Mathematics

Each CKMath unit begins with a pre-assessment that helps teachers gauge what students know about both prerequisite and upcoming concepts and skills, so they can make adjustments accordingly. The initial lesson in a unit is designed to activate prior knowledge and provide an easy 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.

The unit design systematically introduces students to representations, contexts, concepts, language, and notation. Thus, as their learning progresses, they are able to:

• make connections between different representations and strategies
• consolidate their conceptual understanding
• see and understand more efficient methods of solving problems

This approach, along with the distributed practice problems, gives students ongoing practice, which also supports developing procedural proficiency.

Students have opportunities to make connections to real-world contexts throughout the CKMath materials. Frequently, carefully-chosen 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.

Additionally, most units conclude with a real-world application lesson, often titled the “Let’s Put It to Work” culminating task.

In some cases, students spend more time developing mathematical concepts before tackling more complex application problems, and the focus is on mathematical contexts. The first unit on geometry is an example of this, Grade 6 Unit 1 Area and Surface Area.

Selected activities throughout the curriculum are structured using Five Practices for Orchestrating Productive Mathematical Discussions (Smith & Stein, 2011), also described in Principles to Actions: Ensuring Mathematical Success for All (NCTM, 2014), and Intentional Talk: How to Structure and Lead Productive Mathematical Discussions (Kazemi & Hintz, 2014).

These activities include a presentation of a task or problem. Students first engage in independent think-time followed by partner or small-group work on the problem. The teacher circulates as students are working and notes groups using different approaches. Groups or individuals are selected in a specific, recommended sequence to share their approach with the class, and finally, the teacher leads a whole-class discussion to make connections and highlight important ideas.

In a productive mathematics class, students should not just learn about mathematics, they should do mathematics. This can be defined as engaging in the mathematical practices:

• making sense of problems,
• reasoning abstractly and quantitatively,
• making arguments and critiquing the reasoning of others,
• modeling with mathematics,
• making appropriate use of tools,
• attending to precision in their use of language,
• looking for and making use of structure, and
• expressing regularity in repeated reasoning.

Students should take an active role, both individually and in groups, to see what they can figure out before having things explained to them or being told what to do. Teachers play a critical role in mediating student learning, but that role looks different than simply showing, telling, and correcting. The teacher’s role is to:

• ensure students understand the context and what is being asked,
• ask questions to advance students’ thinking in productive ways,
• help students share their work and understand others’ work through orchestrating productive discussions, and
• synthesize the learning with students at the end of activities and lessons.

With CKMath, teachers have comprehensive resources and lesson plans to assist their students to do mathematics in a problem-based learning environment.