## ORIGO Stepping Stones 2.0

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### Overall Summary

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials partially meet expectations for rigor and meet expectations for practice-content connections.

###### Alignment
Meets Expectations
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Meets Expectations

### Focus & Coherence

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations that they assess grade-level content and, if applicable, content from earlier grades. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

Each Grade Level Consists of 12 modules. Each module contains three types of summative assessments. Check-ups assess concepts taught in the module, and students select answers or provide a written response. Performance Tasks assess concepts taught in the module with deeper understanding. In Interviews, teachers ask questions in a one-on-one setting, and students demonstrate understanding of a module concept or fluency for the grade. In addition, Quarterly Tests are administered at the end of Modules 3, 6, 9, and 12.

Examples of assessment items aligned to Grade 4 standards include:

• Module 2, Check-Up 2, Problem 3, “Complete each equation. Show your thinking. a. 9\times 35 =  b. 3\times94 = .” (4.NBT.5).

• Module 6, Quarterly Test B, Problem 2, “Choose the operation you would use to solve this problem. Victoria has 26 stamps in her collection. Her brother has 18 more stamps than Victoria. How many stamps are in her brother’s collection? A. Multiplication, B. Division, C. Addition, D. Subtraction.” (4.OA.2)

• Module 8, Performance Task, Problem 1, “a. Three people equally share the cost of this television. How much will each person pay? b. A fourth person joins the group to share the cost of the same television. How much less will each person have to pay?” An image shows the price of the television as 624. (4.MD.2 and 4.OA.3). There are some assessment items that align to standards above Grade 4; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include: • Module 10, Check-Up 1, students add decimals: Problem 1a, 0.4 + 0.2, Problem 1b, 3.15 + 2.50, and Problem 1c, 0.6 + 0.25. (5.NBT.7). • Module 10, Performance Task, students add decimals (5.NBT.7) in the six problems. • Module 12, Quarterly Test A and Quarterly Test B, Problems 12 and 13, students add decimals (5.NBT.7). ##### Indicator {{'1b' | indicatorName}} Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The instructional materials provide extensive work in 4th grade by including different types of student problems in each lesson. There is a Student Journal with problems in three sections: Step In, Step Up, and Step Ahead. Maintaining Concepts are in even numbered lessons and include additional practice opportunities, including Computation Practice, Ongoing Practice, Preparing for Module _, Think and Solve, and Words at Work. Each Module includes three Investigations and, within grade 4, students engage with all CCSS standards. Examples of extensive work from the grade include: • Module 3, Lessons 2 and 6 engage students in extensive work with 4.NBT.4 (Fluently add and subtract multi-digit whole numbers using the standard algorithm.) as students use the standard algorithm to solve addition problems. Lesson 2, Number: Comparing to order four-, five-, and six-digit numbers, Student Journal, Maintaining Concepts and Skills, page 87, Question 1a, “Estimate each total. Then use the standard addition algorithm to calculate the exact total. Estimate ______ 1615 + 1472 =, Estimate ______ 2486 + 1373 =, Estimate ______ 2108 + 2095 =.” Lesson 6, Multiplication: Relating multiples and factors, Student Journal, Maintaining Concepts and Skills, page 99, Question 1a, “Estimate each total. Then use the standard algorithm to calculate the exact total. Estimate______ 4360 + 804 + 273 =, Estimate ______ 36020 + 2654 + 1168 = , Estimate ______ 52789 + 13540 + 3420 =.” Student Journals in Lessons 2, 4, 6, 8, 10, and 12 of each module, include two pages called Maintaining Concepts and Skills that provide all students additional practice in order to engage in extensive work with grade-level problems. • Module 7, Lesson 4, Division: Solving word problems with remainders, engages students with extensive work with grade-level problems with 4.OA.3 (Use the four operations with whole numbers to solve problems). In the Student Journal, Step Up, page 252, Question 1, students solve word problems with remainders. “Solve each problem. Show your thinking. a. Teresa is walking 60 miles for charity. She walks 7 miles a day. How many days will it take to complete the walk? b. 20 balls are packed into cans. There are 3 balls in each can. How many balls are left out?” • Module 9, Lesson 3, Common fractions: Comparing and ordering, engages students with extensive work with 4.NF.2 (Extend understanding of fraction equivalence and ordering). In the Student Journal, Step Up, page 327, Question 3, students use number lines to compare and order common fractions. “Use the number lines in Questions 1 and 2 to help you write these fractions in order from least to greatest. a. \frac{8}{6}, \frac{13}{6}, \frac{6}{4}, \frac{8}{4} b. \frac{5}{4}, \frac{8}{3}, \frac{13}{4}, \frac{2}{3} c. \frac{11}{12}, \frac{18}{10}, \frac{7}{2}, \frac{12}{10} d. \frac{11}{5}, \frac{18}{8}, \frac{4}{5}, \frac{3}{1} e. \frac{11}{4}, \frac{7}{4}, \frac{7}{6}, \frac{12}{6} f. \frac{2}{1}, \frac{24}{8}, \frac{12}{8}, \frac{5}{5}.” The instructional materials provide opportunities for all students to engage with the full intent of 4th grade standards through a consistent lesson structure, including sections called Step In, Step Up and Step Ahead. Step In includes a connection to prior knowledge, multiple entry points to new learning, and guided instruction support. Step Up engages all students in practice that connects to the objective of each lesson. Step Ahead can be used as an enrichment activity. Examples of meeting the full intent include: • Module 3, Lessons 9 and 12 engage students in the full intent of 4.MD.3 (Apply the area and perimeter formulas for rectangles in real world and mathematical problems.) In Lesson 9, Area: Developing a rule to calculate the area of rectangles, Student Journal, Step Up, page 107, students reason about area. Question 2a, “Calculate the area of each rectangle. Show your thinking. 4 yd 12 yd Area ____yd^2.” Question 3a, “Write possible dimensions for each rectangle. ____yd ____yd 36 yd^2.” In Lesson 12, Perimeter/area: Solving word problems, Student Journal, Step Up, page 114, students apply the formulas for area and perimeter. Question 1a, “Measure each side length in centimeters. Then calculate the perimeter and area. Perimeter ____cm Area ____cm^2” There is a rectangle for students to measure. Question 2a, “Solve each problem. Show your thinking. Remember to include the units in your answers. Zoe’s backyard is a rectangle. The short sides are 5 yards long. The long sides are twice as long. What is the area of her backyard?” • Module 7, Lessons 5 and 8 engage students with the full intent of 4.NF.3a (Understand addition and subtraction of fractions as joining and separating parts referring to the same whole). In Lesson 5, Common fractions: Adding with same denominators, Student Journal, Step Up, page 256, Question 1, students use area models to represent the addition of fractions. “Each large rectangle is one whole. Shade parts using different colors to show each fraction. Then write the total fraction that is shaded. a. \frac{3}{8} + \frac{4}{8} = b. \frac{1}{6} + \frac{3}{6} = c. \frac{4}{10} + \frac{2}{10} =.” In Lesson 8, Common fractions: Subtracting with same denominators, Student Journal, Step Up, page 265, Question 2, students use a number line to subtract fractions. “Use this number line to help you write the differences. a. \frac{15}{6} - \frac{4}{6} = b. = \frac{20}{6} - \frac{8}{6} = c. \frac{17}{6} - \frac{2}{6} = d. = \frac{23}{6} - \frac{9}{6} = e. \frac{21}{6} - \frac{16}{6} = f. = \frac{18}{6} - 1 = \frac{18}{6}- 1.” • Module 12, Lessons 2 and 3 engage students with the full intent of 4.OA.5 (Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself). In Lesson 2, Patterns: Investigating square numbers, Student Journal, Step Up, page 437, students analyze numerical and visual patterns. Question 3, “Norton is exploring square number patterns where there is a 2 in the one’s place of the original number. His results are shown in this table. Original number: 12, 22, 32, 42, 52. Square number: 144, 484, 1,024, 1,764, 2,704. a. Look at his pattern. Circle the numbers below that you think are square numbers. 6,241, 5,184, 2,401, 6,724, 9,409, 8,649. b. Explain your thinking.” In Lesson 3, Patterns: Analyzing number patterns, Student Journal, Step Up, page 441, students use a given rule to complete a pattern. Question 1, “a. Read the rule. Then complete the table. Number of circles = Picture number 2. Picture Number: 6, 4, 5, 20, 2, 15, __. Number of Circles: __, 8, __, 40, 4, __, 26. b. Do you think it is possible to record an odd number of circles? Explain your thinking.” • One 4th grade standard, 4.MD.4, does not include opportunities for students to engage with problems that meet the full intent of the standard. (Make a line plot to display a data set of measurements in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}) Solve problems involving addition and subtraction of fractions by using information presented in line plots.) For example, Module 6, Lesson 12, Angles: Estimating and calculating, Student Journal, page 231, students engage with making a line plot to display a set of measurements in fractions of a unit with \frac{1}{2}, but none with \frac{1}{4} or \frac{1}{8}. Student Journal, Ongoing Practice, “These line plots show the distances run by an athlete during training.” Question 1a, “In which month did the athlete train for the greater number of days?” Question 1b, “ In which month did the athlete run the greater total distance?” Question 1c, “What is the difference between the total distances run in April and May?” #### Criterion 1.2: Coherence Each grade’s materials are coherent and consistent with the Standards. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work. ##### Indicator {{'1c' | indicatorName}} When implemented as designed, the majority of the materials address the major clusters of each grade. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days are included. • The approximate number of modules devoted to major work of the grade (including supporting work connected to the major work) is 9 out of 12, which is approximately 75%. • The approximate number of days devoted to major work of the grade (including supporting work connected to the major work, but not More Math) is 126 out of 156, which is approximately 81%. • The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 114 out of 144, which is approximately 79%. A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in. As a result, approximately 79% of the instructional materials focus on major work of the grade. ##### Indicator {{'1d' | indicatorName}} Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Materials are designed so supporting standards/clusters are connected to the major standards/clusters of the grade. These connections are sometimes listed for teachers on a document titled, “Grade __ Module __ Lesson Contents and Learning Targets” for each module. Examples of connections include: • Module 3, Student Journal, Mathematical Modeling Task, page 118, connects the supporting work of 4.MD.A (Solve problems involving measurement and conversion of measurements) to the major work of 4.NBT.B (Use place value understanding and properties of operations to perform multi-digit arithmetic). Students solve word problems with area and price comparisons. “Hailey is buying carpet for three rooms in her house. The carpet for each room will be a different color. The main bedroom is 16 feet long and 12 feet wide. The office is 15 feet long and 9 feet wide, and the family room is 23 feet wide by 35 feet long. At Country Carpets, if you buy less than 250 square feet of the same color carpet, each square foot costs8. If you buy 250 square feet or more of the same color carpet, the cost for each square foot is $6. How can Hailey use mathematics to figure out the total cost for carpeting the three rooms? Show your thinking.” • Module 5, Lesson 12, Length/mass/capacity: Solving word problems involving metric units, Student Journal, Step Up, page 190, connects supporting work of 4.MD.A (Solve problems involving measurement and conversion of measurements) to the major work of 4.NF.B (Build fractions from unit fractions). Students convert between measurements and fractional parts of measurements to solve word problems. Question 1b, “Solve each problem. Show your thinking and be sure to use the correct units in your answer. Before an operation, a dog weighs 3\frac{4}{10} kg. Afterward, it is 3\frac{1}{10} kg. How many grams has the dog lost?” Question 2d “A pitcher holds 1\frac{1}{2} liters of water. Luis pours out some water and there is now 900 mL of water left. How much water was poured out?” • Module 6, Lesson 12, Angles: Estimating and calculating, Student Journal, Ongoing Practice, page 231, connects the supporting work of 4.MD.B (Represent and interpret data) to the major work of 4.NF.B (Build fractions from unit fractions). Students analyze two line plots with fractional values to answer questions. “These line plots show the distances run by an athlete during training.” Question 1a, “In which month did the athlete train for the greater number of days?” Question 1b, “In which month did the athlete run the greater total distance?” Question 1c, “What is the difference between the total distances run in April and May?” • Module 7, Lesson 11, Common fractions: Solving word problems, Student Journal, Step Up, page 275, connects the supporting work of 4.MD.2 (Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expression measurements given in a larger unit in terms of a smaller unit) to the major work of 4.NF.3 (Understand a fraction \frac{a}{b}with a > 1 as a sum of fractions \frac{1}{b}.) Students solve addition and subtraction word problems involving mixed numbers and common fractions. Question 2, “Solve each problem. Show your thinking. a. Oscar cuts 5 oranges into sixths for a picnic. Afterward, there is only \frac{4}{6} of an orange left. How much orange has been eaten? b. Two statues are being packed into a box. One weighs 7\frac{3}{8} lb and the other weighs 9\frac{4}{8} lb. What is their total mass? c. Two full 2-liter bottles of water are placed in a fridge. After four days, one bottle is half full. The other has 1\frac{3}{10} liters left in it. How much water is there in total? d. A chain is 8\frac{5}{12} feet long. It is joined to another chain so the total length is 10\frac{9}{12} feet. How long is the extra piece of chain?” ##### Indicator {{'1e' | indicatorName}} Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Materials are coherent and consistent with the Standards. Examples of connections include: • In Module 2, Lesson 3, Addition: Reviewing the standard algorithm (composing hundreds), students use the four operations with whole numbers to solve problems, 4.OA.A, and use place value understanding and properties of operations to perform multi-digit arithmetic, 4.NBT.B by explaining and discussing the effects of order of operations on an equation. • In Module 4, Lesson 11, Common fractions: Introducing mixed numbers, Teaching the lesson, Lesson notes, students extend understanding of fraction equivalence and ordering, 4.NF.A, and build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers, 4.NF.B, by using equivalence to add fractions. • In Module 7, Lesson 11, Common fractions: Solving word problems, Teaching the lesson, Lesson notes, students extend understanding of fraction equivalence and ordering, 4.NF.A, and, build fractions from unit fractions 4.NF.B, and represent and interpret data by solving real world problems with fractions and mixed numbers, 4.MD.B. ##### Indicator {{'1f' | indicatorName}} Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Materials relate grade-level concepts from 4th Grade explicitly to prior knowledge from earlier grades. These references are consistently included within the Topic Progression portion of Lesson Notes and within each Module Mathematics Focus. At times, they are also noted within the Coherence section of the Mathematics Overview in each Module. Examples include: • Module 1, Mathematics Overview, Coherence, “Lessons 1.8–1.12 focus on reviewing mental multiplication and extending the focus of multiplying by tens, hundreds, or thousands. This work builds on the prior work with multiplication strategies (3.3.3, 3.3.6, 3.5.1–3.5.2, 3.10.7).” • Module 5, Lesson 6, Length: Exploring the relationship between meters and centimeters, Lesson Notes connect 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit) to work from grade 2 (2.MD.1, 2.MD.3, 2.MD.10). “In Lesson 2.9.11, students measure and compare the lengths of longer objects by repeatedly using a 1 meter length. In this lesson (5.6), students consider what the numbers and markings represent on tools that measure unit of length. They express measured lengths in both meters and centimeters, and use abbreviations.” • Module 7, Lesson 1, Division: Halving two-digit numbers, Lesson Notes connect 4.NBT.6 (Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division) to the work from grade 3 (3.OA.3 and 3.OA.7). “In Lesson 3.12.5, students reinforce the think-multiplication strategy to solve division problems beyond the number fact range. In this lesson (7.1), students review strategies to divide by 2. They use base-10 blocks to model sharing situations, and multiplication equations and diagrams to relate the operations of multiplication and division.” Content from future grades is identified within materials and related to grade-level work. These references are consistently included within the Topic Progression portion of Lesson Notes and within the Coherence section of the Mathematics Overview in each Module. Examples include: • Module 6, Lesson 8, Length: Exploring the relationship between miles, yards, and feet, Lesson Notes connect 4.MD.1 (Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit) to grade 5 (5.MD.1). “In this lesson, students focus on the relationships between miles, yards, and feet and the count of the units when converting miles to yards, then to feet. In Lesson 5.4.7, students convert between feet and inches. The lesson builds upon earlier grade level work as students begin to convert lengths that involve fractions. They convert inches to feet.” • Module 10, Lesson 12, Decimal fractions: Solving word problems, Lesson Notes connect 4.MD.2 (Solve problems involving addition and subtraction of fractions by using information presented in line plots) to the work of grade 5 (5.NBT.7). “In this lesson, students solve word problems involving decimal fractions as related to units of measurement. In Lesson 5.5.1, students review strategies to add tenths to tenths, hundredths to hundredths, and tenths to hundredths. The examples do not require regrouping.” • Module 11, Mathematics Overview, Coherence, “Lessons 11.9–11.12 focus on the geometry work of points, lines, line segments, and rays and transformations that involve reflective symmetry. This work builds on experiences with estimating, calculating, and measuring angles (4.6.9–4.6.12) and serves as a foundation for work with parallelograms and triangles (5.5.10–5.5.12).” ##### Indicator {{'1g' | indicatorName}} In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 foster coherence between grades and can be completed within a regular school year with little to no modification. There are a total of 180 instructional days within the materials. • There are 12 modules and each module contains 12 lessons for a total of 144 lessons. • There are 36 days dedicated to assessments and More Math. According to the publisher, “The Stepping Stones program is set up to teach 1 lesson per day and to complete a module in approximately 2\frac{1}{2} weeks. Each lesson has been written around a 60 minute time frame but may be anywhere from 30-75 minutes depending upon teacher choice and classroom interaction.” ###### Overview of Gateway 2 ### Rigor & the Mathematical Practices The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). ##### Gateway 2 Meets Expectations #### Criterion 2.1: Rigor and Balance Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations for rigor. The materials give attention throughout the year to procedural skill and fluency and spend sufficient time working with engaging applications of mathematics. The materials partially develop conceptual understanding of key mathematical concepts and partially balance the three aspects of rigor. ##### Indicator {{'2a' | indicatorName}} Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include some problems and questions that develop conceptual understanding throughout the grade level. Students have limited opportunities to engage with concepts from a number of perspectives, or to independently demonstrate conceptual understanding throughout the grade. Domain 4.NBT addresses generalizing place value understanding for multi-digit whole numbers and using place value understanding and properties of operations to perform multi-digit arithmetic. There are some opportunities for students to work with multiplication and division through the use of visual representations and different strategies. Examples include: • Module 1, Lesson 2, Number: Building a picture of 100,000, Step 2 Starting the lesson, “Project slide 1 as shown. Ask a volunteer to write a five-digit numeral on the board, then have different students draw beads on the abacus to represent the number, starting from the ones. After each representation, discuss the points below: What is this number? What is 10 more than this number? What is 10 less? What is 100 (1,000/10,000) more than this number?” Step 3 Teaching the lesson, “Project the abacus showing 90,000 (slide 2) and ask students to identify the number. Have a student write 90,000 on the board. Then ask, What would happen if you wanted to add another bead to the ten thousands rod? (MP2 and MP4). Organize students into pairs to discuss their thoughts, then invite a pair to share their ideas. Encourage responses such as, “Another bead would be adding 10,000,” “It would equal 10 groups of 10,000,” and “It would require a bead in the hundred thousands place.” Project another, empty abacus and 90,000 + 10,000 = ___ (slide 3) and ask a student to show 90,000 + 10,000 on the second abacus (MP4). Contextualize 100,000 by encouraging students to share some real-world places where they might see or encounter 100,000.” (4.NBT.1). • Module 2, Lesson 3, Addition: Reviewing the standard algorithm (composing hundreds) Investigation 1, “Project slide 1 (537 + 374), as shown, and read the investigation aloud. Organize students into small groups and have them brainstorm all of the different ways that students may choose to solve the problem. Make sure they record the results using different pieces of paper to show each different method. After, have each group share one method at a time until no other methods are offered. Have students post the written methods on the board. Ask questions such as, How are the methods the same (different)? What are the advantages (disadvantages) of the methods? Are there times when you would use one method over the other? Why?” (4.NBT.4). • Module 6, Lesson 2, Multiplication: Using the partial-products strategy (three-digit numbers), Step 2 Starting the lesson, “Ask, What multiplication equation can we write to describe the total number of squares inside the rectangle? Project the equation 5 x 32 = ___ (slide 2) when suggested. Then ask, How can we split the rectangle so that the tens and ones are separated? After several responses, project slide 3 and ask, How many squares are in each part? (There are 5 rows of 30 in the first section and 5 rows of 2 in the second part.) What multiplication equation can we write for each part? Invite volunteers to record the equations 5 × 30 = 150 and 5 × 2 = 10 on the board. Then ask, What is the total number of squares? (160)” Step 3 Teaching the lesson, “Project slide 4. Encourage the students to imagine the 6 rows of 147 small squares. Say, The diagram is just a representation of all of the squares in the rectangle. The dimensions do not show an accurate relationship between them. Discuss the points below: How is this problem like the one we solved in Step 2? How is it different? Could the same strategy be used to solve this problem? Organize students into pairs to make a solution plan, then solve the problem. Encourage them to draw a diagram to represent the problem (MP4). If students struggle to connect the partial-products strategy used in Step 2 with this problem (MP1), ask, How can we split the rectangle to separate the hundreds, tens, and ones? Does it matter where you draw the lines to show the partitions? What equation shows the number of squares in the hundreds part? What equation shows the number of squares in the hundreds part (tens part)? What about the ones part? How would you calculate the total number of squares in the whole rectangle?” (4.NBT.5) Cluster 4.NF.A addresses extending understanding of fraction equivalence and ordering, building fractions from unit fractions by applying and extending previous understandings of operations on whole numbers and understanding decimal notation for fractions, and compare decimal fractions. Multiple Modules present a variety of problems using mathematical representations. Some opportunities exist for students to work with fractions that call for conceptual understanding and include the use of some visual representations and different strategies. Examples include: • Module 4, Lessons 12, Common fractions: Exploring equivalence with mixed numbers, Step 2 Starting the lesson, Project the Flare Number Line online tool and say, Start at 0 and make three jumps to 2. The jumps do not need to be equal-sized. How long is each jump? How do you know? Invite volunteers to draw three jumps, write the length of each jump, and then explain how they figured out what numbers to write. Encourage the students to use common fractions with the same denominator. After one example is written on the board ask, How would we write an equation to match the jumps? For example, the number line shown below would be represented by the equations \frac{1}{2} + \frac{1}{2} + 1 = 2 or \frac{1}{2} + \frac{1}{2} + \frac{2}{2} = 2 (by recognizing 1 is equivalent to a common fraction). Encourage the students to suggest other ways they could write the same fractions to describe the lengths of the jumps.” During the “Step Up” portion of the lesson, students use shaded parts that represent mixed numbers to “write the equivalent mixed number and common fraction” represented by the shaded parts (4.NF.1). • Module 9, Lesson 2, Common fractions: Comparing with different numerators and denominators, students discuss unit fractions as fractions with a numerator of 1 and unit fractions with common denominators are added to make other fractions such as adding \frac{1}{4} + \frac{1}{4} + \frac{1}{4} to get \frac{3}{4}. In the student materials, fractions are represented by fractions strips where the top strip equals 1 whole and each subsequent strip is divided into unit fractions of \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}. Students discuss which fraction is greater and tell how they decide. In the “Step Up” portion of the lesson, students are presented with two fraction strips side by side and compare fractions such as \frac{10}{6} to \frac{10}{12} (4.NF.2). The instructional materials present few opportunities for students to independently demonstrate conceptual understanding throughout the grade-level. In most independent activities students are told how to solve problems. Examples include: • Module 1, Lesson 6, Number: Locating six-digit numbers on a number line, Student Journal, page 21, Step Up, Question 2, students are shown how to plot large numbers on a number line. “Look at each number line carefully. Write the number that is shown by each arrow.”The number lines are provided with correct spacing and students are either placing numbers on the number line or stating which number is being represented on the number line. Placing numbers on a number line does not help students develop the understanding that a digit in the tens place is ten times larger than the digit to its right nor does it help students with their conceptual understanding of rounding. (4.NBT.A) • Module 2, Investigation 1, students determine different written methods to calculate 537 + 374 and record their results to show each of the methods. Enrichment activities provide some opportunity to understand mathematical concepts through exploring ways to spend$750. (4.NBT.B).

• Module 7, Lesson 2, Division: Halving to divide by four and eight, Step 3 Teaching the lesson, “Organize students into groups of three and distribute the base-10 blocks. Project slide 7. Explain that four friends are equally sharing the total cost of the meal. Then discuss the points below: How can we calculate the amount each person should pay? How can we use base-10 blocks to help our thinking? What other strategy could we use to calculate each share? (Repeated halving.) How can we use multiplication to calculate each share? What multiplication equation can we write? (__ × 4 = 92.) Ask one student in each group to model the division with base-10 blocks (MP4), a second student to write a multiplication equation, and the third student applies the halving strategy used in Step 2. Move around the room to encourage students to verbalize how they share the tens and ones blocks, and how they identify the missing factor in the multiplication equation. Ask, What was the first missing factor you chose? What other missing factors did you think about? How did they help you find the eventual answer? Students should describe how equations such as 20 × 4 = 80 and 25 × 4 = 100 can be used to help.”  It is not suggested that students could use other methods such as rectangular arrays or area models to demonstrate conceptual understanding of division. (4.NBT.2)

##### Indicator {{'2b' | indicatorName}}

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Materials attend to the Grade 4 expected fluencies, 4.NBT.2, add/subtract within 1,000,000.

The instructional materials develop procedural skills and fluencies throughout the grade-level. Opportunities to formally practice procedural skills are found throughout practice problem sets that follow the units. Practice problem sets also include opportunities to use and practice emerging fluencies in the context of solving problems. Ongoing practice is also found in Assessment Interviews, Games, and Maintaining Concepts and Skills.

##### Indicator {{'2d' | indicatorName}}

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 the grade.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

There is some evidence that the curriculum addresses standards, when called for, with specific and separate aspects of rigor and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials have an emphasis on fluency, procedures and algorithms.

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:

• Module 2, Lesson 9, Multiplication: Reviewing the fives strategy, (4.NBT.), students use an array model to reinforce the relationship between pairs of tens and fives facts.

• Module 8, Lesson 9, Common fractions: Exploring the multiplicative nature

• (area model), 4.NBT.5, students practice procedural skill and fluency using an area model to multiply whole numbers.

• Each module contains one lesson Solving Word Problems which requires application. For example, in Module 10, Lesson 12, Decimal fractions: Solving word problems, Student Journal, Step Up, students must solve a word problem and show their thinking. Question 1b states, "Vishaya rides 4.6 miles. Jacob rides 8.3 miles more than Vishaya. How far does Jacob ride?"

Examples of students having opportunities to engage in problems that use two or more aspects of rigor include:

• Module 2, Lesson 5, Addition: Using the standard algorithm with multi-digit numbers, Student Journal, students use the standard algorithm to identify steps already completed in a problem, write out the numbers, and explain what the number “11” represents in the problem.

• Module 9, Problem Solving Activity 1, “Rita baked 2 cakes that were exactly the same size for a party. The first cake was a carrot cake which was cut into 8 equal slices. The second cake was a fruit cake which was cut into 12 equal slices. At the party, \frac{3}{8} of the carrot cake was eaten and 6 slices of the fruit cake was eaten. Was more of the carrot cake or fruit cake eaten?” Students need to apply their conceptual understanding of fractions.

• Module 6, Thinking Task, students use information from the chart provided to solve and answer the questions, Question 3, “What group can take the van? Fill in the total miles walked on the table above. Write which group can take the van. Show your thinking.”

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Indicator {{'2e' | indicatorName}}

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices across the year and they are often explicitly identified for teachers in several places:  Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, alongside the learning targets or embedded within lesson notes.

MP1 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 1, Lesson 3, Number: Reading and writing six-digit numbers, Student Journal, page 13 and Step 4 Reflecting on the work, students make sense of problems and persevere in solving them as they reason about place value. Student Journal, Step Ahead, page 13, “Figure out the total number shown by each set of cards. Write the numbers on the expanders below.” Step 4 Reflecting on the work, “Discuss the students’ answers to Student Journal 1.3. Refer to Step Ahead and discuss the points below: How did you decide which digits should be written on the expanders? How did you know where to write each digit? How does the number of groups show on the place-value cards? (MP1 and MP7)”

• Module 4, Lesson 5, Subtraction: Analyzing decomposition across places involving zero (three-digit numbers), Step 3 Teaching the Lesson, students make sense of subtraction problems and persevere in solving them. “Project slide 6, as shown, and discuss the points below: What problem does this algorithm represent? (307 − 118.) (MP2) What do you estimate the difference to be? Will you need to regroup more than once to find the difference? (Yes.) How would you use blocks to show the regrouping? Ask the students to use a strategy of their choice to calculate the difference (MP1 and MP5).”

• Module 6, Lesson 8, Length: Exploring the relationship between miles, yards, and feet, Step 3 Teaching the Lesson, students make sense of equivalence statements involving length, connecting problems to those solved in the previous lessons as they persevere in solving them. “Project slide 2, as shown. Organize students into pairs to work together to find the solutions. Slide: 1760 yards is equal to 1 mile. ___ yards is equal to 2 miles. 1 mile is 1760 times longer than 1 yard. 2 miles is 1760 times as long as ___ yards. 1760 yards is equal to 1 mile. ___ yards is equal to 3 miles. 3 miles is 1760 times as long as ___ yards. If students have difficulty, help them persevere (MP1) by reminding them how similar statements were solved when working with just yards, feet, and inches in the previous lesson. Point to the first relationship and ask, How has the number of miles changed? (It was doubled.) What do we need to do to the number of yards to keep the same relationship? If students are still confused, ask them to write the equation 12 inches = 1 foot and ___ inches = 2 feet, then repeat the questions with these numbers.”

• Module 8, More Math, Problem Solving Activity 4, Word Problems, students make sense and persevere in solving multi-digit division word problems. “Project slide 1 and read the word problem with the students. Ask, What information do we need to solve this problem? What operations will we use? What will we do first? What will we do next? How could you show your thinking? Slide 1: Robert bought a used car for $5,995 and a GPS for$109. He is paying the total in equal monthly amounts for 8 months. How much does he pay each month? Allow time for students to find a solution. Then invite students to share their solution ($763) and explain their thinking.” MP2 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the modules. Examples include: • Module 2, Lesson 7, Addition: Solving word problems, Step 3 Teaching the Lesson, students decontextualize addition word problems to find answers and contextualize numbers to create addition word problems. “Distribute a copy of the support page to each pair of students. Project the two tables of sales information (slide 4) and ask the students to work together to write an addition word problem in the top left corner of the support page using the information on the tables as a guide. Specify that students can only write a problem where a maximum of two addition equations are required to find the solution. Move around the room to ensure that each word problem is suitable and that only addition is used. The word problems can be exchanged among the students and the support page completed. Suggest that the students describe what the word problem is asking them to do (top right), before estimating the total by rounding and adding (as they would do mentally — bottom left), then finding the exact total using a written method of their choice (bottom right). The problems are then returned to the original authors, who check the solutions for accuracy. Select various pairs to present their word problems and solutions (MP1, MP2, and MP4).” • Module 3, Lesson 11, Perimeter: Working with rules to calculate the perimeter of rectangles, Step 2 Starting the Lesson, students reason abstractly and quantitatively as they explain the meaning of the rules to find perimeter. “Project slide 1, as shown, then discuss the points below: P = 2 x L + 2 x W; P = 2 x (L + W) How do these rules describe how to calculate the perimeter of this rectangle? What does L (W) mean? Where is L (W) on the rectangle? Why are the length and width both doubled in the first rule? Why can the length and width be added first then the total doubled in the second rule? Invite volunteers to use the numbers from the diagram and mathematical understanding to explain why each rule makes sense (MP2).” • Module 5, Lesson 8, Length: Exploring the relationship between meters, centimeters, and millimeters, Step 4 Reflecting on the work, students decontextualize word problems involving various lengths, make sense of the relationships between units, and work with symbols to solve the problem. “Discuss the students’ answers to Student Journal 5.8 and the points below: Why is the number of meters less than the number of millimeters? How did you decide which lengths would be equivalent? What did you have to do first to solve the problems in Question 4? (Convert the lengths to the same unit of measurement.) (MP1 and MP2).” • Module 9, Lesson 12, Capacity/Mass: Solving word problems involving customary units, Student Journal, Step Ahead, page 353 and Step 4 Reflecting on the work, students reason abstractly and quantivity as they solve word problems with customary units. “Write numbers to complete the story. Make sure it makes sense. Andrea buys a carton of juice. The curtain holds __ fluid ounces. She fills __ glasses with juice from the carton. Each glass holds __ fluid ounces. There are __ fl oz left in the carton.” Step 4 Reflecting on the work, “Ask, What equations did you use? Is there more than one way the story will work? Compare two cases of the same story where both of the numbers work and ask, “What relationships make both of these stories work? (MP2)” ##### Indicator {{'2f' | indicatorName}} Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to meet the full intent of MP3 over the course of the year as it is explicitly identified for teachers in several places: Mathematical Practice Overview, Module Mathematical Practice documents and within specific lessons, and alongside the learning targets or embedded within lesson notes. Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments. In some lessons, teachers are provided questions and sentence stems to help students critique the reasoning of others and justify their thinking. Convince a friend, found in the Student Journal at the end of each module and Thinking Tasks in modules 3, 6, 9, and 12, provide additional opportunities for students to engage in MP3. Students engage with MP3 in connection to grade level content, as they work with support of the teacher and independently throughout the units. Examples include: • Module 2, Lesson 1, Addition: Making estimates, Step 3 Teaching the Lesson, students construct viable arguments and critique the reasoning of others when they round multi-digit numbers and estimate sums. “How can we use compatible numbers, or rounding, to estimate the total of different combinations of items so that we do not have to find exact totals each time? Are there enough cars for charity? What combination of items will be the closest to 500 without going over? Which two classes collected the most toy cars? Invite groups of students to share their thinking. Highlight the different strategies they used and the estimations they made. Encourage respectful critique by asking questions such as, Do you agree with this group’s estimate? Why/why not? Who used a different strategy? Did your strategy result in a more accurate estimate? How could you explain that strategy in a different way?“ • Module 3, Student Journal, page 119, Convince a friend, students justify their reasoning about prime and composite numbers and then critique the reasoning of a classmate. “Which number does not belong? 9, 27, 36, 17, 51. Show your thinking. The number does not belong. I think this because … Share your thinking with another student. They can write their feedback below. I agree/disagree with your thinking because. . .” • Module 6, Thinking Tasks, Question 5, students construct viable arguments using their understanding of fourths and halves as they design a travel plan and share evidence for why they think their plan will work. “Ms. Lesh’s class will try to earn over 500 points on the field trip day all at once. Is it possible to create a plan for each group that will: Not skip lunch, AND Earn the class 500 total points or more? For this item you need to: Fill in a Walking Plan for each group on the table below. Fill in Total Miles Walked on the table below. Fill in the Total Mileage Club Points on the table below. Write a letter to the class explaining how it is or is not possible to make a plan that will earn 500 points or more?” • Module 10, Lesson 9, Decimal fractions: Adding tenths, Student Journal, page 383, Step Ahead, students construct viable arguments as they reason about adding tenths, “Maka and Lillian ran a relay. Maka ran the first 3.1 kilometers, then Lillian ran the last 3.3 kilometers. a. Did they run greater than or less than 6.05 kilometers in total? b. Write how you know.” • Module 11, Student Journal, page 433, Convince a friend, students construct viable arguments as they draw lines of symmetry and make predictions in real world problems. “Draw all the lines of symmetry in each shape. What do you notice? Use what you know to predict how many lines of symmetry will be in a shape that has 10 sides equal in length. Share your thinking with another student. They can write their feedback below. Discuss how you could prove your prediction.” ##### Indicator {{'2g' | indicatorName}} Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within lesson notes. MP4 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include: • Module 1, Lesson 8, Multiplication: Reviewing the doubles strategy, Step 3 Teaching the lesson, students model with math as they draw pictures or write multiplication equations to justify their thinking. “Invite volunteers to select a price, explain why they chose it, and describe the thinking they would use. For example, “I know double 23 is 46. I doubled 20 and then doubled 3.” Encourage the students to draw pictures on the board or write equations to help explain their thinking to others (MP4). Explore all of the strategies for each price tag. Emphasize strategies such as: Use a known fact: Double 7 is 14 so double 70 is 140. Use a whole quantity: Two 45s is 90 so two 46s is two more, or two 20s is 40 so two 18s is four less. Split into parts: Double 20 is 40 and double 3 is 6.” • Module 2, More math, Problem Solving 4, students model real word multi-step problems and explain the problem and strategy they chose to find a solution. “Project slide 1 and read the word problem with the students. Slide 1: The school sports department purchased 5 stopwatches for$19 each and a set of hurdles for $1,100. How much did they spend in total? Ask, What information do we need to solve this problem? What operations will we use? What will we do first? What will we do next? How could you show your thinking? (For example, use the standard algorithm, draw a diagram, or write an equation.) Allow time for the students to find a solution. Then invite students to share their solution ($1,195) and explain their thinking. Distribute the support page to each student and have them work independently to solve each problem. Remind them to show their thinking.”

• Module 7, Student Journal, page 280, Mathematical modeling task, students model a real- world multi-step problem involving operations with common fractions. “Jessica is sending three packages to her family. The combined mass of the three packages is just less than 2 kg. One package has a mass of \frac{7}{10} kg, another package has a mass of \frac{1}{4} kg. What could the mass of the third package be? Show your thinking.”

• Module 12, More Math, Thinking Task, School Fun Run, students model with math as they debate and justify their ideas about whether more time elapses while students are running or doing other things on the Fun Run day. Question 4, “Some students in Ms. Flanagan’s class are debating the time that is spent running versus the time that is spent at lunch and stretching. Sharon says they already spend twice as long stretching as they spend running. Sandra says they actually spend twice as long running as they spend stretching. Emilio says that if they include the time spent at lunch, each grade level actually spends twice as long eating lunch and stretching as they do running. For this item, write true or false beside each statement. Explain/show your thinking for each using words, numbers, and/or models.”

MP5 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have multiple opportunities to identify and use a variety of tools or strategies, working with the support of the teacher and independently, throughout the modules to support their understanding of grade level math. Examples include:

• Module 2, More Math, Investigation 1, students show all the different strategies they can use as tools to solve a problem. “Project slide 1 and read the investigation question. (Slide 1, What different written methods can be used to calculate 537 + 374?) Organize students into small groups and have them brainstorm all of the different ways that students may choose to solve the problem. Make sure they record the results using different pieces of paper to show each different method. After, have each group share one method at a time until no other methods are offered. Have students post the written methods on the board. Ask questions such as, How are the methods the same (different)? What are the advantages (disadvantages) of the methods? Are there times when you would use one method over the other? Why?”

### Usability

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports, partially meet expectations for Criterion 2, Assessment, and meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

##### Indicator {{'3a' | indicatorName}}

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• ORIGO Stepping Stones 2.0 Comprehensive Mathematics, Teacher Edition, Program Overview, The Stepping Stone structure, provides a program that is interconnected to allow major, supporting, and additional clusters to be coherently developed. “One of the most unique things about ORIGO Stepping Stones is the approach to sequencing content and practice. Stepping Stones uses a spaced teaching and practice approach in which each content area is spaced apart, the key ideas and skills of these topics have been identified and placed in smaller blocks (modules) over time. In the actual lessons, work is included to help students fully comprehend what is taught alongside the other content development. Consequently, when students come to a new topic, it can be easily connected to previous work.”

• Module 1,  Resources, Preparing for the module, Focus, provides an overview of content and expectations for the module. “The work with place value involving whole numbers is extended to six-digit numbers. Students learn to read and write these greater numbers by using an expander and representations of the numbers on an abacus. When asked to write numbers with zeros, students often insert too many zeros. For example, to write the number three hundred four, they might incorrectly write 3004. To clarify these potentially challenging numbers, this module discusses numbers with zeros and teens separately. By using the expander to show six-digit numbers, students can see the group of three places that are collectively called the thousands. They observe that this group of three has similar place names to the group of three places to the right — the hundreds, tens, and ones. The expander is used to help the students write numbers in expanded form. The students locate greater numbers on a number line to reinforce the role of place value to help position the numbers on the line. For example, the digit in the hundred thousands place tells how many steps of one hundred thousand to move from 0, the digit in the ten thousands place tells how many ten thousands farther along the number line to move, and so on. Students focus on place value to identify the value of digits in different places, and increase or decrease digits by 10, 100, 1,000, or 10,000.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Several components focus specifically on the content of the lesson, such as the Step In, Step Up, Step Ahead, Lesson Slides, Step 1 Preparing the Lesson, while other components, like the Step 2 Starting the lesson, Step 3 Teaching the lesson, and Step 4 Reflecting on the work, serve to ensure teachers have the support and knowledge they need to successfully implement the content.” Lesson notes can also highlight potential misconceptions to support teacher planning and practice. Examples include:

• Module 1, Lesson 7, Number: Working with place value, Step 2 Starting the lesson, teachers provide context about equal parts on a number line. “Project the abacus (slide 1). Choose one student to roll the place-value cube. They draw a bead on the abacus to match their roll. Another volunteer rolls the same cube to record a different place value and draws a bead on the abacus to show their value. The values of the two beads are then compared. Ask, What number does each bead represent? What is the relationship between (Patricia’s) number and (Ben’s) number? If necessary, draw (×10) relationship arrows between each rod on the abacus, as shown. Establish that each rod represents a value that is 10 times as much as the value of the rod to the immediate right.”

• Module 5, Lesson 5, Multiplication: Using tape diagrams to solve word problems, Step 3 Teaching the lesson, provides teachers guidance about how to solve problems using the four operations. “Organize students into pairs to solve the problem from Step 2. Make sure they represent the relationships between the ages with tape diagrams and write equations to match. Afterward, invite pairs to share their models and equations on the board. Make sure they explain the connections between the two representations. Project the Step In discussion from Student Journal 5.5 and read aloud to the end of the clues. Say, This is a photo of Brady and his family when he was 8 years old. You will need to use the clues below the photo to figure out the age of each person in the photo. Refer to the clues and highlight how each clue describes a relationship between the ages of two people in the photo. Have the students work in their pairs to first create a solution plan, writing the clues in the order that they will need to use them. Listen to their discussions, assisting where needed with questions such as: Whose age do you know? Which clue refers to Brady’s age? What model will you use to show the relationship between Brady’s age and his little brother’s age? Why is that a suitable model? When students have completed their plan, have them work through it to find the solutions. As they do so, remind them to continually ask themselves, “Does this make sense?” and to adjust their plan if needed. Continue to observe and listen to the pairs as they work. Afterward, invite pairs to present their solutions and methods to the class. Compare and contrast the different methods and models, highlighting the connections between them. Work with the students to analyze conflicting answers to determine how and where the mistakes were made (SMP3). Discuss whether the students’ original solution plans worked or had to be adjusted, and if they were adjusted, discuss how. Read the Step Up and Step Ahead instructions with the students. Encourage them to draw tape diagrams to help model each problem. In doing so, they should consider whether the problem involves part-total thinking or equal-groups thinking. Make sure they know what to do, then have them work independently to complete the tasks.”

• Module 9 Lesson 9, Mass: Reviewing pounds and introducing ounces, Lesson overview and focus, Misconceptions, include guidance to address common misconceptions as students work with units of measure. “If students are struggling with units of measure, provide objects and experiences (pouring water, stacking mass pieces in a pan balance) which will give them concrete experiences with benchmark measurements. "How long does it take to fill a 1 quart container at the water fountain?" "How much does a baseball weigh?" This enables number sense about measurements which will help students solve problems accurately.”

##### Indicator {{'3b' | indicatorName}}

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Origo Stepping Stones 2.0 Grade 4 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.

Within Module Resources, Preparing for the module, there are sections entitled “Research into practice” and “Focus” that consistently link research to pedagogy. There are adult-level explanations including examples of the more complex grade-level concepts so that teachers can improve their own knowledge of the subject. Professional articles support teachers with learning opportunities about topics such as ensuring mathematical success for all, early understanding of equality, and repeating patterns. There are also professional learning videos, called MathEd, embedded across the curriculum to support teachers in building their knowledge of key mathematical concepts. Examples include:

• Module 5, Research into Practice, Multiplication, supports teachers with concepts for work beyond the grade. “Work in this module on multiplicative comparison sets the stage for future work with unit conversion in Grade 5 and equivalent ratios in Grade 6. Unit conversion is an instance of multiplicative comparison (how many times as many inches as feet in a given length, for example) while equivalent ratios are a sequence of multiplicative comparisons. Read more about unit conversions in the Research into Practice sections for Grade 5, Modules 4 and 9. Read more about the ways students understand equivalent ratios in the Research into Practice section for Grade 6 Module 3.”

• Module 6, Preparing for the module, Research into practice, Angles, includes explanations and examples connected to concepts of angles. To learn more includes additional adult-level explanations for teachers. “An angle can be understood in two different ways. In the first way, an angle measures the amount of space based on how far the angle arms are apart from each other. This space is understood as a static shape, and can be visualized as a wedge. In the second conception, an angle measures the amount of turn, or rotation that occurs as the rays move apart from each other. This conception is dynamic in that it focuses on the action of the angle arms moving apart. In this module, students focus on the dynamic, or turning, interpretation of angle, learning to focus their attention on how the opening changes and measuring it using familiar concepts such as quarter and half turns.” To learn more, “Browning, Christine, Gina Garza-Kling, and Elizabeth Hill Sundling. 2007. “What's Your Angle on Angles?” Teaching Children Mathematics 14 (5): 283–87.”

• Module 7, Preparing for the module, Research in practice, Division, supports teachers with concepts for work beyond the grade. “Learning about reminders prepares students to expand the range of values they consider in division and allows them to explore situations where the solution is not a whole number value. This prepares students for dividing fractions and decimals in Grades 5 and 6. It is important to emphasize the meaning of the remainder, particularly when it represents a partial group, to prepare students for dividing fractions in Grade 6. Read more about the development of fraction division in the Research into Practice sections for Grade 5 Module 6 and Grade 6 Module 5.”

• Module 9, Preparing for the module, Research into practice, Measurement, includes explanations and examples connected to the magnitude of various measurement units. To learn more includes additional adult-level explanations for teachers. “It is essential that students develop a sense of the magnitude of various units of measure. Students should be comfortable with the fact that a typical slice of bread weighs about 1 ounce while a baseball weighs about 1 pound. As students think about measuring the same object with different units, they use their multiplicative reasoning skills to understand that the baseball would weigh about 16 ounces since it weighs about 1 pound. The slice of bread would weigh a small fraction of a pound. Working with different units of measure is another example of composing and decomposing. When counting in 1 ounce increments, every 16 counts represents another pound of mass. As students work with measurement units, they also develop a deeper understanding of the operations. Addition and subtraction become tools for comparing measurements (how much more or how much less). Multiplication (how many times as many or as much) becomes the beginning of proportional reasoning, an essential concept developed in the middle grades. Multiplication and fractions both support reasoning about the relative size of different units.” To learn more, “Lehrer, Richard and Hannah Slovin. 2014. Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Grades 3-5. Reston, VA: National Council of Teachers of Mathematics.”

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series and can be found in several places, including the curriculum front matter and program overview, module overview and resources, and within each lesson. Examples include:

• Front Matter, Grade 4 and the CCSS by Lesson includes a table with each grade level lesson (in columns) and aligned grade level standards (in rows). Teachers can search any lesson for the grade and identify the standard(s) that are addressed within.

• Front Matter, Grade 4 and the Common Core Standards, includes all Grade 4 standards and the modules and lessons each standard appears in. Teachers can search a standard for the grade and identify the lesson(s) where it appears within materials.

• Module 10, Module Overview Resources, Lesson Content and Learning Targets, outlines standards, learning targets and the lesson where they appear. This is present for all modules and allows teachers to identify targeted standards for any lesson.

• Module 4, Lesson 1, Subtraction: Making estimates, the Core Standards are identified as 4.OA.A.3 and 4.NBT.A.3. The Prior Learning Standard is identified 3.NBT.A.2. Lessons contain a consistent structure that includes Lesson Focus, Topic progression, Formative assessment opportunity, Misconceptions, Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, and Maintaining concepts and skills. This provides an additional place to reference standards, and language of the standard, within each lesson.

Each module includes a Mathematics Overview that includes content standards addressed within the module as well as a narrative outlining relevant prior and future content connections. Each lesson includes a Topic Progression that also includes relevant prior and future learning connections. Examples include:

• Module 4, Mathematics Overview, Number and Operations in Base Ten, includes an overview of how the math of this module builds from previous work in math. “The first section of this module focuses on using the standard subtraction algorithm with multi-digit numbers. This includes reinforcing the importance of estimation when subtracting multi-digit numbers. Lesson 2 reviews the standard algorithm as studied in Grade 3, decomposing tens or hundreds. The standard algorithm is developed for three-digit numbers with decomposing in any place (regrouping does not extend across a place with a zero). The algorithm is then extended to multi-digit numbers, but does not involve regrouping across a place with a zero, although zeros are included in some numbers.”

• Module 10, Mathematics Overview, Coherence, includes an overview of how the content in fourth grade connects to mathematics students will learn in fifth grade. “Lessons 10.1–10.12 focus on work with common fractions with denominators that are 10 or 100, and reading, writing, comparing, and ordering decimal fractions, as well as, relating common fractions and decimal fractions to carry out addition. This work builds on experiences with identifying common and equivalent fractions less than and greater than one (3.8.6–3.8.9) and serves as a foundation for using addition and subtraction with decimal fractions (5.5.1–5.5.9).”

• Module 5, Lesson 7, Length: Introducing millimeters, Topic progression, “Prior learning: In Lesson 4.5.6, students consider what the numbers and markings represent on tools that measure unit of length. They express measured lengths in both meters and centimeters, and use abbreviations. 4.MD.A.1; Current focus: In this lesson, students learn about the need for a unit of length that is shorter than a centimeter. They use a metric ruler to measure short lengths in centimeters and millimeters. Students then use the relationship between millimeters and centimeters to convert units. 4.MD.A.1; Future learning: In Lesson 4.5.8, students explore the relationship between meters, decimeters, centimeters, and millimeters. Students use the times 10, and divide by 10 pattern to convert between metric units of length. 4.MD.A.1, 4.MD.A.2.” Each lesson provides a correlation to standards and a chart relating the target standard(s) to prior learning and future learning.

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Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provides strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

ORIGO ONE includes 1-minute videos, in English and Spanish that can be shared with stakeholders. They outline big ideas for important math concepts within each grade. Each module also has a corresponding Newsletter, available in English and Spanish, that provides a variety of supports for families, including the core focus for each module, ideas for practice at home, key glossary terms, and helpful videos. Newsletter examples include:

• Module 2, Resources, Preparing for the module, Newsletter, Core Focus, “Addition: Making estimates, Addition: Using the standard algorithm, Multiplication: Extending the fives and nines facts. Estimates - Strategies for adding numbers mentally are important for real-life situations. Students use strategies based on place value to estimate addition totals. Students estimate purchase prices then calculate exact solutions using composing strategies to relate classroom mathematics to real-world uses. Standard algorithm - The standard addition algorithm is the familiar paper-and-pencil procedure for adding multi-digit numbers that most adults were taught in school. What was called carrying is now called regrouping because numbers are regrouped into new place values in order to combine the quantities. Multiplication - Students extend the fives and nines strategies, which are related to multiplying by 10.”

• Module 5, Resources, Preparing for the module, Newsletter, Ideas for Home, “When doubling or tripling a recipe, use multiplicative comparison language: “We need two times as much rice as the recipe calls for, so how much rice is that?” Take turns estimating small lengths or short distances, and then use a meter stick or metric tape measure to check your estimates. Notice together how ×10 and ÷10 work in the metric system. Think of a measure in one metric unit (3 m 23 cm) and practice figuring out what that measure would be in other units (3 m + 23 cm = 323 cm = 3,230 mm; 6 km + 8 m = 6,008 m = 600,800 cm). If you are not familiar with the metric system, we encourage you to learn about it along with your child by practicing conversions between kilograms and grams, liters and milliliters, and meters and millimeters. Check conversions using an online conversion calculator.”

• Module 9, Resources, Preparing for the module, Newsletter, Glossary, “Equivalent fractions are fractions that cover the same amount of area on a shape, or are located on the same point on a number line.” Module 9, Newsletter, Helpful videos, “View these short one-minute videos to see these ideas in action. go.origo.app/j5q8k. go.origo.app/ff ttu.”

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Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Instructional approaches of the program are described within the Pedagogy section of the Program Overview at each grade. Examples include:

• Program Overview, Pedagogy, The Stepping Stones approach to teaching concepts includes the mission of the program as well as a description of the core beliefs. “Mathematics involves the use of symbols, and a major goal of a program is to prepare students to read, write, and interpret these symbols. ORIGO Stepping Stones introduces symbols gradually after students have had many meaningful experiences with models ranging from real objects, classroom materials and 2D pictures, as shown on the left side of the diagram below. Symbols are also abstract representations of verbal words, so students move through distinct language stages (see right side of diagram), which are described in further detail below. The emphasis of both material and language development summarizes ORIGO's unique, holistic approach to concept development. A description of each language stage is provided in the next section. This approach serves to build a deeper understanding of the concepts underlying abstract symbols. In this way, Stepping Stones better equips students with the confidence and ability to apply mathematics in new and unfamiliar situations.”

• Program Overview, Pedagogy, The Stepping Stones approach to teaching skills helps to outline how to teach a lesson. “In Stepping Stones, students master skills over time as they engage in four distinctly different types of activities. 1. Introduce. In the first stage, students are introduced to the skill using contextual situations, concrete materials, and pictorial representations to help them make sense of the mathematics. 2. Reinforce. In the second stage, the concept or skill is reinforced through activities or games. This stage provides students with the opportunity to understand the concepts and skills as it connects the concrete and pictorial models of the introductory stage to the abstract symbols of the practice stage. 3. Practice. When students are confident with the concept or skill, they move to the third stage where visual models are no longer used. This stage develops accuracy and speed of recall. Written and oral activities are used to practice the skill to develop fluency. 4. Extend. Finally, as the name suggests, students extend their understanding of the concept or skill in the last stage. For example, the use-tens thinking strategy for multiplication can be extended beyond the number fact range to include computation with greater whole numbers and eventually to decimal fractions.”

• Program Overview, Pedagogy, The Stepping Stones structure outlines the learning experiences. “The scope and sequence of learning experiences carefully focuses on the major clusters in each grade to ensure students gain conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply this knowledge to solve problems inside and outside the mathematics classroom. Mathematics contains many concepts and skills that are closely interconnected. A strong curriculum will carefully build the structure, so that all of the major, supporting, and additional clusters are appropriately addressed and coherently developed. One of the most unique things about ORIGO Stepping Stones is the approach to sequencing content and practice. Stepping Stones uses a spaced teaching and practice approach in which each content area is spaced apart, the key ideas and skills of these topics have been identified and placed in smaller blocks (modules) over time. In the actual lessons, work is included to help students fully comprehend what is taught alongside the other content development. Consequently, when students come to a new topic, it can be easily connected to previous work. For example, within one module students may work on addition, time, and shapes, addressing some of the grade level content for each, and returning to each one later in the year. This allows students to make connections across content and helps students master content and skills with less practice, allowing more time for instruction.”

Research-based strategies within the program are cited and described regularly within each module, within the Research into practice section inside Preparing for the module. Examples of research- based strategies include:

• Module 2, Preparing for the module, Research into practice, “Addition: In Grade 4, students work to master a standard algorithm for addition. This builds from work in previous grades around modeling addition on the number line or with base-10 blocks and now extends to multi-digit numbers and strings of multiple numbers where these physical and visual representations are less practical. Computational estimation is an important part of this process because it provides students with an effective way to check their work. Students use rounding as one method of estimating computational results. Supporting students to see what happens in the standard algorithm, with base-10 blocks or other representations, builds conceptual understanding of the algorithm. Allowing alternate notations can also build confidence and competence as the students see the connections between the symbolic representation and the models they have built in the past. Multiplication: Grade 4 students extend their knowledge of multiplication facts to use the same principles with multi-digit numbers. This is an important structural element of the base-ten place-value system. Problem solving situations allow students to generalize their understanding to work with multi-digit numbers in a practical way. Strategies, such as multiplying by ten and then halving the solution to find the product when multiplied by five, take on new life when students see that they also work with multi-digit numbers. To learn more: Kling, Gina and Jennifer M. Bay-Williams. 2015. “Three Steps to Mastering Multiplication Facts.” Teaching Children Mathematics 21(9): 548-559. O’Connell, Susan and John SanGiovanni. 2014. Mastering the Basic Math Facts in Multiplication and Division. Portsmouth, NH: Heinemann. Problem Solvers: Problem 2015. “Eggsactly How Many?” Teaching Children Mathematics 21 (9): 521-523. References: Fuson, Karen C. and Sybilla Beckmann. 2012. “Standard algorithms in the Common Core State Standards.” National Council of Supervisors of Mathematics Journal of Mathematics Education Leadership 14(2): 14-20. Lefevre, Jo-Anne, Stephanie L Greenham, and Nausheen Waheed. 1993. “The Development of Procedural and Conceptual Knowledge in Computational Estimation.” Cognition and Instruction 11(2): 95-132.”

• Module 9, Preparing for the module, Research into practice, “Common fractions: As students consolidate their understanding of fraction comparison, they bring together a number of strategies. Common numerators, common denominators, and referencing benchmark fractions are all effective strategies for comparing fractions. The number line is an effective tool for illustrating fraction comparisons, in part because it provides a strong foundation for understanding the magnitude of fractions and their relative value when based on the same whole. Strategies for finding common denominators (or common numerators) become important as students compare fractions when a known strategy will not work at first sight. Measurement: It is essential that students develop a sense of the magnitude of various units of measure. Students should be comfortable with the fact that a typical slice of bread weighs about 1 ounce while a baseball weighs about 1 pound. As students think about measuring the same object with different units, they use their multiplicative reasoning skills to understand that the baseball would weigh about 16 ounces since it weighs about 1 pound. The slice of bread would weigh a small fraction of a pound. Working with different units of measure is another example of composing and decomposing. When counting in 1 ounce increments, every 16 counts represents another pound of mass. As students work with measurement units, they also develop deeper understanding of the operations. Addition and subtraction become tools for comparing measurements (how much more or how much less). Multiplication (how many times as many or as much) becomes the beginning of proportional reasoning, an essential concept developed in the middle grades. Multiplication and fractions both support reasoning about the relative size of different units. To learn more: Bray, Wendy S., and Laura Abreu-Sanchez. 2010. “Using Number Sense to Compare Fractions: Reflect and Discuss.” Teaching Children Mathematics 17 (2): 90–97. Freeman, Daniel W. and Theresa A. Jorgensen. 2015. “Moving Beyond Brownies and Pizza.” Teaching Children Mathematics 21 (7): 412–20. Lehrer, Richard and Hannah Slovin. 2014. Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Grades 3-5. Reston, VA: National Council of Teachers of Mathematics. References: National Research Council. 2001. Adding It Up: Helping Children Learn Mathematics. Jeremy Kilpatrick, Jane Swafford, and Bradford Findell (eds.). Washington, D.C.: National Academy Press.”

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Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. In the Program Overview, Program components, Preparing for the module, “Resource overview - provides a comprehensive view of the materials used within the module to assist with planning and preparation.” Each module includes a Resource overview to outline supplies needed for each lesson within the module. Additionally, specific lessons include notes about supplies needed to support instructional activities, often within Step 1 Preparing the lesson. Examples include:

• Module 2, Preparing for the module, According to the Resource overview, teachers need, “base-10 blocks (hundreds, tens, and ones) in lessons 2 and 3, base-10 blocks (thousands, hundreds, tens, and ones) in lessons 4, 5, and 6, scissors and Support 16 in lesson 11. Each pair of students needs base-10 blocks (hundreds, tens, and ones) in lessons 3 and 8, cube labeled: 15, 18, 24, 28, 34, 35 in lesson 10, a cube labeled: 90, 150, 160, 180, 210, 240 in lesson 8, a cube labeled: 5, 5, 5, 10, 10, 10 in lesson 10, a cube labeled: 1, 2, 3, 4, 5, 6 and a cube labeled: 7, 7, 8, 8, 9, 9 in lesson 9, a cube labeled: halve, halve halve, double, double, double in lesson 8, paper and Support 13 in lesson 7, scissors in lesson 11, Support 14 in lesson 9, and Support 15 in lesson 10. Each individual student needs counters in lessons 9 and 10, scissors in lessons 11 and 12, the Student Journal in each lesson, and Support 17 in lessons 11 and 12.”

• Module 2, Lesson 9, Multiplication: Reviewing the fives strategy, Lesson notes, Step 1 Preparing the lesson, “Each pair of students will need: 1 copy of Support 14, 2 cubes labeled: (Note: Retain for Extra Practice.) cube A: 1, 2, 3, 4, 5, 6, cube B: 7, 7, 8, 8, 9, 9. Each student will need: 10 counters (a different color for each student) and Student Journal 2.9.” Step 3 Teaching the lesson, “Organize students into pairs and distribute the resources. Students take turns to roll the cubes, then choose one of the numbers to multiply by 5. A counter is then placed on that square.”

• Module 4, Preparing for the module, According to the Resource overview, teachers need, “base-10 blocks (thousands, hundreds, tens, ones) in lessons 4 and 6, cube labeled: 1, 2, 3, 4, 5, 6 and cube labeled: 4, 5, 6, 7, 8, 9 in lesson 6, and The Number Case in lesson 9. Each group of students needs paper in lesson 6. Each pair of students needs base-10 blocks (hundreds, tens, and ones) in lessons 2 and 3, blank sheet of paper in lesson 7, non- permanent markers in lesson 6, paper in lesson 5, Support 33 in lesson 8, and The Number Case in lesson 6. Each individual student needs adhesive tape or glue, a ruler, several strips of paper and construction paper in lesson 9, paper in lessons 2, the Student Journal in each lesson, and Support 32 in lesson 5.”

• Module 4, Lesson 4, Subtraction: Reviewing the standard algorithm (decomposing tens or hundreds), Lesson notes, Step 1 Preparing the lesson, “Each pair of students will need: base-10 blocks (hundreds, tens, and ones); Each student will need: Student Journal 4.2.”

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This is not an assessed indicator in Mathematics.

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This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations for Assessment. The materials identify the standards, but do not identify the mathematical practices assessed for the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for follow-up. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

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Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

While Check-ups, Quarterly tests, Performance tasks, and Interviews consistently and accurately identify grade level content standards within each Module assessment overview, mathematical practices are not identified. Examples from formal assessments include:

• Module 2, Preparing for the module, Module assessment overview, Check-up 1, denotes standards addressed for each question. Question 1, 4.OA.3, “Color the bubble beside the closest estimate of each total. a. 957 + 468. ___less than 1,300, ___ less than 1,500, ___ greater than 1,600. b. 723 + 286. ___ less than 900, ___ about 1,000, ___ about 1,200.”

• Module 6, Assessment, Quarterly test, Test A, denotes standards for each question. Question 9, 4.NBT.4, “Use the standard subtraction algorithm to calculate the difference between 8,786 and 85,097.”

• Module 8, Preparing for the module, Module assessment overview, Interview, denotes standards addressed. 4.NBT.6, “Steps: Write 39 \div 3 and say, I can break this number into parts that are easier to divide. Rewrite the number sentence as 30 \div 3 = ___ plus 9 \div 3 = ___. Discuss how to add the answers to solve 393. Ask students to use the same method to solve the following: 48 \div 4 = ___, 70 \div 5 = ___, 162 \div 6 = ___, 1,052 \div 4 = ___. Draw a ✔ beside the learning the student has successfully demonstrated.“

• Module 10, Preparing for the module, Module assessment overview, Performance task denotes the aligned grade level standard. 4.NF.5, “Figure out each total. Show your thinking. a. 0.4 + 0.5 = ___, b. 3.2 + 0.4 = ___, c. 2.35 + 3.12 = ___, d. 2.03 + 0.04 = ___, e. 0.6 + 0.02 = ___, f. 4.05 + 0.3 = ___.”

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Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meets expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Summative Assessments, such as Check-ups and Quarterly tests, provide an answer key with aligned standards. Performance Tasks include an answer key and a 2-point rubric, which provides examples of student responses and how they would score on the rubric. A student achievement recording spreadsheet for each module learning target is available that includes: Individual Achievement of Learning Targets for this Module, Whole Class Achievement of Learning Targets for this Module and Individual Achievement of Learning Targets for Modules 1 to 12. While some scoring guidance is included within the materials, there is no guidance for teachers to interpret student performance or suggestions for teachers that could guide follow-up support for students. Examples from the assessment system include:

• Module 2, Assessments, Check-up 2, Question 3, “Complete each equation. Show your thinking. a. 9 \times 35 =___ . Answer: 315. b. 39 \times 4 = ___. Answer. 156.” The answer key aligns this question to  4.NBT.5.

• Module 6, Assessments, Quarterly test B, Question 12, “Write the number that makes this equation true. Use the number line to show your thinking. 1\frac{5}{8} = \frac{}{8}.” The answer key shows the answer as \frac{13}{8} and aligned to 4.NF.1.

• Module 9, Assessments, Performance task, students reason with fractions to solve word problems. Question 3, “Jessica eats \frac{2}{4} of the Gooey Chewy bar. Caleb eats \frac{3}{4} of the Crunchy Munchy bar. Jessica knows that \frac{3}{4} is more than \frac{2}{4} so she says Caleb has eaten more than she has. Caleb thinks he has eaten less than Jessica. Who is correct? Explain your answer.” The Scoring Rubric and Examples state, “2 Meets requirements. Shows complete understanding. The answer for Question 3 made some reference to the size of the whole being different and identified Caleb as correct. 1 Partially meets requirements. Answered Question 3 and showed some correct reasoning about fractions but did not refer to the sizes of the wholes being different. Caleb may have not been identified as being correct. 0 Does not meet requirements. Shows no understanding.”

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Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative Assessments include Pre-test, Observations and discussions, and Journals and Portfolios. Summative Assessments include Check-ups, Interviews, Performance tasks, and Quarterly tests. All assessments regularly demonstrate the full intent of grade level content and practice standards through a variety of item types: multiple choice, short answer, and constructed response. Examples include:

• Module 2, Check-up 1 and Performance task and Module 4, Performance task, develop the full intent of standard 4.NBT.4, fluently add and subtract multi-digit whole numbers using the standard algorithm. Check-up, Question 2, “Use the standard algorithm to calculate the totals. a. 25714 + 3205; b. 57023 + 27894.” Performance task, Question 2, ”A student made a mistake when using the standard addition algorithm. Describe the error. 3621 + 2835 = [5] [14] [5] [6]” Module 4, Performance task, Question 1, “Use the standard subtraction algorithm to calculate the difference between each pair of numbers. a. 8.756 and 3,621; b. 67,384 and 4,313.” Question 2, “A student made a mistake when using the standard subtraction algorithm. Describe what they did wrong. 47602 - 31281 = 16421.”

• Module 6, Quarterly test questions support the full intent of MP4, model with mathematics, as students use a tape diagram to represent multiplication and division. Question 1, “Nicole has 42 game tokens. She has 6 times as many as Dixon (D). How many tokens does Dixon have? Choose the equation that would not help you solve this problem. A. D \times 6 = 42, B. 42 \div 6 = D, C. 6 \times D = 42 D. D \div 6 = 42.”

• Module 10, Interview 1 and Check-up 2, develop the full intent of 4.NF.6, use decimal notation for fractions with denominators 10 or 100. Interview 1, “Steps: Display the number line. Draw an arrow toward one of the increments between 3 and 4. Ask, What number would be here? How did you figure that out? Repeat with an arrow at a position between an adjacent pair of increments. Make sure the arrows are not close to one another. Repeat with one other arrow. Indicate two of the arrows on the number line and say, Write a number that is between these two numbers. Show me where it is on the number line. Repeat with another pair of arrows. Ensure the student does not choose a number that only involves ones and tenths. Draw a ✔ beside the learning the student has successfully demonstrated.” Check-up 2, Question 1, “Write the common friction. a. 0.8 = ___   b. 0.50 = ___.”

• Module 12, Quarterly test B questions support the full intent of MP6, attend to precision, as students add numbers written in decimal form. Question 12, “Complete the equation. Show your thinking. 0.31 + 0.5 = ___.” Question 13, “Complete the equation. Show your thinking. 1.08 + 2.49 = ___.”

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Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Origo Stepping Stones 2.0 Grade 4 provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. According to the Program overview, Grade assessment overview, “ORIGO Stepping Stones 2.0 provides online student assessments for each instructional quarter, Grades 1–5. Each assessment offers a variety of technology-enhanced item types, such as open-response visual displays, to monitor and guide achievement.” In addition to technology- enhanced items, the online assessments include the ability to flag items, magnify the screen, and utilize a screen reader for text to speech. The digital assessments are authored through Learnosity and the screen readers are an add-on feature, housed outside of the Origo platform.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics, multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity, and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. In each Module Lesson, Differentiation notes, there is a document titled Extra help, Extra practice, and Extra challenge that provides accommodations for an activity of the lesson. For example, the components of Module 5, Lesson 9, Length: Introduction kilometers, include:

• Extra help, “Activity: Invite a student to write digits in each place on the expander and share their length with the class. Repeat as time allows. As students gain confidence have them close the expander and read the length.”

• Extra practice, “Activity: Organize students into pairs and distribute the cards. Have one student write a length in kilometers (for example, 3 km) on a card. The other student then writes the equivalent length in meters (for example, 3,000 m) on another card. After five rounds, students alternate roles and repeat the activity until all their cards are used. The cards can then be used to play mix-and-match games. (Note: Collect and retain the cards for use in the differentiation activity for Lesson 5.12.)”

• Extra challenge, “Activity: Organize students into pairs and distribute the cards. Have one student write a length including tenths of a kilometer (for example, 3\frac{6}{10} km) on a card. Another student then writes the equivalent length in meters (for example, 3,600 m) on another card. After five rounds, students alternate roles and repeat the activity until all their cards are used. The cards can then be used to play mix-and-match games. (Note: Collect and retain the cards for use in the differentiation activity for Lesson 5.12.)”

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Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

While there are no instances where advanced students do more assignments than classmates, materials do provide multiple opportunities to investigate the grade-level content at a higher level of complexity. The Lesson Differentiation in each lesson includes a differentiation plan with an extra challenge. Each extra challenge is unique to an activity completed in class. Examples include:

• Module 2, Lesson 1, Addition: Making estimates, Differentiation, Extra Challenge, “Organize students into pairs. Project the four cars (slide 1). Inform the students that you will write a number above each car that tells the number of cars of that color in the sales lot and they will have 15 seconds to consider the numbers, then write their estimate of the total number of cars. (Note: This amount of time can be increased or decreased to suit the students.) Write three three-digit numbers and one four-digit number. Students then show their estimates to their partner and work together to calculate the exact total. The difference between each student's estimate and the exact total is the number of points that they receive. The student with fewer points after five rounds wins.”

• Module 5, Lesson 4, Multiplication: Making comparisons involving division and subtraction (tape diagram), Differentiation, Extra Challenge, “Have students write comparison problems that involve division or subtraction. The examples should be similar to those on page 167 of Student Journal 5.4. The problems can then be exchanged and completed.”

• Module 10, Lesson 10, Decimal fractions: Adding hundredths, Differentiation, Extra Challenge, “Distribute the resources. Have students cut out various food items showing prices from the food catalog and place them faceup on the table. Then have them cut out the wallets and place those facedown in a pile. Students then turn over one wallet. They race to see who can collect food items to meet the approximate amount the wallet allows without going over the amount. After students have selected items, they add up the amounts. The student whose total is closest to the wallet amount will win the wallet and receive a point. If a student goes over the wallet value, they lose a turn in the next round. Students repeat the activity until all the wallets have been collected. The student with the most points at the end wins.”

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Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provide various approaches to learning tasks over time and variety in how students are expected to demonstrate their learning, but do not provide opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways: Student Journal Steps, Investigations, Problem-solving Activities, Step It Up 2.0, and within Thinking Tasks, a key component for the program. According to the Program Overview, “ORIGO Thinking Tasks break this mold by presenting students with rigorous, problem-solving opportunities. These problems may become messy and involve multiple entry points as students carve out a solution path. By placing emphasis on the complexity of problem solving, we strive to create a culture for all learners that engages and inspires while developing their confidence and perseverance in the face of challenging problems.” Examples of varied approaches include:

• Module 1, Lesson 6, Number: Locating six-digit numbers on a number line, Student Journal, page 20, Step Up, students connect numbers to their positions on a number line. Question 1 states, “Draw a line to connect each number to its position on the number line. 403,000, 405,000, 408,000, 409,000, 411,000, 412,000, 415,000, 417,000.”

• Step It Up Practice, Grade 4, Module 3, Resources, Lesson 5, Number: Building a picture of one million, Question 1, students use estimation strategies and place value understanding when thinking about the most accurate distance. “Color the bubble for the answer that makes sense. a. The distance from New York to Miami is about … bubble 1,000,000 miles, bubble 100,000 miles, bubble 1,000 miles.”

• Module 6, More Math, Thinking Tasks, Question 1, students use multiplication strategies to compare two amounts. “Use the information from the State Capital Field Trip Plan to solve. Compare the amount that the adults and students pay to go on the field trip. Describe the relationship between the two amounts. Show your thinking.”

• Module 11, More Math, Investigation 2, students use different strategies to multiply two digit by two digit numbers. The materials state, “What different strategies could be used to multiply 35 by 18? Project slide 1 and read the investigation question. Organize students into small groups and have them work together to complete the task. Encourage the students to think of all the different multiplication strategies they have learned and investigate different ways to do the calculation.”

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provide opportunities for teachers to use a variety of grouping strategies.

Suggested grouping strategies are consistently present within lesson notes and include guidance for whole group, small group, pairs, or individual activities. Examples include:

• Module 1, Lesson 4, Number: Reading and writing six-digit numbers (with teens and zeros), Step 3 Teaching the lesson, “Organize students into small groups and distribute the resources. Direct the students to assign each task to a person. Project the Step In discussion from Student Journal 1.4 and work through the questions with the whole class.”

• Module 6, Lesson 5, Multiplication: Solving word problems, Step 2 Starting the lesson, “Project slide 1. Organize students into groups and assign one equation to each group. Challenge each group to calculate the answer then write a word problem to match their equation.” Step 3 Teaching the lesson, “have the students work in their pairs to create a solution plan, then solve the problem. Project the Step In discussion from Student Journal 6.5 and work through the questions with the whole class.“

• Module 11, Lesson 5, Multiplication: Using the associative property with two two-digit numbers (double and halve), Step 1 Preparing the lesson, “Each pair of students will need: several copies of Support 58, scissors, adhesive tape, 1 ruler. Each student will need: Student Journal 11.5.” Step 3 Teaching the lesson, “Organize students into pairs and distribute the resources. Project the Step In discussion from Student Journal 11.5 and work through the questions with the whole class.”

##### Indicator {{'3q' | indicatorName}}

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Although strategies are not provided to differentiate for the levels of student language development, all materials are available in Spanish. Guidance is consistently provided for teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards.  According to the Mathematics Overview, English Language Learners, “The Stepping Stones program provides a language-rich curriculum where English Language Learners (ELL) can acquire mathematics in a natural second-language progression by listening, speaking, reading, and writing. Each lesson includes accommodations to be aware of when teaching the lesson to ensure scaffolding of content and misconceptions of language are addressed. Since there may be several stages of language development in your classroom, you will need to use your professional judgement to select which accommodations are best suited to each learner.” Examples include:

• Module 3, Lesson 4, Number: Rounding four-, five-, and six-digit numbers, Lesson notes, Step 2 Starting the lesson, “ELL: Pair the students with fluent English-speaking students. Encourage them to think aloud as they find the missing answers. Encourage the students to listen to the answers given and then say if they agree or disagree and why.” Step 3 Teaching the lesson, “ELL: Provide time for the students to process the questions, formulate an answer, then speak about their thoughts to another student before presenting their ideas to the class. Pair the students with fluent English-speaking students. During the activity, have students discuss the concepts in their pairs, as well as repeat the other student’s thinking. Allow the students to work in their pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Allow pairs of students to discuss their thinking for the question, Can you think of other occasions when rounding to estimate may be useful? Then, give them an opportunity to explain their thinking to the class.”

• Module 9, Lesson 9, Mass: Reviewing pounds and introducing ounces, Lesson notes, Step 2 Starting the lesson, “ELL: Say the words mass, weight, and pound slowly and clearly. Invite the students to read each word with you one or two times. Ensure students understand the difference between the words weight as in mass, and wait as in being patient; and the difference between mass as in weight, and mass as in a religious event.” Step 3 Teaching the lesson, “ELL: Pair the students with fluent English-speaking students to discuss the concepts, as well as repeating the other student’s thinking. Say the word ounce slowly and clearly. Invite the students to read each word with you one or two times. Encourage them to explain what they are learning to check that they understand the concept. When the students are holding the mass pieces, ensure they make the connection between the physical objects and the word weight associated with the mass.” Step 4 Reflecting on the work, “ELL: Allow pairs to discuss their response to the questions, What is heavier, a pound or a kilogram? An ounce or a gram? Invite them to explain their thoughts to the class.”

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provide a balance of images or information about people, representing various demographic and physical characteristics.

The characters in the student journal represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Names include multi-cultural references such as Fatima, Jie, Hiro, and Anoki and problem settings vary from rural, to urban, and international locations. Each module provides Cross-curricula links or Enrichment activities that provide students with opportunities to explore various demographics, roles, and/or mathematical contexts.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

While there are supports in place to help students who read, write, and/or speak in a language other than English, there is no evidence of intentionally promoting home language and knowledge. Home language is not specifically identified as an asset to engage students in the content nor is it purposefully connected within mathematical contexts.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for ORIGO Stepping Stones 2.0, Grade 4 provide some guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Spanish materials are consistently accessible for a variety of stakeholders, including ORIGO ONE Videos, the Student Journals, the glossary, and the Newsletters for families.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provide some supports for different reading levels to ensure accessibility for students.

Each module provides support specific to vocabulary development, called ‘Building vocabulary’. Each Building vocabulary activity provides: “Vocabulary term, Write it in your own words, and Show what it means”. While the Lesson overview, Misconceptions, and Steps within each lesson may include suggestions to scaffold vocabulary or concepts to support access to the mathematics, these do not directly address accessibility for different student reading levels. Examples of vocabulary supports include:

• Module 1, Lesson 1, Number: Reading and writing five-digit numbers, Lesson overview and focus, Misconceptions, “Some students may incorrectly insert the word and when reading a number aloud or writing it in word form. This frequently happens between the hundreds and tens digits. For example, students might read 37,512 as "Thirty-seven thousand, five hundred and twelve." In mathematics, we use the word and as a separator dividing the whole number portion of a number from the fractional part. Typically, this means we use the word and only when we see a decimal point in a number.”

• Module 2, Lesson 7, Addition: Solving word problems, Step 3 Teaching the lesson, “The word problems can be exchanged among the students and the support page completed. The problems are then returned to the original authors, who check the solutions for accuracy. Select various pairs to present their word problems and solutions (SMP1, SMP2, and SMP4).”

• Module 7, Lesson 11, Common fractions: Solving word problems, Lesson overview and focus, Misconceptions, “If students struggle to solve word problems with fractions, it may help to encourage them to say the problem with whole numbers. This can help students identify the underlying structure and decide what to do to solve the problem. Then students can use those steps with the fractions given in the problem to find the solution.”

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 meet expectations for providing  manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials consistently include suggestions and/or links, within the lesson notes, for virtual and physical manipulatives that support the understanding of grade level math concepts. Examples include:

• Module 2, Lesson 3, Addition: Reviewing the standard algorithm (composing hundreds), Step 2 Starting the lesson, references an online game to support two and three digit addition strategies. “To review two- and three-digit addition strategies, organize the class into two groups and project the online Fundamentals game Jump On for students to play as a class. Discuss mental strategies with students to compose tens as required while they play (SMP8).”

• Module 6, Lesson 9, Angles: Identifying fractions of a full turn, Step 3 Teaching the lesson, references a “tester” as a strategy to support students when measuring angles. “Distribute copies of the support page and have the students cut out the top tester. Work through the instructions beside the tester on the support page to demonstrate how to fold it into a fan-like object. Demonstrate how the tester can be used to measure a wide range of angles and emphasize that the unit of measure is based on one-eighth of a full turn.”

• Module 10, Lesson 8, Decimal fractions: Comparing and ordering, Step 3 Teaching the lesson, references a handout, colored pencils and scissors to support comparing and ordering decimal fractions. “Organize students into five small groups. Distribute the resources and project slide 4. Assign each group one number and have them work together to represent their number on the page. Afterward, the page is cut into strips along the dotted lines.”

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 integrate some technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 integrate some technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable. Examples include:

• While all components of the materials can be accessed digitally, some are only accessible digitally, such as the Interactive Student Journal, Fundamentals Games and Flare Online Tools.

• ORIGO ONE videos describe the big math ideas across grade level lessons in one minute clips. There is a link for each video that makes them easy to share with various stakeholders.

• Every lesson includes an interactive Student Journal, with access to virtual manipulatives and text and draw tools, that allow students to show work virtually. It includes the Step In, Step Up, Step Ahead, and Maintaining Concepts and Skills activities, some of which are auto-scored, others are teacher graded.

• The digital materials do not allow for customizing or editing existing lessons for local use, but teachers can upload assignments or lessons from the platform.

• Digital Student Assessments allow for Progress Monitoring. Teachers can enter performance data and then monitor student progress for individual students and/or the class.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

While teacher implementation guidance is included for Fundamentals games and Flare online tools, there is no platform where teachers and students collaborate with each other. There is an opportunity for teachers to send feedback to students through graded assignments.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provide a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within modules and lessons that supports student understanding of the mathematics. Examples include:

• Each lesson follows a common format with the following components: Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, Maintaining Concepts and Skills, Lesson focus, Topic progression, Observations and discussions, Journals and portfolios, and Misconceptions. The layout for each lesson is user-friendly as each component is included in order from top to bottom on the page.

• The font size, amount and placement of directions, and print within student materials is appropriate.

• The digital format is easy to navigate and engaging. There is ample space in the Student Journal and Assessments for students to capture calculations and write answers.

• The ORIGO ONE videos are engaging and designed to create light bulb moments for key math ideas. They are one minute in length so students can engage without being distracted from the math concept being presented.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Program Overview includes a description of embedded tools, how they should be incorporated, and when they can be accessed to enhance student understanding. Examples include:

• Program Overview, Additional practice tools, “This icon shows when Fundamentals games are required.” Lessons provide this icon to show when and where games are utilized within lesson notes.

• Program Overview, Additional practice tools, “This icon shows when Flare tools are required.” Lessons provide this icon to show when and where these tools are utilized within lesson notes.

## Report Overview

### Summary of Alignment & Usability for ORIGO Stepping Stones 2.0 | Math

#### Math K-2

The materials reviewed for Origo Stepping Stones 2.0 Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 1 and 2 meet expectations for Usability, Gateway 3, and the materials reviewed for Origo Stepping Stones 2.0 Kindergarten partially meet expectations for Usability, Gateway 3.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 6-8

The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Origo Stepping Stones 2.0 Grades 3-6 meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

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###### Usability
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