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

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

Writing learning targets on the board before class begins 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 can use learning targets in a number of ways, including:

• 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.

The materials provide many opportunities and tools for both formative assessment and summative assessment. The majority of the assessment tools are purely formative. Tools that may be used for summative assessment also can be used formatively.

• Each unit begins with Check Your Readiness, a diagnostic assessment of concepts and skills prerequisite to the unit, as well as a few items that assess what students already know of some key contexts and concepts addressed by the unit.
• Commentary on expected student responses and potential misconceptions accompany each classroom activity. Adjust instruction, depending on what students are doing in response to the task. Ask the suggested questions to gain insight into students’ thinking.
• Each lesson concludes with a Cool-down—analogous to an exit slip or an exit ticket—to assess how well students understand the work of the day. Use this as a formative assessment to provide feedback or to plan further instruction.
• A set of cumulative Practice Problems for each lesson is included. Use these problems for homework or in-class practice, as needed. Either collect and grade these or use them simply to provide feedback to students.
• A one- to three-problem Checkpoint assesses the learning goals of each section. Use this as a formative assessment to plan further instruction.
• Each unit includes a written End-of-Unit Assessment that students complete individually. Longer units also include a Mid-Unit Assessment that follows a designated lesson in the middle of the unit.

At the start of each unit is Check Your Readiness, a pre-unit diagnostic assessment. These assessments vary in length. Most problems address prerequisite concepts and skills for the unit. Use these problems to identify students with particular below-grade needs, or topics to carefully address during the unit. Check Your Readiness also may include problems that assess what students already know of the upcoming unit’s key ideas. Use these to pace or tune instruction. In rare cases, they may signal the opportunity to move more quickly through a topic to optimize instructional time.

What if a large number of students can’t complete the same pre-unit assessment problem? Address below-grade 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 below-grade skills. Look for opportunities within the upcoming unit to address the target skill in context. For example, an upcoming activity might require solving an equation in one variable. Strategies might include:

• Ask a student who can do the skill to present their method.
• Add additional questions to the Warm-up, with the purpose of revisiting the skill.
• Add a few related equations to the Launch, for students to solve before they need to do this while working on an activity.
• Pause the class while working on the activity to focus on the portion that requires solving an equation.

Then, attend carefully to students as they work through the activity. If difficulty persists, add more opportunities to practice the skill, by adapting tasks or practice problems.

What if all students do well on Check Your Readiness? This is an indication that students are ready for the work ahead, and special attention likely doesn’t need to be paid to below-grade skills.

Each lesson ends with a Cool-down to formatively assess students’ thinking in relation to an important math concept from the day’s learning. Each Cool-down is accompanied by guidance on how to continue teaching grade-level content, with appropriate and aligned practice and support for students.

The guidance falls into three categories, with suggestions on next steps if most students struggle with the Cool-down:

• More Chances is a signal that students will see the content of the Cool-down again and there is no need to alter planned instruction for the class.

• Points to Emphasize suggests small adjustments to build into future lessons. For example, inviting more students to share strategies in an upcoming activity, reviewing a specific practice problem with the whole class, or altering a Launch to address a common error from the Cool-down before students see the same type of thinking again.
• Press Pause is used to mark a Cool-down that has content with which students may need to spend more time before moving forward with new lessons. This type of Cool-down may suggest adding in specific optional activities or lessons, or revisiting content of past lessons or sections.

If results from a Cool-down suggest most students are struggling with a key concept, consider implementing one or more of these strategies:

• During the next lesson, display the work of a few students on that Cool-down. Anonymize their names, and show both correct and incorrect work. Ask the class to observe what each student did well and what they could have done better. Consider using the MLR 3: Critique, Correct, Clarify structure.
• Give each student brief, written feedback on a Cool-down that nudges them to re-examine their work. Ask students to revise and resubmit.
• Identify a common error and create a sample response to the Cool-down, with the error, for students to identify and correct.
• Review activities and lessons, with related work, for optional content not yet used in class. Include this work in future lessons to give students additional time and different ways to make sense of key concepts.

Checkpoints

Each section ends with a Checkpoint of one to three problems that assess the section learning goals. Each Checkpoint item is accompanied by guidance on how to continue teaching grade-level content, with appropriate and aligned practice and support for students.
The guidance falls into the same three categories as guidance for the Cool-down, with suggestions on next steps if most students struggle with the Checkpoint. See the Cool-down section for more details on the forms this guidance takes.

At the end of each unit is the End-of-Unit Assessment. These assessments have a specific length and breadth, with problem types that 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 assessment, keep the format of the provided problem types, which helps students know what to expect and ensures each assessment will take approximately the same amount of time.

In longer units, a Mid-Unit Assessment is also available. This assessment has the same form and structure as an End-of-Unit Assessment. In these units, the End-of-Unit Assessment includes the breadth of all content for the full unit, with emphasis on the content from the second half of the unit.

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. Restricted constructed-response and extended-response items include a rubric. Unlike formative assessments, problems on summative assessments generally do not prescribe a method of solution.

A note about technology use on assessments: Some assessments require use of technology, some allow it, and some prohibit it. These affordances or restrictions are communicated in each Assessment Narrative and in the instructions to students. The use of technology is prohibited on assessments of standards that require students to sketch a graph by hand or use mathematical properties to rewrite expressions. Conversely, some standards specify that students must use technology for certain tasks, such as generating a best-fit line and correlation coefficient. When these skills are assessed, technology is required. This approach is in keeping with many state and national standardized assessments that include calculator-allowed and calculator-prohibited portions. Streamlining this approach, technology is either allowed or prohibited on an entire assessment in the IM curriculum—no single assessment contains both technology-allowed and technology-prohibited portions.

Design Principles for Summative Assessments

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, 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 relating to the assessed content. Serving a diagnostic function, the distractors quickly reveal most common errors that students make. There are no “trick” questions, and the phrases “all of the above” and “none of the above” are never used, since they do not give useful information about the methods a student used.

Multiple-response prompts always include 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 careful 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 arithmetic or algebra, use of representations (tables, graphs, diagrams, expressions, and equations), and explanation.

Rubrics for Evaluating Student Answers

Restricted constructed–response and extended-response items have rubrics to evaluate the level of student responses.  

Restricted Constructed Response

• Tier 1 response: Work is complete and correct.
• Tier 2 response: Work shows general conceptual understanding and mastery, with some errors.
• Tier 3 response: Significant errors in work demonstrate lack of conceptual understanding or mastery. Two or more error types from Tier 2 response can be given as the reason for a Tier 3 response instead of listing combinations.

Extended Response

• Tier 1 response: Work is complete and correct, with complete explanation or justification.
• Tier 2 response: Work shows good conceptual understanding and mastery, with either minor errors or correct work with insufficient explanation or justification.
• Tier 3 response: Work shows a developing but incomplete conceptual understanding, with significant errors.
• Tier 4 response: Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.

Typically, sample errors are included. Acceptable errors, listed at any tier (as an additional bullet point), notably Tier 1, specify exclusions.