## ORIGO Stepping Stones 2.0

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### Overall Summary

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

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

### Focus & Coherence

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 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 6 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 6 meet expectations that they assess grade-level content and, if applicable, content from earlier grades.

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 6 standards include:

• Module 2, Check-Up 2, Problem 4, “Calculate the answer. a. 4.62\times 71, b. 9.3\times 5.12.” (6.NS.3)

• Module 6, Quarterly Test B, Problem 18, “Write an equation to the word problem. Hugo is given $25 to attend the school concert. He pays$7 for each entry ticket and $2.50 for each soda. Hugo pays for his ticket and drink and also for his little brother’s ticket and drink. How much change will Peter receive? Let c represent Hugo’s change.” (6.EE.2). • Module 8 Performance Task, Problem 1, “This machine holds 150 gumballs with different flavors. Solve each word problem. Show your thinking. a. One-fifth of the gumballs are orange flavored. What percentage of the gumballs are orange? b. Forty percent of the gumballs are cherry flavored. How many gumballs are cherry? c. What is the difference between the number of orange and cherry gumballs?” (6.RP.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 6 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 6th 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 6, students engage with all CCSS standards. Examples of extensive work from the grade include: • Module 2, Lesson 3, Algebra: Order of operations involving exponents, engages students with extensive work with 6.EE.1 (Write and evaluate numerical expressions involving whole- number exponents). In the Student Journal, Step Up, page 51, Question 4, students evaluate numerical expressions that involve whole-number exponents. “Complete each equation. Show your thinking on page 80. a. 4(12 - 7)^2 b. (18 - 14) \cdot 2^2 \cdot10 c. 9 \cdot 8 - 7 \cdot 6 - 5^2.” • Module 4, Lessons 4 and 6 engage students in extensive work with 6.NS.6 (Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.) as students reason about rational numbers. In Lesson 4, Algebra: Evaluating expressions given the value of the variable, Student Journal, Maintaining Concepts and Skills, page 131, Question 1a, “Write < or > to complete each statement. Use the number line to help your thinking. 0.3 ___ -0.4.” In Lesson 6, Algebra: Solving equations given a set of possible values, Student Journal, Maintaining Concepts and Skills, page 137, Question 1a, “Write <, >, or = to complete each statement. Use the number line to help. \left|-12\right|____$$\left|12\right|$$.” 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 10, Lesson 2, Statistics: Measuring variability using quartiles and interquartile range, engages students with extensive work with 6.SP.3 (Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number). In the Student Journal, Step In, page 360, students describe the spread of data in a dot plot using what they have learned about interquartile range. “Some students are asked about the number of hours that they spend on social media each week. The results are then recorded. Hours spent on social media: 7, 3, 5, 12, 10, 9, 2, 6, 0, 1, 5, 3. How could you display the data? What types of questions could this data answer? What does the distance between the first quartile and the third quartile indicate? What percentage of the values fall between the first and third quartiles?” An interquartile range is provided for students. The instructional materials provide opportunities for all students to engage with the full intent of 6th 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 1, Lessons 6-8 engage students with the full intent of 6.NS.6 (Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.) In Lesson 6, Number: Interpreting the negative symbol, Student Journal, Step Up, page 21, Question 2b, students reason about opposite numbers on a number line. “Interpret each expression. Then write the number that is opposite. Use the number line to help your thinking. -30 ___.” In Lesson 7, Number: Comparing and ordering positive and negative numbers, Student Journal, Step Up, page 25, Question 4a, students order integers using a number line. “Shade five numbers. Then write the numbers that are shaded in order from least to greatest. You can draw a number line on page 42 to help your thinking. -6, 1, 3, -4, -7, 0, -1.” In Lesson 8, Number: Introducing absolute value, Student Journal, Step Ahead, page 27, students use absolute value to reason about integers. “The temperatures of two different cities were measured at the same time. The absolute value of each city in degrees Fahrenheit is 8. Write the possible pairs of temperatures for the cities in the chart. Show your thinking.” • Module 3, Lesson 3 and Module 5, Lesson 10 engage students with the full intent of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.) In Lesson 3, Ratio: Examining equivalence using tables, Student Journal, Step Up, page 89, Question 2a, students reason about ratios from a real world problem. “Read each story then answer the questions. Use a table to show your thinking. A math test has 7 multiplication questions for every 2 addition questions. Calculate the number of multiplication questions to addition questions for the following number of test questions: 27 Questions ____ : ____ ; 45 Questions ____ : ____.” In Lesson 10, Ratio: Using a given ratio when the total is known, Student Journal, Step Up, page 814, Question 1a, students reason about ratios using a tape diagram. “Draw a tape diagram to represent each problem. You do not need to calculate the answer. A 15-bag pack of potato chips has a 1:4 ratio between plain chips and BBQ chips. How many packs of each flavor are there?” • Module 7, Lessons 6, 8, and 10 engage students with the full intent of 6.EE.7 (Solve real- world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers). In Lesson 6, Algebra: Solving addition equations, Student Journal, Step Up, page 259, Question 2, students reason about and solve one step equations. “Calculate the value of each variable. Show your thinking and be sure to show each step. a. p + 3 = 21, b. 41 = m + 1, c. 65 = a + 5, d. w + 1.5 = 4.2, e. z + \frac{12}{20} = 2\frac{6}{10}, f. 48 + 3 = p + 30, g. z + 1.20 + 0.08 = 7.8, h. 58 + 34 = 26 + p + 30.” In Lesson 8, Algebra: Solving multiplication equations, Student Journal, Step Up, page 265, Question 1, students continue to reason and solve one step equations. “Calculate the value of each variable. Show your thinking. a. 2d = 16, b. 27 = 9y, c. 3h = 4.5, d. 32 + 24 = 7r, e. 55 = 4g + 7g, f. z + 8z = 4 + 32, g. 5\frac{2}{10} = 4g, h. 2z + z + 5z = 4.” In Lesson 10, Algebra: Solving word problems (addition and multiplication), Student Journal, Step Up, page 271, Question 2a, students write and solve an equation in the form of px = q for a real-world problem. “A machine assembles 60 bicycles in 4 hours. A person assembles 60 bicycles in 9 hours. How many bicycles does the machine assemble each hour? Let b represent the number of bicycles.” #### 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 6 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 6 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 11 out of 12, which is approximately 92%. • 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 114 out of 156, which is approximately 73%. • The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 103 out of 144, which is approximately 72%. 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 72% 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 6 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 1, Lesson 11, Number: Calculating distance on a coordinate plane, Student Journal, Step Up, page 36 and 37, connects the supporting work of 6.G.3 (Draw polygons in the coordinate plane given coordinates for the vertices) to the major work of 6.NS.8 (Understand a rational number as a point on the number line. Students use a coordinate plane to graph polygons and find the perimeter.) Question 1, “Plot each set of coordinates on page 37. Then draw lines to connect the dots in alphabetical order. Shape 1 A(-4,10), B(8,10), C(8,6), D(-4,6). Shape 2 E(-8,3), F(-4,3), G(-4,-6), H(-8,-6). Shape 3 I(3,3), J(10,3), K(10,-4), L(3,-4). Question 2, “Calculate these side lengths. Shape 1 Side AB, Shape 2 Side EH, Shape 3 Side LK.” Question 3, “Dallas wrote this equation to help calculate the side length of one of the shapes \left|3\right| + \left|-4\right| = 7. a. Which shape and side length did she calculate? b. What steps could she now follow to calculate the perimeter?” • Module 2, Lesson 8, Mass: Algebra: Using the distributive property, Step Up, page 65 connects the supporting work of 6.NS.B (Compute fluently with multi-digit numbers and find common factors and multiples) to the major work of 6.EE.A (Apply and extend previous understandings of arithmetic to algebraic expressions). Students use greatest common factors to represent expressions. Question 3c, “Find the greatest common factor. Then use the distributive property to rewrite each expression. 75 + 99, = (___ x ___) + ( ___ x ___), = ___ ( ___ x ___).” • Module 9, Lesson 6, Statistics: Identifying the mode, Student Journal, Step Up, page 334, connects the supporting work of 6.SP.2 (Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape) and 6.SP.3 (Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number) to the major work of 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, eg., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.) Students use ratio reasoning to answer questions about statistical data represented on a dot plot. Question 1, “Look at the dot plot on the right above and answer the following questions. a. What is the mode? b. What fraction of the words are above the mode? c. What fraction of the words are below the mode? d. Based on your answers for the previous two questions, do you think the mode is a good measure for that data set? Explain your answer.” • Module 10, Lesson 9, Volume: Rectangular-based prisms with one fractional side length, Student Journal, Step Up, page 382, connects the supporting work of 6.G.2 (Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems) to the major work of 6.EE.6 (Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.) Students use a formula to calculate the volume of rectangular prisms. Question 1, “Calculate the volume of each object. Show your thinking. a. 6in, 5in, and \frac{1}{4} in. b. 7m, 25m, and \frac{1}{5}m.” ##### 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 6 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Materials are coherent and consistent with the Standards. Examples of connections include: • In Module 2, Lesson 8, Algebra: Using the distributive property, Teaching the lesson Lesson notes, students apply and extend previous understandings of arithmetic to algebraic expressions, 6.EE.A, tand compute fluently with multi-digit numbers and find common factors and multiples, 6.NS.B to by solving word problems involving common factors and algebraic expressions. • In Module 4, Lesson 2, Algebra: Writing equations to match word problems, Teaching the lesson, Lesson notes, students apply and extend previous understandings of arithmetic to algebraic expressions, 6.EE.A, and reason about and solve one-variable equations and inequalities, 6.EE.B by solving real-life problems using their knowledge of expression to solve one-variable equations. ##### 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 6 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 6th 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, Lesson 2, Number: Reviewing fractions, Lesson Notes connect 6.NS.5 (Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation) to previous work in grade 5 (5.NBT.4). “In Lesson 5.3.11, students round decimal fractions with up to three decimal places to the nearest whole number and nearest tenth. In this lesson, students work to explore decimal fractions beyond thousandths.” • Module 8, Lesson 3, Ratio: Introducing percentage (area model), Lesson Notes connect 6.RP.3 (Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations) to the work from grade 5 (5.NF.2). “In Lesson 5.4.6, students are encouraged to use a range of strategies to solve multistep word problems involving the comparison of two or more common fractions. In this lesson (8.3), students are introduced to the concept of percentage using a hundredths square. They learn that a percentage is a representation of a number of parts out of 100 parts.” • Module 9, Mathematics Overview, Coherence, “Lessons 9.5–9.8 focus on introducing statistics and interpreting a set of data with mean, median, and mode. This work builds on interpreting data using line plots (5.3.12, 5.4.12, 5.9.12).” 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 2, Lesson 8, Algebra: Using the distributive property, Lesson Notes connect 6.NS.4 (Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor) and 6.EE.2 (Write, read, and evaluate expressions in which letters stand for numbers) to work in grade 7 (7.EE.1). “In this lesson, students use the distributive property to model equivalent expressions. They also build on the content from the previous lesson by using the greatest common factor to represent an equivalent expression using the distributive property. In Grade 7, students apply the properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.” • Module 3, Overview, “Lessons 3.1–3.7 focus on ratios as part-part and part-whole relationships. This work builds on previous work with relationships in numerical patterns (5.11.1–5.11.6) and serves as a foundation for comparing, measuring, and solving problems with ratios (6.5.8–6.5.12).” • Module 10, Lesson 12, Volume: Solving word problems, Lesson Notes connect 6.G.2 (Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems) to the work of grade 7 (7.G.6). “In this lesson, students review how to calculate the volume of rectangular-based prisms with fractional side lengths. They then solve multistep word problems involving volume. In Grade 7, geometry, students solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.” ##### 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 for Origo Stepping Stones 2.0 Grade 6 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 6 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 6 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. The materials partially 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 6 meets expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. The materials include problems and questions that develop conceptual understanding throughout the grade level. Cluster 6.RP.A addresses understanding ratio concepts and using ratio reasoning to solve problems. Multiple modules explore a variety of real-world applications using a few mathematical representations. Some opportunities exist for students to work with ratios that call for conceptual understanding and include the use of some visual representations and different strategies. Examples include: • Module 6, Lesson 8, Ratio: Developing the concept of rate, Step 3 Teaching the lesson, “A car travels 200 miles in 4 hours. How far does it travel in 1 hour? Project slide 3 and read the problem aloud. Ask, What does this problem want you to find? How would you solve it? What strategy or model could you use? Allow pairs to try different strategies to solve the problem (MP4). They may choose to draw a diagram or use a table to model their results. Invite volunteers to share their thinking, using the board if needed. If a table isn’t suggested, project the table (slide 4) and ask, How could this help us solve the problem? Confirm that a table can be used to organize rates to calculate the answer. Invite volunteers to share their ideas on how to complete the table. The image below shows two strategies for using the table. Ideas could include repeating the pattern, or finding out how long it takes Amy to run 10 laps. Confirm that the answer is 30 minutes.” Module 3, Lesson 2, Ratio: Building equivalent ratios pictorially, Step 3 Teaching the lesson, “Allow students time to work with a partner and create a representation for the scenario using a tape diagram for one sandwich first, then for two. Invite volunteers to share their responses with the class. Ask, What do you notice about the relationship between the amounts? Does the ratio change? Establish that there are more slices of ham in total, but because there are more sandwiches, the ratio stays the same. Say, Ratios describe a constant relationship between quantities. This relationship stays constant as the quantities change. This means equivalent ratios have the same relationship between each quantity.” (6.RP.1). • Module 3, Lesson 1, Ratio: Introducing ratio, Step 3 Teaching the lesson, “Ask, When might you use a ratio? What are some real-world examples of ratios? Allow students time to discuss and invite volunteers to share their thinking. If students have difficulty thinking of a context for this, provide examples such as birthday parties (guests, drinks, food), sports teams (scores, players) or school (classes, lessons) to assist with this. Have students work in pairs to create their own example of a scenario describing a relationship between two quantities (for example, for every x girls in the class, there are y boys). Have them write their example on a blank card and collect them to be used later in the lesson. Shuffle and distribute the cards to pairs of students (ensure that all students have a card that they did not create). Have the students work with the relationship of the quantities written on the cards, creating different representations of the ratio. This could include drawing tape diagrams, writing sentences describing the ratio, or writing the ratio as x:y. Allow time for students to work on their cards, moving around the room to ensure all students know what to do. Bring students back together and invite volunteers to share their ratio and related representations. Invite students to critique the reasoning of others.” Students relate abstract to concrete examples (6.RP.1). • Module 8, Lesson 1, Ratio: Linking part-whole ratios to fractions, Step 3 Teaching the lesson, “Distribute the cubes. and say, You will be building a character with some or all of your cubes. But first you need to count how many of each color cube you have. Ask students to build a character with their cubes. Afterward, have them write as many different ratios as they can about the cubes used to build the character. Encourage them to include part-part and part-whole ratios. Project the statement and table (slide 3), and read the scenario aloud. Analyze the fraction of profits ($$\frac{1}{4}$$) being donated. Then ask, What part of the fraction represents the total? What part represents the amount donated? How much is remaining? Project slide 4 to show these numbers in the table. Point out that if only$4 profit is made, then only 1 is donated to charity. Then ask, What numbers can we write to complete the table? Work with the students to write the missing values. For each value, ask, How did you figure out that amount? Look for students who have identified the multiplicative relationships in each column of the table.” (6.RP.1) Cluster 6.EE addresses the need to be able to apply and extend previous understandings of arithmetic to algebraic expressions, reason about and solve one-variable equations and inequalities and represent and analyze quantitative relationships between dependent and independent variables. Multiple Modules explore a variety of real-world applications using a few mathematical representations. Some opportunities exist for students to work with expressions and equations that call for conceptual understanding and include the use of some visual representations and different strategies. Examples include: • Module 2, Lesson 1, Algebra: Reviewing language and conventions, Step 3 Teaching the lesson, “Invite groups to share their working definitions from Step 2. Then discuss the points below: What is the difference between an expression and an equation? What is the difference between a product and a sum? What examples can you give for each? Establish that an expression can be a number by itself, or a combination of numbers and operations that do not have a relationship. Whereas an equation shows that two expressions are equal.” (6.EE.1) • Module 7, Lesson 1, Algebra: Simplifying expressions, Step 2 Starting the lesson, students are presented with a visual representation of 16 blocks representing 4 squared. “To review square numbers, project slide 1 and discuss the points below: What number does this picture represent? What expression can we write to match? (4 • 4, 16, or 42.) What type of number is 16? (Square number.) What other square numbers do you know?” Step 3 Teaching the lesson, “Distribute the resources and say, These are called algebra tiles. They are used to represent expressions. Ask students to examine the tiles and look for relationships between the different sizes (MP7). Display a small square tile. Say, The length of each side of this square is 1. What do we know about the area of this tile? (1 by 1.) 1 by 1 is 1 so this tile is called 1. Display the long tile end-to-end with the small square tile. Ask, What is the width of this rectangle? (1.) We could try to determine an exact length of this tile but we want this tile to represent a variable so we will think of it as a tile that can change length according to the unknown amount it is representing. Since we do not know the exact length of the tile, we will use the variable x to label, so the area is 1x or just x. Display the large square tile aligned to the length of the long tile. Say, We know the length of the long tile is x, so the side length of the large square tile is also x. What can we write to represent the area of the large square tile? (x2.) Emphasize that each tile should be treated as a single quantity.” (6.EE.3) • Module 7, Lesson 4, Algebra: Simplifying expressions with more than one variable, Step 3 Teaching the lesson, “ Organize students into groups of three or four and distribute the cubes to each group. In turn, each student rolls the cubes and uses the result to form a term, such as 2a for a roll of 2 and a, or 6 or 9 for a roll of 3 and 3. A roll of a and b would result in the two terms a + b. After there are at least two terms with differing variables, have the students work independently to write one expression to represent the total of all the individual terms, for example, for the terms 2a, 6, 4b, and 8, they could write 2a + 4b + 14. Encourage them to use factors to write the expression a different way where possible, for example, 2(a + 2b + 7), and to check the equivalence by substitution. Observe and listen to the students as they work, to identify and support those using incorrect thinking. Afterward, have the students compare their expressions and explain the steps they used. Encourage them to compare and contrast the different methods, if any.” (6.EE.3) ##### 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 6 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. 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 6 expected fluencies: 6.NS.2, multi-digit division and multi-digit decimal operations; 6.NS.3, add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation; and 6.EE.A, apply and extend previous understandings of arithmetic to algebraic expressions. Examples include: • In Module 3, Lessons 8-12, students use multi-digit division of whole numbers and decimals (6.NS.2,3). • In Module 5 interview, students calculate quotients in expressions that include fractions and whole numbers (6.NS.2,3). • Module 2, Lesson 8, Algebra: Using the distributive property, includes using <, >, or = to compare expressions that include skills such as subtracting or multiplying decimal numbers. • In Module 2, Lessons 9-12, students solve problems using the standard algorithm for performing mathematical operations with decimals (6.NS.3). • Module 3, Lesson 10, Division: Terminating and repeating decimal fractions, students add and subtract decimals, and multiply or divide numbers as they convert units. In Module 2, Lessons 9-12 provide practice for solving problems using the standard algorithm for performing mathematical operations with decimals (6.NS.3). • Module 4, Lesson 2, Algebra: Writing equations to match word problems, provides practice in writing equations to match word problems. For example, “What variable can you use to represent the value?” and “What operations will we use to calculate that value?” (6.EE.A) In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluencies. Examples include: • 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. • Each module contains a summative assessment called Interviews. According to the program, “There are certain concepts and skills , such as the ability to route count fluently, that are best assessed by interviewing students.” For example, in Module 9 Interview, students must demonstrate fluency of finding the mean, median, and mode of a data set. • Some lessons provide opportunities for students to practice procedural skills during the “Step Up” section of the student journal. • “Fundamentals Games” contains a variety of games that students can play to develop grade level fluency skills. ##### 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 6 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 6, Lesson 8, Ratio: Developing the concept of rate, Student Journal, Step In, page 216, addresses the standard 6.RP.3, “Antonio mixes teaspoons of yellow and red paint in the ratio of 12:4. How much yellow paint will be used for 1 teaspoon of red?” • Module 5, Lesson 2, Division: Common fractions (same denominators), Student Journal, Step Up, page 161, Problem 2b, addresses the standard 6.NS.1, “A straw is ten-twelfths of a foot long. Nicole cuts the straw into shorter pieces that are each two-twelfths of a foot long. How many pieces did she cut?” • Module 7, Lesson 10, Algebra: Solving word problems, Student Journal, page 271, Problem 2b, address the standard 6.EE.7, “Three friends enter a 15-mile fun run. Dwane runs the first 4 1/2 miles. Natalie runs the next 3\frac{1}{4} miles. Reece runs the rest of the distance. How far did Reece run? Let r represent the unknown distance.” • Module 4, Lesson 11, Algebra: Identifying independent and dependent variables, Student Journal, Step Up, page 151, Problem 2c, addresses the standard 6.EE.9, “In a math test, a student scores 5 points for each correct answer. What is a student’s score if they get 15 correct answers?” (identifying dependent and independent variables). • Module 9, Lesson 12, Area: Solving word problems, Student Journal, Step Up, page 353, Problem 2a, address the standard 6.G.4, “The roof of a cottage needs refurbishing. One side of the roof is 30 ft long by 12.5 ft wide. If a bundle of shingles can be purchased to cover 24 ft2, how many bundles are needed?” • Module 12, Lesson 10, Algebra: Generating and graphing variables (non-equivalent ratios), Student Journal, Maintaining Concepts and Skills, Ongoing Practice, page 463, Problem 2a, “Andrea wants to buy a guitar that costs150. The music store has a 25% off sale. When she buys the guitar she is given an extra 5% off. What amount does she pay for the guitar?”

• Module 3, Lesson 7, Algebra: Generating and graphing variables (non-equivalent ratios), Teaching the lesson, Investigation 2, students work in pairs to answer, “Emily has beetles to feed her lizards. Altogether she has a total of 52 legs. How many lizards could Emily have? What is the ratio of lizards to beetles?” (6.RP.1).

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

• Module 3, Lesson 12, Division: Adjusting to divide with decimal fractions, Teaching the lesson, Thinking Task, Problem 1, students read points on a coordinate grid to fill in a table showing the cost of a phone bill per month. Question 3 asks, “Riku investigates the call rate for Option B. It will cost $0.30 for each minute that she spends on the phone. She decides to calculate the total cost of a six-minute call. Which of these displays is most likely to show the total cost? Explain your thinking.” This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts. • Module 6, Lesson 12, Ratio: Comparing rates, Teaching the lesson, Thinking Task, Problem 2 inquires, “An architect hired by the school district draws up these plans (design shown). She decides to split the hall into three areas: stage, auditorium, and entrance. The stage needs wooden flooring and the auditorium will be carpeted. The school has a budget of$900 to spend on the wooden stage flooring. One dimension of the stage is 8m. They would like the other dimension to be somewhere between 3 and 5 meters. Given their budget, write the dimensions for the largest stage the school can afford to build. Show your thinking.” This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.

• Module 9, Lesson 12, Area: Solving word problems, Teaching the lesson, Thinking Task, students find the surface area of a greenhouse with dimensions given and identify the net that matches the greenhouse design. Problem 3 asks, “Archie plans to build the garden bed in this picture (3ft x 6ft x 6in deep). The measurements are taken from inside the garden bed. He will need to buy the wood to build it and the soil to fill it. He has all the other tools and materials that are necessary. What is the cost of building the garden bed?” This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.

• Module 12, Lesson 12, Algebra: Generating and graphing variables (non-linear), Teaching the lesson, Thinking Task, students are provided a collection of data in two tables. Number of vehicles that drive past the school at certain times during the day, the other set of data is a record of each vehicle’s speed. Problem 1 asks, “How many vehicles traveled at a speed that is equal to or greater than 25 miles per hour?” 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 6 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

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

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

• Module 2, Lessons 9-12, address addition and multiplication of decimal fractions. This standard is assessed in Module 2, Check-Up 2 (6.NS.2).

• Module 4, Lesson 11, Algebra: Identifying independent and dependent variables, (6.EE.3), students demonstrate conceptual understanding when they respond to, “Can independent variables involve fractions? Why?”

• Module 3, Lesson 3, Ratio: Examining equivalence using tables, (6.RP.1), students use tables to represent and reinforce equivalent ratios. Given a muffin recipe students find “how much of each ingredient is needed to bake 20 muffins”. A table is used to record the equivalent relationship between quantities.

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

• Module 5, Lesson 4, Division: Whole numbers by common fractions, Maintaining Concepts and Skills, Words at Work, students engage with all three aspects of rigor as they solve, “In his backyard, William is planting the same vegetables together in patches that are 2/3 of a yard wide and 1 yard long. The available space in his backyard measures 6 yards by 9 yards. William uses division to figure out the greatest number of vegetable patches he can have while allowing a walking space of \frac{1}{2} yard going in one direction between rows of vegetable patches.”

• Module 12, Lesson 10, Algebra: Generating and graphing variables (non-equivalent ratios), Maintaining Concepts and Skills, Question 2, students engage with conceptual understanding and application to solve, “Andrea wants to buy a guitar that costs $150. The music store has a 25% off sale. When she buys the guitar she is given an extra 5% off. What amount does she pay for the guitar?” • Module 3, Lesson 2, Ratio: Building equivalent ratios pictorially, (6.RP. 1), students apply their understanding of equivalent ratios using tape diagrams to solve several real-world problems during the Step Up discussion. In Ongoing Practice, students independently solve word problems using tape diagram models. • Module 12, Thinking Task, students are provided a collection of data in two tables. Number of vehicles that drive past the school at certain times during the day, the other set of data is a record of each vehicle’s speed. Question 2, “Show the number of vehicles that drove past the school throughout the morning in this graph. You will need to add the following information that is missing: title, labels for the x-axis and the y-axis, values along each scale.” #### 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 6 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 6 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 2, Lesson 6, Number: Finding the least common multiple, Step 3 Teaching the Lesson, students make sense of problems involving multiples and look for efficient ways to represent and solve them. “Project slide 2 and deconstruct the problem by asking questions such as, What do you know? What do you need to find out? How will you solve the problem? (MP1): A school cafeteria serves burgers every third school day and burritos every fourth school day. Both meals were served today. How many days until both meals are again served on the same day?” The teacher asks, “What is this problem asking you to do? Have you solved a problem like this before? What steps have you used to this point? What other strategies could you try? What other math tools could you use?” • Module 3, Lesson 7, Ratio: Solving word problems with part-part and part-whole situations, Step 2 Starting the Lesson, students make sense of problems and persevere in solving them as they draw upon their understanding of equivalent ratios. “Project slide 1, as shown, and read the word problem aloud (MP1). Ask, What steps do you need to take to solve the problem? Is the question referring to a part-part situation or part-whole? How do you know? Review the language used in the problem to determine that it is a part-whole situation, and the steps students will need to take to solve it. Allow students time to work with a partner to solve the word problem. Invite volunteers to share their solutions and confirm the ratio is 32:48, making the answer to the problem 80 club members.” • Module 5, Lesson 5, Division: Whole numbers by common fractions (with remainders), Step 2 Starting the Lesson, students analyze given word problems with division of whole numbers and fractions and check that their solution makes sense in the situation. “Project slide 1 as shown, and discuss the point below (MP1): A snail can travel at \frac{7}{10} of a mile each day. How many days would it take to travel 14 miles? What do you know about this problem? (A snail can travel \frac{7}{10} of a mile each day.) What do you need to find out? (How far can it travel in 14 days?) What expression can you write to match the problem? (14 ÷ \frac{7}{10.) What picture could you draw to help solve the problem? (14 rectangles split into tens.) How can you use the diagram to help you change the expression to whole numbers? (Multiply the whole number (dividend) and the fraction (divisor) by the same amount.) What amount would you multiply the numbers by? Why? (The value of the denominator because that will create a numerator that is a multiple of the denominator. The resulting fraction will be equivalent to a whole number.) Invite a student to complete the diagram to show the multiplication. What is the equivalent whole number expression? (140 ÷ 7.) What is the solution to the problem? (20 days.)” • Module 11, More Math, Problem Solving Activity 4, Word Problems, students make sense and persevere in solving multi-step ratio word problems. “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 will we do first? What will we do next? How could you show your thinking? Allow time for the students to find a solution. Then invite students to share their solution (1:2:2) and explain their thinking. Slide 1: There are 200 cars parked in a parking lot. 20% are blue, \frac{2}{5} are red, and the rest are white. What is the ratio of blue, red, and white cars in the parking lot?” 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 3, Number: Reviewing abbreviations for numbers greater than one million, Step 2 Starting the Lesson, students reason abstractly and quantitatively as they contextualize numbers, identifying real-world contexts for millions, billions, and trillions. “Project slide 1. Have the students list everyday examples for millions, billions, and trillions. Encourage debate around each suggestion (MP2). For example, a country’s population may be recorded with billions, millions, or even thousands depending upon its size and density. Then ask, How do we record these numbers? Do we write the whole number or do we just abbreviate the number? Bring out that numbers greater than one million are often abbreviated, especially when being reported to the public. For instance, a large company may have a reported net worth of 7.2 billion.” • Module 4, Lesson 5, Algebra: Order of operations involving variables, Step 3 Teaching the Lesson, students reason abstractly and quantitatively as they write an expression to match a given word problem and write a word problem to match a given expression. “Project slide 2 and read the problem aloud. Slide: Vishaya runs the same distance Monday through Friday. She then runs 12 miles on Saturday.” Notes include, “What expression could you write to represent the total number of miles that Vishaya runs each week? Organize the students into pairs to brainstorm ideas. Then have pairs write their expression (for example, 5m + 12) on the board (MP2) and explain how it matches the problem. Point to one expression and discuss the points below: What part of the expression will you calculate first? How do you know? What is a reasonable value we could substitute for the variable?” • Module 6, Lesson 1, Area: Exploring parallelograms, Step 2 Starting the Lesson, students reason abstractly and quantitatively as they contextualize a given scenario into a word problem. “Project slide 1 as shown and ask, What do you know about calculating the area of a rectangle? Organize the students into pairs to discuss their ideas. Then invite responses. Emphasize the understanding that the area of a rectangle is calculated by multiplying the length and width together. Project the grid overlaid on the rectangle (slide 2) and ask students to calculate the area of the shape. Invite responses to confirm the answer is 40 ft2. Ask pairs to work together again to create a word problem based on calculating the area of the shape shown on the slide (MP2). Bring students back together and invite volunteers to share their word problems with the class.” • Module 7, Lesson 3, Algebra: Simplifying expressions using distributive property, Student Journal, Step Up, page 251, Question 2, and Step 4 Reflecting on the work, students reason abstractly and quantitatively as they simplify expressions using the distributive property. “Write an expression to match each problem. a. There are 5 equal rows of fruit trees. In each row, there are 15 apple trees and some plum trees, with the same number of plum trees in each row. Let p represent the number of plum trees in each row. How many fruit trees are there in total? b. Each concert ticket costs$49 plus a $5 service fee. Ethan buys a ticket for himself and a group of friends. Len nrepresents the number of tickets that he bought. What is the total cost of the tickets? c. A garden path is 1\frac{1}{2} yards wide. The first 10 yards of the path are concrete. The rest of the path is gravel. Let prepresent the length in yards of the path that is gravel. What is the total area of the path?” Step 4, “Discuss the students’ answers to Student Journal 7.3. For Question 2, have students write their expressions on the board and relate each term back to the 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 6 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 1, Lesson 7, Number: Comparing and ordering positive and negative numbers, Step 3 Teaching the lesson, students critique the reasoning of others as they compare and order positive and negative numbers on a number line. “Make sure students justify the position of each number on the number line. In doing so, they should justify which side of the 0 to which the number is attached, the distance of the number to 0 and the relative position of the number in relation to other numbers. Encourage the remaining students to critique their reasoning using the sentence stems shown below (MP3). I have a different opinion, I think, I agree (disagree) because, and That makes sense, but...”. • Module 3, Thinking Tasks, Question 4, students construct viable arguments as they analyze linear relationships in order to determine the best cell phone plan. “Riku asks her friend Thomas about his cell phone usage. He says that he rarely makes any phone calls, but he sends a lot of texts. He estimates that he sends at least 300 text messages each month! If Riku uses her phone in much the same way Thomas does, which cell phone option should she choose? Show your thinking in the space below. Then justify your decision.” • Module 4, Student Journal, page 157, Convince a friend, students create expressions and equations to solve problems and then critique the reasoning of classmates. “Deana is 3 years older than her brother Marcos, and 2 years older than her pet dog, Hailey. Marcos is 8 years old. Deana reads that one human year is equivalent to 7 dog years. Marcos says that Hailey is over 70 years old in dog years. Do you agree or disagree with Marcos? Explain why. I agree/disagree with Marcos because ...Share your thinking with another student. They can write their feedback below. I agree/disagree with your thinking because … Feedback from:” • Module 7, Student Journal, page 281, Convince a friend, students construct a viable argument and critique the reasoning of others as they determine equivalent expressions in real-word and mathematical problems. “James and Gemma are talking about expressions. Gemma says that 7a + 10b can be rewritten as 17ab in the same way that 10 + 7 = 17. James agrees that 10 + 7 = 17 but he says it is more accurate to write 7a + 10b as 17 + ab. Who do you agree with? Explain your thinking. Share your thinking with another student. They can write their feedback below. Discuss how the feedback you received will help you give better feedback to others.” • Module 9, Student Journal, page 357, Convince a friend, students construct an argument and critique the reasoning of others while interpreting measures of center in real-world and mathematical problems. Noah asks his classmates to contribute to his math project. He creates a dot plot showing the age of one parent of each in his class so he can try to calculate the overall age. Mary says that calculating the median gives the most accurate measure of center. Do you agree or disagree with Mary? Share your thinking with another student. They can write their feedback below. Discuss how the feedback you received will help you give better feedback to others.” ##### Indicator {{'2g' | indicatorName}} Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Students have opportunities to engage with the Math Practices throughout the year. The MPs are often explicitly identified for teachers in several places: Mathematical practice overview, Module Mathematical practice documents, Mathematical modeling tasks, Thinking tasks, and within specific lessons, alongside the learning targets or embedded within lesson notes. MP4 is identified and connected to grade level content, and there is intentional development of the MP to meet its full intent. Students have many opportunities to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include: • Module 5, Lesson 9, Ratio: Comparing ratios in tables and graphs, “students use a ratio table or coordinate plane to model a real world problem”. Step 3 Teaching the lesson, “Organize the students into pairs and distribute the resources. Project slide 3. Pairs then solve the problems (90 dokkins from Store A or 72 from Store B for$48; 60 dokkins for $36 at Store A; 60 dokkins from Store B will cost$40). Organize pairs into groups to share answers and analyze methods used. Ask, Who created a ratio table to find equivalent values? Who created a coordinate plane and plotted ordered pairs to compare the prices? Who worked with the numbers in another way to solve the problems? (MP4) Make sure students justify their choices.”

• Module 7, Student Journal, page 280, Mathematical modeling task, students model a real- world situation with equations. “Ten year old Ricardo and his family are going to a show at the theater. His mom, dad, and five-year-old sister are all attending. They have $130 to spend on the family night out. How would you spend the money to ensure everyone has a ticket, a treat, and a drink? Explain your thinking.” An image shows: Theater tickets: Adults$23.50, child (8-17 years) $19.50, child (2-7 years)$16.50, Booking fee $3.50/ticket, Family ticket (includes booking free)$95.00. Another image shows Refreshment prices: Popcorn $5.50, Chocolate$2.50, Small drink $3.00, Large drink$4.50.

• Module 8, Lesson 9, Ratio: Finding the whole given a part and the percentage, students use a double number line or relationship diagram to represent a problem and explain the connections between the two models. Step 3 Teaching the lesson, “Organize students into pairs. Project slide 6 and read each problem aloud. One student in each pair uses a double number line to solve the first problem, then draws a relationship diagram to solve the second problem. The other student uses a relationship diagram to solve the first problem, and a double number line for the second problem. Listen and observe as they work. Ask questions to gauge their understanding of the models and calculations. Afterward, have the pairs debate the efficiency and effectiveness of each diagram and their methods (MP3). Then ask the class, What is the same about the two models? (MP4) What is different? Which do you prefer? Why?”

• Module 9, Student Journal, page 356, Mathematical modeling task, students model a real-world surface area problem. “Pamela wants to paint the outside of her dog’s kennel. The kennel is shaped like a rectangular-based prism and she would like to cover the sides only with one coat of paint. The paint cans sold at her local store contain enough paint to cover about 2,500 square inches per can. a. Pamela buys two cans of paint from the store. Does she have enough paint for her project? b. If the kennel was twice as long, would Pamela need exactly twice as much paint? c. Explain your thinking.”

• Module 12, More Math, Thinking Task, School Crossing, students model with math as they graph ratio percentages. “The principal of Sunnydale Elementary is concerned about the increased traffic around the school. She has asked the city council to install a set of traffic lights to help. The council explains they must first study the traffic flow around the school before they can agree. The following Monday, two traffic inspectors arrive. One of the inspectors records the number of vehicles that drive past the school. The other inspector records the speed that each vehicle travels. The results are shown below. Show the number of vehicles that drove past the school throughout the morning in this graph. You will need to add the following information that is missing: title labels for the x- and y-axis values along each scale.”

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

• Module 3, Lesson 7, Ratio: Solving word problems with part-part and part-whole situations, students choose between a model or diagram as a tool to represent ratio and solve ratio word problems. Step 3 Teaching the lesson, “Project slide 2, as shown, and read the word problem aloud. Cathy makes bouquets with 23 flowers in each to sell at a local market. She can make 6 bouquets in 4 hours. If she needs to make 54 bouquets by the weekend, how many hours will she need to work? Encourage students to solve the problem, choosing a model or diagram to show their thinking (MP5).”

• Module 7, Student Journal, page 194, Mathematical modeling task, students consider and choose from the available tools to solve a real world problem. “Samuel is playing an online game where he can trade the goods he collects for other items he needs. He has some oranges, but he would like to trade them for fish. He knows that: one loaf of bread is worth the same as one apple and two fish, five oranges are worth the same as two loaves of bread, four loaves of bread are worth the same as fourteen fish, and six fish are worth the same as two cantaloupes. How many fish can Samuel trade for five oranges? Explain your thinking. Discuss the different tools, representations, and/or strategies students used to solve the problem. For example, some students may have used tables to represent each relevant clue as a ratio then used equivalent ratios to allow comparison, as shown, and concluded that Samuel can trade 5 oranges for 7 fish. Other students may have simply started with the second clue, because Samuel has 5 oranges, then analyzed the third clue and determined that Samuel can trade 5 oranges for 7 fish.”

• Module 7, Lesson 2, Algebra: Simplifying expressions using the commutative and associative properties, Slide 1, students simplify algebraic expressions and choose a tool to represent the problem. “Victoria is decorating her backyard for a party. She arranges balloons individually or in bunches of the same number. Afterward, there are three bunches of silver balloons and six individual silver balloons. There are also four bunches of purple balloons and three individual purple balloons. How many balloons has she arranged in total?” Step 3 Teaching the Lesson, “What might help you model this problem? Have students work individually to model the problem using any method of their choice. (MP5)”

### Usability

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 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 6 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities.

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 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.”

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 5, Number: Introducing positive and negative numbers, Step 2 Starting the lesson, teachers are provided context about positive and negative integers. “Project slide one and ask, What two numbers on this number line have a difference of 5? Encourage students to give pairs of numbers. Decimal fractions or common fractions may be included. Write each  pair of numbers on the board.”

• Module 4, Lesson 2, Algebra: Writing equations to match word problems, Step 3 Teaching the lesson, provides teachers guidance about how to set up equations to match word problems. “Project slide 2 as shown, and discuss the points below. Organize the students into pairs to write an equation to match the word problem. Invite one pair to write their equation on the board and explain what each part represents. Continue until all variations of the equation (for example, 65 – (5 • 5.50) = t, (5 • 5.50) + t = 65, 65 – t = (5 • 5.50), or t + (5 • 5.50) = 65) are written on the board. Project the word problem (slide 3) and read it aloud. Say, Three students wrote these equations to match this word problem. Have the pairs determine which of the equations is correct. Afterward, invite pairs to share and justify their findings, including why the other equations are incorrect. Encourage the other students to ask questions to clarify, if necessary, and to critique their reasoning.”

• Module 8, Lesson 6, Ratio: Percentages of collections, Lesson overview and focus, Misconceptions, include guidance to address common misconceptions as students work with percentages. “Because these examples focus on percentages less than 100%, students may develop the misconception that percentages are only used in this range. When examples arise in the news or through classroom conversation, discuss percentages greater than 100% to help students recognize that these are valid values as well.”

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

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

The materials reviewed for Origo Stepping Stones 2.0 Grade 6 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, Preparing for the module, Focus, Operations, explains concepts connected to operations with decimal fractions. “In the last part of Module 2, students review addition and subtraction of decimal fractions before exploring multiplication of decimals. In Lesson 2.9, students add and subtract decimals with regrouping, emphasizing the need to align decimal points to ensure place-value columns are correct. In Lesson 2.10, students are encouraged to use partial products for multiplying a decimal fraction by a whole number. The situation can be described by the expression 4 × 8.2, and students partition this to 4 × 8 and 4 × 0.2. This strategy is compared with the standard algorithm for multiplication. It is important to note that students place the decimal point in these lessons by reasoning about its position, not by counting digits to the right of the decimal point. If the product of 4 × 8.2 is 328 (without the decimal point), it makes sense that the product would be 32.8 because it would be a bit more than 32. In Lessons 2.11 and 2.12, students work with greater factors. They are still asked to reason about an estimated product and then to place the decimal point using their estimation. The standard multiplication algorithm is used for calculations. Some of the problems given require regrouping.”

• Module 5, Research into Practice, Ratio, supports teachers with concepts for work beyond the grade. “As the Mathematics Focus suggests, this work with ratio sets the stage for the ongoing work with ratio (Modules 6, 8, 11, and 12) and provides a foundation for learning about proportional relationships in Grade 7 in the major cluster 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. In preparation, provide every opportunity for students to investigate, represent, and describe part-part and part-whole relationships in context. Read more in the Research into Practice sections of Modules 6, 8, 11, and 12.”

• Module 11, Preparing for the module, Research in practice, Ratio, supports teachers with concepts for work beyond the grade. “As the Mathematics Focus suggests, the work in this and previous modules serves as a foundation to the introduction of percentages greater than 100% and percentage discounts/markups (Module 12). It provides the groundwork for learning about proportional relationships in Grade 7 in the major cluster 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. Provide many opportunities for students to investigate and discuss different ways of representing a problem in context as they work toward a solution. For example, drawing a picture to help their understanding, or using different symbolic representations (decimal and/or common fractions, or percentages) to make the calculations easier (30% of 4⁄5 = 0.3•0.8). Read more in the Research into Practice section of Module 12.”

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

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

The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 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 6 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 6 and the Common Core Standards, includes all Grade 6 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 6, 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, Division: Interpreting division situations, the Core Standard is identified as 6.NS.A.1. The Prior Learning Standard is identified 4.MD.A.2. Lessons contain a consistent structure that includes Lesson Focus, Topic progression, Formative assessment opportunity, Misconceptions, Step 1 Preparing the lesson, Step 2 Starting the lesson, Step 3 Teaching the lesson, Step 4 Reflecting on the work, and Maintaining concepts and skills. This provides an additional place to reference standards, and language of the standard, within each lesson.

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

• Module 5, Mathematics Overview, The Number System, includes an overview of how the math of this module builds from previous work in math. “Module 5 begins with an exploration of fraction division. Students have experience dividing a whole number and a fraction from Grade 5. They extend their learning now to fraction by fraction division. Lessons 5.1 and 5.2 ask students to write division expressions for problem situations and to draw models of those situations. Students should recognize that the actual division problems are similar to those they have solved in the past, except now there are more fractions. Making this connection to whole number division helps many students reason effectively about these problems. Students solve the problems using visual models and reasoning in this module. They do not need the algorithm at this stage.”

• Module 10, Mathematics Overview, Coherence, includes an overview of how the content in sixth grade connects to mathematics students will learn in seventh grade. “Lessons 10.8-10.12 focus on calculating volume of rectangular-based prisms with up to three fractional side lengths. This work extends from finding and calculating volume of prisms (5.2.7- 5.2.12) and solving volume word problems (5.11.12) and serves as a foundation for solving real-world problems involving angle measure, area, surface area, and volume in Grade 7.”

• Module 12, Lesson 3, Ratio: Using complementary percentages, Topic progression, “Prior learning: In Lesson 6.12.2, students review percentages greater than 100%. They assess situations to determine where it makes sense to have a percentage greater than 100%, and complete equivalency statements to match. 6.RP.A.3, 6.RP.A.3c; Current focus: In this lesson, students relate a percentage reduction of an item to the amount to be paid (for example, 25% off an item means 75% of the total will be paid). They then calculate an answer using a preferred method. 6.RP.A.3, 6.RP.A.3c; Future learning: In Lesson 6.12.4, students relate a percentage increase of an item to the amount to be paid (for example, a 20% increase in the cost price of an item means that 120% of the cost price will be paid). 6.RP.A.3, 6.RP.A.3c” Each lesson provides a correlation to standards and a chart relating the target standard(s) to prior learning and future learning.

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

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

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

• Module 2, Resources, Preparing for the module, Newsletter, Core Focus, “Algebra: Reviewing and extending understanding of the order of operations, Number: Finding the least common multiple, and the greatest common factor, Operations: Adding, subtracting, and multiplying decimal fractions using the standard algorithm. Algebra - Students begin by revisiting the terms relating to algebra. They work through examples of expressions and equations using this to review the idea that the = sign means: is equal to, is equivalent to, or balances. They also learn that in algebra the multiplication symbol may be confused for the letter x. This is why an expression such as 5 × (3 + 7) can be recorded as 5 \cdot (3 + 7), or 5 (3 + 7). Following this, students review and extend their understanding of the order of operations. Students begin to work with expressions that include exponents, common fractions, and decimal fractions. Number - Students review factors and multiples to help identify least common multiples (LCM), and greatest common factor (GCF). Students explore factors and multiples by describing the relationship in both directions (for example, 5 is a factor of 75, and 75 is a multiple of 5). Students also label factors as prime or composite. Students list the multiples of any two given numbers to identify the least common multiple. Similarly, they find the greatest common factor by listing the pairs of factors for given numbers. Operations - In the final lessons of this module, students review the addition and subtraction of decimal fractions by applying the standard algorithm. They then explore the multiplication of decimal fractions by relating the partial-product strategy to the standard algorithm.”

• Module 6, Resources, Preparing for the module, Newsletter, Glossary, “Parallelograms: The base (b) of a parallelogram can be any side. The perpendicular height (h) forms a right angle with the base and is the distance from the base to the opposite side. The rule for calculating the area is bh, or bh. Any polygon: Split the polygon into the least number of triangles and/or rectangles. Calculate the area of these shapes individually. Add the areas to find the area of the original polygon. Triangle: The base (b) of a triangle can be any side. The apex is the vertex opposite the base. The perpendicular height (h) forms a right angle with the base and is the distance from the base to the apex. The perpendicular height can be inside the triangle or outside, as shown below. The formula for calculating the area is (b \cdot h) \div 2 or \frac{bh}{2}. A rate describes the relationship between two quantities when the value of one of the quantities is 1. Rates may be expressed in different ways, but all have one quantity as 1. For example, 8 for 1 ticket, 2 cups of flour for every 1 cup of milk, 3 miles per hour, or 4/lb.” Module 6, 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, “Have your child collect a set of data about something that interests them (e.g. number of points scored by their favorite football team for one season) and have them create a box plot to show the information. Have your child find a box around the home and measure the length, width, and height using centimeters. Once they have done the measurements, have them calculate the volume of the box.” ##### Indicator {{'3e' | indicatorName}} 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 6 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, “Algebra: In Grade 6, students are expected to understand the order of operations more deeply. For many students, the order of operations is an acronym (PEMDAS) rather than a meaningful way of thinking about mathematics. There are four common misconceptions about the order of operations: Multiplication must come before division; Addition must come before subtraction; Operations must be performed from left to right; and Parentheses come first. Students must understand that multiplication and division are done in the order they appear from left to right, as are addition and subtraction. A multiplication to the right of an addition (2 + 3 × 4) is done before the addition — operations are not all done in one left to right sequence. Finally, grouping symbols (not just parentheses) are used to re-sequence operations. In (2 + 3) × 4, the parentheses push the addition to the beginning of the sequence. In 3 × 4 ÷ (1 + 2), the multiplication of 3 and 4 or the addition of 1 and 2 could happen first. The parentheses mean to add before you divide. Number: Students learn about factors as the numbers (often prime) that are multiplied together to make a product. While the procedures of factoring are simple, students are sometimes challenged to use what they know about factors to solve problems, including finding the Greatest Common Factor (GCF) or Least Common Multiple (LCM). Students may not realize that a number with both 2 and 3 as prime factors also has 6 as a factor. They may work only with the factors that are visible, ignoring factors that are products of prime factors. Operations: Students use their understanding of place value to add and subtract decimal fractions. This understanding of place value also supports multiplication of decimals. Students reason about the approximate size of a product in order to place the decimal point correctly in a product. This supports developing strong operation sense around decimal multiplication. Decimal multiplication challenges the common misconception (present even in many adults) that multiplication makes things bigger and division makes things smaller. To learn more: Dupree, Kami M. 2016. “Questioning the Order of Operations.” Mathematics Teaching in the Middle School 22 (3): 152–59. Feldman, Ziv. 2014. “Rethinking Factors.” Mathematics Teaching in the Middle School 20 (4): 230–36. Jeon, Kyungsoon. 2012. “Reflecting on PEMDAS.” Teaching Children Mathematics 18 (6): 370–77. Empson, Susan B. and Linda Levi. 2011. Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH: Heinemann. References: Vamvakoussi, Xenia, Wim Van Dooren, and Lieven Verschaffel. 2013. “Educated Adults Are Still Affected by Intuitions about the Effect of Arithmetical Operations: Evidence from a Reaction-time Study.” Educational Studies in Mathematics 82, no. 2: 323–30.” • Module 6, Preparing for the module, Research into practice, “Area: Just as students have learned to compose and decompose numbers, they can also compose and decompose shapes. Once students understand that measuring area is about counting the number of square unit tiles inside a shape, formulas can be figured out by reasoning based on what students already know. The area of a rectangle is a simple calculation. The use of visual images allows students to develop and use the formulas for the area of parallelograms and right triangles. They can then extend this understanding to reason about any quadrilateral or triangle — in fact, any polygon. Even if students have access to a formula list during high- stakes assessment, these experiences reasoning about the formulas will minimize confusion between area and perimeter as well as use them more effectively (and accurately) because they understand them. Ratio: Unit rate is one of the first ways students reason proportionally. By asking, “How much for one?” students are able to figure out solutions to complex problems in ways that make sense to them. Rates are composed units (e.g. miles per hour or dollars per pound) that describe a relationship. Unit rates have been simplified to include a one in the relationship. Depending on the situation, it may be appropriate to leave the rate in whole numbers other than one. Students build proportional reasoning skills by using these skills to solve problems. They must understand that there are multiple strategies for solving a problem and they will come to understand that these different strategies are related to one another. For example, students can use a common multiple or a unit rate when comparing prices. Both methods work because common multiples build on unit rates. To learn more: Beigie, Darin. 2016. “Dare to Compare.” Mathematics Teaching in the Middle School 21 (8): 460–69. Sinclair, Nathalie, David Pimm, Melanie Skelin, and Rose Mary Zbiek. 2012. Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 6-8. Reston, VA: National Council of Teachers of Mathematics. References: Cramer, Kathleen and Thomas Post. 1993. “Making Connections: A Case for Proportionality.” The Arithmetic Teacher 40 (6): 342–46. de la Cruz, Jessica A. and Sandra Garney. 2016. “Saving Money Using Proportional Reasoning.” Mathematics Teaching in the Middle School 21 (9): 552–61. Van de Walle, John, Karen Karp, and Jenny Bay-Williams. 2013. Elementary and Middle School Mathematics: Teaching Developmentally (8th Edition). Boston: Pearson.” ##### Indicator {{'3f' | indicatorName}} Materials provide a comprehensive list of supplies needed to support instructional activities. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 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, “ten-sided dice in lesson 11 and The Number Case in lesson 6. Each student uses a blank card in lesson 9, counters in lesson 5, Student Journal in each lesson, Support 8 in lesson 11, and Support 12 in lesson 5.” • Module 2, Lesson 5, Number: Reviewing factors and multiples, Lesson notes, Step 1 Preparing the lesson, “Each student will need: 1 copy of Support 8, counters, and Student Journal 2.5.” Step 3 Teaching the lesson, “Distribute the support page. Explain that you are going to read some clues and that you want them to use the hundred chart to find the mystery number. They can place their counters on top of numbers that may match the clues below: Clue 1: I am a composite number. Clue 2: I am a multiple of 8. Clue 3: I have 7 factors. Clue 4: I am greater than 60 but less than 70. • Module 5, Preparing for the module, According to the Resource overview, teachers need, “non-permanent markers in lesson 9 and The Number Case in lesson 9. Each pair of students needs access to water, blue and red paint cotton tips, eye droppers, a non-permanent marker, a paint tray or plastic lid, and The Number Case in lesson 8. Each student will need a strip of paper or ribbon in lesson 1.” • Module 7, Lesson 9, Algebra: Solving division equations, Lesson notes, Step 1 Preparing the lesson, “Each pair of students will need: 1 pan balance card from The Number Case; Each student will need: 1 set of algebra tiles (Note: If not available, use cut-outs from Support 34.) Student Journal 7.9” ##### Indicator {{'3g' | indicatorName}} This is not an assessed indicator in Mathematics. ##### Indicator {{'3h' | indicatorName}} 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 6 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. ##### Indicator {{'3i' | indicatorName}} Assessment information is included in the materials to indicate which standards are assessed. The materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 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 4, 6.NS.4, “Write the greatest common factor. a. 60; 45 greatest common factor ___. b. 52; 26 greatest common factor ___ c. 35; 10 greatest common factor ___.” • Module 6, Assessment, Quarterly test, Test A, denotes standards for each question. Question 21, 6.EE.5, “Choose the value that would make the equation true. (25 - x)2 = 144 A. 10, B. 15, C. 13, D. 17.” • Module 8, Preparing for the module, Module assessment overview, Interview, denotes standards addressed. 6.RP.3 and 6.RP.3d, “20% of 130 \Box Provides a correct answer. (26) \Box, Shows evidence of an effective strategy. 40% of 5m \BoxProvides a correct answer. (200cm or 2m) \BoxShows evidence of an effective strategy. 30% of 2\frac{1}{4}m \BoxProvides a correct answer. (75cm or 0.75m) \BoxShows evidence of an effective strategy. 70% of 3 \BoxProvides a correct answer. (2.1) \BoxShows evidence of an effective strategy.” • Module 10, Preparing for the module, Module assessment overview, Performance task denotes the aligned grade level standard. Question 1, 6.G.2, “Unlike most pools, Kasem’s pool does not have a shallow end and a deep end. Instead, it is all the same depth. The pool is 15.25 m longer, 10 m wide, and 1.8 m deep. How much water does the pool hold if filled to a depth of 1.6 meters? Show your thinking.” ##### Indicator {{'3j' | indicatorName}} 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 6 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 2a, “Write the missing numbers to balance the expression. 35 + 84 = 7( ___ + ___ ). Answer: 5 + 12.” The answer key aligns this question to 6.NS.4 and 6.EE.2. • Module 6, Assessments, Quarterly test B, Question 12, “Complete the equation. Show your thinking. \frac{9}{15}\div\frac{3}{15}= ?” The answer key shows the answer as 3 and aligned to 6.NS.1. • Module 9, Assessments, Performance task, Question 2, students use ratio strategies to solve multi-step problems. “Solve the word problem. Show your thinking. Then write the answer. Monique is asked to fill this machine with gumballs. She counts seventy-five gumballs that are either orange or cherry flavor. Monique says that this number represents 30% of the total number of gumballs in the machine. How many gumballs are not cherry or orange flavored in this machine?” The Scoring Rubric and Examples state, “2 Meets requirements. Shows complete understanding. Correctly solves multistep word problems that include calculating a whole when given a part and the percentage. 1 Partially meets requirements. Shows little evidence of understanding when solving a multistep word problems that include calculating a whole when given a part and the percentage. 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 6 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 6.NS.7, understand ordering and absolute value of rational numbers. Check-up 1, Question 4, “Color the bubble beside the statement that is true. a. -7 > -2, -7 > 2, -2 > -7, 2 < -7. b. -2 = 2, -7 < 2, 9 < -7, -2 > 9.” Performance task, ”Olivia is housesitting for a friend in Canada. She notices that both the fridge and freezer show a temperature of 0°C. She decides to change the temperature on the controls. A few hours later, the temperature of the fridge is 3°C, while the temperature of the freezer is -9°C. Question 1, Circle the part of the fridge that records the greatest change in temperature. fridge; freezer. Question 2, Use this open number line to prove your thinking. Question 3, Olivia writes this statement to compare the magnitude of the temperature change. -9 < 3.” • Module 6, Quarterly test questions support the full intent of MP2, reason abstractly and quantitatively, as students reason abstractly and quantitatively about ratios. Question 3, “Circle the best offer. Show your thinking. Image shows 4 spaghettis for2.80 or 6 spaghetti for \$3.90.” Question 6, “Which watermelon has a greater ratio of seeds to slices? Show your thinking. Tyler eats 3 slices of watermelon and counts 8 seeds. Beatrice eats 4 slices of watermelon and counts 10 seeds.

• Module 9, Interview 1, develops the full intent of 6.SP.2, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. “Steps: Provide the student with the support page. Explain that screen time is the amount of time that is spent each day in front of any screen. Ask the student to describe what the results show. If necessary, prompt them to make reference to the shape and spread of data. Ask the student to identify the mode, median, and mean. Encourage students to verbalize their thinking as they calculate each measure of center. Draw a ✔ beside the learning the student has successfully.”

• Module 12, Quarterly test questions support the full intent of MP6, attend to precision, as students identify and calculate the mean average deviation for a data set. For example, Question 23, “Calculate the mean average deviation (MAD) for the data set. Round your answer to the nearest hundredth. 1, 3, 5, 7, 9, 11, 13.”

##### 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 6 do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

There are no accommodations on student assessments.

#### 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 6 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 6 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 5, Division: Whole numbers by common fractions (with remainders), include:

• Extra help, “Activity: Have each student cut out their three foldables, then fold the ends in so the expression is on the front as shown. Instruct them to open one foldable, and draw an area model picture to help solve the expression. They then write the mixed number quotient in the answer box on the front. Repeat for the other two foldables. Then have them share and compare their completed foldables to check each other’s work.”

• Extra practice, “Activity: Have the students work individually to write a word problem to match each equation in Question 3 of the Student Journal. Explain that they must make sure the mixed number solution makes sense. They then exchanged problems with another student to check each other’s work.”

• Extra challenge, “Activity: Organize the students into pairs. They take turns to write an equivalent whole number expression for one expression on the game board. For example, for 7\div\frac{5}{3} they would write 21\div5 on a blank card. Allow them to make notes as needed. They continue until they have written an equivalent expression for each expression on the game board. The cards are then mixed and placed facedown in a pile. Students take turns to flip a card and place a counter on the equivalent expression on the game board. They then say the quotient. If the quotient is not correct they must remove their counter. Otherwise play continues until one student places 3 adjacent counters in one row or column to win the game, or until all the cards are used. The cards can be remixed and the game played again.”

##### 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 6 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: Using exponents greater than 2, Differentiation, Extra Challenge, “Review what the students already know about square numbers and list some of these examples on the board (e.g. 1, 4, 9, 16). Say, Square numbers are generated with exponents of two. Cubic numbers are generated with exponents of three. Ask, What are some cubic numbers that you know? Have the students list the first few cubic numbers on the board (e.g. 1, 8, and 27). Once familiar, groups of 3 students can be challenged to a) find the cubic numbers less than 250, and b) find the cubic number that is nearest 500.”

• Module 5, Lesson 2, Division: Common fractions (same denominators), Differentiation, Extra Challenge, “Organize the students into pairs. Have each student write a quotient in the form of a proper fraction or whole number (less than 10). They then exchange cards and write a matching expression involving division. For example, one student writes the quotient \frac{1}{12} and the other student writes the expression \frac{5}{12}\div5. Encourage them to write expressions in the different formats discussed in the lesson, for example, \frac{4}{8}\div4, \frac{4}{8}\div\frac{2}{8}, and \frac{4}{8}\div\frac{1}{8}. The activity continues until all the cards are used. Retain the cards for use in the later differentiation activities.”

• Module 10, Lesson 4, Statistics: Consolidating box plots, Differentiation, Extra Challenge, “Organize students into pairs. Explain that students are to select an international city to research temperature data for the 1st to the 15th of the previous month, then complete a five-number summary, box plot, and report to describe the variation in temperature.”

##### 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 6 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 2, Lesson 1, Algebra: Reviewing language and conventions, Student Journal, page 44, Step Up, students determine if two expressions are equivalent. Question 1, “Circle the two expressions in each equation. Then write true if they are equivalent. a.”15 = 45 \div 3, b. 4(3 \div 3) = 38, c. 60 = 12(1 + 4), d. 5 + 11 + 4 = 30, e. 18 = 2 \times 3 \times 3, f. 8 \times\frac{1}{4}= 2, g. 1.8 + 9.2 = 10, h. 5 = 100 \div 20.”

• Module 6, More Math, Thinking Tasks, Question 4, students determine seating arrangements using dimensions that were given to them in a previous problem, “Use your answer from Question 3 to solve this problem. The architect allows 0.5 m2 for each seat and has been asked to seat as many people as possible. Draw a picture to show the possible seating arrangements in each area. You can draw to show each seat. Then justify the seating arrangement that you decided to draw.”

• Module 11, More Math, Investigation 1, students compare ratios with 3 parts. “How does the ratio of boys to girls to teachers vary from Pre-K to Grade 6? Project slide 1 and read the investigation with the students. As a class, discuss how students are going to answer the investigation question. When the students understand what they need to do, organize students into pairs and allow time for them to answer the investigation question. Afterward, bring the class back together and discuss the results.”

##### 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 6 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 3, Lesson 1, Ratio: Introducing ratio, Step 1 Preparing the lesson, “Each pair/group of students will need: paper, blank cards. Each student will need: Student Journal 3.1.” Step 2 Starting the lesson, “Project slide 1, and read the scenario aloud. Ask, How could you represent this information using a diagram? Have students discuss ideas with the person beside them and make notes on paper if necessary. Then invite volunteers to share their thinking.” Step 3 Teaching the lesson, “Shuffle and distribute a card to each pair of students making sure the card was not written by them. Pairs then create different representations of the relationship between the quantities shown (MP2). This could include drawing tape diagrams, writing sentences describing the ratio, or writing the ratio symbolically (x:y). Move around the room to ensure all students know what to do. Afterward, invite volunteers to share their ratio and related representations. Encourage other students to critique their reasoning.”

• Module 5, Lesson 2, Division: Common fractions (same denominators), Step 3 Teaching the lesson, “Organize students into pairs to solve the problem. Encourage students to use the Flare Fractions (Area) online tool to act out the problem, if needed. Project the third word problem (slide 5), and have the pairs work together to write a matching equation showing the solution (for example, \frac{8}{10}\div\frac{2}{10} = 4) (MP2). Afterward, invite students to share and justify their methods. Encourage them to use the Flare Fractions (Area) online tool to demonstrate the division. Ask an individual to write the equation on the board.”

• Module 12, Lesson 9, Algebra: Generating and graphing variables, Step 3 Teaching the lesson, “Project slide 2 of the Step In, as shown, and read them aloud. Allow students time to discuss in pairs, then invite responses. Project slides 3 to 9 of the Step In and work through the questions with the class. Place students into small groups and explain that they are to work together to complete an experiment. Outline the three stations using the support pages, then distribute the relevant support pages to each group (Note: Groups are to complete one of the three activities.). Allow students to work in their groups to complete their activity in Student Journal 12.9.”

##### 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 6 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: Using exponents greater than 2, Lesson notes, Step 2 Starting the lesson, “ELL: Pair the students with fluent English-speaking students. Allow them to discuss the question, How could you use exponents to represent the number one hundred? Create an anchor chart representing Exponents and display it in the classroom.” Step 3 Teaching the lesson, “ELL: Allow the students to think about the questions being asked. Then give them the opportunity to tell their partner their answer before presenting to the group. Allow the students to use hand gestures (such as thumbs up or down) to show they understand, or are confused by, the language being used. Allow pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Encourage the students to listen to other students’ answers and tell their partner why they agree or disagree.”

• Module 12, Lesson 3, Ratio: Using complementary percentages, Lesson notes, Step 3 Teaching the lesson, “ELL: Encourage the students to think about the questions being asked, then share their answers with their partner before presenting to the group. Allow pairs to complete the Student Journal, if necessary.” Step 4 Reflecting on the work, “ELL: Encourage the students to listen to other studnet’s answers, then rephrase them.”

##### 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 6 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 Dwane, Jacinta, Jamar, and Samuru 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 6 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 6 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 6 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 7, Number: Finding the greatest common factor, Lesson overview and focus, Misconceptions,  “If students struggle to distinguish Least Common Multiple (LCM) from Greatest Common Factor (GCF), support them to state the entire phrase (not just the acronym) and reason about each word, emphasizing the words least and greatest, respectively. Number pairs could have many factors or multiples in common. The first word tells if the solution is the least or greatest in the list.”

• Module 3, Lesson 3, Ratio: Examining equivalence using tables, Step 3 Teaching the lesson, “Project the word problem (slide 3) and read it aloud. Ask, How can you solve this problem? How does the table model the problem? Encourage students to describe the problem, then invite volunteers to write the missing numbers (SMP1). Ask, Do we need to skip count? What is the relationship between 3 and 15? Students should identify that 15 is a multiple of 3, because 3 × 5 = 15. Therefore, 4 × 5 (20) will tell the number of trucks. Confirm that 20 + 15 = 35, which matches the number of vehicles (trucks and cars).”

• Module 8, Lesson 5, Ratio: Simple percentages of quantities, Lesson overview and focus, Misconceptions, “If students struggle to connect 25% with \frac{1}{4}, for example, support them to use the definition of percentage (a fraction of 100) to write \frac{25}{100} and then see if \frac{1}{4} is an equivalent fraction.”

##### 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 6 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 5, Number: Reviewing factors and multiples, Step 2 Starting the lesson, references the Flare Number Board to review the relationship between factors and multiples. “Open the Flare Number Board online tool. Invite students to shade all multiples of 6. Choose a multiple of 6 and ask, What are some other factors of (36)? Repeat for other multiples of 6 on the chart.”

• Module 4, Lesson 3, Algebra: Writing equations with two variables, Step 3 Teaching the lesson, describes the use of physical items as a way for students to explore the relationship between variables and their equations. “Organize the students into pairs or groups of three. Distribute one balance card to each pair or group. Have them work together to explore the relationship between the mass of the items in each bag, and to write an equation to show that relationship (SMP2). Then have them figure out which bag holds the lightest single item. Afterward, invite pairs or groups to share their equation and explain how they figured out the lightest single item.”

• Module 11, Lesson 1, Ratio: Introducing ratios with three parts, Step 3 Teaching the lesson, identifies the use of connecting cubes to create patterns and explore ratios. “Organize students into pairs and distribute the connecting cubes. Say, I want you to use the cubes to create a color pattern that has three parts (colors) and that has at least eight cubes in the repeating element. As the students are working, distribute the table cards and markers. When their patterns are complete, have the students create a ratio table to show how their pattern can be extended.”

#### 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 6 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 6 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.

##### 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 6 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 6 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 6 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

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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