The instructional materials reviewed for Kindergarten meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessment sections of each module.

• No above-grade-level content was assessed on mid-module or end-of-module assessments.
• All assessments, rubrics and topics relate to Kindergarten standards.
• All interview questions are related to Kindergarten standards.
• The summative assessments focus on grade-level topics.
• The first module assesses one-more and one-less than a given number between 6 and 10.
• The fourth module assesses students' ability to add and subtract within 10.
• Appropriately, there are no assessments on telling time, which is a Grade 1 standard.

The instructional materials reviewed for Kindergarten meet the expectation for focus by spending the majority of the time on the major clusters of the grade. This includes all clusters within the following domains: K.CC, K.OA and K.NBT.

• While some lessons include multiple standards, approximately 113 out of 152 lesson days are devoted to major work.
• More than 70% of the lessons are explicitly focused on major work, with major work often included within supporting work lessons as well.
• Of six modules, modules 1, 4, and 5 address major work almost exclusively. Module 3 devotes more than half of the lessons to major work.
• The two shortest modules, 2 and 6, are devoted to supporting and additional work.
• Of the 45 assessment days, 39 are devoted to major work.

The instructional materials reviewed for Kindergarten meet the expectations for their use of supporting content as a way to enhance coherence. For Kindergarten, reviewers focused on the use of counting and addition/subtraction within the K.MD and K.G domains.

• In module 1, students are classifying and then counting objects.
• In module 2, students are asked to use shapes to count sides, quantity and attributes.
• In module 2, students are expected to count sides to distinguish between shapes and to use counting to answer questions about shapes.
• In module 2, students are asked to use varying numbers of circles to practice adding and subtracting.
• In module 3, students are using counting to count heights and lengths using words like "greater than" and "less than." They are also expected to count and compare group sizes with shapes.
• In module 6 students are asked to draw shapes with a specific number of sides, add those shapes to another group of shapes and write the appropriate equation for that addition.

The instructional materials reviewed for Kindergarten meet the expectation for this indicator by providing a viable level of content for one school year.

• Materials provide for 180 days of instruction and assessment.
• Lessons are expected to be 50 minutes.
• Lessons include fluency practice, application problems, concept development and a student debrief.
• The materials are structured so that a teacher could make modifications if necessary.
• While a district, school or teacher would not need to make significant changes to the schedule set forth, reviewers expressed concerns about the volume of lessons.
• Some lessons may take longer than indicated.
• Days are included at the end of the year for culmination activities and preparation for summer practice.

The instructional materials reviewed for Kindergarten are consistent with the mathematical progressions in the standards meeting the expectation for this indicator.

• Students work on their understanding of the number 5 before moving on to the number 10.
• Students work extensively on the domain of K.CC before working with K.OA and K.NBT.
• Pre-Kindergarten standards are offered as foundational standards for Kindergarten.
• Students are expected to practice writing numbers 21-100 but, appropriately, they are not assessed on this content.
• Problem sets in each module offer students extensive work on grade-level problems.
• Within the differentiation sections teachers are given suggestions for supporting struggling students while continuing to expect that students work on grade-level problems.
• Suggestions for supporting English language learners (ELLs) continued to reflect high expectations for these students.
• The teacher notes include suggestions for advanced students to continue working within their grade level while deepening their understanding of the content.

The instructional materials reviewed for Kindergarten foster coherence through grade-level connections.

• Topic titles and lesson titles are informed by cluster headings.
• Module 1 includes a topic called "Classify to Make Categories and Count," which is informed by the cluster heading "Classify Objects and Count the Number of Objects in Each Category."
• Module 3 includes a lesson called "Compare Objects Using the Same as...," which is similar to the cluster heading "Count to Tell the Number of Objects."
• Module 5 includes a lesson called "Model with Objects and Represent Numbers from 10-20 with Place Value or Hide Zero Cards." This is similar to the cluster heading "Work with Numbers 11-19 to Gain Foundations for Place Value."
• Module 1 connects the K.CC and K.OA domains with K.MD.B.
• Module 3 connects K.CC and K.MD. Module 6 connects K.CC with K.G.
• Module 6 asks students use counting and cardinality to make shapes.
• Module 3 connects comparison of length with comparisons of numbers.
• Module 1 asks students to sort objects (shapes) into categories and count the number in each.

The materials reviewed in Kindergarten for this indicator meet the expectations by attending to conceptual understanding within the lessons.

• Within the concept development sections of each lesson, the mathematical topic is developed through understanding as indicated by the standards and cluster headings.
• In module 1, specific lessons are devoted to the understanding of zero.
• In module 4, significant time is spent developing an understanding of addition and subtraction using a variety of settings. For example, students are asked, “How did we use the number bond to show putting things together?”
• In module 5, students work with models to develop conceptual understanding of the teen numbers.

The materials reviewed in Kindergarten for this indicator meet the expectations by attending to fluency and procedural work within the lessons. In Kindergarten this includes K.OA.A.5 "Add and subtract within 5."

• Within the distribution of instructional minutes the schedule allows for 10-20 minutes per day to practice fluency. This varies according to the timeline of the school year and the focus mathematics in the module.
• As described within the "how to implement" documents, "Fluency is usually first-by beginning class with animated, adrenaline-rich fluency, students are more alert when presented with the Concept Development and Application Problems."
• Attention is paid to the use of the words "fluency" and "fluent" within the standards.
• Required fluencies are listed within the section called "Curriculum Overview Sequence."

The materials reviewed in Kindergarten for this indicator meet the expectations by attending to application within the lessons.

• Application problems occur in almost every lesson depending upon the focus mathematics of the lesson. This is expected to last around five minutes for each lesson in Kindergarten.
• If the focus standard of the lesson includes language requiring application, the application problem will become the major portion of the lesson.

The materials reviewed in Kindergarten for this indicator meet the expectations by providing a balance of rigor. The three aspects are not always combined, nor are they always separate.

• The distribution-of-minutes chart and the structure of the lessons show a balance of the three aspects of rigor.
• Application problems often call for fluency and procedural skills.
• Fluency work and application problems are used to develop conceptual understanding.
• Conceptual problems often involve procedures.

The Standards for Mathematical Practice (MPs) are often identified and often used to enrich mathematics content, however, it only partially meets expectations. There are many missed opportunities for identifying MPs and some instances where they are misidentified.

• MPs are listed at the beginning of each module with a description of the explicit connection to the mathematics of the module.
• Module 6 describes MP7, one of the focus standards in this module: "Students make use of their understanding of a shape's attributes to build three-dimensional from two-dimensional shapes."
• MPs are listed in the margins of the teacher notes, mostly in the "Concept Development" and the "Student Debrief" portions of some lessons.
• While reviewers appreciate that the MPs are not over-identified or used in contrived situations, there are many missed opportunities for identifying MPs as a way enrich the content in these lessons.
• The debrief section of the lessons offers an opportunity to highlight, for both teachers and students, how they might reason abstractly and quantitatively (MP2) and construct arguments and critique the reasoning of others (MP3).

The materials only partially meet the expectations. While they often attend to the full meaning of each practice, there are instances where the students are not using the practice as written. For example, there are many lessons where the tools are chosen for the students or the modeling expected is a simple representation.

• Students are using MPs when engaging with the content as designed, fully meeting Publisher's Criteria #9.
• Throughout the lessons the debrief section includes opportunities to construct viable arguments and critique the reasoning of others (MP3).
• The overview of module 1 describes MP4-related activity: "Students model decompositions of three objects as math drawings and addition equations (page v)." There is no mention of a contextual situation.
• MP4 ("Model with Mathematics") is irregularly applied. There is ambiguity over whether "model" means to draw a picture or whether it means to create a mathematical representation in a real-world context.

The materials reviewed for Kindergarten meet the requirement of this indicator by attending to the standards' emphasis on mathematical reasoning.

• Each module lists terminology for the module including "new or recently introduced terms" and "familiar terms and symbols."
• In module 2, students are asked to be explicit about the attributes of shapes.
• In module 4 the debrief section includes a question focused on language: "How did we use our math words to talk about what happened in the song?"

The materials reviewed for Kindergarten meet the expectations of this indicator by attending to the standards' emphasis on mathematical reasoning.

• Students are prompted within problem sets, interviews and application problems to explain, describe, critique and justify.
• In module 1 the debrief section suggests using the frame "we have zero_______ in our classroom" to talk about items in or not in the classroom.

The materials reviewed for Kindergarten meet the requirement of this indicator by attending to the standards' emphasis on mathematical reasoning.

• Each lesson includes a debrief section with questions for the teacher to use in facilitating classroom discussion about the mathematical content. For example, when working on teen numbers and place value, students are asked, "How does finding parts help you to understand big numbers better?"
• In module 4, students are asked if there were many different answers today or if there were different ways to solve to get an answer.

The materials reviewed for Kindergarten meet the requirement of this indicator by attending to the standards' emphasis on mathematical reasoning.

• Each module lists terminology for the module including "new or recently introduced terms" and "familiar terms and symbols."
• In module 2, students are asked to be explicit about the attributes of shapes.
• In module 4 the debrief section includes a question focused on language: "How did we use our math words to talk about what happened in the song?"

The design of the materials reviewed for Kindergarten meets the expectations for this indicator by providing students with ongoing opportunities to practice previously learned skills alongside their learning of new content. These materials use problem sets and application problems to develop student understanding of new mathematics. They use homework, application problems and fluency sessions to practice previously learned concepts.

• Problems sets within the lessons include guidance on how to select and sequence the exercises.
• Fluency exercises within the lessons include guidance on the purpose of each activity, allowing the teacher to determine the necessary activities for the students.
• The "how to implement" document provides information for the teacher on the purpose for each lesson section.
• Page 12 of the "how to implement" document states, "The primary goal of the problem set is for students to apply the conceptual understanding(s) learned in the lesson."
• Page 23 of the "how to implement" document states, "The bank of fluency activities for each lesson is intentionally organized so that activities revisit previously-learned material to develop automaticity, anticipate future concepts, and strategically preview or build skills for the day's Concept Development."
• Page 13 states, "The homework gives students additional practice on the skills they learn in class each day. The idea is not to introduce brand-new concepts, but to build student confidence with the material learned in class."
• Page 9 states, "A Story of Units doesn't wait months to spiral back to a concept. Rather, once a concept is learned, it is immediately spiraled back into the daily lesson structure through fluency and applications."

The materials reviewed for Kindergarten meet the expectations of this indicator by using intentional sequences in the design.

• Problem sets, exit tickets and homework relate to the mathematical concept developed in the lessons each day.
• Once a concept is developed, it is spiraled back into the daily structure within the fluency and application portion.
• The sequence of topics within each module is intentional, going from working with a variety of concrete and pictorial representations to more abstract work with numbers and computation. For example, module 1 starts with counting and numerals to 5, moves to the concept of zero, and then works with numbers 6-8, then 9 and 10. It finally ends with one more than "zero minus 10" and one less than "zero minus 10."
• The Kindergarten materials develop a solid foundation for K.CC.A, B before moving on to deeper concepts within addition and subtraction.

The materials reviewed for Kindergarten meet the expectations of this indicator by providing a variety in what students are expected to produce.

• Students are expected to produce answers and solutions throughout the fluency sections and some of the problem sets.
• Students are expected to provide arguments and explanations within the problem sets, exit tickets and homework.
• Students are asked to provide a variety of mathematical responses. In module 3, for example, students are expected to color items with fewer than a specified number (3.B.9); draw a stick that is longer than a specified stick (3.B.17); draw or cross out items to make a total of 5 (3.C.7); and to circle to represent a specified quantity (3.D.22).
• Arguments and explanations are the basis for the debriefing section of each lesson.
• The "Read, Draw, Write" procedure requires students to represent the problem in a drawing and make connections between the drawing and the equations.
• Throughout the modules and lessons students produce a variety of solutions, using concrete, pictorial and abstract representations.

The materials reviewed for Kindergarten meet the expectations of this indicator by using manipulatives and models as faithful representations of the mathematics they are used to represent.

• The materials use a limited set of concrete and pictorial models throughout the program.
• Each module lists suggested tools and representations that apply to the mathematics in the module.
• Students use a variety of manipulatives including rekenreks, counting objects, five and ten frames, pattern blocks, 2-D and 3-D shapes, and linking cubes. They are connected with written methods.
• Students are frequently asked to color, draw or circle shapes rather than write.

The materials reviewed for Kindergarten meet the expectations of this indicator by using a design that supports students in engaging thoughtfully with the subject.

• The visual design is clean and simple and supports students in engaging with the mathematics.
• There are no distractions on the student pages or teacher pages.
• Student pages contain only mathematical problems and pictures/diagrams as part of the problems.
• The materials have very minimal pictures.

The materials reviewed for Kindergarten meet the expectations for this indicator by supporting teachers in using questions to guide mathematical development.

• Materials provide quality suggested questions throughout the debriefing section of each lesson. For example, in module 4, students are asked, “How did you decide what number should go in the mystery box? Did your friend do the same thing?” In module 5, students are asked, “When you make a teen number in parts? What do you notice? Which is always biggest, the parts or the total, the whole?”
• Quality questions are also included in the concept development portion, application problems and problem sets of the lessons.

The materials reviewed for Kindergarten meet the expectations for this indicator.

• Teacher editions have many annotations and examples on how to present the content.
• The concept development sections include a sample script to help the teacher understand what might happen when presenting the material. These scripts can sometimes mask the mathematical concepts at hand, leading teachers to think that the script is exactly what should happen. A summary of the process and concept before the script would be useful.
• Within the lessons, aside from the teacher script and wording in the teacher directions, most lessons have pictures or other graphics with annotations, demonstrating the concepts for the teacher and providing guidance on how to present content.
• There are answer keys for all the student problem sets, exit tickets, homework and tests, including written annotations to show what student work should look like.
• There are also boxes in the sidebar of many lessons that annotate information about how to present content.
• There is a repeated process for solving word problems called the "Read, Draw, Write," approach, which the manual explains in the module overview.
• The overview of each module has several suggestions for delivering instruction.

The materials reviewed for Kindergarten meet the expectations for this indicator by including adult-level explanations and examples of mathematical topics so that teachers can improve their own knowledge of the subject, if necessary.

• In the teacher edition for each module, there is an overview section that has narrative information about the mathematical content of the module.
• In each module, at the start of each topic, there is another section of narrative that gives an explanation of the mathematical content in the topic.
• These topic-level explanations and overviews include mathematical coherence within and between grade levels.
• In the document called "How to Implement A Story of Units," there are adult-level explanations of the models and representations used.

The materials reviewed for Kindergarten partially meet the expectations for this indicator. There are a few specific descriptions of the coherence of the mathematics, however there is no discussion of the grade-level content's role in Kindergarten through Grade 12.

• There are explanations of the role previous content plays in each module. This is listed in the module overview in the "Foundational Standards" section.
• In the document called "A Story of Units: A Curriculum Overview for Grades P-5," there is a description of the module sequence which includes the connection to the previous grade and the next future grade. No connection is made to other grade levels.

The materials reviewed for Kindergarten provide information on connected content standards and pacing.

• Within each module overview there is a section called "Overview of the Module Topics and Lesson Objectives." It contains lessons broken down by topic and cross-references the standards at the topic level.
• This overview also lists the number of days for each topic as well as the total number of instructional days for the entire module, including assessments.
• Lessons include a time frame for each activity in the lesson.
• There is a yearly summary of standards and pacing.

The materials reviewed for Kindergarten include information and suggestions for parents.

• Eureka has a web page for parents that contains general information about the curriculum as well as a few informational videos.
• The web page also has a section called "Eureka Math Tips for Parents," which gives information organized by grade level and module.

The materials reviewed for Kindergarten contain explanation of the instructional approaches of the program.

• The Eureka web page has a section called "Reports," which details key research reports on mathematics instruction and learning.
• There is annotation about the curriculum as it relates to these reports.
• There is information about the instructional approaches and research connection in the documents called "How to Implement A Story of Units" and "A Story of Units."
• The opening letter from Executive Director Lynne Munson addresses some of the research and philosophy behind the curriculum.

The materials reviewed for Kindergarten do not meet the expectations for this indicator.

• Foundational standards are listed for most modules, but there are no directions for using these standards to assess prior knowledge.
• There are not systematic ways to gather information about prior knowledge.
• There are no diagnostics included other than within the rubrics for the summative assessments.
• There are no module pretests.

The materials reviewed for Kindergarten meet the expectations for this indicator by including strategies to identify and address common student errors and misconceptions.

• Each summative assessment includes a chart of "Progression toward Mastery" to help teachers with the coherence towards mastery.
• On page 13, "How to Implement A Story of Units" says this about support: "Distractors for such questions are written to illuminate common student errors and misconceptions."
• The intent of the lesson's student debrief section is to get students to reflect and process the lesson. Strategies include partnering to guide students in conversation to debrief the problem set and process the lesson.
• The marginal notes often suggest ways to support students as a whole and subgroups of students who might need support. In particular, the "Multiple Means of..." notes tend to focus on student misconceptions.

The materials reviewed for Kindergarten meet the expectations for this indicator by including ongoing review and practice.

• Ongoing review and practice is included within the fluency section of lessons.
• Exit tickets can provide feedback depending upon how the teacher uses them.
• Review and practice, also within the problem sets and homework, are included in every lesson.
• The summative assessments contain rubrics to provide feedback to the teacher and student on a student is progressing toward mastery.

The materials reviewed for Kindergarten partially meet the expectations for this indicator. The summative assessments meet the expectations, but the formative assessments do not.

• For the mid-module and end-of-module assessments, there are rubrics for scoring the items, as well as an answer key with sample answers.
• Rubrics and scoring guides are clear and helpful. Examples of student work receiving top grades on the rubric are included.
• In the "Progression toward Mastery" section of the summative assessments there is a detailed rubric for grading student mastery from 1 to 4. If the student does not achieve total mastery (step 4), then the teacher can look at the next steps to see what or how to follow up with the student. For example, when a student's mastery is step 2, teachers can look at steps 3 and 4 to guide follow-up instruction.

The materials reviewed for Kindergarten partially meet the expectations for this indicator. The summative assessments meet the expectations, but the formative assessments do not.

• Mid-module and end-of-module assessments align each item to specific standard(s).
• There are standards listed for each lesson; sometimes multiple standards are listed.
• There are no specific standards listed within the lesson's exit tickets, which could include multiple standards.

The materials reviewed for Kindergarten partially meet the expectations for this indicator. The summative assessments meet the expectations, but the formative assessments do not.

• For the mid-module and end-of-module assessments, there are rubrics for scoring the items, as well as an answer key with sample answers.
• Rubrics and scoring guides are clear and helpful. Examples of student work receiving top grades on the rubric are included.
• In the "Progression toward Mastery" section of the summative assessments there is a detailed rubric for grading student mastery from 1 to 4. If the student does not achieve total mastery (step 4), then the teacher can look at the next steps to see what or how to follow up with the student. For example, when a student's mastery is step 2, teachers can look at steps 3 and 4 to guide follow-up instruction.

Materials reviewed for this indicator do not include self-monitoring for students. There is one exception within the fluency sprints. Students complete the sprint twice with a goal of increasing their score on the second round.

The materials reviewed for Kindergarten meet the expectations for this indicator by including strategies to help teachers sequence and scaffold lessons.

• The lessons are sequenced to build from conceptual understanding, using representations ranging from concrete and pictorial to the more abstract.
• The marginal notes often suggest ways to support students as a whole and subgroups of students who might need extra support. This includes support for vocabulary, representations, engagement options and materials.
• Lessons and mathematical topics are sequenced according to the CCSSM "Progressions of Learning."
• A description of the module sequence and layout is provided.

The materials reviewed for Kindergarten meet the expectations for this indicator by including strategies for meeting the needs of a range of learners.

• The lessons are sequenced to build from conceptual understanding, using concrete and pictorial representations as well as more abstract ones.
• The marginal notes often suggest ways to support students as a whole and subgroups of students who might need extra support. This includes support for vocabulary, representations, engagement options, and materials.
• Page 13 of "How to Implement A Story of Units" describes a variety of scaffolds and accommodations.

The materials reviewed for Kindergarten meet the expectations for this indicator by providing tasks with multiple entry points that can be solved in a variety of ways.

• Application problems, problem sets and homework are included in almost all lessons. Students can choose their own solution strategy and/or representation from a variety of options.
• The embedded tasks show the students multiple representations using drawings, charts, graphs, or numbers or words.

The materials reviewed for Kindergarten meet the expectations for this indicator by including support for ELL students and other special populations in order for them to actively participate.

• Notes on multiple means of engagement give teachers suggestions about meeting the needs of ELL students. These margin notes include sentence starters, physical responses and vocabulary support.
• On pages 14-20 of "How to Implement a Story of Units," there are suggestions for working with ELL students and students with disabilities. Page 14 states, "It is important to note that the scaffolds/accommodations integrated into A Story of Units might change how a learner accesses information and demonstrates learning; they do not substantially alter the instructional level, content, or performance criteria. Rather, they provide students with choices in how they access content and demonstrate their knowledge and ability."

The materials reviewed for Kindergarten meet the expectations for this indicator by offering instructional support for advanced students.

• Notes on multiple means of engagement give teachers suggestions about meeting the needs of advanced students.
• The curriculum specifies that not all pieces of each section of a lesson must be used, so advanced students could be asked to tackle problems or sections a teacher does not use for all students.
• On page 20 of "How to Implement A Story of Units," teachers are given suggestions for working with above-grade-level students.

The materials reviewed for Kindergarten meet the expectations for this indicator by providing a balanced portrayal of various demographic and personal characteristics.

• The names and situations in the story problems represent a variety of cultural groups.
• The application problems include real-world situations that would appeal to a variety of cultural and gender groups.
• There is a balanced approach to the use of gender identification.

The materials reviewed for Kindergarten include a variety of grouping strategies.

• Notes within the lessons present the teachers a variety of options for whole group, small group, partner or individual work.
• There are opportunities for different groupings, however the fundamental models are "Modeling with Interactive Questioning," "Guided Practice" and "Independent Practice."
• There are also suggestions for small-group work within the differentiation pages of the "how to implement" document.

The materials reviewed for Kindergarten encourage teachers to make home-language connections and cultural ties in order to facilitate learning.

• There are occasions (mostly with Spanish) where students are encouraged to make connections to words in their home languages.
• The "how to implement" document puts it this way: "Know, use, and make the most of student cultural and home experiences. Build on the student's background knowledge."

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.

Reviews for this series were conducted using print materials, which do not include an instructional technology component. Materials were not reviewed for this indicator.