3rd Grade - Gateway 3

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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 2, Lesson 4, Understand the Meaning of Multiplication, Session 2, Teacher Edition, Connect It, Problem 6, “Use any model to show and find 4\times7. Write a complete multiplication equation and explain what each number in the equation means.” The Teacher Edition provides guidance for the teacher in the Exit Ticket, “Look for a model that shows 4 equal groups or rows of 7 with the complete equation 4\times7=28. Common Misconception: If students draw a model that shows 4\times4=16 or 7\times7=49, then help them to self-correct by asking them how each factor in their equation relates to their model. Remind them to always ask themselves if their answer makes sense.”

• Unit 4, Lesson 21, Understand Fractions on a Number Line, Develop, Session 2, Teacher Edition, Discuss It, teacher supports partner discussions about how to place fractions on a number line. The Teacher Edition provides guidance for the teacher, “Encourage students to discuss how they determined the fraction at A on each number line. Support as needed with questions such as: How did you decide the denominator of each fraction? The numerator? What does it mean if the numerator is less than the denominator? If it is greater than the denominator.”

• Unit 5, Beginning of Unit, Prepare, Unit and Lesson Support, teachers are provided with guidance in connecting skip-counting to telling time. “Use skip-counting to briefly review telling time to the nearest 5 minutes. Point out that although it might seem like students are counting by ones when moving from 1 to 2 on an analog clock, they are actually skip-counting by 5- minute intervals since there are 5 equal-size spaces between 1 and 2. Skip-counting will support students when they learn to tell time to the nearest minute. For example, if the minute hand is one tick mark past the 7, students can skip-count by 5s seven times to get 35, and then add one more minute to get 36.”

• Unit 6, Lesson 33, Partition Shapes into Parts with Equal Areas, Session 2, Teacher Edition, Develop, Apply It, “For all problems, encourage students to be prepared to explain how they got their answers.” Exit Ticket, “Error Alert If students choose answer choices A or E, then redraw each shape, shading two adjacent parts instead of the ones shown. Trace around the other 2-part sections that have the same shape to show that 1 out of 4 sections is shaded in choice A and that 1 out of 3 sections is shaded in choice E.”

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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 1, Use Place Value to Round, Lesson Overview, Teacher Edition, Solve Word Problems withTwo-Digit Numbers - Full Lesson, Learning Progression:

  • “In Grade 2 students relied on place-value understanding to compare three-digit numbers using concrete models such as base-ten blocks, place value charts, and pictures. Students then compared numbers by writing equations and inequalities using <, >, and =.”

  • “In this lesson students apply their place-value knowledge to round numbers to the nearest hundred. They learn that rounded numbers can be used to estimate and are easier to use when calculating. Students use models such as a number line and a hundred chart to round two- digit numbers to the nearest ten. They learn the rules for rounding, using the halfway number to decide whether to round a number up or down. Students use similar reasoning and models to round three-digit numbers to the nearest ten or hundred.”

  • “In Grade 4 students will extend their place-value understanding to include the idea that the value of a digit in one place is ten times the value the digit would have in the place to its right. Students will use this extended understanding to compare and to round multi-digit numbers, including rounding four-, five-, and six-digit numbers to the nearest tens, hundreds, thousands, and ten thousands.”

• 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 10, Understand the Meaning of Division:

  • Prior Knowledge: “Insights on: Arrays and Odd and Even Numbers. Students recognize arrays as arrangements of equal rows and columns and connect this understanding to tiling. When exploring arrays, students begin to develop an efficient way to count equal groups. Students will build on previous understandings of skip-counting and develop equations to describe arrays….

  • Current Lesson, “Insights on: Relating Multiplication and Division. Multiplication and division are inverse operations. Multiplication is the combining of equal groups to find a total, and division is the breaking apart of a total into equal groups…”

  • Future Learning, “Insights on: Modeling Division. One way to divide is to make equal groups. When working with larger dividends, it helps to use base-ten blocks. Another way to divide is to use an area model in which students take out equal-size groups…”

• 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 4, Lesson 23, Finding Equivalent Fractions:

  • “Naming parts of shapes as fractional areas of the whole shape builds on previous skills with rectangles and circles divided into halves, thirds, and fourths. In this activity, students learn shapes to show sixths and eighths as well. Students will use what they have learned about combining shapes to make other shapes to see how one shape can be a fractional part of another shape. Building on this understanding, students will recognize that the area of a shape can be divided into equal parts and that each equal part is a fraction of the whole area. This will add a new dimension to students’ understanding of fractions. It also prepares them for understanding symmetry and working with nets and three-dimensional figures.”

  • “Step by Step: 1) Review halves, thirds, and fourths. (followed by two prompts) 2) Explore fractional areas. (followed by three prompts) 3) Introduce sixths and eighths. (followed by three prompts) 4) Break shapes into equal parts (followed by five prompts).”

  • “Check for Understanding: Using pattern blocks, show a trapezoid broken into three triangles. Ask: How much of the area of the whole shape does one part represent? \frac{1}{3} 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 3 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 3, Beginning of Unit, Unit and Lesson Support, the opening narrative provides the content of the unit, “In this unit, students build on their prior knowledge of linear measurement and tiling rectangles as they learn that area measures the space inside a shape. They use multiplication to compute area and also recognize that area is additive. Students use their understanding of the relationship between multiplication and division to solve one-step word problems and use all four operations to solve two-step word problems. They also reexamine bar and picture graphs, understanding that the scale on a graph can represent intervals other than one.” The document continues with Instructional Support identifying specific lessons from prior grades to develop understanding, such as Unit 3, Lesson 19, “These lessons build on students’ work with multiplication and division in Grade 3, Unit 2 and one- and two-step word problems involving addition and subtraction in Grade 2, Units 1 and 2.”fractions in Grade 5, Unit 3: Grade 5, Lesson 22 - Multiply Fractions in Word Problems.” Prerequisite Lessons From Grade 2, “Grade 2, Lesson 9 Solve Word Problems with Two-Digit Numbers”

• 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 20, Overview, Learning Progression, “In Grade 2, students used fraction language to describe dividing shapes into equal parts…In Grade 3 students develop a more formal understanding of fractions.  In this lesson, students focus on the meaning of fractions and name fractions by the number of equal parts in the whole such as sixths or eighths…This lesson builds a foundation for subsequent Grade 3 lessons that develop an understanding of fractions as numbers on a numberline and introduce the concepts of equivalent fractions and comparing fractions by reasoning about their size. In Grade 4, students will use their understanding of fractions and fraction equivalency to add and subtract fractions.”

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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 3 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 2, Lesson 9, Session 1, “Materials tab: Math Toolkit base-ten blocks, hundred charts, multiplication models, number lines, Presentation Slides. Differentiation tab: base-ten blocks (10 tens rods).”

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

• Manipulatives List, Unit 5, Lesson 28, identifies marked liter container - 1 per pair, set of base-ten blocks - 1 per pair, counters - 20 per pair, unmarked 2-liter containers - 3 per pair, and marked 6-liter container, - 1 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 3 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 5, Lesson Quiz, Problem 1, “DOK 1, 3.OA.C.7, SMP 8.”

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 3, End of Unit, Assess, Unit Assessment, Form A, Problem Notes, Problem 4, “DOK 2, 3.MD.B.3.”

• Unit 4, End of Unit, Assess, Unit Assessment, Form A, Problem Notes, Problem 10, “DOK 2, 3.NF.A.3d.”

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 2, End of Unit, Assess, Comprehension Check Correlation Guide, Problem 3, “DOK 1, 3.NBT.A.3.”

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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, Lesson 13, Assess, Lesson Quiz, Problem 1, “A, E; Students could solve the problem by applying their knowledge of even and odd numbers to check if the pattern is true with the given rule. B is not correct because the product of an even number and an odd number is always even 7\times2=14 and 14 is always an even number. C is not correct because the rule subtract 1 forms a pattern that alternates odd and even. 7-1=6  and 6 is an even number. D is not correct because the sum of two odd numbers is always even. 7+5=12 and 12 is an even number.”

  • Unit 3, End of Unit, Assess, Unit Assessment, Form A, Problem 10, “62 square meter; See possible student work on the student page.” 

• 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 3, 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 Finding Area (Lesson 14), Multiply to Find Area (Lesson 15), Add Areas (Lesson 16), Multiply and Divide to Solve One-Step Word Problems (Lesson 17). For students who exceed proficiency on the Unit Assessment, choose from the following activities on the Teacher Toolbox. Extend Enrichment Tile Design (Lesson 16), Purple Coins (Lesson 18), Favorite Pet (Lesson 19).”

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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 3 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 3 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 12, Extend, Display of Cans, students are provided with a challenge situation. “You see a shopping cart bump into a display of cans stacked in an array. Many of the cans fall onto the floor. You count 60 cans. You can tell by the cans that are still in place that they were stacked in at least 4 rows with at least 10 cans in each row. Draw a picture and write an equation on the Recording sheet to show how the cans could have been arranged in the display. You are asked to make a similar display for more than 60 cans but fewer than 80 cans using the following rules: The cans are arranged in an array. There must be at least 5 rows of cans. There must be at least 6 cans per row. How many different arrays can you make? Show your displays 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 3, Lesson 16, Session 2, Teacher Guide, Differentiation: Extend - Deepen Understanding, “When discussing the model shown in Picture It, prompt students to compare this method to breaking apart arrays. Ask think of the whole garden as an array. What multiplication expression could model it? Fill in the blanks to show how you could rewrite the expression using 5+4=9 to break apart the array: ___ \times(--- + ___)... How is this way of finding area like breaking apart arrays? How is it different?”

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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. For example: 

• 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 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, 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. 

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

The materials reviewed for i-Ready Classroom Mathematics Grade 3 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 includes Base-Ten Flats, Base-Ten Rods, Base-Ten Units, Rainbow Fraction Tiles, Number Cube, Centimeter Tiles, Pattern Blocks, Fraction Circles, Plastic Rulers, Linking Cubes, Buttons, Color Tiles, \frac{3}{4}-in. Transparent Counters, Six Colors, Number Cubes, Geoboards, Digital Stopwatches. 

• Program Implementation, Manipulative List by Lesson has specific manipulatives listed for each lesson. For example, Unit 2, Lesson 7: Set of base-ten blocks; Unit tiles, Ruler. 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. Linking Cubes could be replaced with Lego bricks). 

• 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.”