8th Grade - Gateway 3

The instructional materials for Ready Grade 8 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

Students engage with problems and exercises through a consistent lesson structure. Use What You Know presents problems where students connect prior knowledge to the new concepts. Find Out More introduces the lesson, followed by Model It, Picture It, Connect It and Try It. This sequence repeats during Learn About as students engage with exercises during modeled and guided instruction. During Independent Practice, students complete problems and apply their learning. Additional problems and exercises are provided in the Practice and Problem Solving Book. For example:

• In Unit 4 Lesson 19 Transformations and Congruence, students are shown models for solving problems and then practice solving problems using the models. In each section, students solve problems with a specific skill.
• In Unit 3 Lesson 12 Understand the Slope Intercept Equation for a Line, students compare, analyze, and verify problems in order to demonstrate their understanding of the slope-intercept form of a linear equation. Students demonstrate their understanding of slope and the slope-intercept form for a linear equation as they examine equations and determine if they are all linear and if they can be written in the form y=mx+b. If they can, students show how. During Independent Practice students use their understanding of proportional relationships to complete a three-part task named, “Put it Together.” In the task, students show different ways to find the slope given points in a table and a graph.
• In Practice and Problem Solving Lesson 25, students solve problems using the Pythagorean Theorem to find the height of a pole and the length of a diagonal in a rectangle. They engage in exercises to find the distance between two points on the coordinate plane.

The instructional materials for Ready Grade 8 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences. Students are presented with a problem at the beginning of each chapter to introduce new concepts and build upon prior knowledge.

The Ready lesson structure is consistent across the series. Within each unit, concept development is sequential. Understand lessons expose students to a concept for the first time and have a heavier emphasis on developing conceptual understanding. There are consistent sections within these lessons that scaffold student learning. Find Out More activities engage students in whole-class examples within a lesson. Learn About reinforces the mathematical concept of the lesson through pictures, models, examples of possible solutions and independent practice. Practice provides ongoing practice of newly learned mathematical concepts and skills as students explain and reflect.

The Ready progression chart shows what students learned in previous grades, what they will learn in their current grade, and how this will relate to future grades. In the Teacher Resource Book at the beginning of each lesson, the Learning Progression restates what had been taught in the previous grade, what is taught in the current grade, and what will be taught in the next grade. Lessons are designed using a scaffolded approach that begins with teacher-guided instruction, moves to working with partners, and concludes with completing problems independently. For example, in Unit 2, the lessons are sequenced to build understanding of functions. Lesson 6 starts with understanding functions. In Lesson 7, students compare functions. In Lesson 8, students are introduced to linear functions, and in Lesson 9, students analyze functions. On the End-of-Unit Performance Task, students apply their understanding of functions to solve a multi-step problem that involves reasoning about how the rates of change for different functions are related.

The instructional materials reviewed for Ready Grade 8 meet expectations that there is a variety in what students produce.

Students respond and produce solutions in a variety of ways. Students provide evidence through drawings, representations, and written explanations. Students analyze and defend the work of others, and they justify their conclusions with verbal statements and mathematical reasoning.

In Picture It, Model It, Connect It, and Try It, students represent the problems in drawings and make connections between the drawings and the equations. In Pair/Share, students discuss approaches to solving problems with another student, promoting students to justify their work and reason through the work of others. Question types vary and include multiple choice, true/false, draw a model, short answer, solve, explain, find the mistake, and multi-step performance tasks. For example:

• In Unit 1 Lesson 5 Operations and Scientific Notation, students individually solve problems using properties of exponents as well as the distributive and associative properties. Students pair up to discuss their solutions with a partner. Students discuss the following: “Would you rather solve this problem with both numbers expressed in standard form or in scientific notation? Explain.”
• In Unit 2 Lesson 7 Compare Functions, teachers pose the following question for students, “Do you think you can compare any two rates? Why or why not?”
• In Unit 5 Lesson 29 Scatter Plots and Linear Models, students invent their own 10-point set of bivariate data. They list all the values in the data set in a table as well as writing a story to describe where they may collect the data. Students produce a scatter plot for the data and trend line. The data set must meet certain provided conditions.

The instructional materials reviewed for Ready Grade 8 meet expectations for providing manipulatives that are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

In the Hands-On Activities found within each lesson, students use a variety of manipulatives such as sticky dots and construction paper. For example:

• In Unit 1 Lesson 2, students illustrate the difference between doubling a number and squaring a number using sticky dots and construction paper. Manipulative use is appropriate for the mathematics content it represents.
• In Unit 3 Lesson 19, students rip a sheet of paper into triangles to describe the conditions that they observed about angles of a triangle. Students make sense of the conditions for drawing triangles.

A detailed Manipulative List is included in the Program Implementation section. For Grade 8 these include centimeter cubes, two or more color counters, number cubes, algebra tiles, tangrams, pan balance, etc. These are used throughout the series to represent mathematical ideas and connect to written methods. For example, in Unit 1 Lesson 2, students draw models of square roots using unit cubes as a reference.

The instructional materials for Ready Grade 8 meet the expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. Support is provided in the following ways:

In Step by Step, each lesson organizes content into chunks for student learning and includes guiding questions, key points, and teacher prompts. For example, in Lesson 21, students are presented information on how same-side interior angles are supplementary and asked to name other pairs of corresponding angles in the given figure. Teachers are prompted with: “Discuss linear pairs. Note that a line measures 180°, so the measures of the angles in a linear pair add to 180°. Ask: What is the name for two angles whose measures add to 180 ̊? [Supplementary]”

The Mathematical Discourse section in each lesson includes questions to engage students and advance their mathematical understanding. For example, the Lesson 29 Mathematical Discourse prompt states: “The relationship shown in the scatter plot appears to be positive and linear. Explain why this may or may not make sense. How might you convince a peer that this is a sensible relationship?” Question 2 asks: “Explain the reasonableness of the line in the scatter plot extending in both directions. Can you provide examples that would make some data points along this line unreasonable? Explain. At which point may this graphic appear unrealistic? Explain.”

The instructional materials reviewed for Ready Grade 8 meet expectations that they contain a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials provide resources to support teacher planning.

• The Teacher Resource Book provides a separate pacing guide for the year, month, week, and day.
• The Unit Overview page includes lesson titles, page numbers, the primary and supporting standards, and content objectives. Two Common Core correlation charts, Ready Instruction Correlation, and Interim Assessment Correlation are included.
• The Cognitive Rigor and Ready Chart lists specific questions identified as DOK level 3.

The Teacher Resource Book contains components to assist with lesson delivery.

• At a Glance explains what students will be doing during each component of the lesson.
• Step by Step organizes the lesson into chunks and provides guiding questions.
• SMP Tips highlight specific Standards for Mathematical Practice.
• Mathematical Discourse includes questions to engage students and advance their learning. Possible answers and key ideas to listen for in student responses are included.
• Try It Solutions provide complete explanations and, in some cases, multiple solutions.
• Concept Extensions, ELL Support, and Visual Models provide support, suggestions, and strategies to engage students with activities that support varied abilities.
• Solutions in the Independent Practice section includes a correct response, at least one possible solution method, and the DOK level for the problems.
• Quick Check and Remediation includes an exit slip to monitor understanding. A chart includes error analysis and remediation suggestions.
• Hands-On Activity extends the concepts and skills, using manipulatives and a collaborative group approach.
• Challenge Activity extends the learning of those students who have mastered the skills and concepts.

The Teacher Toolbox found online contains the following technology components to assist with lesson delivery:

• Interactive Tutorials are referenced as part of Day 1 instruction for most lessons and provide interactive video clips for delivery of student mathematical learning.
• i-Ready Door 24 Plus is a free iPad app for fact fluency practice but is not explicitly included in the Teacher Resource Book for instruction.

i-Ready (available for additional purchase and used by most Ready users) is an Online Diagnostic and Instruction component.

The instructional materials reviewed for Ready Grade 8 meet expectations for containing a teacher edition in print and online that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their knowledge of the subject, as necessary.

In each lesson, information is provided for the teacher to understand and make connections between the mathematical content and practices, errors or misconceptions that may arise, and the rationale behind specific lesson parts.

• In Unit 2 Lesson 10, the Learning Progression states, “In this lesson, students take this analysis further by qualitatively describing a graph by the slopes of its sections. They will discern that steeper slopes represent faster rates, while horizontal segments represent a time of no change or movement. Students will also determine whether a function is increasing, decreasing, or constant; interpret the situation represented by the graph; and solve problems related to the graph. Finally, students will sketch graphs of functions based on verbal descriptions.”
• In Unit 5 Lesson 30, the SMP TIP for MP2 states, “By asking students to explain the meaning of mathematical ideas like slope and y-intercept in terms of the context of an everyday problem, students are learning how to reason abstractly. Students decontextualize by writing an equation for the trend line, and then judge the reasonableness of their answer by going back and considering their answer in light of the original context.”

Throughout Ready Grade 8 there is guidance for teachers that identifies and connects the underlying mathematics of a lesson. These are written in adult language.

The instructional materials reviewed for Ready Grade 8 meet expectations for containing a print teacher edition (in print and in the online Teacher Toolbox) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Each unit begins with a Lessons Progressions Chart. This chart begins by listing lessons on which students are building. These lessons can come from previous grades and from Grade 8. For example, Unit 4 Lesson 27 builds upon Grade 7 Lesson 23 and Grade 8 Lesson 26. The chart also lists standards for which students are preparing. For example, Unit 4 Lesson 23 is preparing students for G-SRT.B.4.

Each Lesson Overview includes a Learning Progression section. This section begins with an explanation of how the lesson builds on prior knowledge from Grade 7. The Learning Progression explains the lesson's overall connection to Grade 8 and the mathematical content of the lesson. This section also explains connections to high school standards.

The instructional materials reviewed for Ready Grade 8 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

The Quick Check and Remediation at the end of a lesson presents a question to monitor understanding of the content of the lesson. This section includes a chart of incorrect answers, common errors, and remediation suggestions.

Lesson Quizzes provide the teacher with a Common Misconceptions and Errors section that describes common misconceptions and errors.

Within lessons themselves, directions instruct teachers to watch for specific errors and misconceptions, and suggestions are provided to address these. For example:

• Unit 2 Lesson 10 Step by Step Error Alert states: “Students who only describe prices as increases and decreases probably don’t understand that a horizontal segment represents no change in price over time.”

The instructional materials reviewed for Ready Grade 8 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Over the course of each lesson, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support within the Guided Practice to independent problem solving within the Independent Practice. With guidance from the Teacher Resource book, feedback is provided to students from the teacher throughout the lessons. Feedback can be given in the Mathematical Discourse section in each lesson. Written feedback can be provided through the rubrics and student quizzes.

The instructional materials reviewed for Ready Grade 8 meet the expectation for offering ongoing formative and summative assessments that clearly denote which standards are being emphasized.

• Standards are clearly noted within assessments found in the Mathematics Assessments Teachers Guide.
• An Interim Assessment is provided for each unit. Interim assessments provide standards correlations for each item. This information is in the Interim Assessment - Teacher section of the Mid-Unit and End-of-Unit Resources tab at the end of each unit.
• Unit Assessments provide standards correlations for each item. Unit Assessments and correlations are found in the Unit Assessment Answer Key - Teacher section of the Mid-Unit and End-of-Unit Resources tab at the end of each unit.
• Lesson quizzes and quick checks are provided for most lessons. These quizzes assess the specific standards being taught in the lesson.

The instructional materials reviewed for Ready Grade 8 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

• Each lesson follows a gradual release model in which scaffolded support is withdrawn as students gain mastery. Each lesson consists of four components: Introduction, Modeled and/or Guided Instruction, Guided Practice, and Independent Practice.
• Lessons are sequenced to build conceptual understanding, using concrete and pictorial representations to more abstract representations.
• The marginal notes in the Teacher Resource book often suggest ways to support students as a whole and subgroups of students who might need extra support. Notes include sections on vocabulary, concept extensions, visual models, hands-on activities, real-world connections, and challenge activities.
• Some lessons contain a Differentiated Instruction page which contains an Intervention Activity, On-Level Activity, and a Challenge Activity.

The instructional materials reviewed for Ready Grade 8 meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The Teacher Resource Book contains the following support:

• Each lesson includes a section called Small Group Differentiation that consists of two subsections: Reteach and Teacher-led Activities. (Some lessons have both subsections while others have one.) Specific lessons from earlier in the material, as well as the previous grade-level material in the series, are identified and can be used to review or fill in gaps in student knowledge. Every lesson also contains a Personalized Learning-Independent section.
• The marginal notes in the Teacher Resource Book suggest ways to support students as a whole and provide specific strategies for subgroups of students who might need extra support. This includes sections on vocabulary, concept extensions, visual models, hands-on activities, real-world connections, and challenge activities.
• Some lessons contain a Differentiated Instruction page that includes an Intervention Activity, On-Level Activity, and a Challenge Activity.
• The student Practice and Problem Solving book includes three levels of problems (basic, medium, challenge) that include verbal, visual, and symbolic representations.

The instructional materials reviewed for Ready Grade 8 meet expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The lesson structure introduces students to different strategies and representations for solving problems, and the embedded tasks use multiple representations (drawings, charts, graphs, numbers, or words) and different solution strategies that provide multiple points of entry to tasks. For example:

• In Unit 3 Lesson 17 Solve Problems Using Systems of Equations, students solve a system of equations by graphing and then solve the same system algebraically. During Guided Practice, students solve systems of equations using specific representations. During Independent Practice, students use what they know about solving systems of equations solved in a graph and algebraically to determine if three lines (given points on the line) intersect another line and how many points of intersection (solutions to the system) there are.
• Unit 4 Lesson 26 Guided Instruction “Lets Explore the Idea” prepares students to compare different formulas for volume. In “Let’s Talk About It,” students work in groups to solve questions that require different entry points, using the formula for a volume of a cylinder. In “Try It Another Way,” students answer questions that relate to components of the volume formula for cylinders and cones, for example, what happens to volume when the radius is doubled. During Independent Practice, students solve problems, “Using Volume Formulas,” where they compare and describe relationships of volume to determine the volume of given figures.

Performance Tasks on interim assessments and Practice and Problem Solving include opportunities to engage with tasks with multiple entry points. For example:

• Practice and Problem Solving Book Lesson 10 problem 4 presents students with two different payment options, one presented as a narrative and the other graphically. Students determine which plan has a greater monthly payment.
• In the Unit 4 Interim Assessment Performance Task, students are given the dimensions of a cone used to hold popcorn at a movie and asked to determine what happens to the cone if the volume was to be doubled, showing and explaining their considerations to double the volume. Students then need to determine whether a container that is triple the volume of the original container is a reasonable size to hold popcorn, and if not, how to change the dimensions of the cone to be reasonable.

The instructional materials reviewed for Ready Grade 8 meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

• ELL strategies can be found throughout the curriculum to build language development and understanding. For example, in Unit 2 Lesson 7, the “Find Out More” section of the lesson includes two prompts for teachers to support English Language Learners: “Write the following on the board: initial value: 2 inches. Guide students to understand this is the point at which the graph starts.” and “Ask students to find the change in y-values and the change in x-values between several pairs of points on the graph to verify that the ratios are all equivalent to 1.5/1.”
• Performance tasks found at the end of every unit provide students with a graphic organizer to help build vocabulary.
• In each lesson, there are tips for using visual models in order to provide support, suggestions, and strategies to engage students with activities that support varied abilities.
• Some lessons include a Differentiated Instruction section that includes an Intervention Activity, On-Level Activity, and a Challenge Activity.
• Small Group Differentiation guidance is also included in the Lesson Pacing Guide. For example, in Unit 4 Lesson 23 Understand the Pythagorean Theorem, Small Group Differentiation identifies prerequisite lessons from Grade 7 and Grade 8.

The instructional materials reviewed for Ready Grade 8 meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Materials offer the following instructional support for advanced learners:

• Each lesson of the Teacher Resource Book includes a Challenge Activity that provides students who have mastered the concepts and skills of the lesson with a more sophisticated problem. For example, in Unit 2 Lesson 10 Graphing Functional Relationships Challenge Activity, students write a scenario that a given graph could represent.
• Concept Extensions provide an opportunity for students to extend their learning at a greater depth. In Lesson 30, the Concept Extension includes introducing domain and range: “Now that students are encountering a situation where the input and output values are restricted, explain to students the meaning of domain and range. Explain that the range represents all of the possible values for the y-variable. For the water height, the range is 0 less than or equal to y which is less than or equal to 19.”

The instructional materials reviewed for Ready Grade 8 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics.

• The names of characters and the context of real-world situations in problems represent a variety of cultural groups.
• Interactive Tutorials found in the online Teacher Toolbox represent students of both genders and various ethnicities.
• Cartoon characters presented in the student edition represent students of both genders and various ethnicities.