The instructional materials reviewed for Zearn Grade 5 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific cluster headings, such as 5.NBT.A, 5.NF.B, and 5.MD.C.

Students expand their understanding of fractions to include addition and subtraction of fractions with unlike denominators (5.NF.A) as well as multiplication and division of fractions for limited cases (5.NF.B).

• In Mission 3, Small Group Lesson 3, students develop a conceptual model of fraction addition. Students fold pieces of paper and shade sections of the paper to represent each fraction that will be added together.
• In Mission 4, Small Group Lesson 6, students develop an understanding of finding a fraction of a set. Students use a tape diagram to show an understanding of the solution to the following problem, “In a class of 24 students, ⅚ are boys. How many boys are in the class?”
• In Mission 4, Small Group Lesson 25, students develop a conceptual model of division with fractions. Students are asked to solve and model the following problem: “Tien wants to cut ¼ foot lengths from a board that is 5 feet long, How many board can he cut?”

The use of multiple representations and understanding the similarities and differences between representations is used extensively throughout the instructional materials to help students build conceptual understanding.

• Mission 1 focuses on 5.NBT.A. Place value charts and vertical number lines are used to introduce the fractional unit of thousandths as well as place value understanding to round a decimal to any place.
• Mission 5 focuses on 5.MD.C. Students use centimeter grid paper, centimeter cubes, and isometric dot paper to build and represent solid figures of a given volume as well as to find the volume of a given rectangular prism.
• Throughout the Grade 5 Missions and Lessons, students are frequently asked to draw and make conclusions based on their drawings.
• Optional Problem Sets include opportunities for students to draw pictures and make models to show understanding. For example, the Mission 4 Problem Set for Small Group Lesson 16, asks students to, “Solve and show your thinking with a tape diagram” when multiplying fractions within a word problem.

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 using place value, concrete models, and the properties of arithmetic.

The instructional materials reviewed for Grade 5 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.

• In Mission 2, Teacher-Led Instruction Whole Group Fluency Lesson 4 (5.NBT.5), students practice decomposing multiplication sentences such as 12 x 3 =____ into (8 x 3) + (____ x 3) = _____. They practice writing the value of the new equation and using addition to solve. They repeat the process for 14 x 4, 13 x 3, and 15 x 6.
• In Mission 2, Independent Digital Lesson 5 Blast, students practice solving two-digit whole numbers multiplied by 10. During Blast, students solve multi-digit multiplication (5.NBT.5).

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 5 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.

Mission 4, Multiply and Divide Fractions and Decimals (5.NF.B) represents major work for the grade. The Application Problems in this mission are specifically designed as a bridge between deepening concept development on multiplication and division and applying their understanding to multiplication and division of fractions. For example, in Teacher-Led Instruction, Whole Group Word Problems, Topic E: Multiplication of a Fraction by a Fraction, “Topic E introduces students to multiplication of fractions by fractions -both in fraction and decimal form (5.NF.4a, 5.NBT.7).” The topic includes six lessons that have application problems. For example:

• Lesson 15: “Kendra spent ⅓ of her allowance on a book and ⅖ on a snack. If she had four dollars remaining after purchasing a book and snack, what was the total amount of her allowance?” The teacher note states, “This problem reaches back to addition and subtraction of fractions, as well as fractions of a set.”
• Lesson 17: “Ms. Casey grades 4 tests during her lunch. She grades ⅓ of the remainder after school. If she still has 16 tests to grade after school, how many tests are there?” The teacher note states, “Today’s Application Problem recalls Lesson 16’s work with tape diagrams.”
• Lesson 18: “An adult female gorilla is 1.4 meters tall when standing upright. Her daughter is 3 tenths as tall. How much more will the young female gorilla need to grow before she is as tall as her mother?” The teacher note states, “This Application Problem reinforces that multiplying a decimal number by tenths can be interpreted in fraction or decimal form (as practiced in Lesson 17). Students who solve this problem by converting to smaller units (centimeters or millimeters) should be encouraged to compare their process to solving the problem using 1.4 meters.”

Throughout Grade 5 students deepen their understanding of multiplication and division as they practice multiplication and division of fractions. The Application Problems link the four operations of arithmetic and the properties of arithmetic to major work of the grade.

The instructional materials reviewed for Grade 5 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. Mission 2, Teacher-Led Instruction, Whole Group Fluency Lesson 14 builds on understandings from Grade 4 to help students review the multiplication of unit fractions. In Independent Digital Lessons Mix and Match, students practice multiplication of multi-digit whole numbers.
• Conceptual understanding is consistently embedded into lessons. In Mission 3, Teacher-Led Instruction, Lesson 8, students use the number line when adding and subtracting fractions greater than or equal to 1. During Independent Digital Lessons, Tower of Power Lesson 8, students use the number line when adding and subtracting mixed numbers and whole numbers.
• Application problems are consistently embedded into lessons and often call for students to model their thinking and make connections to procedural skills. The Mission 5, Teacher-Led Instruction, Whole Group Word Problems Lesson 3 states: “An ice cube tray has two rows of 8 ice cubes. How many ice cubes are in a stack of 12 ice cube trays? Draw a picture to explain your reasoning.”.

The instructional materials for Zearn Grade 5 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 5 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 multiplication of multi-digit numbers before multiplying fractions.
• Concepts are developed in Teacher-Led Instruction. These may be extended into Independent Digital Lessons.

The instructional materials for Zearn Grade 5 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 1, Teacher-Led Instruction Lesson 1, students describe and explain why their solutions demonstrate their understanding, using words, pictures, or place value chart. The Independent Digital Lesson 1 also encourages students to engage with material to use manipulatives and drawing.

The instructional materials for Zearn Grade 5 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 Independent Digital Lessons and Teacher-Led Instruction to represent mathematical ideas and build conceptual understanding. Examples include 2-sided counters, centimeter cubes, and tape diagrams. They are often connected to written representations.

For example, in Mission 3, Independent Digital Lesson 3, students use an electronic tool to divide rectangles into equal parts so that students can combine like fractions. The students take notes and draw a model in the virtual student workbook.

The instructional materials for Zearn Grade 5 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 5 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. During Teacher-Led Instruction and Independent Digital Lessons, there are:

• 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. If 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 5 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 5 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 5 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.
  • In Mission 2, Topic B, Small Group, Lesson 4, “Multiple Means of Action and Expression” states, “This lesson requires students to work mentally with two-digit and three-digit numbers. If basic multiplication facts are not yet mastered, be prepared to adjust numbers in calculations to suit the learner’s level. Spending time working on basic facts (with flash cards, computer games, etc.) may be necessary prior to this lesson.”

The materials reviewed for Grade 5 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 5 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 5 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 5 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.