7th Grade - Gateway 3

The instructional materials for Ready Grade 7 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 2, Lesson 10, Understand Proportional Relationships, students compare, apply, and analyze proportional relationships during Guided Practice using both graphs and tables. During Independent Practice students use their understanding of proportional relationships to complete a task to generate one table of data that compares side length and perimeter and another that compares side length and area. They analyze the data using both ratios and graphs to determine if the data are proportional.
• In Unit 3, Lesson 16, Solve Problems with Equations, students are provided with models and strategies for solving problems and then practice solving problems using the models.
• In Unit 5, Lesson 27, Making Statistical Inferences, students compare and analyze forms of random samples to develop a definition of a random sample. During Guided and Modeled Instruction, they see models of different ways to represent distributions of data (tables, line plots, box plots) that represent their random samples.

The instructional materials for Ready Grade 7 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 1, the lessons are sequenced to build understanding of operations with integers. Lesson 1 builds understanding of addition of positive and negative integers. In Lesson 2, students build understanding subtracting integers, and in Lesson 3 they do both addition and subtraction with integers. Lesson 4 finishes the sequence with dividing and multiplying integers. Each lesson includes opportunities for students to apply their knowledge about integers to solve real-world problems.

The instructional materials reviewed for Ready Grade 7 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: Iin the Practice and Problem Solving Book Lesson 19 Problem 6 students draw the rectangle on the coordinate grid. In Problem 1 students complete a table. For example:

• In Unit 2, Lesson 11, Math Discourse, the teacher poses the following question for students: “How do you think the graph of this proportional relationship might be like other graphs? How might it be different? Explain.”
• In Unit 3, Lesson 16, Problem 5, students are given the side lengths (as an algebraic expression) of an isosceles triangle, as well as the perimeter. Students draw and label the triangle, write an equation, solve the equation, and find the length of all three sides based on the given information.
• In Unit 4, Lesson 21, Reflect, students “Use your own words to explain how to find the circumference of a circle with a radius of 4 inches. Include a drawing in your explanation.”
• In Unit 5, Lesson 31, Think/Pair Share, students individually solve the problems using the information provided and then discuss their solutions with a partner. Students discuss the following: “Would you get the same prediction if you wrote the probability as 1/5 instead of 4/20? Why or why not?”

The instructional materials reviewed for Ready Grade 7 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 including number cubes, coins, painter’s tape, index cards, and integer chips. For example:

• Unit 1, Lesson 3 presents numerous opportunities for students to use manipulatives:
  • In the Hands-On Activity, students use red and yellow integer chips to review addition of integers.
  • In the Unit 1, Game in the Practice and Problem Solving Book, students plan an Operation Game involving integers. They use two number cubes to show representations of negative and positive numbers.
  • Students walk on a large number line on the floor to model integer addition during the lesson.
  • Students engage with visual models using a number line and integer chips to model subtraction.
• In Unit 5, Lessons 31 and 32, students use manipulatives to collect and represent data:
  • In Lesson 31, students collect their own data by rolling number cubes. They gather the results into a frequency table.
  • In Lesson 32, Modeled and Guided Instruction, students use a coin-toss simulation to create an experimental and theoretical probability model for determining the gender of a baby and explain the connection between the different probabilities.

A detailed Manipulative List is included in the Program Implementation section. For Grade 7 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.

The instructional materials for Ready Grade 7 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:

Step by Step in each lesson organizes content into chunks for student learning and includes guiding questions, key points, and teacher prompts. For example, Lesson 24 Picture It provides teachers with guidance and questions: “What shapes make up the greenhouse? You may need to prompt students by saying: Let’s start with rectangles, how many rectangles do you see?” In Lesson 24, teachers are provided Pair/Share questions to use: “How could you check to see if your answer is reasonable?” Teachers are directed to have students discuss their solutions to these questions with a partner or in a group.

The Mathematical Discourse section in each lesson includes questions to engage students and advance their mathematical understanding. In Lesson 11, Equations for Proportional Relationships, the Mathematical Discourse, Question 2 states, “How do you think ratios and proportions are related? Do you think they are similar or different, and in what ways?” The step-by-step directions include, “In problem 6, ask students to explain how they used the equation to find the amount of seltzer.”

The instructional materials reviewed for Ready Grade 7 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 7 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. For example:

• In Unit 4, Lesson 24, the Learning Progression states, “Earlier in Grade 7 students continued their work from Grade 6, solving real-world and mathematical problems involving surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. In this lesson, students use formulas and write equations to calculate the areas of rectangles and triangles that compromise the three-dimensional figures.”
• In Unit 2, Lesson 11, the SMP TIP for MP1 states, “When students understand what the data in a table represent they are making sense of the problem. Encourage students to question what different values in a representation mean, and use other models to check their understanding.”

Throughout Ready Grade 7 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 7 meet expectations for containing a 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 lists lessons that students are building upon. These lessons come from previous grades and from Grade 7. For example, Unit 3, Lesson 17 builds upon Grade 6, Lesson 20 and Grade 7, Lessons 12 and 16. The chart also identifies the standards the lesson is preparing for: Standard 7.EE.4b, and Standard 7.EE.3.

Each Lesson Overview includes a Learning Progression section. This section begins with an explanation of how the lesson builds on prior knowledge from Grade 6. The Learning Progression explains the lesson's overall connection to previous Grade 7 lessons and lessons in Grade 8, including the mathematical content of the lesson.

The instructional materials reviewed for Ready Grade 7 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 teachers 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, in Unit 4, Lesson 24, the Error Alert states, “Students who wrote 36 may have divided the surface area by 6 to come up with the area of a face and stopped there.”

The instructional materials reviewed for Ready Grade 7 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 throughout the lessons from the teacher. 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 7 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, providing standards correlations for each item, is located 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 7 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 7 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 7 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 1, Lesson 5, Terminating and Repeating Decimals, students explore equivalent forms of unit fractions, fractions, and decimals. During Modeled and Guided Instruction students look at situations where representing fractions as decimals is more efficient, study models for dividing fractions to find decimals, and analyze patterns to understand decimals that terminate and those that repeat. During Independent Practice, students identify equivalent fractions and decimals, complete a table, and describe the patterns they see in repeating decimals.

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

• In the Unit 3 Performance Task, students are given information on the cost for printing 500 calendars and the ideal price point between $10 and $12. To complete the task, students need to decide on an appropriate selling price, write an equation to find the amount of money the shelter receives for each calendar it sells, show the amounts received for different numbers of calendar sales, and finally, determine the number of calendars sold to pay for the printing costs and explain. Students can use any method to solve the task, and there are multiple entry points for students to solve the problem. Furthermore, students need to justify their selling price and explain why they used the model they did.

The instructional materials reviewed for Ready Grade 7 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, the Unit 5, Lesson 31, Experimental Probability, “Find Out More” section includes three prompts for teachers to support English Language Learners and an explanation of everyday and academic vocabulary: “Everyday terms have a different meaning in the mathematics classroom. Write the word ‘trial’ on the board, and ask students to explain what they know the word means in everyday speech. Explain that the word means something different in mathematics. Give several examples of different types of trials such as rolling a number cube and spinning a spinner.”
• 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, an On-Level Activity, and a Challenge Activity.
• Small Group Differentiation guidance is also included in the Lesson Pacing Guide. For example, in Unit 2, Lesson 9, Ratios Involving Complex Fractions, Small Group Differentiation identifies Grade 6 Lessons 1 and 2 as prerequisite lessons.

The instructional materials reviewed for Ready Grade 7 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 3, Lesson 15, Writing Linear Expressions Challenge Activity, students find the percent discount when given the sale price and the original price of a shirt.

Concept Extensions provide an opportunity for students to extend their learning at a greater depth. In Unit 4, Lesson 22, Scale Drawings, the Concept Extension states: “Connect scaled drawings to equations of proportional relationships: Tell students that what they learned about proportional relationships earlier this year also applies here. You can write an equation that relates the size of the photograph to size of its enlargement. First, find the constant of proportionality. Ask the class to look at the problem on the student book page and find the constant of proportionality. The constant could either be 4 or ¼. Tell students to use 4 inches for the enlargement (x) to 1 inch of the original (y). The equation is e = 4y. To find the width of the enlargement, substitute 4 inches for y; so, e = 4 x 4 = 16.”

The instructional materials reviewed for Ready Grade 7 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.