representations meaningfully to solve problems.