Alignment: Overall Summary

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for focus and coherence within Gateway 1, and they partially meet expectations for rigor and the mathematical practices in Gateway 2. Since the materials partially meet expectations for Gateway 2, they are not reviewed for usability in Gateway 3.

See Rating Scale
Understanding Gateways

Alignment

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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
12
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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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

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Gateway One Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 5 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, are consistent with the progressions in the standards, and 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 5 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The materials include some assessment questions that were above grade-level, but these could be omitted without affecting the underlying structure of the materials.

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 5 meet expectations that they assess grade-level content. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

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

The following questions assess grade-level standards:

  • In Module 3, Check-up 2, Question 2, “Color the circle below to show the greatest number in each group.” (5.NBT.3).
  • In Modules 4-6, Quarterly Test A, Question 17, “Package A weighs 3/12 kilogram, Package B weights 1 5/6 kilograms, and Package C weighs 3/4 kilograms. What is the total mass of Package A and C? Show your thinking.” (5.NF.2).
  • In Module 9, Performance Task, Question 2, “A student thinks that 1/5 divided by 6 is equivalent to 1/5 ≅1/6. Are they correct? Draw a picture or write sentences to explain your answer.” (5.NF.B).

The following questions assess above-grade-level standards and would need to be omitted or modified to meet grade-level standards:

  • In Module 12, Check-Up 1, Questions 2a, 2b, and 2c, students use the standard algorithm for division (6.NS.3).
  • In Module 12, Performance Task, directions for the assessment state, “Use the standard algorithm to calculate the quotient.” (6.NS.3).
  • In Module 12, Quarterly Tests A and Test B, Questions 10, 11, and 12, the directions state, “Use the standard algorithm to divide.” (6.NS.3).

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 5 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 5 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 9 out of 12, which is approximately 75%.
  • The approximate number of days devoted to major work of the grade (including supporting work connected to the major work, but not More Math) is 128 out of 156, which is approximately 82%.
  • The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 116 out of 144, which is approximately 81%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in.  As a result, approximately 81% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

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

The instructional materials for ORIGO Stepping Stones 2.0 Grade 5 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 5.G.3 and 5.G.4 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 5 partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to Grade 5. 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, the standard for the lesson is stated and connections are not made.

Connections between supporting and major work:

  • Module 9, Lesson 6, major work connects to (5.NF.B), applying and extending previous understandings of multiplication and division to multiply and divide fractions, with supporting work (5.OA.A), writing and interpreting numerical expressions. Students use knowledge and work with numerical expressions to perform operations with multi-digit whole numbers and to divide unit fractions when working with equations like this: 4 x (⅕ /6)=____.
  • Module 1, Lesson 6, major work connects to (5.NF.A), using equivalent fractions as a strategy to add and subtract fractions, with supporting work (5.MD.B), representing and interpreting data. Students interpret the population and connect those given populations to an equivalent fraction.
  • Module 1, Lesson 7, major work connects to (5.NBT.A), understanding the place value system, with supporting work (5.MD.B), representing and interpreting data. Students place the data they are provided on a number line.
  • Module 1, Lessons 11-12, major work connects to (5.NBT.B), performing operations with multi-digit whole numbers and with decimals to hundredths, with supporting work (5.OA.A), writing and interpret numerical expressions. Student solve word problems.

Missed connections between supporting and major work:

  • Module 9, Lesson 8, does not connect the major work of (5.NBT.A), understanding the place value system, with supporting (5.MD.A), convert like measurement units within a given measurement system. Students make metric conversions but connections to using powers of 10 to calculate conversions is not addressed.
  • Module 9, Lesson 12, does not connect the major work of (5.NF.A), using equivalent fractions as a strategy to add and subtract fractions, with supporting (5.MD.B), representing and interpreting data. Students create, describe, and interpret line plots, but line plots using fraction sets with the same denominator are missing. The opportunity to connect adding and subtracting mixed numbers/fractions to interpret line plots is also missing.

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 5 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 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.”

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 5 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 9, students investigate fractions involving division. In Grade 4, Module 8, students master Solving Division Problems and Solving Common Fraction Word Problems.
  • Focus found at the beginning of each module identifies 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. For example, in Module 1, a table identifies Standards 4.NBT.1, 4.NBT.2, and 4.NBT.3 as prerequisites for the 5th grade content in the module. The table for Module 5 lists 4.NBT.4 and 4.MD.6 as prerequisite standards for the grade 5 skills taught in that module.
  • 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 3, the Newsletter states, “Students extend their understanding to decimal fractions in the thousandths, visualizing how place value in our number system decreases as we move to the right in writing numbers, and increases as we move left in writing numbers.”

The instructional materials provide students with extensive grade-level work, although there is no evidence of Standards 5.G.3 and 5.G.4 being addressed 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.
  • In Maintaining Concepts and Skills page 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 Grade 5, Module 1, Lesson 2, preparing for the next module identifies 4.NF.3c (adding fractions with the same denominators) as the prerequisite for Module 6 where students are adding and subtracting fractions with unlike denominators.
  • 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 5 meet expectations that materials foster 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 standard cluster headings.

  • In Module 1, Lesson 5, students understand the place value system (5.NBT.A).
  • In Module 2, Lesson 7-12, students  understand concepts of volume and relate volume to multiplication and to addition (5.MD.C).
  • In Module 4, Lesson 1-5, students use equivalent fractions as a strategy to add and subtract fractions (5.NF.A).
  • In Module 6, Lesson 8-10,  students apply and extend previous understandings of multiplication and division to multiply and divide fractions (5.NF.B).

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

  • In Module 4, Lesson 7, students use equivalent fractions as a strategy to add and subtract fractions (5.NF.A) and convert like measurement units within a given measurement system (5.MD.A) by measuring different times and comparing them.
  • In Module 6, Lesson 10, students perform operations with multi-digit whole numbers and with decimals to hundredths (5.NBT.B) and apply and extend previous understandings of multiplication and division (5.NF.B) to multiply and divide fractions by working with decimal remainders.
  • In Module 11, students understand concepts of volume and relate volume to multiplication and to addition (5.MD.C) and convert like measurement units within a given measurement system, (5.MD.A) by using volume in like measurements to solve real-life problems.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 partially meet expectations for Gateway 2. The instructional materials partially 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.
6/8
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Criterion Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 partially 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 engage students in non-routine application problems, but the instructional materials inconsistently embed opportunities for students to independently develop conceptual understanding. 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.
1/2
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-
Indicator Rating Details

The instructional materials for ORIGO Stepping Stones 2.0 Grade 5 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include some problems and questions that develop conceptual understanding throughout the grade-level. Students have little access to concepts from a number of perspectives or to independently demonstrate conceptual understanding throughout the grade.

Domain 5.NBT addresses understanding the place value system and performing operations with multi-digit whole numbers and with decimals to hundredths. Multiple modules explore a variety of real-world applications using a few mathematical representations. Opportunities exist for students to work with place value that call for conceptual understanding and include the use of some visual representations and different strategies. For example:

  • In Module 1, Lesson 5, begins with a discussion of a place value table and students talk about the places that are grouped into three digits such as millions and thousands and how those places make a pattern of hundreds, tens, and ones. Students select random digits and place them onto a place value expander to create a 9-digit number. Students read the number then engage in a discussion that includes saying the tens and ones together in each grouping of numbers (5.NBT.1).
  • In Module 3, Lesson 8, comparing and ordering thousandths, the class is divided into two teams and the students play the game “Near or Far”. Each member of the team comes forward, spins the cubes, and creates the largest possible decimal number. Then students place the numbers created in order from greatest to least. In the Student Journal, students place numbers in order using a number line, which is provided, or make comparisons using greater than, less than, or equal. Students do not discuss the conceptual understanding that digits to the left are 10 times larger than digits to the right when making their comparisons (5.NBT.1).

Cluster 5.NF uses equivalent fractions as a strategy to add and subtract fractions. Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Multiple modules explore a variety of real-world applications using a few mathematical representations. Opportunities exist for students to work with fractions that call for conceptual understanding and include the use of some visual representations and different strategies. For example:

  • In Module 6, Lesson 10, students discuss remainders and the context in which they may be used to answer a questions. For instance, when a remainder of 4 must be divided as units of fertilizer between 6 trees, how could this be done? (5.NF.3).
  • In Module 8 Lesson 3, students find a fraction of a whole number with unit fractions using number lines (5.NF.1).

The instructional materials present few opportunities for students to independently demonstrate conceptual understanding throughout the grade-level. In most independent activities students are told how to solve problems. For example:

  • In Module 9, Lesson 5, students divide 3 by 1/2 and are shown a pot that is divided into 3 quarts and then divided into 1/2 quarts to see 6 servings. Students then divide 1/2 by 3. They are shown a pot with 1/2 a quart which is then divided into thirds to see each friend will get 1/6 quarts of soup. Students are then shown the same process using bar diagrams. In the Student Journal, students solve five problems using bar diagrams which are provided. Since the diagrams are provided and the questions mirror the example, students do not demonstrate conceptual understanding (5.NF.2).
  • In Module 12, Lesson 2, students do not have the opportunity to demonstrate conceptual understanding of division and place value. Students are taught the standard algorithm for division (5.NBT.2).

Indicator 2b

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 Stone 2.0 Grade 5 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. Materials attend to the Grade 5 expected fluencies (5.NBT.2), multi-digit multiplication.

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

The materials attend to the Grade 5 expected fluencies, fluently multiply multi-digit numbers using the standard algorithm (5.NBT.5). For example, in Module 2, Lessons 2-5, extends knowledge of the standard algorithm for multi-digit multiplication through multi-digit by multi-digit multiplication. In Investigations 1, 2, and 3, students build procedural skill and fluency involving multi-digit numbers. In Activities 1, 2, and 4, students work with the standard algorithm to multiply multi-digit numbers.

In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency:

  • Fundamentals Games contains a variety of games that students can play to develop grade level fluency skills. For example, Use a Ten Fact (multiplication with two-digit numbers), develops fluency in multi-digit multiplication.
  • The Stepping Stones 2.0 overview 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. In Module 10, Lesson 2, provides computation practice with multi-digit dividends and one-digit divisors.
  • 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’s 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.
  • Assessments also give problems that call for fluency and procedural skill. For example, in the Module 2 performance task, students use the standard algorithm to complete multi-digit by multi-digit multiplication.

Indicator 2c

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 5 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 8, Lesson 3, addresses the standard 5.NF.2, “The cost of a hamburger is one-sixth the price of a family meal. What is the cost of one hamburger if the family meal costs $12?”.
  • In Module 4, Lesson 6, addresses the standard 5.NF.1, “Lisa has 2 red apples and 2 green apples. She cuts the red apples into fourths, and the green apples into eighths. She eats 2 pieces of red apple and 3 pieces of green apple. Which color of apple has more left over?”.
  • In Module 9, Lesson 11, addresses the standard 5.MD.3, “Three packages are each filled with 400 g boxes. Each package weighs 2 kg. How many 400g boxes were used?”.
  • In Module 5, Activity 2, students work in pairs to discuss the problem and addresses the standard 5.NBT.7, “A weather research center records temperatures to the nearest hundredth of a degree (table provided). On which day was there the greatest variation in temperature? Show your thinking.”.

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 states, “Nancy begins the game by building this tower (students refer to the picture). What is the volume? Show your thinking." This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
  • In Module 6, Thinking Task, Question 2 states, “The Marathon organizers will purchase energy powder. The Leadership Team will prepare a 10 gallon cooler of energy drink for each water stop. One three-pound tub of energy drink powder makes 24 quarts and costs $8.50. How many tubs will they have to buy and how much will it cost?” Students must use the Course Map provided to solve. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
  • In Module 9, Thinking Task, Question 1 states, “What is the difference in height between the tree with the greatest growth and the tree with least growth?” Students use a line plot provided to solve. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
  • In Module 12, Thinking Task, students are given two portable building options with different dimensions (Building A 7m x 5.3m Building B 15m x 9 m). The students must help the school decide which building is the better option for the school to purchase. Question 1 states, “Calculate the floor area for building A. Show your thinking. Remember to write the unit of measurement.” This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.

Indicator 2d

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 5 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the materials, but there is an over-emphasis on procedural skills and fluency.

There is some evidence that the curriculum addresses standards, when called for, with specific and separate aspects of rigor and evidence of opportunities where multiple aspects of rigor are used to support student learning and mastery of the standards. There are multiple lessons where one aspect of rigor is emphasized. The materials have 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 6, Lesson 6, students explain, “Does it make more sense to write the answer in the format of improper fractions or mixed numbers? Why?”
  • In Module, 12 Lesson 2, “Division: Developing the standard algorithm,” students use the standard algorithm for division.
  • In Module 12, Problem Solving Activity 4, “Three families are vacationing together. They are equally sharing the hotel cost which is $2,634. Thomas’ family is also renting a car for $348. How much will Thomas’ family have to pay for the car rental and hotel together?”

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

  • In Module 7, Lesson 4, Maintaining Concepts and Skills states, “Deon bought a bag of apples that weighed more than 3 kilograms but less than 4 kilograms. Monique bought a bag of apples that weighed 7/8 of a kilogram less than Deon’s bag of apples. Hunter bought the same amount of apples as Deon and Monique together. What could be the mass of the apples each person bought?”
  • In Module 2, Problem Solving Activity 2, “Between 1,200 and 1,300 people will attend the Freemont High School graduation. The chairs need to be arranged in a rectangular array and 18 to 23 chairs can fit into a row. How many rows and how many chairs in a row are needed to make sure they have enough chairs for all the people?”
  • In Module 3, Thinking Task, Question 3 states, “Nancy stacks a total of 160 blocks to build two towers. Tower A is shaped like a cube. Tower B is shaped like a rectangular-based prism. Write the possible dimensions for each tower. Show your thinking" (two different dimension prisms are provided for students to label with length, width, and height).
  • In Module 9, Thinking Task, Question 3 states, “In order to see which type of tree grew the most over the course of one year the club will combine the growth data of each tree measured. For this item: Solve using the order of operations. Compare the total growth of the four types of trees.”

Criterion 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 5 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 5 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
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 1, Lesson 2, students use expanders to help read and write seven-digit numbers.
  • In Module 2, Lesson 7, students use base ten blocks to build prisms and explore concepts of volume. Students should evaluate the utility of models to determine which models are most useful and efficient to solve problems, in this lesson students are given the model.
  • In Module 4, Lesson 1, students use area models to identify equivalent common fractions. In the Student Journal, an area model is used in the example to show how to find equivalent fractions.

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 1, Lesson 7, students use the halfway point between two multiples on a number line to help them round.
  • In Module 3, Lesson 10, students are rounding decimal fractions to the nearest tenth, hundredth, and thousandth. Students are told to “use the thousandths square on the support page with thousandths models or draw number lines to help their thinking. Some students may prefer place value strategies.” Students are given and told what tools to use to round decimal fractions.
  • In Module 5, Lesson 3, students apply the standard algorithm to add decimal fractions with a varying number of places. Students are given place value chart templates and told to estimate before solving. Steps directions states, “Encourage them to first estimate the total for each example, then use their estimate to check the reasonableness of their answer.” Students are given specific tools to add decimals.
  • In Module 9, Lesson 3, students calculate division of any whole number by a unit fraction. Instructional Steps state, “Emphasize that when they know how many one-sevenths are in a whole it is only the case of multiplying that number by 8 to determine the number in 8 wholes” (8 ÷ 1/7 ). Students are not given any other way to solve the problem, and the materials state that having students compare their solutions and discuss as a class meets MP5.

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
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 1, Lesson 4, the teacher chooses five students to come up and grab a number card and hold them facing the class. The teacher then asks the following questions of students, “If you read this number from left to write, what would you say? How could we rearrange the numbers to show the greatest number possible? How did you decide what order to place the cards? How could we rearrange the cards to show the least number possible? How could we rearrange the cards to show a number close to 300,000? What odd number between 60,000 and 70,000 could we show?”
  • In Module 3, Lesson 12, students record results of the amount of time (reaction time) it takes them to grab a ruler that is dropped. Once all the student data is collected, the teacher asks, “Imagine that were were asked to compare our results with the class next door. What single length best represents the reactions of our class?”. The suggested answer is to find the most common or middle reaction time.
  • Module 9, Lesson 2, the teacher projects slide 2 which shows 24 ÷ 8 and asks the class, “What questions could this equation be representing?” Then students state what the solution would be.

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
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Indicator Rating Details

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 2, Lesson 2, students multiply 3 and 4-digit numbers by a 1 digit number. Teachers encourage critical thinking and respectful critique by asking questions such as, “Do you agree with the method (Peter) chose? How is it different from the method you would use? and What other problems could you solve (or not solve) using this method?”.
  • In Module 2, Lesson 5, students extend the standard algorithm to multiply 2 3-digit numbers. Teachers encourage respectful critiquing of ideas by providing sentence stems such as, “I have a different opinion. I think, I agree (disagree) because, and that makes sense, but...”.
  • In Module 4, Lesson 6, students solve multi-step word problems that involve the comparison of two or more common fractions. Teachers encourage students to use examples and non-examples to support their arguments, and to critique the reasoning of their peers by asking, “Do you agree or disagree with (Jie)? Why? What is another example that would support (Lillian’s) thinking? Who can explain why (Susan’s) example makes sense? and How is (Jerome’s) thinking similar to (Rita’s)? How is it different?”.
  • In Module 10, Lesson 5, students share and justify the strategies they used to calculate the area of various rooms. Teachers encourage critical thinking and respectful critique by asking questions such as, “Do you agree with the method (Jerome) chose? How is it different from the method you would use? What other problems could you solve (or not solve) using this method?”.

Indicator 2g.iii

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

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 5 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 are 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 12 vocabulary includes words such as division, algorithm, and division bracket.
  • 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 6, Lesson 4, common denominator is present in the Student Journal, but the definition is not introduced in any lesson in Module 6.

Gateway Three

Usability

Not Rated

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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
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Additional Publication Details

Report Published Date: 05/28/2019

Report Edition: 2017

Title ISBN Edition Publisher Year
The Number Case 9.78192E+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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