4th Grade - Gateway 3

The instructional materials reviewed for Ready Grade 4 meet expectations for distinguishing between problems and exercises. Each problem or exercise has a purpose.

Students are learning new mathematics and solving problems in the beginning stages of each lesson in the Use What You Know, Find Out More, Reflect, Picture It, and Model It sections. At the conclusion of lesson instruction, students complete exercises in the Guided Practice and Independent Practice that engage them in exercises to practice skills and in problems to apply learning.

The instructional materials provide problems and exercises in both the Ready Instruction book and the Practice and Problem Solving Book. For example, in Unit 3 Lesson 12 Modeled and Guided Instruction students complete division problems using an area model and partial products methods that include making meaning of remainders. During Guided Practice students solve division exercises with remainders using area models and partial quotients. During Independent Practice students solve multiple choice problems that require them to demonstrate their use and understanding of division with and without remainders.

The instructional materials reviewed for Ready Grade 4 meet the expectations that the design of assignments is not haphazard and that the exercises are given in intentional sequences.

Problem sets and daily practice exercises relate to the mathematical concept developed in each lesson. The sequence of topics in each unit is intentionally planned to move from working with concrete and pictorial representations to more abstract work with numbers and computation. Each unit has a progressions chart showing what students have learned in previous grades connected to what they will learn in Grade 4 and how this will relate to what they will learn in future grades. Each lesson has a Learning Progression section in the lesson overview of the Teacher Resource Book which states what was learned in the previous grade, what students are learning in Grade 4 how it relates the current lesson, and what will happen in the next grades.

Concepts are explored and developed in daily lessons and reinforced through partner work and independent practice. Lessons are designed using a scaffolded approach. Students are guided by the teacher in the beginning of instruction, move toward work with partners or in small groups, and finally work independently. For example, in Unit 3 lessons are sequenced to build understanding of and fluency with multiplication and division with multi-digit whole numbers. Instruction begins in Lesson 11 with students multiplying one-digit and two-digit numbers by multiples of ten before multiplying two two-digit factors using area models, partial sums and the standard algorithm. In Lesson 12 students divide using the same area model representations and are asked to provide the related multiplication equations. Finally, students use the various strategies learned for multiplying and dividing in Unit 3 to complete the Math In Action lesson where they use and apply all operations with whole numbers as well as estimation.

The instructional materials reviewed for Ready Grade 4 meets expectations that there is a variety in what students are asked to produce.

Students are expected to respond and produce solutions in various ways. They are asked not only to produce answers but to provide evidence through drawings, representations, and written explanations. Students are often asked to analyze and defend the work of others. They must justify their conclusions with verbal statements and mathematical reasoning.

Lessons are designed with a consistent routine that includes whole group, partner, and independent work. The Picture It, Model It, Connect It, and Try It portions of each lesson require students to represent the problem in a drawing and make connections between the drawing and the equations. The Pair/Share portion of each lesson asks students to discuss their 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. Students are asked to produce various answers for the mathematical content that is the focus of each lesson. For example, in Lesson 25 students complete open-ended questions based on reading a short paragraph, use bar models, pictures, and number lines to solve problems, solve problems involving measurement conversions, and answer multiple choice questions.

The instructional materials reviewed for Ready Grade 4 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, unit cubes, fact triangles, hundreds charts, base-ten blocks, place value charts, number cards, clocks, stopwatches, volume containers, pattern blocks, and square tiles. Students are frequently asked to look at a manipulative model and create a math equation from the representation. For example, in Lesson 20 students add fractions of tenths and hundredths by looking at pictures of base-ten blocks shaded to represent the fractions.

Throughout the materials, various manipulatives are introduced and used in lessons. Their use is appropriate for the mathematics content represented. For example, in Lesson 17 students use fraction circles to model addition of fractions in the Hands on Activity. Students discuss and make sense of the models, connecting them to the written expression the teacher is instructed to write on the board.

The instructional materials reviewed for Ready Grade 4 meet 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, in Lesson 15 students explore fractions on a number line. During Guided Instruction teachers are prompted to ask: “Can you think of another way to show finding a difference on a number line?” Teachers are told, “Students may mention adding up to subtract.”
• The Mathematical Discourse section in each lesson includes questions to engage students and advance their mathematical understanding. For example, Lesson 11 Mathematical Discourse asks: “If you have a multiplication problem such as 100 x 12, will it change your answer if you write it as 12 x 100?” Teachers receive information on why the answers are the same and how this is an example of the commutative property. “Students may understand the concept, but may not know the name. It states that regardless of the order in which you multiply two numbers, the product is always the same.”

The instructional materials reviewed for Ready Grade 4 meet expectations that they contain a teacher's 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, prerequisite skills, content objectives, learning progressions, lesson vocabulary, and a detailed pacing guide for whole and small group instruction for each lesson.
• 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 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 4 meet expectations for containing a teacher’s 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 4 Lesson 22 the SMP TIP for MP8 states, “Students make use of regularity in repeated reasoning by applying the same processes that they developed in earlier grades to compare whole numbers. Ask students why this process works for decimals but not for fractions. [Decimals use the principles and patterns of base ten place value, but fractions often have denominators that are not multiples of ten.]”
• In Unit 6 Lesson 33 the Learning Progression states, “In this lesson students build on their understanding to reason about lines of symmetry in two-dimensional figures. … In Grade 5 students will extend their understanding of geometric concepts when they solve mathematical problems using the coordinate plane.”

Throughout Ready Grade 4 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 4 meet expectations for containing a print teacher’s edition (in print and in the on-line 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 that students are building upon. These lessons can come from previous grades and from Grade 4. For example, Unit 4 Lesson 15 builds upon Grade 3 Lessons 16 and 17 and Grade 4 Lesson 13. The chart also lists lessons that students are preparing for. For example, Unit 6 Lesson 32 is preparing students for Grade 5 Lessons 30 and 31.

Each Lesson Overview includes a Learning Progression section. This section begins with an explanation of how the lesson builds on prior knowledge from Grade 3. The Learning Progression explains the lesson's overall connection to Grade 4 and the mathematical content of the lesson. This section also explains connections to Grade 5 and, if appropriate, to other future grades.

The instructional materials reviewed for Ready Grade 4 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

• The Quick Check and Remediation section 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 errors and misconceptions. For example, in Lesson 5 students are assessed on multiplicative comparison and the following misconceptions are noted: “Students may find a sum or difference instead of finding the comparison; they may confuse the meaning of the factors in the model; or they may look at the position of the factors without considering the meaning of the context.”

The instructional materials reviewed for Ready Grade 4 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Each lesson provides approximately one week of instruction. Over the course of the week, responsibility for the learning process transfers from the teacher to the student. Students move from scaffolded support to independent problem solving. Review and practice is incorporated in each lesson within the Ready Instruction Book and in each homework assignment within the Practice and Problem Solving Book.

Feedback is provided to students throughout lessons. Frequent feedback opportunities to address skills and concepts are provided in the Teacher Resource Book. The Quick Check and Remediation activity within each lesson provides teachers with sample errors and remediation strategies to address those errors. Assessments and Performance tasks include rubrics that can also be used to provide feedback.

The instructional materials reviewed for Ready Grade 4 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 can be found on the Interim Assessment Correlations chart in the Teacher Resource Book.
• Unit Assessments provide standards correlations for each item. Unit Assessments and correlations are found online in the Teacher Toolbox.
• 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 4 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 Guided Instruction, Guided Practice, and Independent Practice.
• Lessons are sequenced to build from 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, and real-world connections.
• Each lesson contains a Differentiated Instruction page which contains an Intervention Activity, On-Level Activity, and a Challenge Activity.
• Center Activity PDF’s can be found online in the Teacher Toolbox to help further differentiation.

The instruction materials reviewed for Ready Grade 4, 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 three subsections: Reteach, Teacher-led Activities, and Student-Led Activities. 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. Student–led Math Center activities in three different levels are referenced for additional instruction, if needed.
• 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, and challenge activities.
• The Math In Action section for each unit has a Differentiated Instruction page that includes an Intervention 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.

Grade 4 Ready instructional materials meet expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

When solving problems, students often choose their own solution strategy and/or representation. The embedded tasks are presented using multiple representations (drawings, charts, graphs, numbers or words) and different solution strategies.

• In Unit 2 Lesson 6 students are guided through a multiplication word problem using a bar model and the context of the problem to build the equation.
• In Unit 4 Lesson 20 Hands-on Activity students use 10-inch squares of paper to mark intervals of 10 vertically to create and explore a model of tenths and then horizontally to explore hundredths. In Lesson 21 Visual Model the teacher uses a place value chart and guides students in finding parallels between tens and tenths, and hundreds and hundredths.
• Unit 3 Math in Action features open-ended problems with many entry points and more than one possible solution. For example, students are given data about worms (how much they eat in one day, cost of 1050 and 2950 worms, and how much food is available). Students then tell how many and what size package of worms can be purchased to use the amount of food available. Students are encouraged to solve the problem in different ways.

The instructional materials reviewed for Ready Grade 4 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.

The Teacher Resource Book and online Teacher Toolbox contain the following support:

• ELL Support Tips are found in the margin notes of each lesson of the Teacher Resource Book. For example, Unit 2 Lesson 9: “Throughout this lesson you will need to provide extra support to give English Language Learners confidence to participate in class discussions. Give all students time to think through their response to a question. Wait at least 5 seconds, and up to 30 seconds, before calling on any student to answer. If a student’s comment is unclear try 're-voicing' the student’s comment.”
• Prerequisite lessons include specific ELL support as needed. For example, in Unit 4 Lesson 20 there is one prerequisite lesson. Prerequisite Lesson 14 (Grade 3) includes an English language Learners support that states: “Some students, especially ELL students, may need additional support with understanding and using the word unit. Connect the term to the base-ten blocks they use. Remind them the ones blocks are called 'unit' cubes.”
• A Differentiated Instruction page is included in some lessons of the Teacher Resource Book. For example, Unit 5 Lesson 28 Understand Angles includes an Intervention Activity, On-Level Activity, and a Challenge Activity.
• Math Center Activities are provided On Level, Below Level, and Above Level.

The instructional materials reviewed for Ready Grade 4 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 provides 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 12 Challenge Activity students are solving two-step word problems involving division. Three problems with contexts that include remainders are given. For example, “Jeremy had a bag of 300 raisins. He kept 20 for himself. He wanted to evenly split the rest among 7 friends. How many raisins was Jeremy able to give each of his friends?”
• The Math In Action section for each unit of the Teacher Resource Book has a Differentiated Instruction page that includes a Challenge Activity. For example, Unit 4 Math in Action: Use Fractions and Decimals Challenge Activity Sports Picture Frame asks students if they can design a frame from five craft sticks without changing the instructions. If it cannot be done, students must explain how the instructions could be changed to complete the project.
• A Differentiated Instruction page that provides Challenge activities is included in some lessons of the Teacher Resource Book. For example, Unit 1 Lesson 1 Understand Place Value includes a Challenge Activity to find numbers around them and present the numbers using base-ten clues in two different ways. Students also write each number in standard form, word form, and expanded form.

The instructional materials reviewed for Ready Grade 4 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics.

• The names and situations in the story problems represent a variety of cultural groups.
• Student edition pictures include students from a variety of cultures.
• The Let’s Talk About It section in each lesson includes four faces of various demographics and represents both genders.
• The application problems include real-world situations that are appropriate to a variety of cultural and gender groups.
• Interactive tutorials found online in the Teacher Toolbox represent students of both genders and various ethnicities.