Curriculum modules in mathematics are marked by in-depth focus on fewer topics. They integrate the CCLS, rigorous classroom reasoning, extended classroom time devoted to practice and reflection through extensive problem sets, and high expectations for mastery. The time required to complete a curriculum module will depend on the scope and difficulty of the mathematical content that is the focus of the module (first priority cluster area for a given grade level). For example, the curriculum module relating to Grade 3 multiplication and division introduces initial ideas of multiplication and division in a brief period at the start of the year, continues to develop strategies and problem solving throughout the year, and includes materials to be used throughout the year for helping students reach fluency by the end of the year with single-digit multiplication and related division.
Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content
The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.
The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.