The instructional materials reviewed for Zearn Grade 3 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings, such as 3.OA.A, 3.OA.B and 3.NF.A.

Cluster 3.OA.B states that students are to understand properties of multiplication and the relationship between multiplication and division.

• Mission 1 uses pictures and arrays to develop conceptual understanding of multiplication and division. In Mission 1, Teacher-Led Instruction, Lesson 1 students use their arms to relate skip counting to repeated addition to ten groups of two.
• Missions 1 and 3 use counters, tape diagrams, arrays, and drawings to help visualize division and connect it to multiplication. In Mission 3, Teacher-Led Instruction, Lesson 6 students model the distributive property on whiteboards and tape diagrams to show multiplication of 6 and 7. Using the “break apart” method, students break larger numbers into smaller numbers to compute the product of 6 x 7, arriving at different ways to demonstrate the distributive property (i.e. 6x4 + 6x3 or 6x5 + 6x2).

Cluster 3.NF.A states students will develop understanding of fractions as numbers. In Mission 5, Fractions as Numbers, the lessons use concrete models to demonstrate partitioning shapes into equal parts.

• In Teacher-Led Instruction, Lesson 9 students use drawings and fractions strips to model how an orange can be partitioned into fourths. Students explore questions such as the following:
  • “What is our unit?"
  • "How many fourths are in two oranges?"
  • "Are you sure our unit is still fourths? Talk with your partner.”
• These questions and prompts help students articulate the relationship of parts to whole and what happens when there is more than one whole, as in this case with two oranges with a unit of one-fourth of one orange.

Overall, lessons within Missions, whether Teacher-Led Instruction or Independent Digital Lessons, present opportunities for students to develop conceptual understanding of the mathematical concepts for the grade. Students use place value concepts to round numbers and perform multi-digit addition and subtraction within 1,000 (as described in Table 1 of the CCSSM). Students link multiple representations of multi-digit whole numbers to place value charts and decomposing and recomposing of numbers with hands-on and virtual manipulatives, and these representations are connected to addition and subtraction sentences within 1,000. Students develop an understanding of fractions as numbers by exploring fractional parts of a whole and the relationship between unit fractions and their whole.

The instructional materials reviewed for Grade 3 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, Blast, Totally Times, and Multiply Mania, and in Small Group Instruction, with Fluency activities for most lessons.

• Mission 2, Teacher-Led Instruction Whole Group Fluency includes activities (3.NBT.2) where students use part-whole thinking with metric units (Lesson 15), count forward and backwards by nines to 90 (Lesson 17), and use the subtraction algorithm within 1000 with various units (Lesson 19).
• In Mission 2, Independent Digital Lessons students add measurements using the standard algorithm to compose larger units and subtract measurements including three-digit minuends.

Overall, Zearn includes time in every lesson during Independent Digital Lessons in Number Gyms and lesson-specific activities to build fluency. Most Teacher-Led Instruction lessons include a Whole Group Fluency Lesson as well. These lessons are designed to complement one another, reinforcing student development of procedural skills and fluency.

The instructional materials reviewed for Grade 3 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.

During Teacher-Led Instruction in every Mission, there are Whole Group Word Problems (Application Problems) for most lessons. These Application Problems represent the Addition and Subtraction Situations described in Table 1 of the CCSSM, and the Multiplication and Division Situations described in Table 2 of the CCSSM. For example, Cluster 3.OA.A represents major work of the grade. Mission 1, Whole Group Word Problems for Topic B, "Division as an Unknown Factor Problem" connects multiplication and division situations to different applications from Lessons 4 through 6. For example:

• The Lesson 4: “The student council holds a meeting in Mr. Chang’s classroom. They arrange the chairs in 3 rows of 5. How many chairs are used in all?” The teacher note states, “This problem reviews relating multiplication to the array model from Lesson 2. This application word problem connects multiplication to a division situation asking how many in each group?“
• The Lesson 5: “Stacey has 18 bracelets. After she organizes the bracelets by color, she has 3 equal groups. How many bracelets are in each group?” The teacher note states, “This problem reviews the meaning of the unknown as the size of the group in division from Lesson 4. It also provides a comparison to Problem 1 in the Concept Development, where the unknown represents the number of groups in division.”
• The Lesson 6: “Twenty children play a game. There are 5 children on each team. How many teams play the game? Write a division sentence to represent the problem.” The teacher note states, “... where the unknown represents the number of groups.”

Throughout Grade 3 students develop their understanding of multiplication and division through a variety of multi-digit addition and subtraction. The Application Problems link the four operations of arithmetic to the CCSSM Tables 1 and 2 and to the major work of the grade.

The instructional materials reviewed for Grade 3 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, Independent Digital Lesson 6, Multiply Mania, students have two minutes to answer problems for multiples of six and seven. Problems are not always presented sequentially. For example, students may solve a string of problems 6 x 6, 6 x 9, 6 x 6, 6 x 8, 6 x 5, 6 x 9, 6 x 8, etc. During Teacher-Led Instruction students practice multiplying by 6 and counting forward and backwards from different starting points, for example, from 30 to 90.
• Conceptual understanding is embedded into every lesson. In Mission 3, Teacher-Led Instruction, Lesson 6, students apply the distributive property to multiply using units of 6 and 7. Students rewrite expressions into known facts. For example, 7 x 6 is rewritten into 5 x 6 and 2 x 6 so that 7 x 6 = (5 x 6) + (2 x 6). Students use this understanding to rewrite the division problem 48 ÷ 6 as the sum of two quotients (30 ÷ 6) + (18 ÷ 6).
• 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 are presented with the problem: “Mabel cuts 9 pieces of ribbon for an art project. Each ribbon is 7 centimeters long. What is the total length of the pieces of ribbon that Mabel cuts?” This problem builds on the procedural fluencies working with multiples of six and contextualizes the concept development on the distributive property.

The instructional materials for Zearn Grade 3 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 3 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 with numbers and computation.
• Progressions are clear, as in focusing on multiplying numbers between 2 and 5 along with 10, before extending to multiplying all numbers within 10.
• Concepts are developed in Teacher-Led Instruction. These may be extended into Independent Digital Lessons.

The instructional materials for Zearn Grade 3 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 2, Teacher-Led Instruction Lesson 4, students describe and explain why their solutions demonstrate their understanding, using words, pictures, or number lines. The Independent Digital Lesson 4 also encourages students to engage with material to use manipulatives and drawing.

The instructional materials for Zearn Grade 3 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, Mission 5, Independent Digital Lesson 2 Learning Lab begins with students cutting a sandwich into equal parts. The virtual tools let students determine where to cut and sets the stage for students considering how to determine equal parts. The written work provides models and pictures that are created to enhance the math concept. Students are encouraged to create their own models; however, the digital lessons are limited to prescribed tools and virtual manipulatives.

The instructional materials for Zearn Grade 3 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 instructional materials for Zearn Grade 3 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 3 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 3 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 instructional materials for Zearn Grade 3 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 Grade 3 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 instructional materials for Zearn Grade 3 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 for Zearn Grade 3 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 for Zearn Grade 3 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.