6th Grade - Gateway 3

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. 

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• i-Ready Classroom Central, Preparing for a Unit of Instruction, “Before delivering each unit of instruction, make sure to peruse the unit-level resources in your Teacher’s Guide. Learn about the unit goals by reading the Unit Opener, take note of the vocabulary and language supports, and study the mathematics in the unit by watching the Unit Flow and Progression Video or reading the Math Background pages.” 

  • Program Overview provides the teacher with information on program components and description of i-Ready classroom Mathematics implementation. 

  • Plan is broken down into Unit, Lesson, and Session. 

  • Teach gives information on practice, and differentiation. 

  • Assess includes support for the diagnostic, reports, and data. 

  • Leadership informs the teacher on getting started, building routines, fostering discussions, making connections, and top leader actions. 

• Program Implementation includes numerous supports such as digital math tools, videos, discourse cards, vocabulary, language routines, graphic organizers, games, correlations with standards and practices, etc.

• Each unit has a Beginning of Unit document that provides the teacher with extensive information on Unit Flow and Progression, Unit Resources, Unit Opener, Unit Prepare For, Unit Overview, Lesson Progression, Prerequisites Report Overview, Professional Development, Understanding Content Across Grades, Language Expectations, Math Background, Cumulative Practice, Yearly Pacing for Prerequisites, and Unit Lesson Support. Examples include:

  • Unit Opener, Self Check, “Take a few minutes to have each student independently read through the list of skills. Ask students to consider each skill and check the box if it is a skill they think they already have. Remind students that these skills are likely to all be new to them and that over time, they will be able to check off more and more skills.”

  • Prerequisites Report Overview, “Diagnostic data generates the Prerequisites report, which helps you identify students’ prerequisite learning needs and provides guidance on how to best integrate prerequisite instruction into your grade-level scope and sequence for the year.” These are specific to current students and classes providing valuable data about entry points for students. 

  • Under the Prepare column, there is a Unit and Lesson Support document that provides multiple On-the-Spot Teaching Tips for each Unit. These tips provide information on what to reinforce from prior learning promoting scaffolding to current content.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Throughout each lesson planning information, there is narrative information to assist the teacher in presenting student materials throughout all phases of the unit and lessons. Examples include:

• Program Implementation, Teaching & Learning Resources, Discourse Cards, provides instruction on how to use the Math Discourse Cards. “These questions and sentence starters provide a way to engage all students in meaningful mathematical conversations. These cards will help students initiate, deepen, and extend conversations with partners, small groups, or the whole class. Each card has two questions or sentence starters on it-one on the front and one on the back. With each question, be sure to have students explain their reasoning for their response.”

• Unit 2, Lesson 8, Session 1, Teacher Edition, Connect It, Problem 3, “How is using the standard algorithm similar to using partial quotients to divide a three-digit number by a one-digit number? How is it different?” The teacher’s edition provides guidance for the teacher in the Exit Ticket, “Look for understanding that the standard algorithm does not use zeros as placeholders in the quotient; instead each part of the quotient is written in its corresponding place value as the division occurs. Error Alert: If students struggle to identify the place value of each digit in the quotient of the standard algorithm and place the digits of the quotient in the wrong position, then have them organize their work on grid paper to maintain alignment. Provide place-value charts so students can match the digits in their quotients to the corresponding place values.”

• Unit 3, Lesson 13, Session 2, Teacher Edition, Apply It, students answer questions about equivalent ratios. The Teacher’s Edition provides guidance for the teacher, “For all problems, encourage students to use a model to support their thinking. Allow some leeway in precision; drawing number lines with equal spacing between tick marks can be difficult, and precise measures are not necessary to determine a solution to the problem.”

• Unit 4, Beginning of Unit, Unit Prepare For, teachers are provided with guidance in using the graphic organizer included for students. This includes guidance in analyzing the term “comparing ratios” and how to build academic vocabulary throughout each lesson in the unit. “Next, have students meet with a partner to share ideas and add new information to the organizer. Circulate and validate responses and clarify any misconceptions.”

• Unit 5, Lesson 22, Session 2, Teacher Edition, Develop, Discuss It, teachers are prompted to support partner discussion. “After students work on Try It, encourage them to respond to Discuss It with a partner. If students need support in getting started, prompt them to ask each other questions such as: In your equation, how did you represent the number of days? The cost for a day? How can you organize the information to find a pattern? How can you test whether your equation makes sense?” Common Misconception: “Listen for students who are not precise when defining variables. For example, students may say d = dollars, instead of d = dollars to feed 8 meerkats for n days. As students share their strategies, have partners discuss and reinforce understandings of variables and the need for precise descriptions of the meaning of variables.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for  containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. 

The Beginning of Unit section for every unit provides an abundance of information for teachers, including sections to support teachers with adult-level understanding of the content:

• Math Background includes Unit Themes, Prior Knowledge, and Future Learning. In the Math Background, as well as throughout the teacher materials, there are insights on the concepts taught, Common Misconceptions, and Error Alerts to watch for when students are incorrectly applying skills. 

• Lesson Progression links each lesson within the current unit to a prior and future lesson so teachers know what students need to know to be successful with the current work as well as what the current work is preparing students for. This is important for a teacher’s complete understanding of how to scaffold and bridge the current content. For example, Unit 3, Lesson 13, Lesson Overview, Teacher Edition, Find Equivalent Ratios - Full Lesson, Learning Progression:

  • “In Grade 5, students extended their use of multiplication to scale a quantity, which means to increase or decrease by multiplying a factor. In the previous lesson, students were introduced to the concept of ratio, ratio notation, and ratio language. They compared quantities and examined relationships using ratios. 

  • In this lesson, students merge their understanding of multiplication as scaling and ratio concepts to identify and generate equivalent ratios. Students find missing values in tables of equivalent ratios and solve problems using double number lines or tables. They represent ratios as ordered pairs and then graph them as points in the coordinate plane. 

  • Later in Grade 6, students will use tables to compare ratios, and they will apply their understanding of ratio to the ideas of rate and unit rate. They will analyze relationships between dependent and independent variables using graphs. In Grade 7, students will apply ratio reasoning to explore proportional relationships and calculate probabilities.”

• Understanding Content Across Grades provides explanations of instructional practices as well as information about necessary prior knowledge and concepts beyond the current course for teachers to improve their own knowledge of the subject. For example, Unit 2, Beginning of Unit, Understanding Content Across Grades related to Lesson 7:

  • Prior Knowledge: “Insights on: Adding and Subtracting Decimals. Students learn to add and subtract decimals using the same variety of models and strategies they used to add and subtract whole numbers. Common Error - When students add and subtract decimals using the standard algorithm, they may line the numbers up by the end digits, rather than by place- value. A place-value chart is an excellent tool to help students focus on the value of each digit.” This information is accompanied by example problems worked out using a number line, a 100s place value grid, and the algorithm. 

  • Current Lesson, “Insights on: Adding, Subtracting, and Multiplying Decimals. Multiplying Decimals - When multiplying decimals, students use both decimal and fractional forms of the factors to make sense of the placement of the decimal point in the product.” This information is accompanied by an example problem worked out using the relationship between decimals and fractions to understand decimal multiplication.

  • Future Learning, “Insights on… Understanding addition with positive and negative numbers. Students use integer chips to observe a key difference between adding two numbers with different signs and adding two numbers with the same sign. When the addends have different signs, they can cancel out zero pairs. When the addends have the same sign, all the chips are of the same type, so there are no zero pairs.” This is accompanied by an example problem solved using integer chips.

• Each lesson includes a Reteach section with several pages called “Tools for Instruction” that provide explicit teacher guidance related to the current work and to prerequisite skills. These pages include adult explanations, step-by-step guidance for teaching, and check for understanding. For example, Unit 6, Lesson 24, Compare Positive and Negative Rational Numbers:

  • “Rational numbers are numbers that can be written as fractions. The set includes whole numbers and fractions, as well as terminating and repeating decimals, both positive and negative. Students will be familiar with number lines from early grades… Concepts such as temperature, money in a bank account, and depth below or height above sea level give context to negative numbers… Using the number line provides a base for understanding positive and negative rational numbers and operations, absolute value, and the use of all quadrants of the coordinate plane.”

  • “Step by Step: 1) Create a number line. Have the students draw a vertical number line from -10 to 10. Ask the student to draw a horizontal line at zero across the number line. Tell the student to imagine that the horizontal line is the surface of the ground. The negative numbers are below ground, and the positive numbers are above ground. 2) Compare integers on the number line. (followed by three prompts) 3) Compare positive and negative decimals. (followed by two prompts) 4) Compare positive and negative fractions. (followed by two prompts)”

  • “Check for Understanding: Have the student use the “greater than” symbol to compare -18 and -16.” Then an error analysis chart is provided: “If you observe… the student may… Then try…”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

In Program Implementation, correlation information is present for the mathematics standards addressed throughout the grade level using multiple perspectives. For example: 

• The Correlations document for Content Focus in the Common Core State Standards (CCSS) describes lesson correlation to the CCSSM through multiple lenses. The document identifies the major and supporting areas of focus within the CCSSM and corresponding lessons that address those standards. Additionally, a table is provided that correlates each lesson with the standards addressed, designating standards as “Focus”, “Developing”, or “Applied” within each lesson. 

• The Correlations Document also identifies the Standards of Mathematical Practice that are included in each lesson; one table is organized by MP, and another is organized by lesson. 

• The Unit Review Correlation identifies the associated standard and lesson to each problem within the Unit Review, along with their Depth of Knowledge level. 

• Digital Resource Correlations, Comprehension Check Correlations, and Cumulative Practice Correlations identify the lesson and a statement of the part of the standard it aligns to. 

• The WIDA PRIME V2 correlates the WIDA Standards Framework to examples in the material with descriptions of how they connect. 

• The English Language Arts Correlations provides a table that offers evidence of how the Common Core State Standards for English Language Arts are supported in every lesson and unit of the i-Ready Classroom Mathematics material.

In each Beginning of Unit section, there are numerous documents provided that contain explanations of the role of the specific grade-level mathematics in the context of the series. For example: 

• The Lesson Progression provides a flow chart delineating how each standard in the current lesson builds upon the previous grade levels and connects to future grade levels. This is developed in detail with examples in the Understanding Content Across Grades document. 

• There is a Unit Flow and Progression video for teachers that provides background about the content covered in the unit. 

• The Unit and Lesson Support document provides descriptions of the standards addressed in each unit with connections to prerequisites and teaching tips about prior knowledge. For example, Unit 2, Beginning of Unit, Unit and Lesson Support, the opening narrative provides the content of the unit, “In this unit, students use what they know about adding, subtracting, and multiplying decimals to hundredths to extend their understanding of computing with decimals. They learn the standard algorithm for whole number and decimal division and use both visual models and equations to divide with fractions. They will also build on their prior understanding of volume and of multiplying with fractions to find volumes of rectangular prisms with fractional side lengths.” The document continues with Instructional Support identifying specific lessons from prior grades to develop understanding, such as Unit 2, Lesson 8, “These lessons build on students’ work with multiplying fractions and dividing unit fractions in Grade 5, Unit 3: Grade 5, Lesson 22 - Multiply Fractions in Word Problems.”

• In every teacher's Lesson Overview, the Learning Progression identifies how the standard is addressed in earlier grades, in the current lesson, next lesson, and in the next grade level. For example, Unit 4, Lesson 17, Overview, Learning Progression, “In earlier grades, students used models to represent, write, and identify equivalent fractions. Earlier in Grade 6, students generated and identified equivalent ratios… In this lesson, students understand that a percent is a special type of rate in which the second quantity is 1 unit that is divided into 100 equal parts… In the next lesson, students will use their understanding of percents and models of percents to find the percent of a number and to find the whole when a percent and part are known. In Grade 7, students will choose to represent percents as fractions or decimals as they solve a variety of percent problems.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

There are thorough explanations about the instructional approaches of the program. These are easily found under Program Implementation and in Classroom Central. For example:

• Program Implementation contains “Try-Discuss-Connect Routine Resources.” This routine is embedded throughout the program, “i-Ready Classroom Mathematics empowers all students to own their learning through a discourse-based instructional routine. Lessons are divided into Explore, Develop, and Refine sessions and are taught over the course of a week. In Explore and Develop sessions teachers facilitate mathematical discourse through a Try-Discuss- Connect instructional routine.” In i-Ready Classroom Central, there are videos modeling the six steps of the Try-Discuss-Connect routine as well as an Exit Ticket.

• Program Implementation, User Guide, Protocols for Engagement describes multiple protocols and identifies the traits each protocol validates to help all students “feel accepted and included.” Further, “Protocols provide structure for activities so that all students have a chance to think, talk, and participate equally in classroom activities. Each protocol incorporates modes of communication common to one or more culture and leverages those behaviors for a particular instructional purpose.” For example, “Stand and Share: Students stand when they have something to share with the class. Validates: spontaneity, movement, subjectively, connectedness.” Protocols can be found in the Lesson Overview section of the Teacher Guide.

• Program Implementation, i-Ready Classroom Central, Building Community, Promote Collaborative Learning, has resources such as using Lesson 0 to introduce the Try-Discuss-Connect Routine and language routines, questions to support discourse, videos about sharing math ideas, ideas for promoting mathematical practices, and creating a positive mindset. 

• Program Implementation, i-Ready Classroom Central, has a link in the upper right under the search box called Explore the Resources page that has all of the additional resources organized in a list of links by category that provide abundant information, including a section called Program Overview.

Materials include relevant research sources. In Program Implementation, Supporting Research, “i-Ready Classroom Mathematics is built on research from a variety of federal initiatives, national mathematics organizations, and experts in mathematics.” A table describes 16 concepts that are embedded in the program with examples of how and where each is used, an excerpt from the research that supports it, as well as an extensive reference list. Examples include: 

• “The Concrete-Representational-Abstract (CRA) Model is a three-part instructional model that enhances students’ mathematical learning.” This model is built into all i-Ready Classroom Mathematics lessons in the Try It, Discuss It, Connect It, and Hands-On Activities. “Using and connecting representations leads students to deeper understanding. Different representations, including concrete models, pictures, words, and numbers, should be introduced, discussed, and connected to support students in explaining their thinking and reasoning.” (Clements and Sarama, 2014)

• “Collaborative learning (partner or small group) encourages students to present and defend their ideas, make sense of and critique the ideas of others, and refine and amend their approaches.” Lessons provide multiple opportunities for collaborative learning during Discuss It and Pair/Share. “Research tells us that when students work collaboratively, which also gives them opportunities to see and understand mathematics connections, equitable outcomes result.” (Boaler, 2016)

• “An instructional framework supports students in achieving mathematical proficiency and rigor within a collaborative structure to develop greater understanding of how to reason mathematically.” The Try-Discuss-Connect instructional framework is foundational in this program. “Instructional routines are situated in the learning opportunity itself, providing students with a predictable frame for engaging with the content…”  (Kelemanik, Lucenta, & Creighton, 2016)

• Program Implementation, User Guide, Routines that Empower Students identifies 9 research-based language routines. Each routine includes the purpose, the process, and which part of the Try-Discuss-Connect Routine it can be used with. For example, Say It Another Way is used with Try It, “Why: This routine helps students paraphrase a word problem or text so they know if they have understood it. It provides an opportunity to self-correct or to ask for clarification and ensures that the class hears the problem or story more than once and in more than one way.”

• Program Implementation, i-Ready Classroom Central, Explore the Resources page (near search box), Program Overview,Building Effective Mathematics Teaching Practices within Classrooms, explains how NCTM’s Effective Teaching Practices are integrated into i‑Ready Classroom Mathematics. “When teachers use the program with integrity… they naturally engage in the Top Teacher Actions. This ensures students have access to high-quality mathematics instruction every day… The intentional design of the Teacher’s Guide provides teachers with the opportunity to consistently implement NCTM’s Teaching Practices each day.”

The materials reviewed for i-Ready Mathematics, Grade 6 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Lesson Overview for the teacher provides a Materials Required column for each lesson on the Pacing Guide; additional materials are listed in the Differentiation column. Any materials that need to be printed are also provided in the Overview, such as grid paper or double number lines. For example:

• Unit 3, Lesson 13, Session 1, “Materials tab: Math Toolkit connecting cubes, counters, grid paper, Presentation Slides. Differentiation tab: 25 two-color counters per group.”

Under Program Implementation, a Manipulatives List provides a document identifying manipulatives needed for each lesson K-8. For example: 

• “Manipulatives List, Unit 3, Lesson 13, identifies connecting cubes - 60 per pair, and counters - 60 per pair.”

Program Implementation also includes digital math tools, discourse cards and cubes, activity sheets, data sets, and graphic organizers.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

In the Teacher Toolbox, each lesson includes Assess which provides Lesson Quizzes & Unit Assessments. Lesson Quizzes, Teacher Guide lists information for each problem: tested skills, content standards, mathematical practice standards, DOK levels, error alerts, problem notes, Short Response Scoring Rubric with points and corresponding expectations, and completed problems. For example:

• Unit 5, Lesson 20, Lesson Quiz, Problem 2, “DOK 1, 6.EE.B.5, SMP 2.”

Assess, End of Unit, Unit Assessments, Teacher Guide, Forms A and B are provided and include the content item with a solution. Form A includes Problem Notes, completed problems, DOK levels, content standards, mathematical practices, Scoring Guide, Scoring Rubrics, and Responding to Student Needs. Form B appears to parallel all of the correlations provided for Form A, though it is not labeled. It is noted in the Scoring Guide, “For the problems in the Unit 4 Unit Assessments (Forms A and B), the table shows: depth of knowledge (DOK) level, points for scoring, lesson assessed by each problem, and both the CCSS standard and Mathematical Practice Standards addressed.” For example:

• Unit 1, End of Unit, Assess, Unit Assessment, Form A, Scoring Guide, Problem 5, “DOK 2, 6.G.A.1, SMP 6.”

• Unit 7, End of Unit, Assess, Unit Assessment, Form A, Scoring Guide, Problem 12, “DOK 2, 6.SP.A.2, SMP 7.”

Digital Comprehension Checks “can be given as an alternative to the print Unit Assessment. For this comprehension check, the table below provides the Depth of Knowledge (DOK), standard assessed, and the corresponding lesson assessed by each problem.” While the Comprehension Checks identify the content standards, they do not identify the mathematical practices. For example:

• Unit 1, End of Unit, Assess, Comprehension Check Correlation Guide, Problem 5, “DOK 2, 6.G.A.1.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

The assessment system provides opportunities to determine students’ learning that include teacher support for interpreting student performance in the Problem Notes and Rubrics provided, though the rubrics are generic rather than specific to the lesson. Examples include:

• Problem Notes for each problem in the Lesson Quizzes and Form A of the Unit Assessment provide guidance on steps to solve the problem and what students may have done incorrectly. For example:

  • Unit 1, Lesson 5, Assess, Lesson Quiz, Problem 2, “C is correct. Students could solve the problem by identifying that there are 2 additional factors of 3 in 3^{21}, and 3\times3=9. A is not correct. This answer represents the difference between the exponents. 21-19=2. B is not correct. This answer represents the repeated factor instead of the product of the repeated factors. D is not correct. This answer represents three factors of 3 instead of two factors of 3.”

  • Unit 6, End of Unit, Assess, Unit Assessment, Form A, Problem 6, “Students could also solve the problem by considering the placement of each layaway balance on the number line and identifying the balance that is farthest from 0.” 

• Lesson Quizzes contain a Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric and a Short Response Scoring Rubric. The Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric states: “2 points if all answers are correct, 1 point if there is 1 incorrect answer, and 0 points if there are 2 or more incorrect answers.” The Short Response Scoring Rubric states: 2 points if the “Response has the correct solution and includes well-organized, clear and concise work demonstrating thorough understanding of mathematical concepts and/or procedures.” 1 point for “Response contains mostly correct solution(s) and shows partial understanding of mathematical concepts and/or procedures.” 0 points if the “Response shows no attempt at finding a solution and no effort to demonstrate an understanding of the mathematical concepts and/or procedures.”

• Unit Assessments contain the Extended Response Scoring Rubric (if there is an extended response question included in the assessment), Short Response Scoring Rubric, and a rubric for Fill-in-the-Blank/Multiple Select/Choice Matrix. For example, the Extended Response Scoring Rubric, a response should earn 4 points if, “Response has the correct solution(s) and includes well-organized, clear and concise work demonstrating thorough understanding of mathematical concepts and/or procedures.” This same expectation scores a 2 on the Short Response Scoring Rubric. The Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric is the same as the Lesson Quizzes.

The Lesson Quizzes and Unit Assessments provide sufficient guidance to teachers to follow-up with students, although there is no follow-up guidance for the Comprehension Checks. The follow up suggestions reference previous work rather than new material. For example:

• Unit 2, Lesson 10, Assess, Lesson Quiz provides three types of differentiation for possible follow up depending on student performance: Reteach, Reinforce, and Extend. “Reteach: Tools for Instruction, Students who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction. Grade. Reinforce: Math Center Activity, Students who require practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities (available in on-level, below-level, and above-level versions). Extend: Enrichment Activity, Students who have achieved proficiency with concepts and skills and are ready for additional challenges will benefit from group collaborative games and activities that extend understanding.” The Reteach section directs teachers back to Lesson 10, Divide Fractions. The Reinforce section directs teachers back to Lesson 10, Use Fraction Division. The Extend section directs teachers back to Lesson 10, Pumpkin Pairs.

• Unit 2, End of Unit, Assess, Unit Assessment, Form A, provides a section called Responding to Student Needs. This section directs teachers back to the relevant lessons for review and where teachers can access the Review, Reinforce, and Extend options. “For students who answer problems incorrectly on the Unit Assessment, choose from the following resources on the Teacher Toolbox for additional support.””Reteach: Tools for Instruction, Multiply Multi-Digit Decimals (Lesson 7), Divide Multi-Digit Decimals (Lesson 8), Understand Division with Fractions (Lesson 9), Divide Fractions (Lesson 10). For students who exceed proficiency on the Unit Assessment, choose from the following activities on the Teacher Toolbox.””Extend: Enrichment Activities, Tacos for All! (Lesson 9), Pumpkin Pairs (Lesson 10), Turn Down the Volume (Lesson 11).”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

There are formative and summative assessments provided as PDFs as well as comparable assessments provided online. Lesson Quizzes and Unit Assessments provided include a variety of item types for students to demonstrate grade-level expectations. For example:

• Fill-in-the-blank

• Multiple select

• Matching

• Graphing

• Constructed response (short and extended responses)

• Technology-enhanced items, e.g., drag and drop, drop-down menus, matching 

Throughout the lessons, there are opportunities to demonstrate critical thinking, develop arguments, or apply learning in a performance task, though these are not typically on the assessments.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

• i-Ready Classroom Central, Teach, Differentiate, has information to support the teacher in planning for all special populations. Address Unfinished Learning provides multiple links to guidance resources, data analysis resources, and instructional resources. i-Ready Personalized Instruction has resources for students who have taken the Diagnostic and will have access to online learning and instructional paths tailored to their individual needs to reinforce prerequisite skills and build grade-level skills. Support Every Learner, “Every student can excel in mathematics with the right supports. Access these resources to find ideas and strategies for organizing groups and adapting your instruction to meet the unique needs and learning styles of all students.” There are seven links related to grouping students and adapting instruction. For example:

  • Reference Sheet: Supporting Differentiated Needs before the Unit or Lesson is a 4-page document with numerous strategies including addressing prerequisites, integrating assessments, supporting English learners, and differentiating that links to practice, games, enrichment, literacy, tutorials, and more.

  • Reference Sheet: Supplemental Tools for Accessible Mathematics Instruction is a 5-page table that provides support ideas for every aspect of the lesson. For example, during Try It, a suggested support is, “Offer multiple means of representation, engagement, and action and expression such as: highlight important numbers, words, and phrases; Invite volunteers to act out the problem for the class; Offer options for how students express their ideas.” During Discuss It, “Use hand signals to agree, disagree, or share an idea.”

• In Refine, the last session of each lesson, the teacher’s edition provides suggestions to Group & Differentiate, “Identify groupings for differentiation based on the Start and problems 1-3. A recommended sequence of activities for each group is suggested below. Use the resources on the next page to differentiate and close the lesson.” Resources are suggested for groups Approaching Proficiency, Meeting Proficiency, and Extending Beyond Proficiency. 

• At the end of the Lesson Quiz in the teacher’s edition, there is a section for differentiation that provides suggestions for Reteach (Tools for Instruction), Reinforce (Math Center Activity), and Extend (Enrichment Activity). Reteach, “Students who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.” Reinforce, “Students who require practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities (available on-level, below-level, and above-level versions).” Extend, “Students who have achieved proficiency with concepts and skills and are ready for additional challenges will benefit from group collaborative games and activities that extend understanding.” 

• Program Implementation, i-Ready Classroom Central, Differentiate, Support Every Learner, Reference Sheet: Supplemental Tools for Accessible Mathematics Instruction, Accessibility and Accommodations with i-Ready Classroom Mathematics, Accessibility and Accommodations Update document which states, “To make i-Ready Classroom Mathematics accessible to the widest population of students, we offer a range of accessibility supports that may also meet the requirements of a number of student accommodations.” The table provided lists the Universal Supports, Designated Supports, and Accommodations that are both embedded and not embedded in the program. For example, embedded supports include audio support, closed captioning, calculator, zoom in/out, highlighting, and more. Available non-embedded supports include native language translation of directions, noise buffer, alternate response options, scribe, and more.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity. 

• Each lesson has an Extend: Enrichment Activities column that provides a challenge task. For example, Unit 1, Lesson 2, Extend, Building Shapes, students are provided with a challenge question, “How can you build different polygons with given areas using triangles, rectangles, and parallelograms?” followed by related tasks such as, “What is the fewest number of triangles needed to build a 4-sided polygon with an area of 12 square units? Explain. Draw one possible way to do this.”

• Refine sessions at the end of each lesson provide recommendations for students that demonstrate understanding “Extending Beyond Proficiency” to engage in problems for reinforcement and a challenge. The number of problems is the same as the work for students who are considered to be “Meeting Proficiency.” Additional Enrichment Activities can be found online in the Small Group Differentiation Extend section. In addition, Refine sessions include at least one problem identified as DOK 3 where students utilize strategic thinking. 

• In Explore and Develop sessions in each lesson, the materials contain Differentiation: Extend, Deepen Understanding or Challenge for the lesson’s key concepts through the use of discourse with students. For example, Unit 5, Lesson 21, Session 3, Teacher Guide, Differentiation: Extend, Deepen Understanding, “Prompt students to compare differences between a hanger diagram for an addition equation and one for a multiplication equation...Ask: In what situations could a hanger diagram be used to represent addition or multiplication? When could it only represent addition?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing strategies and support for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. Examples include: 

• Program Implementation, i-Ready Classroom Central, Differentiate, Support All Learners, Reference Sheet: Supports for English Learners explains where to find and how to use all of the supports built into the Teacher Guide for every lesson to “address the strengths and needs of ELs” such as, Build Your Vocabulary, Connect Language Development to Mathematics, Language Objectives, Connect to Community and Cultural Responsiveness, and Connect to Language Development.

• Program Implementation, Program Overview, Integrate Language and Mathematics shows where teachers can access tips for targeted support using Language Routines in the Teacher Guide for every lesson.

• Program Implementation, Program Overview, Language Development and Discourse Support provides “support at the word/phrase, sentence, and discourse levels so that all students can engage in rigorous mathematics and communicate effectively.”

• Program Implementation, User Guide, Resources for Language Development describes nine features that are embedded in the teacher materials to “build academic language of all students, especially English learners. These supports help students learn how to communicate effectively across the language domains.”

• Program Implementation, User Guide, Routines that Empower Students provides nine language routines. “While these routines support English learners, they are designed to be used by all students as they access mathematical concepts and their growing mathematical understanding.” Three routines, in particular, are differentiated for English Learners: Act it Out, Co-Constructed Word Banks, and Stronger and Clearer Each Time. 

• Program Implementation, User Guide, Support for Academic Discourse describes “a variety of ways to support students in communicating with academic and math-specific vocabulary and language.”

• Program Implementation, Discourse Cards provide sentence starters and questions to help students engage in conversations with their partners, small groups, or the whole class such as, “Did anyone get a different answer?; What would you add to what was said?”

• All classroom materials are available in Spanish.

• Program Implementation, Multilingual Glossary is available in Arabic, Chinese, Haitian Creole, Portuguese, Russian, Tagalog, Urdu, and Vietnamese. There is a Bilingual glossary in the student textbook that includes mathematics vocabulary in English and Spanish.

• Beginning of Unit, Language Expectations is a chart that “shows examples of what English Learners at different levels of English language proficiency can do in connection with one of the Common Core State Standards (CCSS) addressed in this unit. As you plan for this unit, use these examples of language expectations to help you differentiate instruction to meet the needs of English Learners.”

• Beginning of Unit, Unit Prepare For, Build Academic Vocabulary includes a chart of academic words for the units paired with their Spanish cognates. There are three routines provided in Professional Development to support vocabulary development: Academic Vocabulary, Cognate Support, and Collect and Display. 

• Each lesson in Lesson Overview, Teacher Guide’s Full Lesson includes Language Objectives, Connect to Culture, and Connect to Language. 

• Session 1 of every lesson uses graphic organizers to help students access prior knowledge and vocabulary they will develop in the lesson. Support for Academic language is used during the “Try-Discuss-Connect Language” routines in each lesson. 

• All sessions throughout the lesson embed support including references back to previously listed items.

The materials reviewed for i-Ready Classroom Mathematics, Grade 6 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Students have access to both virtual and physical manipulatives throughout the program. For example:

• Program Implementation, Digital Tools are available for students. These tools include Counters and Connecting Cubes, Base-Ten Blocks, Number Line, Multiplication Models, Perimeter and Area, and Fraction Models. Geometry Tool, Scientific Calculator, and Graphing Calculator. Also in Program Implementation, support videos are available for each of the digital tools, explaining how they may be used and their functions. 

• Program Implementation, Manipulative Kit includes algebra tiles, plastic rulers, centimeter cubes, base ten blocks, number cubes, rainbow color tiles, two color counters, and connecting cubes. A la carte items are available. The materials state that these items may only be used once, may be common to classrooms, or print options are available. A la carte items include fraction bars, tangrams, geoboards, geosolids, and rainbow fraction circle sets. 

• Program Implementation, Manipulative List by Lesson has specific manipulatives listed for each lesson. For example, Unit 6, Lesson 24 lists 1 Set of Algebra Tiles, 20 Two-color counters, and 1 Number cube per pair. There is also a Manipulative Suggestions for At-Home Use document that provides ideas for using items commonly found at home or easily created that could be used in place of the actual manipulative (e.g. Attribute Buttons and Connecting Cubes could both be replaced with Lego bricks). 

• Program Implementation, Activity Sheet Resources includes a 52-page document full of visual models such as number lines, graphs, grid paper, nets, graphic organizers, etc. These are also provided as a link in lessons where they would be expected to be a helpful resource. 

Program Implementation, Try-Discuss-Connect Routine Resources, Understanding the Try-Discuss-Connect Instructional Routine, the foundational “Try-Discuss-Connect” routine is designed to “encourage proficiency and rigor within a collaborative structure.” A primary purpose is to “expose students to a number of representations and approaches” to help them make connections, develop mathematical language and thinking, and improve written and oral communication skills. This routine helps students transition from manipulatives to written methods. For example: 

• In the Try It activity, “students have access to a variety of tools and manipulatives to use to represent the problem situation.” During the Discuss It activity, “Students present and explain their solution methods and listen to and critique the reasoning of others, models and representations.” During the Connect It activity, “Students write their answers to Connect It questions independently (or in pairs to support language production, as needed) to solidify understanding and make further connections.” 

• “Tip: If students are struggling with writing responses…. have multiple students share answers orally while writing key words or phrases on the board. Have students use these key words and phrases to write their own response to the question in their worktexts.”

• “Tip: Encourage students to represent and solve problems in more than one way to build flexibility in their thinking.”

The “Try-Discuss-Connect” routine also integrates the Concrete-Representational-Abstract (CRA) model, for example:

• Try It, “Students may use concrete, representational, or abstract strategies to solve the problem, based on their understanding of the problem or mathematical concept.”

• Discuss It, “Students who use more concrete approaches begin to make connections to representational or abstract approaches as they engage in partner discussions.”

• Connect It, “Through the Connect It questions, students connect concrete and representational approaches to more abstract understanding as they formalize their connections.”