Learning Goals and Learning Targets
Each lesson has teacher facing learning goals, student facing learning goals, and learning targets.
Teacher Facing Learning Goals
These appear at the top of lesson plans. They describe the specific lesson learning goals in teacher-level language.
Student Facing Learning Goals
These provide an invitation to the work of the day. They appear at the top of every student lesson and begin with the word “Let’s . . .”
These are more specific than student facing learning goals, but written in more student-appropriate language than the teacher facing learning goals. They appear at the top of the teacher lesson plan, and in student materials, at the end of the unit in reflection pages. Uses may include student self-assessment or targets for standards-based grading. Teachers can decide when and how to use these learning targets.
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 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.
Pre-Unit Diagnostic Assessments
At the start of each unit is a pre-unit diagnostic assessment. These assessments vary in length. Most of the problems in the pre-unit diagnostic assessment address prerequisite concepts and skills for the unit. Teachers can use these problems to identify students with particular below-grade needs, or topics to carefully address during the unit. Teachers are encouraged to 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 only addresses below-grade skills. The pre-unit diagnostic assessment also may include problems that assess what students already know of the upcoming unit’s key ideas, which teachers can use to pace or tune instruction; in rare cases, this may signal the opportunity to move more quickly through a topic to optimize instructional time.
What if a large number of students can’t do the same pre-unit assessment problem? Look for opportunities within the upcoming unit where the target skill could be addressed in context. For example, an upcoming task might require fraction addition. Ask a student who can do the skill to present their method, then attend carefully to students as they work through the task. If difficulty persists, add more opportunities to practice the skill, by adapting tasks or practice problems.
What if all students do really well on the pre-unit diagnostic assessment? Great! That means they are ready for the work ahead, and special attention doesn’t likely need to be paid to below-grade skills.
Each lesson includes a “cool-down” (also known as an exit slip or exit ticket) to be given to students at the end of the lesson. This activity serves as a brief checkpoint to determine whether students understood the main concepts of that lesson. Teachers can use this as a formative assessment to plan further instruction.
What if the feedback from a cool-down suggests students haven’t understood a key concept? Look at the next lesson to see if the cool-down concept is followed through, which may give a second opportunity to learn the concept. Highlighting the different work students did on the cool-down during the next lesson can also help bring the discussion back to the concept. Look for practice problems that are similar to, or involve the same concepts as the cool-down, then assign those problems over the next few lessons.
At the end of each unit is the end-of-unit assessment. These assessments have a specific length and breadth, with problem types that are intended to 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.
Teachers may choose to grade these assessments in a standardized fashion, but may also choose to grade more formatively by asking students to show and explain their work on all problems. Teachers may also decide to make changes to the provided assessments to better suit their needs. If making changes, teachers are encouraged to keep the format of problem types provided, 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 longer units, the end-of-unit assessment will include 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 standard alignment. Multiple-choice and multiple response problems often include a reason for each potential error 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.
Design Principles for Summative Assessments
Students should get the correct answer on assessment problems for the right reasons, and get incorrect answers for the right reasons. To help with this, our assessment problems are targeted and short, use consistent, positive wording, and have clear, undebatable correct responses.
In multiple choice problems, distractors are common errors and misconceptions directly relating to what is being assessed, since problems are intended to test whether the student has proficiency on a specific skill. The distractors serve as a diagnostic, giving teachers the chance to quickly see which of the most common errors are being made. 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 for teachers to understand which common errors students are making.
Short answer, restricted constructed response, and extended response problems are careful to avoid the “double whammy” effect, where a part of the problem asks for students to use correct work from a previous part. This choice is made to ensure that students have all possible opportunities to show proficiency on assessments.
When possible, extended response problems provide multiple ways for students to demonstrate understanding of the content being assessed, 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 that can be used 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.
Notes: Typically, sample errors are included. Acceptable errors can be listed at any Tier (as an additional bullet point), notably Tier 1, to specify exclusions.
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.
Each unit has a culminating lesson where student have an opportunity to show off their problem-solving skills or apply the mathematics they have learned to a real-world problem. The end unit assessments, combined with students’ work on the culminating lessons, will show a multi-faceted view of students’ learning over the course of the unit.