ORIGO Stepping Stones 2.0

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Usability
Our Review Process

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Report for 4th Grade

Overall Summary

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations for alignment to the CCSSM. The instructional materials meet expectations for focus 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.

Alignment
Partially Meets Expectations
Not Rated

Focus & Coherence

The instructional materials for ORIGO Stepping Stones 2.0 Grade 4 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 also 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.

Gateway 1
Meets Expectations

Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 4 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.

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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.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 2, Check-Up 2, Question 3, students complete the equation and show their thinking for 9 x 35 and 39 x 4 (4.NBT.5).
• In Modules 4-6, Quarterly Test B, Question 2, “Victoria has 26 stamps in her collection. Her brother has 18 more stamps than Victoria. How many stamps are in her brother’s collection?” (4.OA.2).
• In Module 8, Performance Task, Question 1a, “Three people equally share the cost of this television. How much will each person pay?” (4.MD.2).
• In Module 4, Interview students estimate the difference between numbers such as 482-57 or 6,835-743 (4.OA.3).
• In Module 3, Check-Up 2, Item 3, students solve word problems about perimeter such as, “Riku is making a rectangular picture frame. Each short side is 8 inches. Each long side is twice as long as each short side. What is the perimeter of the picture frame?” (4.MD.3).

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

• In Module 10, Check-Up 1, students add decimals: Question 1a, 0.4 + 0.2, Question 1b, 3.15 + 2.50, and Question 1c, 0.6 + 0.25 (5.NBT.7).
• In Module 10, Performance Task, students add decimals  in the six questions (5.NBT.7).
• In Module 12, Quarterly Test A and Quarterly Test B, Questions 12 and 13, students add decimals (5.NBT.7).

Criterion 1.2: Coherence

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.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 4 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.

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Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 126 out of 156, which is approximately 81%.
• The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 114 out of 144, which is approximately 79%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work with no additional days factored in.  As a result, approximately 79% of the instructional materials focus on major work of the grade.

Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials for ORIGO Stepping Stones 2.0 Grade 4 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 or future grades is clearly identified, and the materials explicitly relate grade-level concepts to knowledge from prior grades. 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.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 partially meet the expectations for engaging students in mathematics at a level of sophistication appropriate to Grade 4. 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 3, Lesson 9, work connects to (4.OA.A), use the four operations with whole numbers to solve problems, with supporting work (4.OA.B), gaining familiarity with factors and multiples. Students are instructed to use multiplication to calculate the area of a rectangle using length times width, “use your rule to calculate the area of a rectangle that is 7 yards wide and 9 yards long.”
• Module 3, Lessons 1-5, work connects to (4.NBT.B), using place value understanding and properties of operations to perform multi-digit arithmetic, with supporting work (4.MD.B), representing and interpreting data. Students use data from charts to compare numbers.
• Module 10, Lesson 7, work connects to (4.NF.C), understanding decimal notation for fractions, and comparing decimal fractions, with supporting work (4.MD.B), represent and interpret data. Students interpret data from a chart to comparing fraction decimals, the students take decimals from a chart and plot the decimals on a number line.

Missed connections between supporting and major work:

• Module 3, Lesson 7, does not connect the work of (4.OA.4), using the four operations with whole numbers to solve problems, with supporting cluster (4.MD.A), solving problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Students find factor pairs but a connection of using arrays to solve larger multiplication problems is not made.
• Students miss the opportunity to make a line plot to display a data set of measurement in unit fractions, and therefore, miss the opportunity to interpret the data (4.MD.4) and use operations of fractions (4.NF.B).
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The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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.”

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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.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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, under the mathematics tab, Focus, prior content needed for the module is identified in the section Coherence: Prerequisite Skills from Prior Grades. For example, in Module 6, students learn how to separate rectangles to form partial products. Students must have mastered lessons in Grade 3, Module 6 to be successful (Create, describe, and interpret line plots).
• Focus, found at the beginning of each module describes connections to learning from prior grades and makes connections to future grade-level standards. For instance, a table is included in the Focus documents that accompany each module. For example, in the Focus document for Grade 4, Module 1, the table identifies 3.OA.7 as a prerequisite for 4th grade skills in this module. The table for Module 6 lists 3.OA.3 and 3.MD.4 as prerequisite standards for the grade 4 skills taught in that module. The table for Module 12 lists 3.MD.1 and 3.NBT.2 as prerequisites.
• 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 8, the Newsletter states, “Students extend their skill with division by building on what they know about the relationship between multiplication and division. Just like multiplication, division can be represented using a rectangular area model.”

The instructional materials provide students with extensive grade-level work. 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.

• In Module 5, Lesson 4, Multiplication: Making Comparisons Involving Division and Subtraction is connected to Grade 3, Module 3, Introducing Multiplication Facts.
• In Module 6, the Focus tab includes a table identifying 3.OA.3 and 3.MD.4 as prerequisite standards for the grade 4 skills taught in this module.
• In Module 12, the Focus tab includes a table identifying 3.MD.1 and 3.NBT.2 as prerequisites for that module.
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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.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 1, Lesson 10, students use place value understanding and properties of operations to perform multi-digit arithmetic (4.NBT.B).
• In Module 2, Lesson 1, students use the four operations with whole numbers to solve problems (4.OA.A).
• In Module 2, Lesson 2, students use place value understanding and properties of operations to perform multi-digit arithmetic (4.NBT.B).
• In Module 4, Lesson 9, 10, and 12, students extend understanding of fraction equivalence and ordering (4.NF.A).
• In Module 5, Lesson 11, students build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (4.NF.B).
• In Module 10, students understand decimal notation for fractions, and compare decimal fractions (4.NF.C).

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 3, students use the four operations with whole numbers to solve problems (4.OA.A) and use place value understanding and properties of operations to perform multi-digit arithmetic (4.NBT.B) by explaining and discussing the effects of order of operations on an equation.
• In Module 4, Lesson 11, students extend understanding of fraction equivalence and ordering (4.NF.A) and build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers (4.NF.B) by using equivalence to add fractions.
• In Module 7, Lesson 11, students extend understanding of fraction equivalence and ordering (4.NF.A) and use place value understanding and properties of operations to perform multi-digit arithmetic (4.NF.B) and represent and interpret data by solving real world problems with fractions and mixed numbers (4.MD.B).

Rigor & Mathematical Practices

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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.

Gateway 2
Partially Meets Expectations

Criterion 2.1: Rigor

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.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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.

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

The instructional materials for ORIGO Stepping Stones 2.0 Grade 4 partially meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

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

Domain 4.NBT addresses generalizing place value understanding for multi-digit whole numbers and using place value understanding and properties of operations to perform multi-digit arithmetic. Opportunities for students to work with multiplication and division through the use of visual representations and different strategies are included. For example:

• In Module 1, Lesson 2, students write a 5-digit number; then draw a representation of that number on an abacus. Students are led in a discussion of what adding a bead to 90,000 in the ten-thousands place would do and are led to discuss that this would result in a number that is 10 times 10,000 (4.NBT.1).
• In Module 2, Investigation 1, students come up with different strategies to add “537 + 374” (4.NBT.4).
• In Module 6, Lesson 2, introduces a partial product strategy for students to use to solve 3-digit by 1-digit multiplication. Student partition the three-digit factor using place value to multiply (4.NBT.5).

Cluster 4.NF.A addresses extending understanding of fraction equivalence and ordering, building fractions from unit fractions by applying and extending previous understandings of operations on whole numbers and understanding decimal notation for fractions, and compare decimal fractions. Multiple modules present a variety of problems using mathematical representations. 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 4, Lessons 12, students begin the lesson by making three jumps on a number line between 0 and 2, deciding how long each jump is, then writing an equation to represent the three jumps. For example, an equation might be 1/2+1/2 +1/2=1 1/2 . During the Step Up portion of the lesson, students use shaded parts that represent mixed numbers to “write the equivalent mixed number and common fraction” represented by the shaded parts (4.NF.1).
• In Module 9, Lesson 2, students discuss unit fractions as fractions with a numerator of 1 and unit fractions with common denominators are added to make other fractions such as adding 1/4+1/4+1/4 to get 3/4 . In the student materials, fractions are represented by fractions strips where the top strip equals 1 whole and each subsequent strip is divided into unit fractions of 1/2, 1/3, 1/4, 1/5. Students discuss which fraction is greater and tell how they decide. In the Step Up portion of the lesson, students are presented with two fraction strips side by side and compare fractions such as 10/6 to 10/12 (4.NF.2).

The instructional materials present 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 1, Lesson 6, Number: Locating 6-digit numbers on a number line, students are shown how to plot large numbers on a number line. For all problems in the Student Journal, number lines are provided with correct spacing and students are either placing numbers on the number line or stating which number is being represented on the number line. Placing numbers on a number line does not help students develop the understanding that a digit in the tens place is ten times larger than the digit to its right nor does it help students with their conceptual understanding of rounding (4.NBT.A).
• In Module 1, Lesson 2, students have little opportunity to build conceptual understanding with the number 326,417. Students are to write it in expanded form and work in pairs to record the different addition expressions (4.NBT.A).
• In Module 2, Investigation 1, students determine different written methods to calculate 537 + 374 and record their results to show each of the methods. Enrichment activities provide some opportunity to understand mathematical concepts through exploring ways to spend $750 (4.NBT.B). • In Module 7, Lesson 2, students are shown boxes with arrows to assist them in halving numbers, then given base ten blocks and a bill for$92 and told to use the blocks to determine how much each of the four friends will pay. Students then find the answer of 72 divided by 4 by finding half of 72. In the Student Journal students solve division problems using boxes to half enough times to calculate the answer when dividing by four or eight. It is never suggested that students could use other methods such as rectangular arrays or area models to demonstrate conceptual understanding of division (4.NBT.2).
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Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

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

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

The materials attend to the Grade 4 expected fluencies, fluently add and subtract multi-digit whole numbers using the standard algorithm (4.NBT.4). For example, in Module 2, Lesson 3, addresses the addition component of the standard. Investigations 2 and 3 provide opportunities to build students’ procedural fluency. In Activity 1, students choose three items that add together to get close to $875 without going over using the standard algorithm. In Activity 2, students examine work of their peers to determine who used the standard algorithm correctly and identify possible mistakes. In addition, the instructional materials embed opportunities for students to independently practice procedural skills and fluency: • 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 5’s Interview, students must demonstrate fluency of subtracting decimals. • Fundamentals Games contains a variety of games that students can play to develop grade level fluency skills. For example, in Jump On, students add multi-digit numbers. • Some lessons provide opportunities for students to practice procedural skills during the Step Up in the student journal. Indicator {{'2c' | indicatorName}} 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 The instructional materials for ORIGO Stepping Stones 2.0 Grade 4 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 2, Lesson 7, addresses the standard 4.OA.3, “The record number of cell phones sold over a 12 month period is 1,089. Gloria beat the record by 94 sales. How many cell phones did she sell?”. • In Module 7, Lesson 4, addresses the standard 4.OA.3, “A roll of plastic wrap is 70 meters long. Thomas cuts the plastic wrap into lengths of 9 meters. How many of these lengths can he cut?”. • In Module 9, Lesson 12, addresses the standard 4.OA.3, “Deon buys 3 16 oz boxes of raisins. He shares the raisins equally among 4 bowls. What is the mass of raisins in each bowl?”. • In Module 9, Lesson 8, addresses the standard 4.NF.1, “Maintaining Concepts and Skills” includes “imagine you wanted to lay turf in this barnyard. Calculate the area. Show your thinking.” The materials present a rectangle labeled “barnyard” with perimeter measurements given. • In Module 5, Lesson 2, addresses the standard 4.OA.3, “Emily has saved$15 to buy a guitar. The guitar costs four times as much as she has saved. What is the price of the guitar?”.
• In Module 3, Problem Solving Activity 4, addresses the standard 4.NBT.6, “One yard is 25 ft long and 10 ft wide. Another yard is 22 ft long and 10 ft wide. What is the difference in area?”.
• In Module 10, Lesson 12, addresses the standard 4.MD.1, students solve a word problem and show their thinking. For example, Question 1b states, “Vishaya rides 4.6 miles. Jacob rides 8.3 miles more than Vishaya. How far does Jacob ride?”.
• In Module 7, Enrichment Activity 1 includes routine one-step problems and addresses standard 4.NBT.2). For example, ‘There are 43 strawberries to place onto toothpicks. Each toothpick can hold 2 strawberries. How many toothpicks will be needed to hold all the strawberries.”.

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, “Abigail buys one roll of chicken wire. She runs the chicken wire around the outside of the posts to make four walls. How much chicken wire will she use?” Students use information provided to answer. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
• In Module 6, Thinking Task, Question 1 states, “Compare the amount that the adults and students pay to go on the field trip. Describe the relationship between the two amounts. Show your thinking.” The problem states that student pay $4 and adults pay$12. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
• In Module 9, Thinking Task, Question 2 states, “In the Fresh-Fruit Punch, how much more cranberry juice is there than lemon juice? Show your work.” Students must use the information for the Drink Recipes to solve. This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
• In Module 12, Thinking Task, Question 1, students use time, money, fractions/decimals, and information from School Fun Run to solve. The question states, “The students in Ms. Yorba’s class want to each raise $5.00. They are trying to calculate the number of laps needed to reach$5.00, and what distance that will be. For this time: Show how many laps each student must run to raise \$5.00. Show the distance in miles.” This non-routine question prompts students to apply mathematical knowledge/skills to real-world contexts.
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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.

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

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

Examples of conceptual understanding, procedural skill and fluency, and application presented separately in the materials include:, students practice procedural skill and fluency using an area model to multiply whole numbers.

• In Module 2, Lesson 9 (4.NBT.), students use an array model to reinforce the relationship between pairs of tens and fives facts.
• In Module 8, Lesson 9, 4.NBT.5, students practice procedural skill and fluency using an area model to multiply whole numbers.
• Each module contains one lesson Solving Word Problems which requires application. For example, in Module 10, Lesson 12, students must solve a word problem and show their thinking. Question 1b states, "Vishaya rides 4.6 miles. Jacob rides 8.3 miles more than Vishaya. How far does Jacob ride?"

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

• In Module 2, Lesson 5, Student Journal Activity, students use the standard algorithm to identify steps already completed in a problem, write out the numbers, and explain what the number “11” represents in the problem.
• In Module 9, Problem Solving Activity 1, “Rita baked 2 cakes that were exactly the same size for a party. The first cake was a carrot cake which was cut into 8 equal slices. The second cake was a fruit cake which was cut into 12 equal slices. At the party, 3/8 of the carrot cake was eaten and 6 slices of the fruit cake was eaten. Was more of the carrot cake or fruit cake eaten?” Students need to apply their conceptual understanding of fractions.
• In Module 6, Thinking Task, students use information from the chart provided to solve and answer the questions, “What group can take the van? Fill in the total miles walked on the table above. Write which group can take the van. Show your thinking.”

Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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.

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The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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.

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Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 5, Lesson 3, students are told to use tape diagrams to model the mathematics.
• In Module 6, Lesson 3, students use arrays to model partitioning strategies for multiplication. Students do not have opportunities to connect the arrays to different representations.
• In Module 10, Lesson 8, students are given models to compare decimals. A support page is provided for the students with number lines, area models, and place value “expanders” for students to use to compare decimals. Students do not have the opportunity to choose or come with their own model and strategies to compare decimals.

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 9, students use tiles and rulers to determine the area of rectangles. Students are directed which tool they should use.
• In Module 7, Lesson 8, students choose a calculation method but are told which tools to use from the online tool “Flare” with access to number line cards, to find the difference between two numbers.
• In Module 9, Lesson 7, students are locating decimal fractions to the tenths and hundredths on a number line. Students are provided number lines which are already numbered on which to place the decimals.
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 do not meet the expectations 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 5, the teacher projects the 6-digit slide and asks, “What can you tell me about this number? How would you write this number in expanded form?” Then the teacher invites students to come to the board and show the different ways to record the number, explaining their thinking as they do.
• In Module 5, Lesson 2, the teacher projects four word problems and has the students read the problems aloud and analyze the language and structure of each problem. Then the teacher asks, “Which word problems involve multiplication? Which word problems involve addition? What words help you decide?”.
• In Module 10, Lesson 3, after completion of Student Journal pages 364-365 Question 2, the teacher is instructed to ask, “How did you decide how much more was needed to be shaded to make one whole? Did you focus on the unshaded region, or did you think about how many tenths and hundredths were already shaded?”.
Indicator {{'2g.ii' | indicatorName}}
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.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 1, students round 3-digit numbers to estimate totals. Teachers encourage respectful critique by asking questions such as, “Do you agree with this group’s estimate? Why/why not? Who used a different strategy? Did your strategy result in a more accurate estimate? and How could you explain that strategy in a different way?”.
• In Module 2, Lesson 6, students use the standard algorithm to add 3 addends. Teachers encourage discussion and respectful critique by asking, “I can see why you thought that, but, I disagree because, and I know my answer is correct because.”.
• In Module 6, Lesson 4, students are placed in pairs to brainstorm different ways to partition rectangles. The teacher is guided to prompt the students to demonstrate their strategies and then the class discusses the advantages and disadvantages of different partitioning strategies.
Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grade 4 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 not 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 10, vocabulary includes words such as decimal, decimal fractions, hundredths, and tenths.
• 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 7, Lesson 6, mixed number is present in the Student Journal, but the definition is not introduced in any lesson in Module 7.

Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Not Rated

Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator {{'3a' | indicatorName}}
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.
Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator {{'3c' | indicatorName}}
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.
Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator {{'3g' | indicatorName}}
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.
Indicator {{'3h' | indicatorName}}
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.
Indicator {{'3i' | indicatorName}}
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.
Indicator {{'3j' | indicatorName}}
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).
Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.
Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator {{'3u' | indicatorName}}
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).
Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator {{'3aa' | indicatorName}}
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.
Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator {{'3ac' | indicatorName}}
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.
Indicator {{'3ad' | indicatorName}}
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.).
Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

Report Overview

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

Math K-2

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Kindergarten through Grade 2 partially meet the expectations for alignment to the CCSSM. In Gateway 1, the instructional materials meet the expectations for focus, but partially meet expectations for coherence. In Gateway 2, the instructional materials for each grade partially meet the expectations for rigor and practice-content connections. Since the materials for each grade partially meet expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.

Kindergarten
Alignment
Partially Meets Expectations
Not Rated
Alignment
Partially Meets Expectations
Not Rated
Alignment
Partially Meets Expectations
Not Rated

Math 3-5

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grades 3 through 6 partially meet the expectations for alignment to the CCSSM. The instructional materials meet the expectations for Gateway 1 as they meet the expectations for focus and partially meet expectations for coherence, except for Grade 4 which meets expectations for coherence. In Gateway 2, the instructional materials partially meet the expectations for rigor, except for Grade 6 which meets expectations for rigor, and the instructional materials partially meet the expectations for practice-content connections. Since the materials for each grade partially meet expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.

Alignment
Partially Meets Expectations
Not Rated
Alignment
Partially Meets Expectations
Not Rated
Alignment
Partially Meets Expectations
Not Rated

Math 6-8

The instructional materials reviewed for ORIGO Stepping Stones 2.0 Grades 3 through 6 partially meet the expectations for alignment to the CCSSM. The instructional materials meet the expectations for Gateway 1 as they meet the expectations for focus and partially meet expectations for coherence, except for Grade 4 which meets expectations for coherence. In Gateway 2, the instructional materials partially meet the expectations for rigor, except for Grade 6 which meets expectations for rigor, and the instructional materials partially meet the expectations for practice-content connections. Since the materials for each grade partially meet expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.

Alignment
Partially Meets Expectations
Not Rated

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Overall Summary

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Usability
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