• Students have mathematical ideas. The curriculum supports all students in developing and expanding those ideas.

• Teachers are engaged in ongoing learning about mathematics content, pedagogy, and student learning. The curriculum supports them in this learning.

• Teachers collaborate with the students and curriculum materials to create the curriculum as enacted in the classroom. The curriculum provides a clear, focused, and coherent mathematical agenda and supports teachers in implementing in a way that accommodates the needs of their particular students.

Developing an understanding of what it means to do mathematics is fundamentally about the practices of the discipline. Investigations has always integrated into the learning sequence those core mathematical practices that focus on reasoning, communication, and making sense. Investigations 3 makes explicit the Mathematical Practices (as defined by the CCSS) that have always been embedded in the materials. Support material for teachers—an essay about the two practices highlighted and assessed in each unit and sidebars that indicate opportunities for engaging students in all of the practices—provides images of what these practices look like in the elementary classroom, explain how math practices interact with math content, and offer guidance for helping young students learn how to use these practices in their mathematical work.

Investigations 3 supports teachers in assessing what students do and do not yet know in a variety of ways. There are daily opportunities for formative assessment (i.e. Observing the Students at Work). There are also three kinds of formal assessment: checklists to track information about the Mathematical Practices and about Benchmarks that can best be assessed via observation (K-5); brief Quizzes every 8-10 Sessions that familiarize students with a variety of test question formats (1-5); and embedded assessments that ask students to show and/or explain their work (1-5). Assessment Teacher Notes accompany embedded assessments, and provide analysis of student work that meets, partially meets, or doesn’t yet meet the benchmark, as well as suggestions for what to do with students in the latter two categories.

All teachers are faced with the challenge of meeting the needs of the range of learners in their classrooms, which can include students who struggle or excel in certain areas of mathematics (but perhaps not in others), students who are learning English, and students who have particular learning needs. Investigations 3 provides such support on several levels. Most Sessions have some combination of activity-specific intervention, extension, and/or ELL suggestions. These are labeled with tags that describe generalizable strategies for differentiation (e.g. suggest a tool, provide sentence stems). An additional Intervention, Practice, and Extension activity is also included at the end of each Investigation (1-5), and a Spanish Companion provides teacher dialogue in Spanish.

From the beginning, Investigations was designed as a tool for teacher as well as student learning. Professional development resources embedded in the curriculum include Teacher Notes and Dialogue Boxes, found at the end of each unit, sidebar notes in the Sessions, and essays at the beginning of each unit about mathematics content and the Mathematical Practices that are the focus of that unit. Together, these resources form a tool for professional development-- a tool that supports teachers in learning about mathematics content and practices, how students learn, and effective pedagogy.