5th Grade - Gateway 3

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 Homepage, Success 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 about 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 1, Lesson 5, Divide Multi-Digit Numbers, Refine, Session 4, Teacher Edition, Apply It, Problem 10, “Which of the following pairs of numbers is a set of partial quotients for 594\div18?” Answer choices: 50 and 5; 40 and 4; 30 and 3; 20 and 15. The Teacher Edition provides guidance for the teacher in the Error Alert, “If students choose A or B, review how to use multiples of 10 times the divisor to estimate the first partial quotient. Remind students that the resulting partial product must be less than or equal to the dividend, but it cannot be greater than the dividend.”

• Unit 2, Lesson 11, Subtract Decimals, Develop, Session 2, Teacher Edition, Discuss It, teacher supports partner discussions about data and line plots. The Teacher Edition provides guidance for the teacher, “Encourage students to use the Discuss It question and sentence starter on the Student Worktext page as part of their discussion. Support as needed with questions such as: How did you know which number to subtract? How could you use estimation to check that your answer is reasonable? Common Misconception Look for students who try to subtract 4.6 from 2.05 because 4.6 has fewer digits than 2.05 or because they use the numbers in the order they are given in the problem to write 2.05-4.6. As students present solutions, have them explain what each number in their model represents.”

• Unit 3, Beginning of Unit, Prepare, Unit and Lesson Support, teachers are provided with guidance in how to connect decimals to money. “Connect decimals to money. Build on students’ Grade 4 with decimals in money contexts. Give students experiences with multiplying or dividing with decimals by posing problems that relate the cost of 1 item to the total cost of 2, 3, or 5 of the item.”

• Unit 5, Lesson 31, Understand the Coordinate Plane, Session 2, Teacher Edition, Develop, Connect It, “Student responses should show understanding that the coordinate plane shows the locations of points and the table shows the coordinates of the points.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 2, Lesson 13, Lesson Overview, Teacher Edition, Subtract Fractions - Full Lesson, Learning Progression:

  • “In the previous lesson students added fractions and mixed numbers with unlike denominators by replacing fractions with equivalent fractions that have like denominators.”

  • “In this lesson students extend the methods for adding fractions and mixed numbers with unlike denominators to subtracting fractions and mixed numbers with unlike denominators. They represent the subtraction with manipulatives and visual models. When necessary to subtract, they regroup mixed numbers to show equivalent mixed numbers with fractions greater than 1.”

  • “In the next lesson students will subtract fractions with unlike denominators to solve word problems, using benchmark fractions and number sense to estimate and assess the reasonableness of their answers. In later grades students will apply and extend understandings of addition and subtraction of fractions to add and subtract rational numbers.”

• 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 23:

  • Prior Knowledge: “Insights on: Multiplying Fractions. Connect students’ initial understanding of multiplying fractions back to repeated addition with like denominators. Provide visual models to allow them to transpose and move the parts of a whole around. In the example shown, students make 2 whole s by taking two one-fourths from the third model…”

  • Current Lesson, “Insights on: Dividing with Unit Fractions. In 5th grade, students only divide with unit fractions, for example 3\div\frac{1}{4} or \frac{1}{4}\div3. Area models are an interesting way to show dividing a fraction by a whole number. Students may notice the relationship between dividing by a whole number and multiplying by a unit fraction…”

  • Future Learning, “Insights on: Dividing Fractions. Continue to support students in thinking of division in terms of multiplication: How many of one quantity does it take to make the other quantity? Bar models help students connect what they already know about multiplying with fractions to dividing with fraction. Help students build confidence in dividing with fractions by reasoning about equivalent fractions with common denominators…”

• 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 5, Lesson 31, Understand the Coordinate Plane:

  • “Students are first introduced to coordinate geometry through learning the related terminology and how to plot and identify points in the first quadrant. This activity builds on students’ knowledge of parallel and perpendicular lines and experience with horizontal and vertical number lines, to teach students vocabulary such as origin, x-axis, y-axis, coordinates, and ordered pairs and graphing and identification of ordered pairs. A firm mastery of the coordinate plane will help students later when they begin constructing scatter plots and using the coordinate plane to study geometric concepts such as symmetry and transformations and algebra concepts such as graphing equations and functions.”

  • “Step by Step: 1) Construct the first quadrant of the coordinate plane. (followed by four prompts) 2) Define coordinate terminology. (followed by five prompts) 3) Locate points for ordered pairs. (followed by five prompts) 4) Identify ordered pairs of plotted points (followed by two prompts).”

  • “Check for Understanding: Have the students use the display grid or draw a grid himself.  Plot an ordered pair on the grid, such as (3,4). Ask the student to label the axes, origin, and the point. For the student who struggles, use the table below to help pinpoint where extra help may be needed: “If you observe… the student may… Then try…”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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, 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 Beginning of Unit for each unit, 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.

• 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 2, Beginning of Unit, Unit and Lesson Support, the opening narrative provides the content of the unit, “In this unit, students build on their prior understanding of decimals (tenths and hundredths) as they read, write, compare, and round decimals through thousandths. They will extend their knowledge of the relation between place values as they think about multiplying and dividing by powers of ten. Then students build on their prior understanding of fractions and decimals. They use what they know about fraction equivalency to add and subtract fractions with unlike denominators. Finally, they solve word problems requiring addition and subtraction of decimals and fractions.” The document continues with Instructional Support identifying specific lessons from prior grades to develop understanding, such as Unit 2, Lesson 6, “These lessons build on students’ prior work with place value and fractions and decimals in Grade 4; Grade 4, Lesson 25 - Fractions as Tenths and Hundredths.”

• 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 3, Lesson 17, Overview, Learning Progression, “Previously in Grade 5 students divided whole numbers with up to four-digit dividends by two-digit divisors. Students learned to recognize division as a missing factor problem in which the quotient is the unknown factor… In this lesson, students apply their understanding of division by dividing with decimals. They use place-value understanding to connect patterns in decimal division and whole-number division… Later in Grade 5 students will use their knowledge of decimal division when they convert from larger units to smaller units. In Grade 6, students will continue to multiply and divide with decimals.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

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

• Program Implementation, “Try-Discuss-Connect Routine Resources”, 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, videos model 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. 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 cultures 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.

• i-Ready Homepage, Success 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. 

• i-Ready Homepage, Success 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.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 4, Lesson 29, Session 1, “Materials tab: Math Toolkit geoboard, grid paper, rubber bands, rulers, tracing paper Presentation Slides. Differentiation tab: For each group: 1 set of index cards, each showing pictures of a parallelogram, square, or rectangle (prepared in various sizes, colors, orientations); For display; masking tape.”

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

• Manipulatives List, Unit 5, Lesson 31, identifies “Set of varied classroom manipulatives (e.g., connecting cubes, counters, or tiles).”

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 5 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 correlated to 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 worked-out problems. For example:

• Unit 2, Lesson 6, Lesson Quiz, Problem 2, “DOK 1, 5.NBT.A.1, SMP 7.”

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, worked-out problems, DOK levels, content standards, 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, standard addressed, and lesson assessed by each problem.” For example:

• Unit 4, End of Unit, Assess, Unit Assessment, Form A, Problem Notes, Problem 4, “DOK 2, 5.G.B.4.”

• Unit 5, End of Unit, Assess, Unit Assessment, Form A, Problem Notes, Problem 9, “DOK 2, 5.OA.B.3.”

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 4, End of Unit, Assess, Comprehension Check Correlation Guide, Problem 10, “DOK 2, 5.MD.B.2.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 2, End of Unit, Assess, Unit Assessment, Form A, Problem 3, “A, C,E; Students could solve the problem by comparing the digits in the hundredths place to 5 to make rounding decisions, or by using number lines or place-value charts. B is not correct because it rounds to 1.4 pounds.”

  • Unit 3, Lesson 22, Assess, Lesson Quiz, Problem 3, “D; Students can find the area by multiplying: \frac{17}{3}\times4=\frac{68}{3}=22\frac{2}{3}. A is not correct because the length and width are added instead of multiplied. B is not correct because 5\frac{2}{3} written as a fraction greater than 1 incorrectly by multiplying the numerator and the whole number. C is not correct because the whole numbers are multiplied and then added to the fraction.”

• 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 Scoring Rubric states: 2 points if, “Response contains the following: correct answer(s).” 1 point if, “Response contains the following: “One answer is correct.” 0 points if, “Response contains the following: Incorrect answers that do not demonstrate the correct mathematical procedures and/or thinking.” The Multiple Select/Choice Matrix Scoring Rubric states: “2 Points All answers are correct, 1 Point 1 incorrect answer, and 0 Points 2 or more incorrect answers.” The Short Response Scoring Rubric states: 2 points if the “Response contains the following: Correct computation,  solutions, and/or calculations; Well-organized work demonstrating thorough understanding of math concepts and/or procedures.” 1 point for “Response contains the following: mostly correct solution(s); Shows partial or good understanding of math concepts and/or procedures.” 0 points if the “Response contains the following: Incorrect solution(s);  No attempt at finding a solution; No effort to demonstrate an understanding of the math 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 computation,  solutions, and/or calculations; Well-organized work demonstrating thorough understanding of math concepts.” 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 11, Assess, Lesson Quiz provides three types of differentiation for possible follow up depending on student performance: Reteach, Reinforce, and Extend. Implementation Guide, Program Overview, Differentiation, “Reteach: Tools for Instruction are mini-lessons for reteaching lesson concepts. Reinforce: learning games offer fun, challenging, and personalized practice and help students develop a growth mindset. Extend: Enrichment Activities challenge students with higher-order thinking tasks.” 

• Unit 4, 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, Convert Measurement Units (Lesson 25), Solve Problems with Fractional Measurement Data(Lesson 27), Classify Plane Figures (Lesson 29). For students who exceed proficiency on the Unit Assessment, choose from the following activities on the Teacher Toolbox. Extend Enrichment How Old Am I? (Lesson 26), Weighing Pumpkins (Lesson 27), Sorting Shapes (Lesson 29).”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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 5 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. i-Ready Success Central provides many suggestions and examples for how to accommodate and support special populations. Lessons have sections called Group & Differentiate to help special populations. Lesson quizzes have suggestions for reteaching. Examples of supports for special populations include:

• i-Ready Homepage, Success Central, Plan & Teach, Differentiate, provides information to support the teacher in planning for all special populations. Personalized Instruction provides 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 Small Group Instruction, “Every student can excel in mathematics with the right supports. Check out the resources below to help you plan for, organize, and facilitate small groups so you can meet the various needs of your students.” Support All Learners, “Every student can excel in mathematics with the right supports. Use the resources on this page to find ideas and strategies for adapting your instruction to meet the unique needs and learning styles of all students.” There are several links to documents to support teachers. For example:

  • Supporting Students' Needs – Reference Sheet, provides information regarding  “Optional built-in supports embedded in i-Ready Classroom Mathematics that educators can choose from to best meet the needs of their students. These resources can be used to: Scaffold instruction by breaking learning experiences into smaller parts to help students reach higher levels of comprehension and skills acquisition with temporary supports along the way Differentiate instruction to meet individual students’ needs by modifying content, altering the delivery method, and/or providing alternate learning tasks.” 

  • Tools for Accessible Instruction – Reference Sheet “Highlights i-Ready Classroom Mathematics supplemental tools and examples of student supports that can be used throughout a lesson and session. Examples of student supports may have some overlap with a student’s IEP/504 plan but should not supersede or contradict it, and they may be useful for students regardless of whether or not they have an IEP/504 plan in place.” 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). Program Implementation, Program Overview, Differentiation, Reteach, “Tools for instruction are mini-lessons for reteaching lesson concepts.” Reinforce, “Learning Games offer fun, challenging, and personalized practice and help students develop a growth mindset.” Extend, “Enrichment Activities Challenge students with higher-order thinking tasks.”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity. 

Materials do not require advanced students to do more assignments than their classmates. Instead, students have opportunities to think differently about learning with alternative questioning, or extension activities. Specific recommendations are routinely highlighted as Teacher Notes within parts of each lesson, as noted in the following examples:

• Each lesson has an Extend: Enrichment Activities column that provides an additional challenge task. For example, Unit 2, Lesson 7, Extend, Broken Calculator, students are provided with a challenge situation. “Imani’s teacher asks her to start with the number 3.735 and then perform an operation on her calculator that results in a whole number answer. When Imani picks up her calculator, she finds that both the addition and subtraction keys are broken. How can Imani still use her calculator to complete her assignment? Write at least three different ways on the Recording Sheet. Imani’s teacher asks her to enter the number 21.6 on her calculator. When Imani picks up her calculator, she finds that the key for the decimal point is broken. How can Imani use another way to get her calculator to show 21.6? Write at least three different ways on the Recording Sheet.”

• 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 1 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 4, Lesson 29, Session 2, Teacher Guide, Differentiation: Extend - Deepen Understanding, “When discussing the table model, prompt students to consider how the number of Xs in each column can help them order the shapes from most general to most specific. Ask How does the number of Xs show which shape is the most general category?...Ask How does the number of Xs show which shape is the most specific subcategory?…Ask If you rearranged the columns from most general to most specific, what pattern would you see in the number of Xs?”

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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.

Guidance is consistently provided for teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. Examples include: 

• i-Ready Homepage, Success Central, Plan & Teach,  Differentiate, Support All Learners, Supports for English Learners – Reference Sheet, explains where to find and how to use all of the supports built in to 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, Connect Language Development to Mathematics, Language Expectations for Differentiation 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, 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: Math Vocabulary, Academic Vocabulary, and Cognate Support. 

• 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.

The materials reviewed for i-Ready Classroom Mathematics, Grade 5 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. 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 List, Manipulative Kit includes  Base-Ten Flats, Base-Ten Rods, Base-Ten Units, \frac{}{4}-in. Transparent Counters, Six Colors, Rainbow Fraction Tiles, Geoboards, Pattern Block Template, 1-in. Cubes, Number Cubes, Ruler, Tape Measure, Measuring Jars, Measuring Cups, Assorted Buttons, $1 Paper Bills, Plastic Pennies, Plastic Nickels, Plastic Dimes, Plastic Quarters. 

• Program Implementation, Manipulative List by Lesson has specific manipulatives listed for each lesson. For example, Unit 1, Lesson 1: Unit cubes, Centimeter cubes. 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. Meter Stick and Yard Stick could both be replaced with a Tape Measure). 

• Program Implementation, Activity Sheet Resources, K-5 Activity Sheet Resources includes a 172-page document full of visual models such as number lines, graphs, grid paper, graphic organizers, etc. 

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.”