# Mathematics

Our Middle School Math curriculum for grades 6-8 has been authored by Illustrative Mathematics, the nonprofit math organization founded by acclaimed mathematician and standards author William McCallum.

The Illustrative Mathematics curriculum is focused, coherent, and rigorous. It is built on carefully crafted and sequenced problems following sound progressions of concepts and skills. The program takes seriously the need for students to develop a balance of conceptual understanding, procedural fluency, and the ability to use mathematics in real-world contexts. Its instructional approach is based on a small but powerful repertoire of teacher moves, adapted to different learning goals.

We offer multiple carefully-crafted professional learning options to provide districts with a robust capacity-building support system as they adopt our materials.

Overview of Illustrative Mathematics curriculum

A Problem-based Curriculum

Most instructional time is dedicated to students working on carefully crafted and sequenced problems. Teachers help students understand the problems and guide discussions to be sure that the mathematical punch line is clear to all. Not all mathematical knowledge can be discovered through deductive reasoning, so direct instruction is sometimes appropriate. On the other hand, some concepts and procedures follow from definitions and prior knowledge, and students can, with appropriately constructed problems, see this for themselves; in the process, they explain their ideas and reasoning and learn to communicate mathematical ideas. Our guiding principle is to give students just enough background and tools to solve initial problems successfully, and then have them solve increasingly sophisticated problems as their expertise increases.

Developing Conceptual Understanding and Procedural Fluency

Each unit begins with a pre-assessment that helps teachers gauge what students know about both prerequisite and upcoming concepts and skills, so that teachers can gauge student readiness and adjust accordingly. The initial lesson in a unit is designed to activate prior knowledge and provide a natural entry to point to new concepts, so that students at different levels of both mathematical and English language proficiency can engage productively in the work. As the unit progresses, students are systematically introduced to representations, contexts, concepts, language and notation. As their learning progresses, they see and understand more efficient methods of solving problems that are supported by purely symbolic representations, indicating the shift towards procedural fluency.

Using Mathematics

Students have opportunities to make connections to real-world contexts throughout the materials. Each arc of concept development concludes with at least one set of real-world application problems. In addition, certain anchor contexts are used to motivate new mathematical concepts, and students have many opportunities to make connections between contexts and the concepts they are learning.

An Inclusive Approach to Teaching Practice

The appropriate instruction for any particular lesson depends on the learning goals of that lesson. Some lessons may be devoted to developing a concept, others to mastering a procedural skill, yet others to applying mathematics to a real-world problem. These aspects of mathematical proficiency must be developed together. Our curriculum is based on a small set of lesson plan types and a carefully selected repertoire of teacher moves that become increasingly familiar to teachers as the year progresses.

— *Phil Daro*