## ORIGO Stepping Stones 2.0

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## Report for 5th Grade

### 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
###### Usability
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 5 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 5 standards include:

• Module 3, Check-Up 2, Question 2, “Color the circle below the greatest number in each group. a. 0.62, 0.6, 0.607. b. 0.317, 0.36, 0.321.” (5.NBT.3).

• Module 6 Quarterly Test A, Problem 17, “Package A weighs \frac{3}{12} kilogram, Package B weights 1frac{5}{6} kilograms, and Package C weighs \frac{3}{4} kilograms. What is the total mass of Package A and C? Show your thinking.” (5.NF.2).

• Module 9 Performance Task, Problem 2, “A student thinks that \frac{1}{5} divided by 6 is equivalent to \frac{1}{5} ≅ \frac{1}{6}. Are they correct? Draw a picture or write sentences to explain your answer.” (5.NF.3 and 5.NF.7).

There are some assessment items that align to standards above Grade 5; however, they can be modified or omitted without impacting the underlying structure of the materials. Examples include:

• Module 12, Performance Task, directions for the assessment state, “Use the standard algorithm to calculate the quotient” (6.NS.3).

• Module 12, Quarterly Tests A and Test B, Problems 10, 11, and 12, the directions state, “Use the standard algorithm to divide” (6.NS.3).

##### 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 5 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 5th 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 5, students engage with all CCSS standards. Examples of extensive work from the grade include:

• Module 5, Lessons 2 and 4 engage students in extensive work with 5.NBT.7 (Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.) as students perform calculations with decimals. In Lesson 2, Decimal fractions: Adding (with composing), Student Journal, Maintaining Concepts and Skills, page 163, Question 2a, “Calculate each total. Draw jumps on the number line to show your thinking. 7.4 + 2.55 =.” In Lesson 4, Decimal fractions: Using the standard algorithm to add more than two addends, Student Journal, Maintaining Concepts and Skills, page 169, Question 2b, “Calculate the total. Show your thinking. $2.50,$3.70.” 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 3, Common fractions: Subtracting (unrelated denominators), engages students with extensive work with 5.NF.2 (Use equivalent fractions as a strategy to add and subtract fractions). In Student Journal, Step up, page 251, Question 3, students subtract common fractions with unrelated denominators. “a. Three-fifths of a field is planted with potatoes. Another second of the field is planted with garlic. Eleven-twelfths of the field is planted in total. What fraction of the field is planted with garlic? b. In a park, \frac{5}{8} of the animals are pigeons and \frac{2}{10} of the animals are squirrels. What fraction of all the animals in the park are not pigeons or squirrels?”

• Module 9, Lesson 11, Length/mass/capacity: Solving word problems (metric units), engages students with extensive work with 5.MD.1 (Convert like measurement units within a given measurement system). In the Student Journal, Step Up, page 359, Question 1, students convert measurement units and solve real-world problems. “a. Sheree pours 2 L of water equally into 10 cups. Each cup can hold 400 mL. There is no water left in the bottle. How much water is in each cup? b. A customer orders 8 bags of rice that each weigh \frac{1}{2} kg, and 12 packets of popcorn that each weigh 150 g. What is the total mass of the order?”

The instructional materials provide opportunities for all students to engage with the full intent of 5th 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 2, Lessons 8-12 engage students with the full intent of 5.MD.5 (Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.) Lesson 9, Volume: Developing a formula, Student Journal, Step Up, page 68, Question 2, “Here are the dimensions of another prism. Length 8 cm Width 3 cm Height 5 cm Write how you can calculate the volume without counting cubes.” Lesson 10, Volume: Finding the dimensions of prisms with a given volume, Student Journal, Step Ahead, page 71, “Prism A is made with inch cubes. It is 4 cubes long, 5 cubes wide, and 2 cubes high. Prism B is made with centimeter cubes. It is 10 cubes long, 2 cubes wide, and 2 cubes high. Which prism has the greater volume? Explain your thinking.” Lesson 12, Volume: Solving real-world problems, Student Journal, Step Up, page 76, Question 1a, “Use the box sizes above. Calculate the total volume that each group of boxes would occupy. Show your thinking. a, 2 large boxes and 3 medium boxes. b. 3 large boxes, 2 medium boxes, 6 small boxes.”

• Module 3, Lessons 1-9 engage students in the full intent of 5.NBT.3 (Read, write, and compare decimals to thousandths.) Lesson 6, Decimal fractions: Recording in expanded form, Student Journal, Step Up, page 96, Question 1a, “Write the missing numbers. 9.164  (___ x 1) + (___ x 0.1) + ( ___x 0.01) + (___ x 0.001)” Question 2, “Write each decimal fraction in expanded form using one of the methods from page 96. a. 6.256 b. 1.907, c. 5.005, d. 1.840.” Lesson 8, Decimal fractions: Comparing and ordering thousandths, Student Journal, Step Up, page 103, Question 2a, “Write each group of fractions in order from least to greatest. Use the number line to help you. 0.505, 0.890, 0.550, 0.915.”

• Module 11, Lesson 3, Algebra: Introducing the coordinate plane, engages students with the full intent of 5.G.1 (Graph points on the coordinate plane to solve real-world and mathematical problems). In the Student Journal, Step In, page 402, students describe points on the coordinate plane. “Imagine you took two number lines and turned one of them 90 degrees so that they intersect at 0. You can identify a point on the horizontal number line, or a point on the vertical number line. You can also identify a point between the two number lines by making a grid. On this grid, the horizontal number line is called the x-axis. The vertical number line is called the y-axis. The origin is where the two number lines intersect. The position of the red point in the grid on the right can be described using coordinates, or an ordered pair. The first number in an ordered pair is the x-coordinate. It tells the distance to move from the origin along the x-axis. The second number is the y-coordinate. It tells the distance to move from the origin along the y-axis. The coordinates of the blue point in the grid are (2, 5). What are the coordinates of the red point?” In Step Ahead, page 403, students solve real-world problems using ordered pairs. “Two teams are trying to find each other’s base in a game. Each team has a map with a coordinate plane on it. Team A has heard that Team B’s base is at a certain position on the map. When added together the coordinates for the base have a total of 7. Write all the possible ordered pairs for Team B’s base.”

• One 5th grade standard, 5.MD.2, 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 measurement in fractions of a unit ($$\frac{1}{2}$$, \frac{1}{4}, \frac{1}{8}). Use operations on fractions for this grade to solve problems involving information presented in line plots) For example, Module 9, Lesson 12, Mass/data: Interpreting a line plot to solve problems, 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}.

#### 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 5 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 5 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 128 out of 156, which is approximately 82%.

• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 116 out of 144, which is approximately 81%.

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 81% 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 5 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 4, Lesson 10, Mass: Converting customary units, Student Journal, Step Up, page 147 connects the supporting work of 5.MD.A (Convert like measurement units within a given measurement system) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths). Students multiply and divide to convert measurements. Question 2a-2c, “Convert pounds to ounces to complete these. Show your thinking. a. 3.5 lb = ___ oz b. 2.75 lb ___ oz c. 4.25 lb ___ oz.”

• Module 5, Lesson 9, Decimal fractions: Subtracting (decomposing multiple places), Student Journal, Step Up, page 183, connects the supporting work of 5.OA.A (Write and interpret numerical expressions) to the major work of 5.NBT.B (Perform operations with multi-digit whole numbers and with decimals to hundredths). Students use operations to solve expressions using parentheses. Question 3a “Solve each problem. Show your thinking. 8\times15.6 + 2.40.”

• Module 8, Lesson 5, Common fractions: Finding a fraction of a whole number symbolically (non-unit fractions), Student Journal, Step Up, page 295, connects the supporting work of 5.OA.1 (Use parenthesis, brackets, or braces in numerical expressions, and evaluate expressions with these symbols) to the major work of 5.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.) Students multiply a whole number and a fraction as they solve problems with grouping symbols. Question 4b, “Solve each problem. Show your thinking. \frac{8}{10}\times(17-2)= __.”

• Module 9, Lesson 7, Common fractions: Solving word problems involving unit fractions, Student Journal, Step Up, page 339, connects the supporting work of 5.OA.2 (Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them) to the major work of 5.NF.7c (Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.) Students solve division word problems involving unit fractions. Question 2, “Write an equation to represent each problem. Use a letter to show the unknown amount. Then calculate the answers. Show your thinking. a. A granola recipe requires \frac{1}{3} of a cup of raisins.  How many batches can be made with 3 cups of raisins? b. Thomas’s shirt costs $8, which is $$\frac{1}{6}$$ of the price of Ruby’s shirt. How much does Ruby’s shirt cost? c. Juan scores 8 goals in \frac{1}{4} hour. Kayla scores 24 in the same time. How many times greater is Kayla’s score than Juan’s score? d. An assembly line produces a new car every 6 minutes. What fraction of an hour is 6 minutes? How many cars are produced in 8 hours?” • Module 9, Lesson 12, Mass/data: Interpreting a line plot to solve problems, Student Journal, Step Up, page 353, connects the supporting work of 5.MD.2 (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}), Use operations on fractions for this grade to solve problems involving information presented in line plots.) to the major work of 5.NF.A (Use equivalent fractions as a strategy to add and subtract fractions.) Students make a line plot and then analyze the data to solve problems using operations with fractions. Question 1, “Draw a dot to represent each mass shown at the bottom of page 352.” A line plot titled “Pumpkins” is labeled with Mass (kg) from 4 to 10 and halves included on the axis and 20 pumpkin measurements provided. Question 3a, “The pumpkins that weigh more than 5\frac{1}{2} kg are put together in a box to sell. What is the total mass of these pumpkins?” ##### 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 5 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 4, Lesson 7, Length: Converting between inches and feet, students use equivalent fractions as a strategy to add and subtract fractions (5.NF.A) and convert like measurement units within a given measurement system (5.MD.A) by measuring different times and comparing them. • In Module 6, Lesson 10 students perform operations with multi-digit whole numbers and with decimals to hundredths (5.NBT.B) and apply and extend previous understandings of multiplication and division (5.NF.B) to multiply and divide fractions by working with decimal remainders. • In Module 11, Lesson 12, Volume: Solving word problems, Student Journal, p. 429 Problem 2c, students understand concepts of volume and relate volume to multiplication and to addition (5.MD.C) and convert like measurement units within a given measurement system, (5.MD.A) by using volume in like measurements to solve real life problems. “Suitcase A is 2.5 feet long, 2 feet wide, and 2 feet high. Suitcase B is 36 inches long, 24 inches wide, and 18 inches high. What is the difference in volume?” ##### 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 5 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 5th 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 5.1.1–5.1.7 focus on reading, writing, comparing, and ordering numbers from six to nine digits, including on a number line and including millions expressed as fractions. This work builds on experiences with six-digit numbers (4.3.1–4.3.4).” • Module 3, Lesson 1, Decimal fractions: Reviewing tenths and hundredths (area model) connects 5.NBT.3 (Read, write, and compare decimals to thousandths) to work from grade 4 (4.NF.7). “In Lesson 4.10.8, students use various strategies and models to compare and order decimal fractions with one or two decimal places (comparison symbols). In this lesson, students use the area model to identify common fractions that can be expressed as tenths and/or hundredths.” • Module 5, Lesson 10, 2D shapes: Identifying parallelograms, Lesson Notes connect 5.G.3 (Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category) and 5.G.4 (Classify two-dimensional figures in a hierarchy based on properties) with work from grade 3 (3.G.1). “In Lesson 3.2.12, students examine shapes whose properties allow them to belong to more than one shape family. Venn diagrams are used to sort shapes. In this lesson, students examine a defining feature of parallelograms.” 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 3, Lesson 11, Decimal fractions: Rounding with unequal decimal places, Lesson Notes connect 5.NBT.4 (Use place value understanding to round decimals to any place) to work in grade 6 (6.NS.5). “In this lesson, students round decimal fractions with up to three decimal places to the nearest whole number and nearest tenth. In Lesson 6.1.2, students explore decimal fractions beyond thousandths.” • Module 7, Lesson 12, Number: Representing whole numbers using exponents, Lesson Notes connect 5.NBT.2 (Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10) to the work of grade 6 (6.NS.5, 6.EE.1). “In this lesson, students use expanded form together with exponents to represent whole numbers. In Lesson 6.1.1, students explore the different ways to represent numbers to one trillion. These representations include number names, numerals, expanded form, and exponents.” • Module 11, Mathematics Overview, Coherence, “Lessons 5.11.1–5.11.6 focus on number patterns and coordinate planes. This work connects to future work of interpreting tables, investigating number patterns and rules, exploring different representations of patterns, identifying independent and dependent variables, and backtracking to solve equations (6.4.8–6.4.12).” ##### 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 5 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 5 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 5 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 5 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 little access to concepts from a number of perspectives or to independently demonstrate conceptual understanding throughout the grade. Domain 5.NBT addresses understanding the place value system and performing operations with multi-digit whole numbers and with decimals to hundredths. Multiple modules explore a variety of real-world applications using a few mathematical representations. Some opportunities exist for students to work with place value that call for conceptual understanding and include the use of some visual representations and different strategies. Examples include: • Module 1, Lesson 5, Number: Reading and writing eight- and nine-digit numbers, Step 2 Starting the lesson, “Project slide 1 and ask, What do you notice about this table? What patterns do you see? Highlight that the places are grouped into threes (millions, thousands, and ones) and that the places within each group repeat in the pattern H, T, O. Project slide 2, and refer to the arrows below the table. Say, Ten is 10 times as many as 1, and one hundred is 10 times as many as 10. What other relationships can you share? Volunteers can draw more arrows to show the relationship between different place values. Say, The size of each place value is ten times as much as the place value just before when we move from right to left in this table. What happens if we move from left to right? Draw arrows in the opposite direction above the table to show that the size of each place value is one-tenth of the size of the place value just before when we move from left to right (MP8).” Step 3 Teaching the lesson “Ask nine volunteers to come to the front and select a counter from the container. Have each student then write their digit in one of the empty places on the expander, as shown. Use paper clips to help fold back each of the place-value names. Then discuss the points below: How do you say the number that is shown on the expander? How do you write the number in words? What numeral could we write to match the number?” (5.NBT.1). • Module 3, Lesson 8, Decimal fractions: Comparing and ordering thousandths, Step 3 Teaching the lesson, “Organize students into two teams. Distribute the decimal fraction cards equally between the two teams. Ask one student from each team to stand and compare their fractions. One point is awarded to the team that holds the greater decimal fraction. Make sure that the students from each team justify their comparisons. If necessary, project slide 3 and compare the position of the two decimal fractions on the number line.” Student Journal, Step Up, Question 1 “Draw an arrow to show the approximate position of each number on the number line.” Question 2 “In each group, circle the greatest fraction.” Question 3 “Write < or > to make each statement true.” Question 4 “Write each group of fractions in order from least to greatest. Use the number line to help you.” Students do not discuss the conceptual understanding that digits to the left are 10 times larger than digits to the right when making their comparisons. (5.NBT.1) Cluster 5.NF uses equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Multiple Modules explore a variety of real-world applications using a few 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 6, Lesson 10, Division: Three- and four-digit dividends and one-digit divisors (with remainders), Step 2 Starting the lesson, “Write the equation 75 ÷ 2 = ___ remainder ___ on the board. Ask, Who can remember working with remainders? How would we solve this problem? What is the remainder? Then write the equation 75 ÷ ___ = 8 remainder 3 on the board. Ask, How could we solve this problem? Invite students to share and explain their thinking. For example, “I start with 75 and subtract the remainder. Then the equation is 72 divided by something is 8. I know 8 times 9 is 72 so the solution is 9.” Step 3 Teaching the lesson, “Project the Step In discussion from Student Journal 6.10 and work through the problems and questions with the whole class. Make sure students comprehend each problem and have them interpret the remainder within each context. Establish that the remainder is disregarded for the roses problem, and it is broken into equal parts to solve the compost problem. Ask, How can we share 4 kilograms of compost equally among 6 trees? Have the students discuss their ideas in their pairs, then invite pairs to share and, if possible, demonstrate their thinking. Refer to the diagram to clarify that each tree is given \frac{1}{6} of each one-kilogram bag. There are four one-kilogram bags, so each tree is given 4 counts of \frac{1}{6}. Say, This means that each tree is given \frac{4}{6} of a kilogram of compost. (5.NF.3). • Module 8, Lesson 3, Common fractions: Finding a fraction of a whole number (unit fractions), Step 3 Teaching the lesson, “Continue the Step 2 discussion. Explain that multiplication can also be used to calculate the answer. Project slide 2, as shown, to show the language of replaced by the multiplication symbol. Then discuss the points below: What turnaround can we write to match this equation? (15 × \frac{1}{5}= __.) How can we calculate the product? How can we prove that the product is equal to 3? What jumps could we make along the number line? Ask a volunteer to come to the front and draw 15 jumps of one-fifth along the number line. Confirm that the final jump points to the position on the number line that shows \frac{15}{5}, which is equivalent to 3. Ask, What is another way to prove that 15 × \frac{1}{5}= 3? Lead a discussion about the different methods. For example, students could draw 15 equivalent shapes, partitioned into fifths, with one-fifth of each shape shaded. Some students may work with the turnaround equation \frac{1}{5} × 15 = 3 and model 15 ÷ 5 with counters. Others may use the distributive property of multiplication to write an equivalent equation \frac{1}{5} × 5 + \frac{1}{5} × 5 + \frac{1}{5} × 5 = 3. Then think \frac{1}{5} × 5 = 1 because 5 ÷ 5 = 1, and 1 + 1 + 1 = 3. Project the equation (slide 3) to repeat the discussion. Establish that this time the final jump extends beyond a whole number and points to the position on the number line that shows \frac{10}{3} or 3\frac{1}{3}. (5.NF.1). 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 9, Lesson 5, Common fractions: Dividing a unit fraction by a whole number pictorially, Step 2 Starting the lesson, “Project slide 1 and read it with the class. Ask, What equation can we write to represent this word problem? Invite responses and write 3 ÷ \frac{1}{2} = S on the board. Ask, How can we use the picture to represent the problem? Work with students to progressively split the pot into 3 equal parts, then split each part in half, as shown. Confirm there will be 6 servings, then have students show how to calculate the answer symbolically, as in previous lessons. Step 3 Teaching the lesson, “​​Project slide 2 and read it with the class. Then discuss the points below: How is this problem different from the previous one? Do you think the quotient will be greater or less than \frac{1}{2}? Why? (Less, because \frac{1}{2} is being split into smaller amounts.) What equation can we write to represent the problem? ($$\frac{1}{2}$$ ÷ 3 = S.)How can we use the picture to represent the problem? (MP4) Explain that the pot holds 1 quart. Work with the students to split the pot in half, then split one-half into three parts, as shown. Discuss how the three parts of \frac{1}{2} results in each part being \frac{1}{3} of \frac{1}{2}. However, the goal is to establish an answer that is a single number (that is, a fraction of a quart) so each part needs to be considered in relation to the whole (1 quart). Continuing to split the whole quart into thirds shows that each friend will get \frac{1}{6} of a quart of soup.” In the Student Journal, students solve 5 problems using bar diagrams which are provided. Since the diagrams are provided and the questions mirror the example, students do not demonstrate conceptual understanding (5.NF.2). • Module 12, Lesson 2, Division: Developing the standard algorithm, Step 3 Teaching the lesson, “Project the completed division equation above the completed division problem using the division bracket (slide 6). Say, Look at these two methods of recording division. What is the same about them? What is different? Encourage students to identify the dividend, divisor, and quotient for each method. Some students may make connections between this division method and the partial-quotients strategy. If so, invite them to explain how they are the same and different. Emphasize that the amount in each share (quotient) is shown above the division bracket.” Students do not have the opportunity to demonstrate conceptual understanding of division and place value. Students are taught the standard algorithm for division (5.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 5 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 5 expected fluencies, 5.NBT.2, multi-digit multiplication. 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. The materials attend to the Grade 5 expected fluencies 5.NBT.5, fluently multiply multi-digit numbers using the standard algorithm. For example, in Module 2, Lessons 2-5 extends knowledge of the standard algorithm for multi-digit multiplication through multi-digit by multi-digit multiplication. Investigations 1, 2, and 3, students build procedural skill and fluency involving multi-digit numbers. Activities 1, 2, and 4, students work with the standard algorithm to multiply multi-digit numbers. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency. Examples include: • “Fundamentals Games” contains a variety of games that students can play to develop grade level fluency skills. For example, Use a Ten Fact (multiplication with two-digit numbers) develops fluency in multi-digit multiplication. • The Stepping Stones 2.0 overview explains that every even numbered lesson includes a section called “Maintaining Concepts and Skills” that incorporates practice of previously learned skills from the prior grade level. In Module 10, Lesson 2, Decimal fractions: Reinforcing strategies for multiplying by a whole number, provides computation practice with multi-digit dividends and one-digit divisors. • Some lessons provide opportunities for students to practice procedural skills during the “Step Up” section of the student journal. • Assessments also give problems that call for fluency and procedural skill. For example, in the Module 2 performance task, students use the standard algorithm to complete multi-digit by multi-digit multiplication. ##### Indicator {{'2c' | indicatorName}} Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step word problems presented in contexts in which mathematics is applied. There are routine problems, and students also have opportunities to engage with non-routine application problems. Thinking Tasks found at the end of Modules 3, 6, 9, and 12, provide students with problem-solving opportunities that are complex and non-routine with multiple entry points. Examples of routine application problems include: • Module 8, Lesson 3, Common fractions: Finding a fraction of a whole number (unit fractions), Student Journal, Step Up, page page 289, Problem 2a, addresses the standard 5.NF.2, “The cost of a hamburger is one-sixth the price of a family meal. What is the cost of one hamburger if the family meal costs$12?”

• Module 4, Lesson 6, Common fractions: Solving word problems, Student Journal, Step Up, page 135, Problem 2d, addresses the standard 5.NF.1, “Lisa has 2 red apples and 2 green apples. She cuts the red apples into fourths, and the green apples into eighths. She eats 2 pieces of red apple and 3 pieces of green apple. Which color of apple has more left over?”

• Module 9, Lesson 11, Length/mass/capacity: Solving word problems (metric units), Student Journal, Step In, page 350, Problem b, addresses the standard 5.MD.3, “Three packages are each filled with 400 g boxes. Each package weighs 2 kg. How many 400g boxes were used?”

• Module 5, Lesson 7, Decimal fractions: Subtracting tenths (decomposing ones), Teaching the lesson, Problem Solving Activity 2, students work in pairs to discuss the problem and addresses the standard 5.NBT.7, “A weather research center records temperatures to the nearest hundredth of a degree (table provided). On which day was the greatest variation in temperature? Show your thinking.”

Examples of non-routine application problems with connections to real-world contexts include:

• Module 3, Lesson 12, Decimal fractions: Interpreting results on a line plot, Teaching the lesson, Thinking Task, Problem 1 asks, “Nancy begins the game by building this tower (students refer to the picture). What is the volume? Show your thinking." This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.

• Module 6, Lesson 12, Division: Three- and four-digit dividends and any two-digit divisor, Teaching the lesson, Thinking Task, Problem 2 asks students, “The Marathon organizers will purchase energy powder. The Leadership Team will prepare a 10 gallon cooler of energy drink for each water stop. One three-pound tub of energy drink powder makes 24 quarts and costs $8.50. How many tubs will they have to buy and how much will it cost?” Students must use the Course Map provided to solve. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts. • Module 9, Lesson 12, Mass/data: Interpreting a line plot to solve problems, Teaching the lesson, Thinking Task, Problem 1 asks, “What is the difference in height between the tree with the greatest growth and the tree with least growth?” Students use a line plot provided to solve the problem. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts. • Module 12, Lesson 12, Division: Calculating unit costs to determine best buys (dollars and cents), Teaching the lesson, Thinking Task, students are given two portable building options with different dimensions (Building A 7m x 5.3m Building B 15m x 9 m). The students must help the school decide which building is the better option for the school to purchase. Problem 1 states, “Calculate the floor area for building A. Show your thinking. Remember to write the unit of measurement.” This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts. ##### 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 5 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 6, Lesson 6, Common fractions: Adding mixed numbers (unrelated denominators), students explain, “Does it make more sense to write the answer in the format of improper fractions or mixed numbers? Why?” • Module, 12, Lesson 2, Division: Developing the standard algorithm, students use the standard algorithm for division. • Module 12, Problem Solving Activity 4, “Three families are vacationing together. They are equally sharing the hotel cost which is$2,634. Thomas’ family is also renting a car for 348. How much will Thomas’ family have to pay for the car rental and hotel together?” Examples of students having opportunities to engage in problems that use two or more aspects of rigor include: • Module 7, Lesson 4, Common fractions: Subtracting mixed numbers (related denominators), Maintaining Concepts and Skills, Words at Work, “Deon bought a bag of apples that weighed more than 3 kilograms but less than 4 kilograms. Monique bought a bag of apples that weighed 7/8 of a kilogram less than Deon’s bag of apples. Hunter bought the same amount of apples as Deon and Monique together. What could be the mass of the apples each person bought?” • Module 2, Problem Solving Activity 2, “Between 1,200 and 1,300 people will attend the Freemont High School graduation. The chairs need to be arranged in a rectangular array and 18 to 23 chairs can fit into a row. How many rows and how many chairs in a row are needed to make sure they have enough chairs for all the people?” • Module 3, Thinking Task, Question 3, “Nancy stacks a total of 160 blocks to build two towers. Tower A is shaped like a cube. Tower B is shaped like a rectangular-based prism. Write the possible dimensions for each tower. Show your thinking" (two different dimension prisms are provided for students to label with length, width, and height). • Module 9, Thinking Task, Question 3, “In order to see which type of tree grew the most over the course of one year the club will combine the growth data of each tree measured. For this item: Solve using the order of operations. Compare the total growth of the four types of trees.” #### 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 5 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 5 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 3, Lesson 9, Decimal fractions: Comparing and ordering with unequal places, Step 2 Starting the Lesson, students make sense of problems that involve comparing decimal fractions and then model their strategies. “Project slide 1. Read the problem aloud and ask, Is it possible for a decimal fraction that has only one decimal place to be greater than a decimal fraction with two decimal places? Encourage students to explain their thinking. Project slide 2 and invite students to shade the squares to support their arguments (MP1). Project slide 3 to repeat the activity. In this problem, the two decimal fractions have an unequal number of places, yet they represent the same number. Again, have the students demonstrate their solutions. However, this time project slide 4 so students can model their solutions on a thousandths square.” • Module 4, Lesson 11, Mass/capacity: Solving word problems (customary units), Step 3 Teaching the Lesson, students analyze multi-step word problems that involve converting customary units of mass and capacity and persevere in solving them. “Project slide 2, as shown. Slowly read the problem aloud, twice through. Slide 2: A bottle of juice holds 64 fl. oz. Naomi pours juice into a pitcher. The pitcher holds 1\frac{1}{2} quarts and is now full. How much juice is left in the bottle? Organize students into pairs then discuss the points below (MP1): What is the problem asking you to do? What information do you know? What information do you need to find out? How will you solve the problem? What steps will you follow? Allow time for the students to solve the problem. Invite volunteers to share their strategies on the board. Emphasize the importance of working with only one measurement unit. Have the students identify the measurement unit that they decided to convert.” • Module 7, More Math, Problem Solving Activity 4, Word Problems, students make sense and persevere in solving word problems involving operations with mixed numbers. “Project slide 1 and read the word problem with the students. Ask questions such as, “What information do we need to solve this problem? What operation will we use? What will we do first? What will we do next? How could you show your thinking? Slide 1: Deon made 3\frac{1}{4} qt of vegetable soup and 2\frac{2}{3} qt of chicken soup. Megan made 3\frac{1}{2} qt of lentil soup and 2\frac{3}{8} qt of potato and leek soup. Who made the greater amount of soup?” • Module 12, Lesson 5, Division: Working with the standard algorithm (with remainders), Step 3 Teaching the Lesson, students make sense and persevere in solving division word problems. “Project side 3 and discuss the points below (MP1): What is the problem asking us to do? What do you estimate the answer will be? Who can solve the problem using the standard algorithm? Slide 3: The path at the golf club is 10,935 yards long. If I have gone half-way around the course, how far have I traveled?” 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 1, Lesson 10, Algebra: Working with expressions (without parentheses), Step 2 Starting the Lesson, students reason abstractly and quantitatively as they represent a word problem as an expression or equation and think of a word problem to match given conditions. “Organize students into pairs and have them work together to write a word problem that involves adding three numbers (MP2). Encourage them to choose numbers that are mentally manageable. Afterward, invite three or four students to share their word problems. As each problem is read, write key points on the board, and then discuss the points below: What expression would you write to match the problem? Is it possible to write more than one expression? When it is written can we arrange the parts to make it easier to calculate an answer? Do we need parentheses? Why not? Repeat for a word problem that involves multiplication and three factors.” • Module 5, Lesson 7, Decimal fractions: Subtracting tenths (decomposing ones), Step 3 Teaching the Lesson, students reason abstractly and quantitatively as they represent a problem symbolically and explain the solution in context of the original problem. “Refer to the tide heights for the first high tide and the first low tide on Sunday. Have pairs calculate the difference between these tides using the standard subtraction algorithm (MP2). Remind them to first estimate the difference and also to align the place values and decimal point. Afterward, project slide 3, as shown. Invite a volunteer to verbalize the procedural steps they followed to calculate the difference.” • Module 6, Lesson 10, Division: Three- and four-digit dividends and one-digit divisors (with remainders), Step 3 Teaching the Lesson, students reason abstractly and quantitatively as they write a word problem to show how remainders can be interpreted differently depending on context, and then interpret the remainders in the context of a word problem. “Review the role that context plays in interpreting remainders. For example, depending upon the context the remainder might be broken up and shared, it might represent the actual answer, or it might be irrelevant to the answer and excluded. Encourage students to provide an example for each situation. Organize students into pairs, then move around the room asking each pair of students to roll the cube. The number that they roll will tell the remainder in the word problem that they must write (MP2). For example, if (Hailey) rolls 2, she will write a word problem that leaves a remainder of 2. Select several word problems and read them aloud. Encourage the students to discuss the problem in their pairs to make sense of what is happening and how the quantities are related (MP1). Then ask students to interpret the remainder in the context of the problem (MP2).” • Module 10, Lesson 12, Decimal fractions: Solving multiplication and division word problems, Step 3 Teaching the Lesson, students decontextualize and contextualize word problems that involve dividing or multiplying decimal fractions. “Slide 2: A gardening machine needs 0.1 gallons of oil for each gallon of gas. How much oil is needed for the gas in this container?” An image shows a 5 gallon container. “A remote-controlled plane uses 0.1 gallons of gas for each half-hour of flight. What is the greatest amount of flying time possible with 5 gallons of gas? Encourage them to use a letter or symbol to represent the unknown amount in each equation. For example, students could write T = 0.1 x 5 for the first word problem, or T = 5\div 0.1\div 2 for the second word problem (MP2). The latter requires two steps, so students should justify why they decided to divide the total number of half-hours of flight (50) by two. Make sure students explain what the solutions represent in the context of each problem (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 5 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, Student Journal, page 81, Convince a friend, students justify their reasoning about the standard algorithm for multiplication and then critique the reasoning of a classmate, “Ashley says when completing the standard algorithm for multiplication the greater factor must be recorded first or the product will be incorrect. Gabriel disagrees with Ashley. Who do you agree with? Explain your reasoning. Share your thinking with another student. They can write their feedback below.” On the journal page, students complete, “I agree/ disagree with your thinking because … ” • Module 4, Lesson 5, Common fractions: Converting mixed numbers to improper fractions, Step 3 Teaching the lesson, students construct arguments and critique the reasoning of others as they develop a rule for rewriting mixed numbers as improper fractions. “Encourage students to develop a general rule that would work to convert mixed numbers to improper fractions (MP8). Allow time for them to test their rule with a few examples. Then invite students to share their rule with the class and justify how it works and why it makes sense conceptually (MP3). Encourage students to use diagrams in their justifications. (Note: Students who cannot describe why the rule works conceptually are not ready to use the rule. Premature use of rules puts students at a disadvantage in later learning.) Prompt students to critique the reasoning of their peers (MP3) by providing sentence stems such as: I agree/disagree with you because … I don’t understand … My rule is different because … So, what you are saying is …” • Module 6, Thinking Tasks, Question 5, students construct viable arguments and critique the reasoning of others as they solve a multi-step real-word problem involving operations with fractions and then determine whose cost plan is the best option. “After the marathon \frac{1}{4} of the Apple Pie Granola Bars and the Fig and Walnut Bars were left. Students calculated how many total bars were sold and how much money they made. They charged0.50 for each bar. Cody predicted that after buying the fruits and nuts, they lost money and should have charged $1.00 for each bar instead. Nancy argued that they did make money and might have sold fewer bars if they were more than$0.50 for each bar. Do you agree with Cody or Nancy? Write a letter to the Leadership Team explaining why.”

• Module 8, Lesson 5, Common fractions: Finding a fraction of a whole number symbolically (non-unit fractions), Step 3 Teaching the Lesson and Student Journal, page 294, Step In, students critique the reasoning of others as they find a fraction of a whole number. Student Journal, “Andre races cars. He has 25 miles of the race left to complete. His pit stop crew tell him he has enough fuel to travel \frac{3}{4} of that distance. How many miles can he travel before refueling? Katherine showed her thinking like this. What steps does she follow? Why does she rewrite 25 as \frac{25}{1}? Why does she decide to convert the improper fraction to a mixed number? Cole and Sara showed their thinking like this (image is shown of their work). What do all the methods have in common? How are they different? Why did Cole and Sara change the order of the factors?“

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

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics 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 5 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. MP6 is 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 whole class lesson notes.

Students have many opportunities to attend to precision in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 2, Lesson 8, Volume: Analyzing unit cubes and measuring volume, Step 4 Reflecting on the work, students use precision when reasoning about volume using unit cubes. “Discuss the students’ answers to Student Journal 2.8. Have the students share their rule for determining the total number of cubes when they know the dimensions of the base and the number of layers. Refer to Step Ahead and ask, Do you think Carlos’s calculation is accurate? Encourage students to cite the gaps and overlaps that are left by the cubes in the container (MP6). Discuss the difficulties of using cubes to measure the volume of containers that have curved sides. Ask, How else could you determine the volume? Encourage suggestions such as, filling the container with sand or rice then pouring the rice into a rectangular-based prism.”

• Module 7, Lesson 10: Number: Working with exponents, Student Journal, page 271, Step Up, students attend to precision as they use exponents to accurately represent powers of 10. Question 3, “Write each number using exponents. a. one hundred, b. one million, c. ten, d. ten million, e. one, f. ten billion.” Step 4 Reflecting on the work, “Have students explain how they identified the correct exponent to use (MP6).”

• Module 9, More math, Thinking tasks, The Ecology Club, Question 1, students attend to precision as they read a line plot and accurately calculate operations with fractions. “The Grade 5 Ecology Club stays after school once a week to maintain the garden and the trees that surround their school. One year ago they hosted a big tree-planting event. Every year they will measure the trees in the grove to see how they are growing and buy new seedlings to replace those that have died. This year, the club measured all of the young trees to compare the heights of all the trees. They measured the growth of the new trees and recorded it on this line plot. The trees that died are not represented. What is the difference in height between the tree with the greatest growth and the tree with the least growth?”

Students have frequent opportunities to attend to the specialized language of math in connection to grade level content as they work with support of the teacher and independently throughout the modules. Examples include:

• Module 2, Module overview, Vocabulary development, students can attend to the specialized language of math as teachers are provided a list of vocabulary terms. “The bolded vocabulary below will be introduced and developed in this module. These words are also defined in the student glossary at the end of each Student Journal. A support page accompanies each module where students create their own definition for each of the newly introduced vocabulary terms. The unbolded vocabulary terms below were introduced and defined in previous lessons and grades. Associative property of multiplication, calculate, centimeter (cm), compare, cubic centimeters (cm3), cubic inches (in3), cubic units, decimal fraction, dimensions, equivalent fractions, estimate, expanded form, feet (ft), fraction, height, inch (in), length, meter (m), multiplication algorithm, multiplication, multiply, number name, one whole, partial products, prism, product, volume, width.” Students are provided with a Building Vocabulary support page. The page includes: Vocabulary term (the bolded terms), Write it in your own words, and Show what it means.

• Module 5, Lesson 11, 2D shapes: Exploring categories of quadrilaterals, Step 3 Teaching the lesson, students use clear and precise language as they examine relationships between different types of quadrilaterals. “Project the Step In discussion from Student Journal 5.11. Review what the students know about tree diagrams. Specifically, highlight how they show the relationship between different categories (MP6). Then discuss the points below: What does the tree diagram show? What does it tell you about the relationship between some of these shapes? What does it tell you about rectangles? What does it tell you about squares? Discuss what the students know about shapes based on their position in the tree diagram. For example, squares have four sides (because they are quadrilaterals), two pairs of parallel sides (because they are parallelograms), four equal sides (because they are rhombuses), and four equal angles (because they are rectangles). Invite students to come to the front and draw examples of the shapes that match the label for each white box. As they draw examples, ask individuals to justify why the shapes they draw belong in a particular part of the tree diagram (MP3). Encourage others to confirm or challenge the shapes drawn by their peers. Protractors and rulers can be used to measure the angles and side lengths of contentious shapes (MP6).”

• Module 11, Lesson 12, Volume: Solving word problems, Step 2 Starting the lesson, students use the specialized language of mathematics in order to communicate ideas about volume. “Project slide 1, as shown, and discuss the points below (MP6): How do we calculate the area of a rectangle? Who can use this image to explain the difference between area and volume? What is the definition of volume? How do we calculate volume? How do we record volume? Why is the record for volume written as cubed?”

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

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, 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 5 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices throughout the year and they 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 whole class lesson notes.

MP7 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 throughout the modules to look for, describe, and make use of patterns within problem-solving as they work with support of the teacher and independently. Examples include:

• Module 2, Lesson 5, Multiplication: Extending the standard algorithm, Step 3 Teaching the lesson, “students relate the procedural step of the standard multiplication algorithm back to the partial-products strategy.” “Project slide 4 and have the students carry out the procedural steps of the standard algorithm. Discuss the points below: What numbers do we multiply in the first row of calculations? What numbers do we multiply in the second row of calculations? What about the third row?  Does any regrouping take place? How should we record the regrouping digit? Why do we write a zero in the ones place of the second row, and then again in the tens place and ones place in the third row? How do we calculate the final total? What numbers do we add? Relate each of the procedural steps back to the partial products in the rectangle (MP7).”

• Module 3, Lesson 10, Decimal fractions: Rounding thousandths, Step 3 Teaching the lesson, “students use benchmarks between two marked numbers on a number line to help them round.” “Project the number line partitioned into thousandths (slide 3) and have the students identify the position of 1.371. If necessary, remind the students that 1.37 is equivalent to 1.370. Ask, How does this number line help us identify the hundredth that is nearest? Again, the students should describe how the halfway point between 1.37 and 1.38 is used as a benchmark to help them decide (MP7).”

• Module 7, Lesson 2, Common fractions: Subtracting (related denominators), Student Journal, page 246, Step Up, Question 1, students make use of structure as they create equivalent fractions. “Rewrite each fraction to calculate the difference. Use the diagram to help. Then write the difference. a. \frac{4}{5} - \frac{7}{10} = , b. \frac{2}{3} - \frac{2}{9} =.”

• Module 11, Lesson 2, Algebra: Examining relationships between two numerical patterns, Step 2 Starting the lesson and Student Journal, page 398, students make use of structure as they work with numerical patterns. “Project the table (slide 1) and have the students identify the two variables being compared. Ask, What are some missing numbers we can write? How many candles are in each box? How do you know? How can we calculate the total number of candles for any number of boxes? What rule could we write? Invite volunteers to write the missing numbers in the table (MP7).” Student Journal, Step Up, Question 1, “Emilio has a favorite fruit punch recipe. To make one glass of punch he uses 2 fl oz of pineapple juice and 6 fl oz of orange juice. Write in this table to help you answer the questions below. a. How much pineapple juice will be used for 5 glasses of punch? b. If 12 fl oz of orange juice is used, how many glasses of punch can be made? c. How much orange juice will be used if 20 fl oz of pineapple juice is used? d. How much pineapple juice will be used if 90 fl oz of orange juice is used?” A table is provided that shows Number of glasses- 1 and then six empty boxes, Pineapple juice (fl oz)- 2, and then six empty boxes, Orange juice (fl oz) - 6, and then six empty boxes.

MP8 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 throughout the materials, with support of the teacher or during independent practice, to use repeated reasoning in order to make generalizations and build a deeper understanding of grade level math concepts. Examples include:

• Module 1, Lesson 5, Number: Reading and writing eight- and nine-digit numbers, Step 2 Starting the lesson, “students apply what they know about the multiply by 10 relationship of the base-ten number system, to work the other way and divide by 10.” “Project slide 1 and ask, What do you notice about this table? What patterns do you see? Highlight that the places are grouped into threes (millions, thousands, and ones) and that the places within each group repeat in the pattern H, T, O. Project slide 2, and refer to the arrows below the table. Say, Ten is 10 times as many as 1, and one hundred is 10 times as many as 10. What other relationships can you share? Volunteers can draw more arrows to show the relationship between different place values. Say, The size of each place value is ten times as much as the place value just before when we move from right to left in this table. What happens if we move from left to right? Draw arrows in the opposite direction above the table to show that the size of each place value is one-tenth of the size of the place value just before when we move from left to right (MP8).”

• Module 6, Lesson 1, Common fractions: Making comparisons and estimates, Step 4 Reflecting on the work, “students make a generalization about how the difference between the numerator and the denominator of a fraction affects the size of the fraction.” “Project slide 4. Discuss the common fractions that the students made. Explain how the difference in value between the numerator and denominator affects the size of the fraction. Students can check this relationship and investigate whether it applies with other collections of four digits. (MP8)”

• Module 8, More math, Investigation 1, Fraction Patterns, students use repeated reasoning as they look for shortcuts for operations with fractions. “What numbers will make these true? \frac{1}{4}\times__ = 15, \frac{2}{4}\times__ = 15, \frac{3}{4}\times__ = 15, \frac{4}{4}\times__ = 15. What other patterns involving fractions and multiplication can you make? Then challenge students to look for patterns in the equations and write other groups of equations that show the same patterns.”

• Module 11, Lesson 6, Algebra: Interpreting coordinate grids, Student Journal, page 411, Step Ahead, students identify and write rules from patterns on coordinate planes. “This rule describes the relationship between the number of cups of water (C) and number of scouts (S) on page 410: S\times6 = C. Write rules to describe the relationship between the items in Questions 3 and 4. a. Distance (D) and Time (T): b. Green beads (G) and Red beads (R):”  Step 4 Reflecting on the work, “They can then share the relationship rules they wrote in Step Ahead. (MP8)”

### Usability

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 5 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.

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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 5 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 students have been introduced to six-digit whole numbers, and have been introduced to the idea of one million and a special place name for this place. The millions place is important because it is the start for the next three places that are described using the word millions. This module begins with a review of six-digit numbers. In Lesson 2, students focus on reading and writing seven-digit numbers to help them see that they now have three main groups of three when saying number names: the millions, the thousands, and the ones. A place-value expander helps to clearly show these groups. The number line is used to provide a picture of seven-digit numbers to help students when they work with these greater numbers. The number line representation stresses the fact that the greatest distance from zero is determined by looking at the place with greatest value, and then the digit in that place. The idea of relative position — what the number line tool displays — is useful when students compare, order, or round numbers. Comparing and ordering involve the position of numbers relative to 0 (the origin.) For rounding, the number line indicates the position of a number relative to nearby multiples of 10, 100, 1,000, and so on. In Lesson 5, the work with seven-digit numbers is extended to eight- and nine-digit numbers, so students become confident with reading, writing, comparing, ordering, and rounding these whole numbers.”

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 6, Number: Working with millions expressed as fractions, Step 2 Starting the lesson, teachers provide context about equal parts on a number line. “Project the number line (slide 1) and say, Draw marks to divide this number line into four equal parts. What number will we write at each of the marks? How do you know? Have a student draw the marks and then encourage other students to describe how they would figure out the value of each number. Erase the numbers and the marks and repeat to divide the number line into five and then eight equal parts.”

• Module 9 Lesson 9, Mass: Converting metric units,  Lesson overview and focus,  Misconceptions, include guidance to address common misconceptions as students work with converting metric units. “For students who struggle with metric conversions, work to separate struggles with decimal fractions from challenges with the units of measure. Provide experience with benchmarks and measuring tools to support those who are not familiar with the units of measure. Provide fraction and place-value support for those who struggle with decimal fractions.”

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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 5 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 2, 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 4, Preparing for the module, Research into practice, Common fractions, includes explanations and examples connected to fraction equivalence and fraction notation. To learn more includes additional adult-level explanations for teachers. “Work with fractions in this module incorporates two understandings of fraction notation. When students work with equivalent fractions, they are building on their understanding of multiplication and building their skills towards proportional reasoning. By looking at fractions in the context of the multiplication table rows, students see that the numerator and denominator in equivalent fractions vary together. The skill of converting improper fractions to mixed numbers begins to suggest the division interpretation of a fraction where 15⁄4 is the numerical value of 15 ÷ 4. Students may come to this understanding as they create groups of four fourths (each one whole) by repeated subtraction and find that 15 fourths can be described as three wholes and 3 more fourths. It is not necessary to teach students this strategy for finding equivalence. Allow them to use their knowledge of numbers and operations to realize what is happening. It may be helpful to some students to relate this to the idea of regrouping used in base-ten place value. When working with fractions, we do not regroup for ten of a given item; we regroup when we reach one whole, whether four fourths, five fifths, or any way the whole is partitioned.” To learn more, “Neumer, Chris. 2007. “Mixed Numbers Made Easy: Building and Converting Mixed Numbers and Improper Fractions.” Teaching Children Mathematics 13 (9): 488–92.”

• Module 5, Preparing for the module, Research in practice, Decimal fractions, support teachers with concepts for work beyond the grade. “As the Mathematics Focus suggests, this work prepares students for the multiplication and division of decimal fractions (Module 10), then for the use of the standard algorithms for addition, subtraction, and multiplication in Grade 6 (Module 2) and for division (Module 3) with decimal fractions. In preparation for this, use every opportunity for students to work with the place value structure of the base-ten system and to internalize the multiplicative relationships between different place values. For example, have them represent 0.527 and 527 with a numeral expander or place-value slider then explain how each number changes as it is multiplied and divided by 10, 100, and 1,000. Be sure students describe how the digits shift, not the decimal point, as its position remains constant. Read more about operating with decimal fractions in the Research into Practice section of Module 10, and in Grade 6 Modules 2 and 3.”

• Module 9, Preparing for the module, Research into practice, Measurement, includes explanations and examples connected to measurements within the metric system. To learn more includes additional adult-level explanations for teachers. “Measurement provides a powerful context for continuing to think about fractions and the relationships they represent. Students must continue to develop a benchmark sense of the measures they know (for example, “How much is 2 liters of soda?” of “How many laps around the track is 1 kilometer?”) They then use this number sense to reason about measuring the same quantity using different units. Because the metric system is driven by base-ten relationships, this reasoning strengthens student understanding of decimal fractions as well.” 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.”

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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 5 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 5 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 5 and the Common Core Standards, includes all Grade 5 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 3, 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 5, Lesson 1, Decimal fractions: Reviewing addition strategies (without composing), the Core Standard is identified as 5.NBT.B.7. The Prior Learning Standards are identified 5.OA.A.2, 5.NF.B.7, 5.NF.B.7c. 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, Measurement and Data, includes an overview of how the math of this module builds from previous work in math. “In Grade 4, students learned the relationships between customary units of length, capacity, and mass, and converted between common units. All answers were whole numbers. This module extends that to converting between units, and includes examples that involve familiar fractions. For example, students convert 8 fluid ounces to one-fourth, one-half, and then three-fourths of one quart. The module concludes with solving word problems involving capacity/mass and, in a separate lesson, data collection activities in which students work with ounces to construct and answer questions related to line plots.”

• Module 10, Mathematics Overview, Coherence, includes an overview of how the content in fifth grade connects to mathematics students will learn in sixth grade. “Lessons 5.10.1–5.10.12 focus on multiplication and division with decimals, utilizing the partial-products strategy and the area model for multiplication, and using models, the relationship between multiplication and division, and place-value strategies for division. This extends the previous work with multiplication and division (4.1.2, 4.5.2–4.5.4) to examples involving decimals with tenths or hundredths and connects to work using the standard algorithm to multiply and divide decimals (6.2.10–6.2.12).”

• Module 4, Lesson 6, Common fractions: Solving word problems, Topic progression, “Prior learning: In Lesson 5.4.5, students use fraction strips and related parts to explain how they can rewrite a mixed number as an improper fraction. They consider general rules that can be applied. 5.NF.A.1; Current focus: In this lesson, students are encouraged to use a range of strategies to solve multi-step word problems involving the comparison of two or more common fractions. 5.NF.A.2; Future learning: In Lesson 5.8.2, students relate finding a unit fraction of a quantity to division. 5.NF.B.3” 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 5 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 1, Resources, Preparing for the module, Newsletter, Core Focus, “Number: Working with seven-, eight- and nine-digit numbers, Algebra: Investigating resolution order with one and two operations and working with expressions (with and without parentheses) Number - Students review reading, writing, and representing six-digit numbers with the use of an abacus and other tools and models. Later, students extend the skills and strategies they have used for six-digit numbers to read and write seven-digit numbers, and use relative position to locate seven-digit numbers on number lines. Students then progress to reading and writing eight- and nine-digit numbers with the help of numeral expanders. Algebra - Students learn that the order of numbers will not affect the answer in addition or multiplication equations, but will affect the answer in subtraction and division. Because of these differences, there is an established order of operations to follow when solving problems that have more than one kind of operation, like 7 + 8 \div 2 - 1. In some cases, parentheses are used to clarify the order in which operations would be completed. The previous example might be rendered like this: 7 + (8 \times 2) - 1, or (7 + 8) \times 2 - 1. These two expressions give different results, 22 and 29, respectively. Students practice the order of operations with real-world situations such as, “We bought five sandwiches for $3 each, and one bag of chips that cost$2. How much did we spend in all?”

• Module 5, Resources, Preparing for the module, Newsletter, Glossary, “The term decimal fraction emphasizes how decimal numbers are part of a whole number, and that the part is a multiple of ten: tenths, hundredths, thousandths. The decimal point is used to indicate decimal fractions. Algorithms are groups of rules used for completing tasks for solving problems. A four-sided polygon is called a quadrilateral.” Module 5, Newsletter, Helpful videos, “View these short one-minute videos to see these ideas in action. go.origo.app/z4lh3. go.origo.app/j5q8k.”

• Module 10, Resources, Preparing for the module, Newsletter, Ideas for Home, “Write a basic multiplication fact such as 7 × 3 = 21. Then adjust one or more of the factors to write as many new equations as possible. E.g. your child could write 0.7 × 3 = 2.1, 0.3 × 0.7 = 0.21, and 70 × 3 = 210. Discuss how you know where to place the decimal point (e.g. 0.7 is one-tenth of 7, so the answer must be one-tenth of 21). Look at weekly supermarket circulars and choose some favorite food items. Ask your child to figure out the price of three, four, or five items. Be sure to ask what strategy they used. Restaurant menus provide a great opportunity for your child to practice with decimal fractions. Ask them to find the total price of two or three items, then find the cost per person if the items are shared by 2 or 3 people. There may be a few cents left over. Use everyday experiences such as cooking (mass or capacity) to create and solve situations involving division. E.g. if a dozen eggs weigh 0.72 kg, how much would one egg weigh?”

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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 5 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, “Multiplication: Students in Grade 5 extend their knowledge of the standard algorithm for multiplication from specific cases to multiplying any pair of whole numbers. Their understanding of place value allows them to extend their models for multiplication to multi-digit numbers, continuing the learning progression begun in Grade 3. Students have a wide range of strategies and methods, including area diagrams and partial products, available to them. Extending area diagrams to three-digit numbers helps students connect their work with specific cases to more general cases with multi-digit numbers. Connecting area diagrams to written records, students see that the same strategies and patterns extend into additional columns of the place-value chart. This supports their work to generalize the algorithm. Students review multiplicative comparison word problems in preparation for work this year with scale factor. These problems help students transition their thinking from an additive model to multiplicative reasoning. When comparing two values, multiplicative thinking emphasizes how many times greater (or lesser) one value is compared to the other. This reasoning lays the foundation for ratio and proportion, a key element of middle school mathematics. Volume: Grade 5 students work with volume as a measurement concept as well as an opportunity to apply and extend their knowledge of multiplication. Students reason about building structures and filling shapes with unit cubes to explore ideas of volume and develop a formula for calculating volume. Students need many concrete experiences filling space with unit cubes before they can visualize the elements of volume and use the formula fluently. To learn more: Farmer, Sherri A., Kristina M. Tank, and Tamara J. Moore. 2013. “Using STEM to Reinforce Measurement Skills.” Teaching Children Mathematics 22(3): 196-199.; Fuson, Karen C. 2003. “Toward computational fluency in multi-digit multiplication and division.” Teaching Children Mathematics 9(6): 300-305. Wallace, Ann H. and Susan P. Gurganus. 2005. “Teaching for Mastery of Multiplication.” Teaching Children Mathematics 12(1): 26-33. References: Battista, Michael T., and Douglas H. Clements. 1996. “Students’ understanding of three- dimensional rectangular arrays of cubes.” Journal for Research in Mathematics Education 27(3): 258-292. 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. McCallum, William, Phil Daro, and Jason Zimba. “K, Counting and Cardinality; K–5, Operations and Algebraic Thinking” in Progressions for the Common Core State Standards in Mathematics. The University of Arizona. https://commoncoretools.files.wordpress.com/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf (retrieved 21 September 2016)”

• Module 8, Preparing for the module, Research into practice, “Common fractions: Students in Grade 5 extend their understanding of fraction multiplication to include multiplying a fraction by a fraction. In many cases, an area model serves as a more accessible representation than an equal groups model for this operation. As with all operations, it is essential that students see the operations in context and reason about their solution process in the context of specific problem situations. Students may have the misconception that multiplication makes things greater, not realizing that multiplication by a fraction less than one results in a product of lesser value. Reasoning in the context of problem situations helps students build confidence in their solutions. When students use an area model to multiply fractions, there are several important ideas to develop. First, the whole changes from a length (units along each side of the rectangle) to an area (square unit area of the rectangle itself). Multiplying the denominators tells how many pieces the new square unit area is divided into. Multiplying the numerators tells how many of those pieces are part of the solution to the problem. These basic principles extend to multiplying mixed numbers as well. It is also important to ensure that the visual model being used is appropriate to the situation and mathematics being represented. Students often require more time to see the relationships between multiplication and division than they needed for addition and subtraction. As students gain experience with fractions, they begin to see that sharing between two people (dividing by two) gives the same result as halving (multiplication by \frac{1}{2}). This shows the inverse relationship between multiplication and division and helps students develop their understanding of this relationship more deeply. To learn more: Webel, Corey, Erin Krupa, and Jason McManus. 2016. “Using Representations of Fraction Multiplication.” Teaching Children Mathematics 22 (6): 366–73. References: Robinson, Katherine M., and Jo-Anne LeFevre. 2012. “The Inverse Relation between Multiplication and Division: Concepts, Procedures, and a Cognitive Framework.” Educational Studies in Mathematics 79 (3): 409–28. Van de Walle, John, Karen Karp, and Jenny Bay-Williams. 2013. Elementary and Middle School Mathematics: Teaching Developmentally 8th ed. Boston: Pearson.”

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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 5 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, “cube labeled: 17, 19, 24, 26, 31, 35 and a cube labeled 15, 20, 25, 30, 35, 40 for lesson 3, small to medium-sized rectangular prisms (such as a toothpaste box, matchbox, soap box, etc.) for lessons 7 and 8. Each group of students need base-10 blocks (ones) for lessons 7, 8 and 11, inch cubes, marbles, counters and coins for lesson 8, small to medium-sized rectangular prisms (such as a toothpaste box, matchbox, soap box, etc.) for lesson 8, and Support 14 for lesson 7. Each pair of students need base 10-blocks (ones) for lessons 7 and 10. Each individual student needs base-10 blocks (ones) for lessons 7 and 9, and Student Journal for each lesson.”

• Module 2, Lesson 9, Volume: Developing a formula, Lesson notes, Step 1 Preparing the lesson, “Each student will need: base-10 blocks (ones) and Student Journal 2.9.” Step 2 Starting the lesson, “Say, Imagine you have 20 cubes. What are some different rectangular- based prisms you could make using all the cubes? What would be the dimensions of the three faces? How would you check that you have used all the cubes in each prism? If necessary, provide cubes so the students can construct the prisms to confirm their thinking.”

• Module 5, Preparing for the module, According to the Resource overview, teachers need, “3.5 meter length of string, 4.25 meter length of string and metric measure tape for lesson 4, a cube labeled: 1, 1, 2, 2, 3, 3, and another cube labeled: O, O, T, T, H, H for lesson 5, a protractor and ruler for lesson 11. Each group of students need crayons or markers and Support 15 in lesson 1 and geostrips and fasteners, paper, and a protractor in lesson 12. Each pair of students needs a protractor in lesson 10, scissors in lesson 7, Support 16 in lesson 3, Support 19 in lessons 7 and 8, and Support 20 in lesson 9. Each individual student needs scissors and glue and Support 21 in lesson 10, and the Student Journal in each lesson.”

• Module 6, Lesson 3, Common fractions: Adding (related denominators), Lesson notes, Step 1 Preparing the lesson, “Each student will need: 1 copy of Support 11, scissors, Student Journal 6.3”

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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 5 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 5 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 2, 5.NBT.5, “A music show sells two types of drum kits. One costs $274 and the other costs 4 times as much. Ruby is saving$23 each week to buy the more expensive kit. How much money will she have saved after 17 weeks? Show your thinking.”

• Module 6, Assessment, Quarterly test, Test A, denotes standards for each question. Question 1, 5.OA.1, “Solve the problem. Show your thinking. 0.8 + 54 \div 9 - 1.02.”

• Module 8, Preparing for the module, Module assessment overview, Interview, denotes standards addressed. 5.NF.4, 5.NF.4a, and 5.NF.4b, “Steps: Write \frac{1}{4} and 24 on a sheet of paper. Ask the student to think of a context that involves multiplying the two numbers. (If necessary, help with a context - it is not vital that they provide one.) Then have them multiply the numbers and state the product, explaining their process as they complete the task. Repeat with the following pairs of numbers. Ensure they demonstrate their thinking with an area model for at least one pair of numbers. \frac{5}{6} and 18, 2\frac{4}{5} and 3, \frac{1}{4} and \frac{5}{6}, \frac{1}{3} and 2\frac{4}{5}. Draw a ✔ beside the learning the student has successfully demonstrated.“

• Module 11, Preparing for the module, Module assessment overview, Performance task denotes the aligned grade level standard. Question 1, 5.MD.1, “Solve each problem. Show your thinking and be sure to write the measurement unit. a. The longer sides of a rectangular barn are each 8 meters. The shorter sides are each 7 meters and the height of the fence is 1.5 meters. What is the area of the barnyard? b. What is the perimeter of the barnyard in Question 1a?”

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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 5 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 5, “Calculate the volume of this prism. Show your thinking. Measurements: 5 cm, 3 cm, 3 cm, 2 cm, and 4 cm. Answer: 34 cm3.” The answer key aligns this question to 5.MD.5 and 5.MD.5c.

• Module 6, Assessments, Quarterly test A, Question 11, “Write this common fraction as a mixed number. Show your thinking. \frac{13}{4} = ?” The answer key shows the answer as 3\frac{1}{4} and aligned to 5.NF.1.

• Module 9, Assessments, Performance task, students use strategies to solve multiplication and division of fractions problems. “Question 2, A student thinks that \frac{1}{5}\div6 is equivalent to \frac{1}{5}\times\frac{1}{6}. Are they correct? Draw pictures or write sentences to explain your answer. Question 3, Another student thinks that \frac{1}{8}\div4 is equivalent to 4\div\frac{1}{8}. Are they correct? Draw pictures or write sentences to explain your answer.” The Scoring Rubric and Examples state, “2 Meets requirements. Shows complete understanding. Clearly identified and explained the correct answers for Questions 2 and 3. 1 Partially meets requirements. Identified correct answers for Questions 2 and 3 but explanations were incorrect or absent. 0 Does not meet requirements. Shows no understanding.”

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

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 5 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 1, Check-up 1 and Performance task, develop the full intent of standard 5.OA.2, write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Check-up 1, Question 2, “Write an equation to represent each problem. Use a letter to represent the unknown value. a. Damon has $80. He buys 3 packs of guitar strings for 12.46 each. How much money does he have left? d. Alejandro buys 3 bags of fruit. There are 5 apples and 2 oranges in each bag. How many pieces of fruit did he buy in total? ” Performance task, Question 2, ”Write an expression to match. You do not need to calculate the answers. a. multiply 6 by 8, then subtract 9. b. Multiply 9 by 2, then multiply by 6. c. add 5 and 7, then divide by 3. d. Divide 40 by 5, then multiply by 2.” • Module 6, Quarterly test A questions support the full intent of MP7, look for and express regularity in repeated reasoning, as students look for patterns converting measurement in a table chart to complete the missing value. Question 21, “Complete this table. Gallons: 1, ___. Quarts: 4, 12. Pints: 8, 24.” • Module 10, Interview 1 and Performance task and Module 5, Check-up 1, develop the full intent of 5.NBT.7, add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Interview 1, “Steps: Say, Think of a problem that involves dividing a whole number by a decimal fraction that you can solve. Encourage the student to describe why they felt confident calculating the quotient for their problem and the thinking they used to calculate it. Depending on the answer you may need to check the extent of the student’s abilities by asking them to solve the following problems and explain their thinking: 3 \div 0.2 =___ 5 \div 0.01 = ___ 2 \div 0.25 = ___ Repeat to have students think of a problem that involves dividing a decimal fraction by a whole number. If necessary, ask them to solve the following problems: 0.8 \div 2 = ___ 0.27 \div 3 = ___ 0.06 \div 2 = ___ Repeat to have students think of a problem that involves dividing a decimal fraction by a decimal fraction. If necessary, ask them to solve the following problems: 0.6 0.3 = ___ 0.24 \div 0.06 = ___ 0.4 \div 0.05 = ___. Draw a ✔ beside the learning the student has successfully demonstrated.” Performance task, Question 2, “Look at this equation. 2 \times 0.6 = 0.12 What is the correct product? Explain your answer.” Module 5, Check-up 1, Question 2, “Use the standard algorithm to figure out each total. a. 8. + 12.72; b. 11.81 + 6.4.” Question 3, “Complete each equation. Show your thinking. a. 9.48 - 5.06 = ___, b. 5.3 - 2.7 = ___, c. 6.9 - 3.25 = ___.” • Module 12, Quarterly test questions support the full intent of MP6, attend to precision, as students describe the attributes of a coordinate plane. For example, Question 27, “Choose the word from the list that makes this sentence true. origin, x-axis, y-axis, quadrant. The second number in an ordered pair represents movement along the ___.” ##### Indicator {{'3l' | indicatorName}} 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 5 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 5 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. ##### Indicator {{'3m' | indicatorName}} 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 5 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 6, Decimal fractions: Using the standard algorithm to subtract, include: • Extra help, “Activity: Organize students into pairs and distribute one card to each student. Have pairs compare their mass pieces, identify the mass that is heavier, and explain their thinking. Encourage each student to then find another student who has a card showing a similar mass, for example, 6.4 kg and 6.09 kg. Establish that 6.4 kg is equivalent to 6.40 kg. The students use this understanding to help calculate the difference. Have students form new pairs and repeat the activity as time allows.” • Extra practice, “Activity: Write the equations 5.42 – 3.2 = ____ and 3.98 – 2.45 = ____ on the board. Have the students work independently to solve each equation using both the standard subtraction algorithm and another method of their choice. Afterward, they should share their alternative methods and place a check mark beside those methods that were more efficient to use than the standard algorithm.” • Extra challenge, “Activity: Organize students into groups and distribute the resources. Have students cut out the cards from the support page and place them facedown on the floor. Ask each student to select two cards. They then calculate the difference between the masses indicated on their cards. One point is awarded to the student who records a difference that is nearest (2). Repeat the activity: give a different whole number and have students select two new cards to form a difference that is nearest the new target number.” ##### Indicator {{'3n' | indicatorName}} 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 5 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 1, Lesson 4, Number: Comparing and ordering seven-digit numbers, Differentiation, Extra Challenge, “Organize students into pairs to play Guess My Number. Ask one student to discreetly write a seven-digit number (where zero is not permitted in the millions place). The other student then asks a series of yes/no questions to figure out the number. For example, “Is your number greater than 5,000,000?” or “Is your number within 100,000 of 3,450,000?” Students keep a tally showing how many questions the student asks before they guess the number (up to 20 questions). When either the number has been determined or 20 questions have been asked, students alternate roles and repeat the game. For each round, the student with the fewest tallies wins. The game is repeated as time allows. Rules may be altered so students are to guess within 10,000 of the secret number.” • Module 4, Lesson 2, Common fractions: Reviewing equivalent fractions (related and unrelated denominators), Differentiation, Extra Challenge, “Organize students into pairs and distribute the strips. Ask each pair to place their multiplication strips facedown on the floor. They take turns to choose two strips to compose several equivalent fractions. The student who records the greater fraction scores one point. A bonus point is awarded if they can identify equivalent fractions that share a common denominator. The first student to record six points wins. For example, in the image below, (Lomasi) scores 1 point because \frac{7}{10} is greater than \frac{3}{6}. She then identifies two equivalent fractions that share a common denominator ($$\frac{42}{60}$$ and \frac{30}{60}) to score a bonus point. (Note: Retain the multiplication strips for Lesson 6.4).” • Module 10, Lesson 4, Decimal fractions: Multiplying with whole numbers using partial products, Differentiation, Extra Challenge, “Organize students into pairs. Have students take turns to write any three single digits. They then use their digits to create three different multiplication expressions. Each expression has one factor that is a whole number and one factor that is a decimal fraction recorded in hundredths. For example, a student writes 3, 9, and 5, and uses these digits to write 3 × 0.95, 5 × 0.39, and 9 × 0.35. Students then calculate each product. One point is awarded to students who form a product nearest a whole number. The student with the most points after five rounds wins.” ##### Indicator {{'3o' | indicatorName}} 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 5 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 11, Algebra: Working with expressions (with parentheses), Student Journal, page 36, Step Up, students match expressions and descriptions. Question 1 states, “Color the bubble beside the expression that matches the steps you would use to calculate the answer to the problem. a.”Each book costs$8 plus 50 cents for tax. How much will you pay for 6 books? bubble 6 × (8 + 0.50) bubble 6 × 8 + 0.50 bubble 8 + 0.50 × 6 bubble (6 × 8) + 0.50.”

• Module 3, More Math, Thinking Tasks, Question 1, students calculate volume from a given context, “Nancy is playing a game on her phone. She plays the game by stacking boxes to build different objects, monuments, houses, and even towns. In the game, each box represents a volume of 1 m3. Tool packs and food packs can also be bought with gold bars earned during play. Tool packs cost 40 gold bars. Food packs cost 25 gold bars. Nancy begins the game by building this tower. What is the volume? Show your thinking.”

• Step It Up Practice, Grade 5, Module 8, Resources, Lesson 1, Common fractions: Reviewing multiplication by whole numbers, Question 1, students shade a shape to match the fraction equation, “Each large shape is one whole. Shade each shape to match the equation. Write the product as a common fraction and then a mixed number.”

• Module 11, More Math, Investigation 2, students determine number patterns in the coordinate plane. “What shapes can number patterns make when graphed? Project slide 1 and read the investigation question. Ask, What will you need to do first for this investigation? (Write some number patterns.) Organize students into pairs and distribute the resources. Have students work together to write number patterns that use any of the four operations. They then graph each pattern using different colors on their coordinate plane.”

##### 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 5 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 7, Number: Rounding numbers with up to nine digits, Step 3 Teaching the lesson, “Encourage discussion. Project slide 2 and ask those who would use a number line to share their strategies. Organize students into pairs and distribute the resources. Have them record a seven-, eight-, or nine-digit number on their expander. Project the Step In discussion from Student Journal 1.7 and work through the questions with the whole class. Ask several volunteers to share their answers and discuss their strategies for rounding.”

• Module 7, Lesson 1, Common fractions: Exploring strategies to subtract (same denominators), Step 1 Preparing the lesson, “Each pair of students will need: 1 copy of Support 22. Each student will need: sticky notes, Student Journal 7.1.” Step 2 Starting the lesson, “Distribute the sticky notes. Ask each student to write an improper fraction or mixed number less than 10 on their sticky note. On your instruction, the students exchange notes then write the equivalent mixed number or improper fraction on the other side of the note.” Step 3 Teaching the lesson, “Organize students into pairs and distribute the support page. Have the students work in their pairs to solve each problem.”

• Module 12, Lesson 7, Division: Working with four-digit dividends and two-digit divisors, Step 2 Starting the lesson, “Organize students into small groups and distribute the support page. Explain that different strategies were used to solve the same division problem. Students work in their groups to analyze and describe each strategy, then use each strategy to calculate 976 \div 8 in the space provided on the sheet.”

##### 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 5 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 1, Lesson 4, Number: Comparing and ordering seven-digit numbers, Lesson notes, Step 2 Starting the lesson, “ELL: Allow students to discuss the meaning of three- and four-digit numbers before moving on with the activity. Demonstrate an example of the word halfway before moving on with the activity.” Step 3 Teaching the lesson, “ELL: Use hand gestures to show left to right as you say the phrase. Ensure students understand the difference between the words right as in direction and write as in transcribing text, and order as in sequence and order as in placing a request for food at a restaurant. Allow students to discuss the words nearest, between, and order before moving on with the activity. 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 thoughts on the question, What rolls will you need to get the closest number? Then, invite the student to explain their thoughts to the class.”

• Module 4, Lesson 1, Common fractions: Reviewing equivalent fractions (related denominators), Lesson notes, Step 3 Teaching the lesson, “ELL: Pair students with a fluent English-speaking partner. During the activity, have students discuss the concepts in their pairs, as well as repeat the other thinking. Encourage them to explain what they are learning in their own words to check for understanding of the concepts. Create an anchor chart about common fractions and display in the classroom for students to reference when necessary. Encourage them to use the words numerator and denominator in a sentence to show understanding of the language. Allow students to work in their pairs to complete the Student Journal, if necessary.”

##### 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 5 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 Jie, Ricardo, Riku, and Shiro 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 5 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 5 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 5 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 2, Lesson 6, Multiplication: Solving word problems, Step 3 Teaching the lesson, “Project slide 2 as shown. Slowly read the word problem twice. Organize students into pairs to solve the problem (SMP1). To help students find an entry point into the problem, discuss the points below: What is the problem asking us to do? What information do we know? What information do we need to find out? Does the problem involve more than one step? What steps will you follow to solve the problem? What expression could we write to solve the problem? How might parentheses be used? If not suggested, guide the students to suggest the solution 16 × (4,025 − 795).”

• Module 3, Lesson 4, Decimal fractions: Reading and writing thousandths (without zeros and teens), Lesson overview and focus, Misconceptions, “Students may struggle with decimal place value because they do not hear the -th that differentiates hundreds from hundredths or thousands from thousandths. Reading the decimal 0.374 as three hundred seventy-four thousandths can further this confusion if a student believes there are hundreds in this very small number. Help students connect this number back to fractions, where 374 is the number of pieces we have and 1000 is the number of pieces the whole has been divided into.”

• Module 11, Mathematics overview, Common errors and misconceptions, Algebra, “In representing real-world situations on the coordinate plane, it may be helpful to connect to science and share that the x-axis is traditionally used for the independent variable (often time or the number of things), and the y-axis is traditionally used for the dependent variable.”

##### 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 5 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 7, Volume: Developing the concept, Step 2 Starting the lesson, identifies cubes to support student understanding of volume. “Organize students into small groups. Distribute base-10 ones blocks and the support page to each group. Project slide 1, as shown. Refer to the first base picture and select one individual in each group to form one base then build up five layers of the same size. Guide the other members of the group to record the number of cubes in the first table on the support page as each layer is added. Repeat for the other two bases.”

• Module 4, Lesson 3, Common fractions: Reviewing the relationship with mixed numbers, Step 2 Starting the lesson, describes the use of number lines in order to represent fractions. “Open the Flare Number Line online tool and locate these amounts on a number line. Emphasize the distance from 0 to 1 represents 1 whole for each case, but the whole changes depending on the context. In the discussion, establish that these are called mixed numbers.”

• Module 10, Lesson 2, Decimal fractions: Reinforcing strategies for multiplying by a whole number, Step 3 Teaching the lesson, outlines the use of tenths and hundredths squares to support multiplication of whole numbers by decimal fractions. “Project slide 2 as shown. Read the word problem aloud and clarify that there are two questions attached to the problem. Organize students into pairs and distribute the resources. Likewise, students who used the tenths and hundredths squares can compare the areas that they shaded.”

#### 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 5 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 5 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 5 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 5 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 5 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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##### Gateway {{ gateway.number }}
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