The instructional materials reviewed for Zearn Grade 2 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The use of visual representations builds conceptual understanding of place value (2.NBT.A) and addition and subtraction (2.NBT.B). During Independent Digital Lessons and Teacher-Led Instruction students engage with visual representations and virtual manipulatives.

• In Mission 3, Counting and Place Value, Independent Digital Lesson 14 students use place value disks to model numbers through 1,000 and then connect these models to reading and writing numbers to 1,000.
• In Mission 5, students add and subtract large numbers. Place value is the underlying concept referenced for each iteration from lesson to lesson as larger multi-digit numbers are introduced. Students use a traditional algorithm, but there is a constant tie to place value. In Lesson 1 students begin adding within 1,000 using a place value chart. Students represent each addend by place value, one over the other, to simulate the standard algorithm. During Independent Digital Lesson 6 students are using the associative property and tape diagrams to subtract numbers such as 330-290. In Independent Digital Lesson 9 students use virtual place value disks to add numbers such as 672+249. The use of multiple representations of place value builds student understanding of grouping and regrouping as they conduct addition and subtraction within 1,000.

Overall, Lessons within Missions, whether Teacher-Led Instruction or Independent Digital Lessons, present opportunities for students to develop conceptual understanding of the mathematics. Students engage in multiple addition and subtraction problems as described in Table 1 of the CCSSM. Students encounter multiple representations of whole numbers through place value, decomposing and recomposing of numbers with hands-on and virtual manipulatives, place value charts, and number bonds, and these representations are linked to addition and subtraction sentences within 1,000.

The instructional materials reviewed for Grade 2 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Missions address procedural skill and fluency in both the Independent Digital Lessons, with Fluency activities titled Number Gym, Sprint, and Blast, and in Small Group Instruction, with Fluency activities for most lessons.

• In Mission 1, Teacher-Led Instruction, Whole Group Fluency, Lesson 1 students play Ten-Frame Flash, Happy Counting using a rekenrek, and finger play. Students also alternate between counting and using the “Say Ten” way where students compose numbers with tens; for example 12 is ten 2.
• In Mission 1, Independent Digital Lesson 1 Sprint students practice making 10 and adding to 10 (2.OA.2).
• In Mission 7, Length, Money, and Data, students participate in Fluency Games during Teacher-Led Instruction. For example, during Lesson 21 students play Roll and Follow the Rule Game where the students are given a base number between 0 and 100 (2.NBT.5). In Lesson 22 students play a mental math game called Compensation where the students add numbers such 420+190 by taking from one number to round the other number to the next hundred (2.NBT.B).

Overall, Zearn includes time in every lesson during Independent Digital Lessons through Number Gyms, Sprints, and Blasts, and in Teacher-Led Instruction Whole Group Fluency Lessons to build fluency. These lessons are designed to complement one another, reinforcing student development of procedural skills and fluency.

The materials meet the expectation for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Missions address application in most Teacher-Led Instruction Lessons through Whole Group Word Problems that model the situations from Table 1 of CCSSM “Common Addition and Subtraction Situations.”

Mission 8, Teacher-Led Instruction, Whole Group Word Problems, Topic B Composite Shapes and Fraction Concepts includes teacher notes on what addition and subtraction situations are represented. The problems address representing and solving problems involving addition and subtraction (2.OA.1). For example:

• Teacher-Led Instruction, Whole Group Word Problems, Lesson 6: “Frank has 19 fewer cubes than Josie. Frank has 56 cubes. They want to use all of their cubes to build a tower. How many cubes will they use?” The teacher note states, “This is a two-step problem with a compare with bigger unknown type problem as one step. Encourage students to draw a tape diagram to help visualize the comparison.”
• Teacher-Led Instruction, Whole Group Word Problems, Lesson 7: “Mrs. Librarian’s students are picking up tangram pieces. They collect 13 parallelograms, 24 large triangles, 24 small triangles, and 13 medium triangles. The rest are squares. If they collect 97 pieces in all, how many squares are there?” The teacher note states, “This is a two-step put together with addend unknown problem type. The numbers in this problem invite students to call upon a variety of strategies to solve.”
• Teacher-Led Instruction, Whole Group Word Problems, Lesson 8: “The students were making larger shapes out of triangles and squares. They put away all 72 triangles. There were still 48 squares on the carpet. How many shapes were on the carpet when they started?” The teacher note states, “This is a take from with a start unknown type of problem. Encourage students to visualize the relationships within the problem.”

The instructional materials reviewed for Grade 2 meet the expectation for balancing the three aspects of rigor. Overall, the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within Teacher-Led Instruction and Independent Digital Lessons.

In each Mission students develop procedural skills and fluency and conceptual understandings, and apply these to solve real-world problems.

• Fluency is embedded into every lesson. In Mission 3, Teacher-Led Instruction Whole Group Fluency, Lesson 6, students practice addition using a meter strip with two-digit numbers, and using tens to add nines. For example 9 + 5 = 10 + 4.
• Conceptual understanding is embedded into every lesson. In Mission 3, Teacher-Led Instruction, Lesson 6, students use place value to understand expanded form in unit order. Students connect expanded form into statements, such as “2 hundreds 4 tens 3 ones.” They count up: “1 hundred 2 hundred 2 hundred ten 2 hundred twenty…” They then reread the number using addition symbols: “100 + 100 + 10 + 10 + 10 + 10 + 1 + 1+ 1.” During the Independent Digital Lesson students write the number from a set of expanded numbers often presented using the commutative property: “10 + 400 + 2 = ______ and decompose numbers into expanded form 385 = _____ + _____ + _____.”
• Application problems are embedded into every lesson and often call for students to model their thinking and make connections to procedural skills. In Mission 3, Teacher-Led Instruction Whole Group Word Problem, Lesson 6, students read the problem with the teacher: “Timmy the monkey picked 46 bananas from the tree. When he was done, there were 50 bananas left. How many bananas were on the tree at first?” Students work with the teacher and a partner to answer questions: “Visualize the problem and talk with your partners. What can you draw with what you see? What is the question asking you? How many bananas were on the tree at first? How many different ways can you find the answer? Etc.” In this task, students use procedural fluency to add and subtract within 100, and they apply their conceptual understanding of addition and subtraction situations to explore different solution strategies.

The instructional materials for Zearn Grade 2 meet the expectation of the underlying design of the materials to distinguish between problems and exercises.

Every lesson includes problems and exercises.

• Problems are included in Teacher-Led Instruction during Small Group Lessons and Whole Group Word Problems.
• Exercises are built into the Teacher-Led Instruction during Whole Group Fluency and Assessment, which can be found in most lessons.
• Independent Digital Lessons include a variety of activities for students to engage with exercises. During Number Gym students solve exercises to build fluency.
• Optional Homework consists of problems and exercises, depending on the content of the mission and/or lesson.

The instructional materials for Zearn Grade 2 meet the expectation the design of the assignments is not haphazard, and the exercises are given in intentional sequences.

• The sequence of topics within each mission is intentional, going from working with a variety of concrete and pictorial representations to more abstract work.
• Progressions are clear, as in focusing on adding and subtracting with 100 before adding and subtracting within 1000.
• Concepts are developed in Teacher-Led Instruction. These may be extended into Independent Digital Lessons.

The instructional materials reviewed for Grade 2 meet the expectation that there is a variety in what students are asked to produce. Students are asked to produce a variety of products in digital and written form.

Students are asked to demonstrate:

• Multiple representations through models, arrays, number lines, equations, etc.;
• Justification of their thinking on Optional Problem Sets and Assessments;
• Completion of timed fluency activities in Teacher-Led Instruction Whole Group Fluency and Independent Digital Lessons;
• During Independent Digital Lessons students solve problems using virtual manipulatives.

For example, in Mission 3, Teacher-Led Instruction Lesson 15, students describe and explain why their solutions demonstrate their understanding, using words, pictures or numbers. The Independent Digital Lesson 15 also encourages students to engage with material to use manipulatives and drawing.

The instructional materials reviewed for Zearn Grade 2 meet the expectation that manipulatives are faithful representations of the mathematical objects they represent and are appropriately connected to written methods. Manipulatives are embedded in both Independent Digital Lessons and Teacher-Led Instruction to represent mathematical ideas and build conceptual understanding. Examples include place value disks, Unifix cubes, and craft sticks. They are often connected to written representations.

For example, in Mission 4, Independent Digital Lesson 9 Learning Lab, students use place-value charts to add 2 two-digit numbers and to add a two-digit number and a three-digit number. The students take notes in their student workbook and model the equations using place-value charts.

The instructional materials reviewed for Zearn Grade 2 partially meet the expectation that materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

In Small Group Lessons the materials note where the content is building on from prior knowledge, whether it be within the grade or from previous grades. This information, as well as regular reports from Independent Digital Lessons, can be utilized as students begin the program and progress toward mastery for each Mission. Informal observation is included in the teacher notes for a lesson and is also used to gather information regarding a student’s prior knowledge. During Small Group Lessons students are regularly asked to comment and share with each other and the whole group by responding to question prompts from the teacher. Information from the daily Exit Tickets that students complete give the teacher an opportunity to check for prior knowledge, review, and provide feedback.

"Independent Digital Lessons include embedded remediation throughout that address gaps in knowledge from both the current and prior grade levels; all students begin on the first Mission of their grade and progress through their grade level sequence at their own pace.", according to page 6 of Zearn Math's Teaching and Learning Approach.

The Zearn Grade 2 instructional materials meet expectations for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials provide many opportunities for review and practice. Teacher-Led Instruction and Independent Digital Lessons include:

• A fluency section to practice and review what has been learned.
• Guided instruction for students to practice new concepts or skills.

The Independent Digital Lessons provide instant feedback to students if they get a problem right or wrong. When a student misses a problem they are given a second chance to get the problem correct. If their second attempt is still wrong, the answer is provided to the student. Students also have a digital notebook which is reviewed by teachers.

In Teacher-Led Instruction, students work with partners to share feedback regarding the instruction for the day.

The materials reviewed for Zearn Grade 2 meet the expectation of assessments clearly denoting standards that are being emphasized. Summative assessments are offered in the middle and at the end of each Mission. Each assessment is followed by a rubric indicating the standards assessed and the progressive indicators for mastery.

For Independent Digital Lessons, formative assessments are offered throughout the online lessons, with reports sent to the classroom teacher on each student’s progress towards mastering the standards.

The materials reviewed for Zearn Grade 2 meet the expectation of assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. Each assessment includes a 4-step rubric indicating the standards assessed and the criteria and indicators for mastery. A Progression Toward Mastery is provided to describe steps that illuminate the gradually increasing understandings that students develop on their way to proficiency. This rubric provides a 4-step process that goes from 1, which shows “little evidence of reasoning without a correct answer,” to a 4, which is “evidence of solid reasoning with a correct answer.” The assessment also includes exemplars of student work.

Although there are no rubrics for activities in the Independent Digital Lessons, the teacher can access information on the digital component of the system at any time. In addition, an alert is triggered when a student struggles repeatedly on the same concept.

The materials reviewed for Zearn Grade 2 meet the expectations for this indicator by including strategies to help teachers sequence and scaffold lessons.

• There is guidance provided in the Curriculum Map to clarify the intended sequence of materials to teachers. The Curriculum Map can be downloaded from the Curriculum Overview.
• A weekly schedule provides suggestions for teachers on how to best modify the sequence of lessons to make the content accessible to all learners. The “Recommended Weekly Schedule,” located on page 18 of Zearn Math’s Teaching & Learning Approach, recommends a flex day for day 5 with suggestions on how to adjust groups and instruction based on the needs of the students.
• There are notes in the Teacher-Led Instruction sections of Whole Group Fluency, Small Group Lessons, and Whole Group Word Problems that provide strategies for the teacher to scaffold the content for all learners.

The materials reviewed for Zearn Grade 2 meet the expectations for this indicator by including strategies for meeting the needs of a range of learners.

• The notes in the margin for the Universal Design for Learning Framework suggest ways to support students in engagement, representations, and action and expression of the content. These adaptations support a wide range of learners and help teachers make materials accessible.
• There is a general list of strategies labeled, “Special Cases of Differentiation” in the “Zearn Math’s Teaching & Learning Approach” document. The strategies listed for struggling students on page 22 include, Whole Group Supports, Small Group Supports, and Independent Digital Lesson Supports. Strategies include: “During Whole Group Word Problem, adjust the difficulty of the problem by offering different number choices or context.”, "Small Group Supports, Allow students to work with concrete manipulatives to model and explain thinking", "Independent Digital Lesson Supports, Ensure students are familiar with the video player in Independent Digital Lesson that can be paused and rewound so students can view the video again." .
• There are notes in the Teacher-Led Instruction sections of Whole Group Fluency, Small Group Lessons, and Whole Group Word Problems that provide strategies for the teacher in meeting the needs of a range of learners.

The materials reviewed for Zearn Grade 2 meet the expectations for this indicator by including support for the English language learner (ELL) and other special populations in order for them to actively participate in learning mathematics.

Within Small Group Lessons, there are notes on Multiple Means of Engagement, Representation and/or Action/Expression that provide timely and direct suggestions for meeting the needs of ELL and special population students. Notes include sentence starters, physical responses, and vocabulary support.

There is a general list of strategies labeled, “Special Cases of Differentiation” in the “Zearn Math’s Teaching & Learning Approach” document. Guidance is provided in the following categories: Whole Group Supports, Small Group Supports, and Independent Digital Lesson Supports. The strategies listed for English Language Learners on page 19 include, “Provide frequent checks for understanding and encourage direct feedback from peers.”, “Allow students to work with concrete manipulatives to model and explain their thinking.”, "Seat students so ELLs work with a variety of learners.", "Ensure students are familiar with the audio buttons in each Independent Digital Lesson that can read text aloud to students.".

The instructional materials reviewed for Zearn Grade 2 meet the expectations of providing opportunities for advanced students to investigate mathematics content at greater depth.

• In Teacher-Led Instruction, some Whole Group Word Problems include extensions.
• In Small Group Lessons, Notes on specific problems to use, Multiple Means of Engagement, Representation and/or Action/Expression, sometimes give teachers suggestions about meeting the needs of advanced students.
• Digital Bonuses are provided in some Missions as Enrichment for students who have met their weekly goals.
• There is a general list of strategies labeled, “Special Cases of Differentiation” in the “Zearn Math’s Teaching & Learning Approach” document. Guidance is provided in the following categories: Whole Group Opportunities, Small Group Opportunities, and Independent Digital Lesson Opportunities. The strategies listed for Enrichment on page 21 include, "Encourage students to solve problems in more than one way or understand someone else's reasoning.", "Adjust the difficulty of problems by changing the numbers or the context.", and "Encourage students to progress beyond the recommended four Independent Digital Lessons each week; students could progress deeper in on-grade level content or complete all previous Independent Digital Lessons in prior grades through their My Stuff page.".

The instructional materials reviewed for Zearn Grade 2 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 Teacher-Led Instruction, Whole Group Word 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 Independent Digital Lessons represent a variety of cultural groups.