Learning Goals

Teacher-facing learning goals appear at the top of lesson plans. They describe, for a teacher audience, the mathematical and pedagogical goals of the lesson.

Student-facing learning goals appear in student materials at the beginning of each lesson and start with the word "Let's." They are intended to invite students into the work of that day without giving away too much and spoiling the problem-based instruction. They are suitable for writing on the board before class begins.

Learning Targets

These appear in student materials at the end of each unit. They describe, for a student audience, the mathematical goals of each lesson.

We do not recommend writing learning targets on the board before class begins, because doing so might spoil the problem-based instruction. (The student-facing learning goals (that start with “Let’s”) are more appropriate for this purpose.)

Teachers and students might use learning targets in a number of ways. Some examples include:

• targets for standards-based grading
• prompts for a written reflection as part of a lesson synthesis
• a study aid for self-assessment, review, or catching up after an absence from school

How to Assess Progress

The materials contain many opportunities and tools for both formative and summative assessment. Some things are purely formative, but the tools that can be used for summative assessment can also be used formatively.

• Each unit begins with a diagnostic assessment (“Check Your Readiness”) of concepts and skills that are prerequisite to the unit as well as a few items that assess what students already know of the key contexts and concepts that will be addressed by the unit.
• Each instructional task is accompanied by commentary about expected student responses and potential misconceptions so that teachers can adjust their instruction depending on what students are doing in response to the task. Often there are suggested questions to help teachers better understand students’ thinking.
• Each lesson includes a cool-down (analogous to an exit slip or exit ticket) to assess whether students understood the work of that day’s lesson. Teachers may use this as a formative assessment to provide feedback or to plan further instruction.
• A set of cumulative practice problems is provided for each lesson that can be used for homework or in-class practice. The teacher can choose to collect and grade these or simply provide feedback to students.
• Each unit includes an end-of-unit written assessment that is intended for students to complete individually to assess what they have learned at the conclusion of the unit. Longer units also include a mid-unit assessment. The mid-unit assessment states which lesson in the middle of the unit it is designed to follow.