Alignment: Overall Summary

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for focus and coherence within Gateway 1, and partially meet expectations for rigor and the mathematical practices in Gateway 2. In Gateway 2, the materials meet expectations for rigor and balance, and partially meet expectations for practice-content connections. Since the materials partially meet expectations for Gateway 2, they are not reviewed for usability in Gateway 3.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
12
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
13
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 6 meet the expectations for Gateway 1. These materials meet the expectations for focus by not assessing above grade-level content and by spending the majority of the time on the major clusters of each grade-level. The materials partially meet the expectations for being coherent and consistent with the standards. The materials include an amount of content that is viable for one school year, and the materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 6 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The assessments do not include any above grade-level items.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that they assess grade-level content.

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.

The following questions assess grade-level standards:

  • In Module 2, Check-Up 2, Question 4, students calculate the answer: “a. 4.62 x 71, b. 9.3 x 5.12“ (6.NS.3).
  • In Module 3, Check-Up 1, Question 3a, “Hiro had 8 fiction books and 3 non-fiction books on a shelf. A year later he has more books in the same ratio. If he now has 12 non-fiction books, how many fiction books does he have?” (6.RP.3).
  • In Modules 4-6, Quarterly Test B, Question 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 with Hugo receive? Let c represent Hugo’s change.” (6.EE.2).
  • In Module 8, Performance Task, Question 1b, “This machine holds 150 gumballs with different flavors. Solve each word problem. Show your thinking. Forty percent of the gumballs are cherry flavor. How many gumballs are cherry flavor?” (6.RP.3).
  • Module 5, Performance Task, “Furniture is often sold in packs that the customer has to put together. Bolts, nuts, and washers are put into each pack to assemble the furniture. 1.) Two long bolts for every three short bolts are needed to put a chair together. A washer and nut are also needed for each bolt. Write the ratio of long bolts to short bolts. 2.) 10 bolts are needed to put some chairs together. The ratio of long to short bolts is the same as Question 1. Write the number of bolts that are long and short. Show your thinking. 3.) A table is sold with chairs. The table has a 2:4 ratio of long bolts to short bolts. There are 12 bolts used in the table. Mika buys the table with some extra chairs. He counts a total of 28 long bolts and 44 short bolts. How many chairs did he buy?” (6.RP.3).
  • In Module 9, Check-Up 1, Question 1, students “Choose the statement that matches each inequality. Let n represent the variable.” Answer choices: “n>5 lb; n<5 lb; 5 lb = n; 5 lb< n” (6.EE.8).

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 6 meet the expectations for having students and teachers using the materials as designed and devoting the large majority of class time to the major work of the grade. Overall, the materials devote at least 65% of class time to major work.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations for spending a majority of instructional time on major work of the 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.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
6/8
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Criterion Rating Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 6 partially meet the expectations for being coherent and consistent with the standards. Supporting work is partially connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and fosters coherence between the grades. Content from prior grades is clearly identified, but there is no evidence of standards 6.NS.7 and 6.NS.8 in the materials. The objectives for the materials are shaped by the CCSSM cluster headings, and they also include problems and activities that connect two or more clusters in a domain or two or more domains.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to Grade 6. Supporting work standard connections to major work standards are not called out in the program. For example, when hovering over the eye in the Steps section of each lesson, only the standard for the lesson is stated and connections are not made.

Connections between supporting and major work:

  • Module 2, Lesson 8, connects major work (6.NS.C), applying and extending previous understandings of numbers to the system of rational numbers, with supporting work (6.NS.B), computing fluently with multi-digit numbers and find common factors and multiples. Students write the greatest common factor then use the distributive property to rewrite mathematical expressions such as 56+21 as (7*8)=(7*3).
  • Module 9, Lessons 6, 7, and 8, connect major work (6.EE.A), applying and extending previous understandings of arithmetic to algebraic expressions, with supporting work (6.SP.A), developing understanding of statistical variability. Students calculate mode, median, and mean with multi-digit numbers as they apply previous understandings to algebraic expressions.
  • Module 3 Lesson 4, connects major work (6.RP.A), understanding ratio concepts and use ratio reasoning to solve problems, with supporting work (6.SP.B), summarizing and describing distributions. Students display ratios of items then describe the distributions of those ratios.
  • Module 7, Lesson 12, connects major work (6.EE.A), applying and extending previous understandings of arithmetic to algebraic expressions, with supporting work (6.G.A), solving real-world and mathematical problems involving area, surface area, and volume. Students solve word problems, such as, building fences, painting, and filling in items.

Missed connections between supporting and major work:

  • Module 10, Lesson 8, does not connect the major work of (6.EE.A), applying and extend previous understandings of arithmetic to algebraic expressions, with the supporting work of (6.G.A), Solve real-world and mathematical problems involving area, surface area, and volume. Students calculate volume of an item but writing, reading, and evaluating variable expressions is not addressed.
  • Module 2, Lesson 7, does not connect the major work of (6.NS.C), applying and extending previous understandings of numbers to the system of rational numbers, with supporting (6.SP.A), developing an understanding of statistical variability.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that the amount of content designated for one grade-level is viable for one year.

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 ½ 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.”

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet expectations for being consistent with the progressions in the standards.

The instructional materials identify content from prior grades and use it to support the progressions of the grade-level standards. Future grade-levels are not identified in the instructional materials. For example:

  • In each module prior content needed for the module is identified in the section Coherence: Prerequisite Skills from Prior Grades. For example, in Module 2, students explore expressions and equations. According to the materials, students should have mastered the following concepts found in Grade 5, Module 1, Lesson 12 to be successful (solve word problems involving order of operations with two types of operations).
  • Focus documents found at the beginning of each module identify the domains addressed and the coherence within each module, and summarizes how the lessons address the targeted standards. Focus explains how the lessons in each module transition through the progressions and make applicable connections to past or future content. Focus also identifies common errors and misconceptions in student work. In Module 2, the table identifies 5.NF.1, add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators, as a prerequisite for the 6th grade skills for performing mathematical operations involving fractions in Module 2.
  • The mathematics tab includes a newsletter for parents, providing parents with information on how the content their child is learning connects to prior grades. In Module 5, the Newsletter states, “Students extend their knowledge of dividing whole numbers and fractions to dividing fractions by fractions.”

The instructional materials provide students with extensive grade level work, although there is no evidence of Standards 6.NS.7 and 6.NS.8 in the materials. The lesson structure presents opportunities for students to explore grade-level mathematics more in-depth:

  • During the Step In Discussion, students engage with grade-level content through guided practice, and complete independent journal tasks during the Step Up and Step Ahead parts of the lesson.
  • Each lesson includes Starting the Lesson, Teaching the Lesson, and Reflecting on the Work which present opportunities for students to engage with content.
  • Ongoing Practice provides additional grade-level activities.
  • Maintaining Concepts and Skills provides practice with prior and current grade-level mathematics.
  • The Preparing for the next module activities include fluency practice, spiral review, and vocabulary activities.

Materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • Focus, specifically identifies where in the module and in the lesson, a prerequisite skill is located.
  • Module 7 identifies 5.OA.2 and 5.NF.5 as prerequisite skills needed for Grade 6 content.
  • In Maintaining Concepts and Skills, there is a “preparing for the next module” problem that is a skill from the previous grade preparing the student for the upcoming module. These problems clearly indicate coherence between grade levels. For example, in Module 4, Lesson 7, length (converting between inches and feet) is connected to Grade 4, and prepares students for Module 6, Lesson 8, length (exploring the relationship between miles, yards, and feet).

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

Overall, the instructional materials identify standards. A comprehensive list of the CCSSM and correlating lessons is found under the drop down menu on the home page. Cluster headings are clearly identified by hovering over the Lesson title.

The materials include learning objectives that are visibly shaped by cluster headings.

  • In Module 2, Lessons 1, 2, and 4, students apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A).
  • In Module 2, Lessons 11 and 12, students apply and extend previous understandings of multiplication and division to divide fractions by fractions (6.NS.A).
  • In Module 3, Lessons 2, 3, 5, 6, and 7, students understand ratio concepts and use ratio reasoning to solve problems (6.RP.A).
  • In Module 4, Lessons 1, 2, 4, and 5, students apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A).
  • In Module 4, Lesson 2 and 6, students reason about and solve one-variable equations and inequalities (6.EE.B).
  • In Module  4, Lessons 7, 9 and 11, students represent and analyze quantitative relationships between dependent and independent variables (6.EE.C).
  • In Module 5, Lessons 1, 2, 5, 6, and 7, students apply and extend previous understandings of multiplication and division to divide fractions by fractions (6.NS.A).

The instructional materials include problems and activities that connect two or more clusters in a domain or two or more domains.

  • In Module 2, Lesson 8, students apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A) and compute fluently with multi-digit numbers and find common factors and multiples (6.NS.B) to solving word problems involving common factors and algebraic expressions.
  • In Module 4, Lesson 2 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.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
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Gateway Two Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet expectations for Gateway 2. The instructional materials meet expectations for reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application, and they partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
7/8
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Criterion Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations for reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. The materials give attention throughout the year to individual standards that set an expectation of procedural skills and fluency, and embed opportunities for students to independently develop conceptual understanding and engage in non-routine application problems. The materials over-emphasize fluency, procedures, and algorithms.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials 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. Opportunities exist for students to work with ratios that call for conceptual understanding and include the use of some visual representations and different strategies. For example:

  • In Module 6, Lesson 8, students discuss as a whole class how to solve, “A car travels 200 miles in 4 hours. How far does it travel in 1 hour?” Students are then shown how to use tables to organize rates. In the Student Journal students find unit rates, it is suggested they use tables (6.RP.1).
  • In Module 3, Lesson 2, students build pictorial representations (tape diagrams) of ratios after discussing their thinking on ratios from prior lessons (6.RP.1).
  • In Module 3, Lesson 1, introduces ratios by giving students real-world examples of ratios and having students describe the relationship between the two amounts. In 3.1, “Mix and Match ratio cards” students match real-world examples of ratio to find corresponding number ratio. Students relate abstract to concrete examples (6.RP.1).
  • In Module 8, Lesson 1, links part-whole ratios to fractions using connecting cubes of two different colors. Student build a character then describe the ratio of colors used to build their character. Next, students analyze the profit of 1/4 being donated to charity and what the ratio of profit to donation would be (6.RP.1).

Cluster 6.EE addresses 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. 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. For example:

  • In Module 2, Lesson 1, students discuss questions such as, “What is the difference between and expression and an equation?" (6.EE.1).
  • In Module 7, Lesson 1, students are presented with a visual representation of 16 blocks representing $$4^2$$. Students are led through discussions such as, “what number does this picture represent?”, “what expression can we write to match?”, and “what type of number is 16?”. The student materials engage students with visual representations of squares and have students write an expression “to name each collection of tiles” (6.EE.3).
  • In Module 7, Lesson 4, students are shown how to find the greatest common factor (GCF) and use the distributive property to simplify expressions. Students then work in groups using rolling algebraic cubes to create expressions and simplify them. In the Student Journal, students first determine the GCF of an expression. Then students use the distributive property to simplify expressions, however, blank number sentences are provided (6.EE.3).

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that they attend to those 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, multi-digit division and multi-digit decimal operations (6.NS.2); add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation (6.NS.3); and apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A). For example:

  • 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).
  • In Module 2, Lesson 8, 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).
  • In Module 3, Lesson 10, 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).
  • In Module 4, Lesson 2, 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:

  • The Stepping Stones 2.0 overview states 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, 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

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that the materials are designed so teachers and students spend time working with engaging applications of the mathematics.

Engaging applications include single and multi-step word problems presented in contexts in which the 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, but are not limited to:

  • In Module 6, Lesson 8, 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?”
  • In Module 5, Lesson 2, 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?”
  • In Module 7, Lesson 10, 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 1/4 miles. Reece runs the rest of the distance. How far did Reece run? Let r represent the unknown distance.”
  • In Module 4, Lesson 11, 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).
  • In Module 9, Lesson 12, 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 $$24 ft^2$$ , how many bundles are needed?”.
  • Maintaining Concepts and Skills includes application exercises. For example, in Module 12, Lesson 10, “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?”
  • In Module 3, 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, but are not limited to:

  • In Module 3, Thinking Task, Question 1, students read points on a coordinate grid to fill in a table showing the cost of a phone bill per month. Question 3 states, “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.
  • In Module 6, Thinking Task 6, Question 2 states, “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.
  • In Module 9, Thinking Task, students find the surface area of a greenhouse with dimensions given and identify the net that matches the greenhouse design. Question 3 states, “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.
  • In 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 1 states, “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

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
1/2
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Indicator Rating Details

The instructional materials 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 a an emphasis on fluency, procedures, and algorithms.

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

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

  • In Module 5, Lesson 4, 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 1/2 yard going in one directions between rows of vegetable patches.”
  • In Module 12, Lesson 10, 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?”
  • In Module 3, Lesson 2 (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 solving word problems using tape diagram models.
  • In 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 states, “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 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
6/10
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Criterion Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. The materials identify the Standards for Mathematical Practice and use them to enrich mathematics content within and throughout each applicable grade, and partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. The materials partially attend to the specialized language of mathematics.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

All eight MPs are clearly identified throughout the materials. For example:

  • The Math Practices are initially identified in the Steps portion of each module course information.
  • Videos for each module can be found under the Resources tab which explains the Math Practices and Habits of Mind.
  • A table is provided to show which mathematical practices are in each lessons.
  • Resources states that each practice standard is, “experienced, practiced, and enhances as a result of working on meaningful problems”.
  • Module Lessons tabs have a Lesson Contents overview that lists each lesson and the standards and mathematical practices in the lesson.

The MPs are used to enhance the mathematical content and are not treated separately from  content in lessons. However, there is limited guidance for teachers on the connections between the MPs and the content standards.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. The instructional materials do not attend to the full intent of MP4 and MP5.

For MP4, students are given models to use and have few opportunities to develop their own mathematical models. In addition, students have few opportunities to compare different models in problem contexts. Examples include:

  • In Module 4, Lesson 7, students complete tables to show the data generated by a pattern. In the Student Journal, students fill in tables that are already created.
  • In Module 3, Lesson 2, students are told to use tape diagrams to model equivalent ratios.
  • In Module 6, Lesson 8, students are given a model to map a constant relationship between variables to determine rate.

For MP5, students are given few opportunities to use tools strategically, as they are most often given the tools to use for a problem. Examples include:

  • In Module 3, Lesson 5, students are instructed to use either equivalent fractions or relationships to calculate and identify equivalent ratios. Instructional Steps state, “Allow students time to use one or both methods to calculate the equivalent ratios.” Students choose one of two models to find the equivalent ratio.
  • In Module 7, Lesson 2, students are provided algebra tiles to represent the problem.
  • In Module 9, Lesson 6, students analyze information presented on dot plots. Students are given a data set and told to work in pairs to represent the data. Students are not given a choice on how to represent the data since they are working with dot plots.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 do not meet the expectation for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

There are no opportunities in the Student Journal or assessments for students to construct viable arguments or analyze the arguments or the work of others. MP3 is identified in the Steps portion of the lesson. Teachers are given sentence stems to provide students to promote construction of arguments and justification of student thinking.

Examples where the materials do not prompt students to construct viable arguments or analyze the arguments of others include, but are not limited to:

  • In Module 2, Lesson 11, after completion of Student Journal pages 74-75, the teacher has students look at question 3 and explain the algorithm steps they followed. Then the teacher asks, “Who likes working with whole numbers, and then adjusting their answers? Who preferred to work with decimal fractions?”
  • In Module 7, Lesson 2, students write expressions to match each group of tiles then write an equivalent expression. Next students explain and compare their expressions, adjusting errors. Students are not constructing arguments or justifying their expressions, and they are not analyzing each other’s work.
  • In Module 12, Lesson 2, the teacher projects a word problem which the students read and discuss. Then the teacher asks, “How did you decide which numbers to write?”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher guidance, questions, and sentence stems for MP3 are found in the Steps portion of the lessons. In some lessons, teachers are given questions that prompt mathematical discussions and engage students to construct viable arguments, and in other lessons, teachers are provided questions and sentence stems to facilitate students in analyzing the arguments of others, and to justify their answers.

Examples where teachers are provided guidance to engage students in constructing viable arguments and/or analyzing the think of others include, but are not limited to:

  • In Module 1, Lesson 7, students compare and order positive and negative numbers on a number line. Teachers encourage students to critique their reasoning using the sentence stems, “I have a different opinion, I think, I agree (disagree) because, and That makes sense, but...”.
  • In Module 4, Lesson 2, students analyze four equations to determine which correctly matches a word problem presented. Teachers ask students to justify their findings, encourage students to ask clarifying questions, and to critique the reasoning students present.
  • In Module 5, Lesson 6, students explore division of common fractions by common fractions with unrelated denominators. Teachers provide sentence stems to encourage critique, “I noticed the same pattern and I also noticed, I don’t think that ... shows a pattern because, and I looked at the equations in a different way.”.
  • In Module 8, Lesson 5, students work independently or in pairs to calculate the percentages and solve the problems on Slide 5. Teachers encourage students to model and record their thinking and to justify their answers. If students do not agree, they are instructed to share their own thinking and justify why it is correct.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 6 partially meet expectations for explicitly attending to the specialized language of mathematics.

Accurate mathematics vocabulary is present in the materials, but there are no instructions on how to use the language of mathematics. While vocabulary is identified throughout the materials, there is no explicit directions for instruction of the vocabulary for the teacher in the Steps portion of the lesson. Examples include but are not limited to:

  • Vocabulary instruction for each module is found under Mathematics, Vocabulary Development. Vocabulary identified in bold print is identified as being developed throughout the module. The targeted module vocabulary words can be printed onto cards under Resources. For example, in Module 1 vocabulary includes words such as nearest absolute value, integers, and negative numbers.
  • Each module contains a parent newsletter. The newsletter highlights key vocabulary and provides the definition for parents in the Glossary section of the newsletter.
  • In Module 1, Lesson 5, integer is present in the Student Journal, but the definition is not introduced in any lesson in Module 1.

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

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

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A

Additional Publication Details

Report Published Date: 05/28/2019

Report Edition: 2017

Title ISBN Edition Publisher Year
The Number Case 9.78176E+12 ORIGO Education
Stepping Stones Student Book B 9.78193E+12 ORIGO Education 2017

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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