8th Grade - Gateway 3

The materials reviewed for i-Ready Classroom Mathematics Grade 8 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.

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

• Each unit has a Math Background document that provides the teacher with information to unpack the learning progressions and make connections between key concepts.

• Each Unit has an Unit Opener that provides the teacher with Unit Big Ideas and describes the themes of the unit.

• Each Unit has a Unit Flow and Progression video that describes how concepts are developed in the unit.

• Each Unit has a Professional Development document that provides guidance on instructional strategies, such as Supporting Math and Academic Vocabulary Development, Establishing Classroom Environments That Support Mathematical Discourse for ALL Learners, Knowing and Valuing Every Learner: Culturally Responsive Mathematics Teaching.

• Each Unit has a Unit Overview that provides the teachers with pacing, objectives, standards, vocabulary and lesson-level differentiation for each of the lessons in the unit.

• The Teacher’s Guide provides in-class instruction and practice included in the teacher’s edition.

• The Teacher’s Guide for Assessments and Reports supports whole group/partner discussion, ask/listen fors, common misconceptions, error alerts, etc.

• DIfferentiation strategies are included before and during the unit/lesson for the teacher. There are recommended resources to support students’ learning needs that are highlighted in the Prerequisites report.

• Unit and Lesson Support includes information about prerequisite lessons to focus on, and identifies the important concepts within those lessons.

• On the Spot Teaching Tips suggest additional scaffolding to support students with unfinished prerequisite learning as they engage with on-level work. 

• Digital Math Tools contain support videos that explain how to use their digital tools.

• Ready Classroom Central is an online teacher portal with resources for professional support such as training videos, planning tools, implementation tips, whitepapers, and discourse support.

• Language Expectations identify examples of what English learners at each level of language proficiency can do in connection with a one grade-level standard. 

• The Unit Prepare For provides teachers with guidance to support students when completing the graphic organizer in the beginning of the unit, Prepare for Unit. There is additional guidance to Build Academic Vocabulary through the use of identified cognates and specified academic terms. 

• The Unit Review includes problem notes for teachers identifying the Depth of Knowledge level of each problem and the standard, along with suggested strategies, and possible misconceptions based on the selected answer. 

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:

• Unit 2, Lesson 6, Session 1, Connect It, Problem 1, “What is m⦟BCF? What types of angle relationships did you use to find m⦟BCF?” The materials provide a diagram of two lines cut by a transversal with some of the angles labeled with degree measures or algebraic expressions. ⦟BCF does not have any measurements or labels. The Teacher’s Edition provides guidance for the teacher, “Look for understanding that the relationship between vertical angles can be used to find x, and then of the expressions x + 15 or 2x, and the relationship between vertical or supplementary angles can be used to find m⦟BCF.”

• Unit 3, Lesson 12, Session 3, Apply It, Problem 1, “A system of linear equations has exactly one solution. What can you say about the slopes of the lines when the equations are graphed? How do you know?” The Teacher’s Edition provides guidance, “Look for understanding that the lines in a system of linear equations with exactly one solution will have different slopes. If two lines have the same slope, they will either not intersect at all, so the system has no solution, or they intersect at every point, so the system has infinitely many solutions.

• Unit 4, Math Background, Functions, identifies common misconceptions for teachers around functions and how to support students in addressing this misconception. “Students may mistakenly believe that if there is more than one input with the same output, then the relationship is not a function. Be sure to include many examples and discussion about this idea.”

• Unit 5, Math in Action, Session 2, Discuss Models and Strategies, teachers are instructed to “Present the Insulating Blanket problem and use Three Reads to help students make sense of it. Have different volunteers take turns reading aloud each section of information. Ask: What is this problem? Listen For: It is about determining the thickness, in inches, of a blanket used to insulate spacecraft from damaging heat and radiation from the sun. Invite volunteers to point out what is known and what they need to figure out. Ask: What do you need to include in your plan and solution? Listen For: The plan needs to include the number of pairs of reflector and separator layers that will be used, as well as the choices for the thicknesses of these layers and of the inner and out covers. The solution will need to include the total thickness of the blanket.”

The materials reviewed for i-Ready Classroom Mathematics Grade 8 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. 

In the Teacher’s Guide, a Lesson Progression table is provided that links each lesson within the current unit to a prior and future grade level lesson. Within the Math Background section, detailed explanations of the mathematical concepts in each lesson are provided. For example, in Unit 4,  Math Background, Understanding Content Across Grades, insights are provided for prior knowledge, current lesson, and future learning starting in Lesson 15:

• Prior Knowledge, Insights on: Slope-Intercept Form of an Equation. For example, “In addition to slope, the other main feature of the graph of a linear relationship is the y-intercept, which is the y-coordinate of the point where the graph intersects the y-axis.” Visual examples are included to show comparisons between proportional relationships and nonproportional relationships, and to understand the slope-intercept form of an equation.

• Current Lesson, Insights on Understanding Functions. For example, “A function is a dependence relationship. The value of the output, y, depends upon the value of the input, x. For example, the cost of renting a kayak is a function of the number of hours. Common Misconception: Students may mistakenly believe that if there is more than one input with the same output, then the relationship is not a function. Be sure to include many examples and discussion about this idea.” Examples include input/output tables that are functions and not functions. 

• Future Learning, Insights on Understanding and Interpreting Function Notation. “In high school, students continue to build their understanding of functions by using formal function notation and by relating what they know of input and output with the function and its domain.” Examples include writing an equation using function notation and evaluating and interpreting the functions.

The materials reviewed for i-Ready Classroom Mathematics Grade 8 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series. 

• The Correlations Document describes lesson correlation to the CCSSM through multiple lenses. The document identifies the major and supporting areas of focus within the CCSSM and the lessons address those standards. There is a table correlating each lesson with the standards covered, 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 while the other 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. 

• The Program Overview provides teachers and explanations for how the standards are addressed in each unit. One section identified is the coherence section titled “Lesson Progression.” 

• At the beginning of each Unit, Lesson Progression shows how each standard connects to and builds upon the previous grade levels. Each standard is identified in each lesson. It is arranged in a flow chart, and connects lessons to future grade levels. 

• In the lesson overview, prior knowledge is identified, so teachers know what standards are linked to prior work. Future grade level content is also identified.

Explanations of the role of specific grade-level mathematics are present in the context of the series. 

• Grade Level Support, Learning Progression identifies prerequisite skills for each lesson and their related standards for the two prior grade levels, when applicable, in a flow chart. For example, Unit 3, identifies a prerequisite skill for the unit as, “Solve multi-step equations”. The standards from grades 6 and 7 connected to the unit are, Understand Solutions of Equations (6.EE.5), Write and Solve One-Variable Equations (6.EE.7), and a designated essential skill, Write and Solve Multi-Step Equations (7.EE.4, 7.EE.4a). These standards are connected to Solve Linear Equations in One Variable (8.EE.7, 8.EE.7b).

The materials reviewed for i-Ready Classroom Mathematics Grade 8 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Materials explain the instructional approaches of the program. Examples include:

• The Teacher’s Guide and the Program Implementation area in the digital platform contains a section “Understanding the Try-Discuss-Connect Routine.” This routine is embedded throughout the program. This document explains how the routine is used. “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.” 

• “Using a Session” in the Teacher’s Guide describes the planning and support features within the Teacher’s Guide. This includes each component of the lesson and teacher’s guide and describes why it is important in the lesson. For example, “SMPs are infused throughout the instructional model. Deepen Understanding is a consistent opportunity to build understanding of a key lesson concept by extending mathematical discourse. The content connects a particular aspect of lesson learning to an SMP, showing how it might look in the classroom.”

• Integrating Language and Mathematics identifies and explains the six language routines embedded within the curriculum. It identifies each routine, why a teacher may use it, the process and what part of the Try-Discuss-Connect Routine it can be used within. For example, for Say It Another Way, “What: A routine to help students paraphrase as a way to process a word problem or other written text and confirm understanding. Why: Paraphrasing helps students figure out whether they have understood something they have read or heard...How: Students read or listen to a word problem or other written text. One student paraphrases the text. Other students give a thumbs-up to show that the paraphrase is accurate and complete.”

Materials reference relevant research sources. Examples include: 

• Boaler, (2016), Mathematical Mindsets

• Council of the Great City Schools, (2016), A Framework for Re-Envisioning Mathematics Instruction for English Language Learners

• Kersaint, (2016), Orchestrating Mathematical Discourse to Enhance Student Learning

• National Council of Teachers of Mathematics, (2010), Teaching and Learning Mathematics

• National Council of Teachers of Mathematics, (2014), Principals to Action

• National Council of Teachers of Mathematics, (2014), Using Research to Improve Instruction

• Richhart, (2009), Creating Cultures of Thinking

Materials include research-based strategies. Examples include: 

• “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.” Examples include, “Ready Classroom Mathematics lessons provide multiple opportunities for collaborative learning, such as Discuss It prompts where students explain and justify their strategies to each other and Consider This prompts where students compare problem-solving approaches, solutions, and reasoning.” The research included to support this is, “Research tells us that when students work collaboratively, which also gives them opportunities to see and understand mathematics connections, equitable outcomes result.” (Boaler, 2016)

• Professional Development, contains an adapted excerpt from Reimagining the Mathematics Classroom, co authored by Dr. Mark Ellis for teachers. The excerpt explains “funds of knowledge” to teachers and how they can apply this knowledge using the materials. “Connect to Culture in the Teacher’s Guide for each lesson offers suggestions for tapping into students’ funds of knowledge and connecting the knowledge to Try It and other problems.”

The materials reviewed for i-Ready Mathematics Grade 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The Teacher’s Guide includes an Activity Sheet in the Table of Contents which provides a list of printable tools and resources. “Dot Paper, Frayer Model 2, Fraction Bars are available to print and copy for each student.” Materials include a Manipulatives List by Lesson for each grade level. For example: 

• Unit 2, Lesson 7: 1 straightedge per student, 15 rulers for the class, and 1 protractor per student.

The materials reviewed for i-Ready Classroom Mathematics Grade 8 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. Assessments include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series. 

The formative and summative assessments include a variety of item types to measure grade-level standards. 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 

Assessments are provided as a PDF or online for teachers that can be provided to students in either format.

The materials reviewed for i-Ready Classroom Mathematics Grade 8 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics

• 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.” The digital platform contains these activities for each lesson.

• In Refine lessons, 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. The resources are found in the digital platform (Reteach, Reinforce, Extend). The following pages also contain descriptions of additional activities in the teacher’s edition for Reteach, Reinforce, and Extend.

The materials reviewed for i-Ready Classroom Mathematics Grade 8 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Refine sessions 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 students who are considered to be “Meeting Proficiency”. Additional Enrichment Activities can be found online in the Small Group Differentiation Extend section.

In Explore and Develop sessions, the materials contain a Deepen Understanding section to extend understanding of the lesson’s key concepts through the use of discourse with students. The section contains teacher prompts and suggestions for what ideas to look for from students. Each Deepen Understanding is labeled with an embedded mathematical practice. Examples include: 

• Unit 4, Lesson 20, Enrichment Activity Grow and Shrink, students are provided with a challenge scenario at the beginning and multiple opportunities to explain their answer, “You are programming a video game in which the character grows or shrinks depending on what color token is used. A blue token makes the character double in size. A red token makes the character shrink to half its size. You must write exponential expressions and equations to represent the character’s changes in size.”

• Refine sessions include at least 1 problem where students utilize strategic thinking. In Unit 4, Lesson 18, Session 4, Problem 6, students explain and justify their thinking about graphs of functions. “In a graph that shows the distance a boat travels as a function of time, why would a vertical section not make sense?”

The materials reviewed for i-Ready Classroom Mathematics Grade 8 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Materials consistently provide strategies and supports for students who read, write, and/or speak in a language other than English to meet or exceed grade-level standards through regular and active participation in grade-level mathematics. Examples include:

• Each Lesson Session includes differentiated support for various levels of English proficiency with level 1-3, levels 2-4, and levels 3-5 identified. Support for Academic language is used during the “Try-Discuss-Connect Language” routines in each lesson. 

• In the Program Overview, language expectations charts are provided that describe the language English Learners can understand and produce in connection with students’ levels of English proficiency. Teachers can use the examples to help meet the needs of English Learners. 

• Each Unit Overview connects with one of the CCSS addressed in the unit and shows an example of how language expectations can help to differentiate instruction to meet the needs of English learners. 

• In the Program Overview, there is an Integrate Language and Mathematics section. “Scaffolded language support for a specific problem is outlined. These suggestions for scaffolding and amplifying language can be applied to other problems as well.” 

• Language objectives are included and students are expected to understand and produce language as they work on lesson objectives. Graphic organizers are used to help students access prior knowledge and vocabulary they build on in the lesson.

• Discourse cards are available in the Teacher Digital Experience under the Ready Classroom Mathematics Toolbox. These cards provide sentence starters and questions to help students engage in conversations with their partners, small groups or the whole class. 

• All classroom materials are available in Spanish.

• 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.

The materials reviewed for i-Ready Classroom Mathematics Grade 8 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.

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, Scientific Calculator and Graphing Calculator are also included but cannot be reviewed as these tools are powered by Desmos. Support videos are available for each of the digital tools, explaining how they may be used and their functions. For example:

• Grade 8 Standard Manipulative Kit includes the most commonly used manipulatives. Manipulatives include Algebra Tiles, plastic rulers, centimeter cubes, tangrams, geoboards, two color counters, and protractors. 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 rainbow tiles, compasses, number cubes, tape measure, pattern blocks, base ten blocks, additional tangrams, and algebra tiles. 

• Visual models such as number lines, graphs, or bars, are also available but cannot be manipulated.

The Try-Discuss-Connect routine embedded throughout every lesson provides students the opportunity to connect and transition from the use of manipulatives to written methods. Inside of the digital platform, Program Implementation, Try-Discuss-Connect Routine Resources, Understanding the Try-Discuss-Connect Instructional Routine, the guide describes how the routine helps students transition from manipulatives to written methods. 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.” “The class then looks at the strategies highlighted in the Picture It and Model It, and students make connections between strategies, their own strategies, and the strategies discussed as a class.” During the Connect It activity, “Students apply their thinking during the lesson to new problems.” The routine integrates the CRA model in the:

• Try It, “Students 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.”