Assessment guidance focuses on what can be clearly observed and uses asset-based language to focus on what students understand about particular math concepts and what they show they can do as it relates to procedural skills, fluency, and application.

The guidance also encourages reliance on the coherence of the math in the curriculum when considering how to address any unfinished learning. Although there may be instances when reteaching concepts is required, guidance focuses on ways to continue teaching grade-level content and to use existing structures to address unfinished learning.

Assessment guidance is provided at the lesson, section, and unit levels.

Learning Goals

Each unit is organized around two or three learning goals that describe the mathematical focus. Unit goals are aligned to the standards. Each section in a unit includes section learning goals that describe the focus of each section. The section learning goals are aligned to the unit learning goals. 

Each lesson includes both teacher-facing learning goals and student-facing learning goals.  

Teacher-facing learning goals describe, for a teacher audience, the mathematical and pedagogical goals of the lesson. These goals also include the important receptive and productive language demands of each lesson. 

Student-facing learning goals appear in the 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 the day, without giving away too much of the mathematical focus and spoiling the problem-based instruction. They are suitable for writing on the board before class begins.
 

Progress toward mastery of grade-level math content is assessed at the lesson, section, unit, and end-of-course levels. Each problem-based lesson offers multiple opportunities to assess how students are thinking about mathematics and progressing toward the lesson, section, and unit goals. Supports focus attention on the important mathematical ideas of each activity:

• The Lesson Narrative and the Activity Narrative provide additional details on the concepts and skills that students are developing, how these concepts are connected to previous and/or upcoming work, and how students may show their thinking.  
• “Monitor for . . .” prompts, included in many activities, give examples of what to look for in students’ work as they engage in a problem-based activity. “Consider asking . . .” prompts also provide examples of ways to investigate what and how students are thinking about the math in the lesson.
• The Activity Synthesis and the Lesson Synthesis are used in every lesson as an opportunity to focus the problem-based lesson on the mathematical goals of the lesson. Each synthesis includes opportunities to assess students’ thinking and advance individual and group understanding toward the learning goals.

The materials offer many opportunities and tools for both formative assessment and summative assessment. The majority of the assessment tools are purely formative, but the tools that can be used for summative assessment also can be used formatively.

Formative-Assessment Opportunities

• In IM Grades 1–5, the Practice Problems for Section A of each unit include several items designated as “pre-unit.” These problems target concepts and skills prerequisite to the unit. While many of them review material from earlier grades, the problems in later units address the important work of the grade.
• Accompanying each instructional task, the Advancing Student Thinking section provides commentary on expected student responses, as well as opportunities to advance students’ thinking. Adjust instruction, depending on what students are doing in response to the task. Ask the suggested questions to gain insight into students’ thinking.
• In IM Grades 2–5, each lesson concludes with a Cool-down to assess what students understand about the lesson’s learning goals. In IM Grade 1, the Cool-down is included frequently, but not in every lesson. In IM Kindergarten, the Cool-down appears in an occasional lesson. In both IM Kindergarten and IM Grade 1, important look-fors from the section Checkpoint checklist (described below) are included in lessons that don’t have the Cool-down.
• Each lesson (starting in Kindergarten, Unit 2), provides one or more Practice Problems. Use these problems for in-class practice, homework, or as a means to assess certain learning on a particular concept. Each section also contains two or more explorations, designed to engage students in thinking creatively about the mathematics of the unit, whether in class or at home.
• In IM Grades 2–5, a three- or four-problem Checkpoint assesses the learning goals of each section. Each Checkpoint item is aligned to at least one section-level goal. Use these problems for extra practice or to check students’ understanding before the end of the unit. Administer all items, or choose specific items that may yield more information for a particular learning goal. Each section also has a monitoring sheet. Use it to indicate students’ progress toward meeting the learning goals. In IM Kindergarten and IM Grade 1, the Checkpoint of each section is a checklist to record students’ progress toward meeting the learning goals. Use the checklist to keep track of evidence throughout the section or to organize your observations at the end of the section. In IM Grades 2–5, monitoring sheets offer another way to keep track of observational data toward the section learning goals

Summative-Assessment Opportunity

• Each unit (starting in Kindergarten, Unit 2) includes a written End-of-Unit Assessment that students complete individually to assess their progress toward the unit learning goals and the grade-level standards for the course. Items are aligned to the relevant grade level standards. In grades K–2, read aloud the assessment to students. Items may be read aloud to students  in other grades, as needed.

These problems address prerequisite concepts and skills for the unit. Use these pre-unit problems to identify unfinished learning to carefully address during the unit. 

What if a large number of students can’t complete the same pre-unit assessment problem? Address prerequisite skills while continuing to work through the on-grade tasks and concepts of each unit, instead of abandoning the current work in favor of material that addresses only prerequisite skills. Look for opportunities within the upcoming unit to address the target skill or concept in context or with a center. For example, an upcoming activity might require adding or subtracting within 100 to compare length measurements. Strategies might include:

• Ask a student, who can reliably add and subtract, to present their method.
• Add additional questions to the Warm-up, with the purpose of revisiting the skill.
• Add a few related addition or subtraction problems to the Launch of an activity, for students to solve before they need to do this in the context of measurement.
• Pause the class while working on the activity to focus on the portion that requires addition or subtraction.

Then attend carefully to students as they work through the activity. If difficulty persists, add more opportunities to practice arithmetic, by adapting tasks or practice problems, including practice problems from a previous unit.
 

Advancing Student Thinking

Many activities include the Advancing Student Thinking section. Use the questions in these sections to assess what students understand about the mathematics in an activity. The questions also work together to provide a just-in-time intervention to help students attend to the mathematics of the activity. The first question is the “assessing” question, designed to assess whether students are on-track with the mathematical focus of the activity. If students’ responses show that they may not be on-track, then subsequent questions direct students’ attention to the concept or skill most important for the activity. 

The Cool-down (analogous to an exit slip or an exit ticket) is given to students at the end of the lesson. This activity serves as a brief check-in to determine whether students understand the main concepts of the lesson. Use this as a formative assessment to plan further instruction.

Each Cool-down includes an example that may show unfinished learning. Guidance for unfinished learning, as indicated by the Cool-down, is provided in two categories: Next-Day Support and Prior-Unit Support. The Next-Day Support offers guidance for ways to continue teaching grade-level content while giving students the additional support they need in the next lesson. The Prior-Unit Support indicates the relevant unit and section on which the lesson builds. Revisit these sections (including those from prior grades) to look for ways to incorporate the language, representations, or activities from prior units to address students’ unfinished learning for students.

In IM Kindergarten, most lessons do not include a Cool-down. Instead, a section Checkpoint in the form of a checklist is used to formatively assess understanding of these lessons. Since activities are shorter, each lesson includes 15–25 minutes of time for centers.

In IM Grade 1, some lessons do not have a Cool-down. Instead, a section Checkpoint in the form of a checklist is used to formatively assess understanding of these lessons.

Checkpoints 

For grades 2–5, each Checkpoint item provides guidance similar to the guidance for the Cool-down. Each item includes observations of students’ understanding that may be seen in their work as it relates to the section-level learning goal and ideas for the Next-Section Support. These supports offer ways to address unfinished learning in upcoming lessons, and include centers.
 

At the end of each unit is the End-of-Unit Assessment. These assessments gauge students’ understanding of the key concepts of the unit while also preparing students for new-generation standardized exams. Problem types include multiple choice, multiple response, short answer, restricted constructed response, and extended response. Problems vary in difficulty and depth of knowledge.

Grade these assessments in a standardized fashion, or grade more formatively by asking students to show and explain their work on all problems. If making changes to customize the assessments,  keep the format of the provided problem types and include problems of different types and levels of difficulty.

All summative-assessment problems include a complete solution and standards alignment. Multiple-choice and multiple-response problems often include a reason for each potential error that a student might make. Unlike formative assessments, problems on summative assessments generally do not prescribe a method of solution.

Students should get the correct answer on assessment problems for the right reasons, and they should get incorrect answers for the right reasons. To help with this, IM assessment problems are targeted and short, use consistent, positive wording, and have clear, undebatable correct responses.

Multiple-choice problems test students’ proficiency in a specific skill. Their distractors are common errors and misconceptions directly related to the assessed content. Serving a diagnostic function, the distractors quickly reveal the most common errors that students make. There are no “trick” questions, and in earlier grades, students are told how many answers to select on multiple-select problems.

When a multiple-response prompt does not give the number of correct responses, it always includes the phrase “select all” to clearly indicate their type. Each part of a multiple-response problem addresses a different piece of the same overall skill, again serving as a diagnostic tool for understanding students’ common errors.

Short-answer, restricted constructed-response, and extended-response problems are carefully designed to avoid the “double whammy” effect, when a part of the problem asks for students to use correct work from a previous part. This ensures that students have all possible opportunities to show proficiency on assessments.

When possible, extended-response problems offer multiple ways for students to demonstrate understanding of the assessed content, through some combination of words, diagrams, and equations.
 

End-of-Unit Assessment Guidance

The End-of-Unit Assessment Guidance includes example observations of students’ unfinished learning and strategies for support in the Next-Unit Support. 

The guidance is organized around evidence for understanding and mastery of the grade-level content standards. Rather than provide item-by-item analysis, the observations encourage analyzing multiple items (when appropriate) to look for evidence of what students understand about the standards. The Next-Unit Support offers ideas for how to address any unfinished learning alongside upcoming grade-level work or before the concept is needed for upcoming grade-level work. These supports include suggestions for questions to ask during activities, representations to use, centers to encourage, and ways to incorporate the End-of-Unit Assessment as an additional learning opportunity. When needed, supports also include ways to revisit activities (for example, a Card Sort) in new ways to build on what students already know and focus on both unfinished and new learning.

End-of-Course Assessment

Each grade includes an End-of-Course Assessment to use at the conclusion of the final unit as a way to assess students’ mastery of the grade-level standards. The assessment also may be used before the final unit. Use the results of this assessment to choose sections from the final unit on which to focus, especially if there is limited time to complete the course.

Each End-of-Course Assessment includes three types of problems:

1. The first and longest portion includes items that assess the major work of the grade and are similar in type and format to those in the End-of-Unit Assessment. 
2. The second type of problem assesses the key fluencies of the grade. These come in two forms: pre-chosen calculations of different levels of difficulty, and games that offer the opportunity to observe the strategies students use.
3. Last are one or two in-depth problems that focus on supporting the work of the grade and provide a context in which students apply the key ideas they have learned over the year. Use these as classroom activities or as entire lessons. They offer additional opportunities to assess not only students' ability to model with mathematics, but also their use of other mathematical practices.