1st Grade - Gateway 3

The Grade 1 Ready instructional materials 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 and Explore Together sections. At the conclusion of lesson instruction, students complete exercises in the Practice Together and Practice by Myself 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 15 students practice adding three digits using ten-frames, number paths, and by completing number sentences in the Practice and Problem Solving Book. During Guided Practice students are presented with the problem: “Jon has 7 apples. Tom has 3 apples. Bo has 5 apples. How many apples do they have?” Students are given a number path and complete three number sentences: 7 + ___ = 10, 10 + 5 = 15, and 7 + 3 + 5 = 15. The Mathematical Discourse states: “Are there other ways you could solve the word problem at the top of the page instead of using a number path to add numbers? Tell about the other ways.”

The instructional materials reviewed for Ready Grade 1 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 1 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 1 and 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, Lessons 1, 2, 6, 9, 11, 13, 14, and 16 relate to adding and subtracting within 20 (1.OA.C). The lessons progress from developing counting on strategies in Lessons 1 and 2 to more sophisticated strategies such as using doubles, doubles plus one, and/or making a ten in subsequent lessons.

The instructional materials reviewed for Ready Grade 1 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, Hands-On Activity, Practice, and Problem Solving portions of each lesson require students to represent the problem in a drawing and make connections between the drawing and the equations. Question types vary and include 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 10 students complete addition equations with missing numbers, determine if equations are true or false and explain their answers in writing, draw pictures to explain their answers, and correct equations that were initially incorrect.

The instructional materials reviewed for Ready Grade 1 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 counters, connecting cubes, attribute blocks, ten-frames, and number bonds. Students are frequently asked to look at a manipulative model and create a math equation from the representation. For example, in Lesson 14 students use ten frames to model addition situations, regroup ones to make a ten, and create equations represented in the models.

Throughout the materials, various manipulatives are introduced and used in lessons. Their use is appropriate for the mathematics content represented. For example, in Lesson 15 students use counters and a ten-frame to represent subtraction problems. Students then connect their representation to a subtraction equation. During Independent Practice students use counters and ten-frames to solve problems in the Student Instruction Book.

The instructional materials reviewed for Ready Grade 1 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 30 teachers are prompted to ask: “What information does this picture graph give us? What do the pictures stand for?” A second prompt guides teachers to ask: “What other questions could you ask and answer about this data?”
• The Mathematical Discourse section in each lesson includes questions to engage students and advance their mathematical understanding. For example, in Lesson 21 Mathematical Discourse teachers are prompted to ask: “'Can 54 be shown as 4 tens and 5 ones?' Explain the 5 in 54 means 5 tens and not 5 ones. The 4 means 4 ones and not 4 tens. 'Why do you think there are more ways to show 54 than 45?'”

The instructional materials reviewed for Ready Grade 1 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 1 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 1 Lesson 5 the Independent Practice Mathematical Discourse includes the following guidance for teachers: “When comparing two quantities, children must find a way to represent the ‘how many more’ or ‘how many less’ (the difference) conceptually and through representation. They need to understand that there are two parts to a comparison question: 1. Which quantity is more (or less)? 2. How much more (or less)? Children should be able to act out the problem, create a visual model, and write an appropriate subtraction sentence to answer both questions.”
• In Unit 2 Lesson 10 the SMP TIP for MP2 states: “Finding equivalent and non-equivalent expressions involves making sense of quantities and their relationships.” The Evaluate portion of the Guided Practice guidance for teachers states: “As children decide whether the number sentences are true, revisit the earlier discussion about addends that make the same total. Guide children to recall that when any two addends on each side of equal sign make the same total, the number sentence is true.”

Throughout Ready Grade 1 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 1 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 1. For example, Unit 2 Lesson 10 builds on Kindergarten Lessons 18, 19, and 20, and the chart also lists lessons that students are preparing for in Grade 2, Lessons 4 and 5.

Each Lesson Overview includes a Learning Progression section. This section begins with an explanation of how the lesson builds on prior knowledge from Kindergarten. The Learning Progression explains the lesson's overall connection to Grade 1 and the mathematical content of the lesson. This section also explains connections to Grade 2 and, if appropriate, to other future grades.

The instructional materials reviewed for Ready Grade 1 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, the Unit 3 Review states: “Watch for those who struggle with the idea of “1 ten and some number of ones.” Help these children identify the ten and ones in each teen number. Have them write, draw, and talk about making a ten as they add.”

The instructional materials reviewed for Ready Grade 1 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 1 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 1 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 carefully 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 1 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. Prerequisite lessons from earlier grades 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 margin 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 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 1 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 1 Lesson 4 Show What I Know students are provided with a number and asked to figure out missing addends. Students fill in a number bond and write a subtraction sentence and addition sentence. The Teacher Resource Book highlights possible answers and also notes that teachers “make sure they understand that there is not just one correct way to color the triangles, so their number bonds and number sentences may be different from others in the class.”
• In Unit 1 Lesson 3 Practice by Myself multiple representations are provided for the students. The students are working on adding and subtracting in word problems and are given two models that are partially completed. Note: Teachers are instructed to review the models and “explain that the models are started for them, and that children can complete them or use some other method they prefer to solve the problem.”
• In Unit 2 Lesson 11 students are building on facts they know. In the Explore It portion of the lesson students solve a mystery and find missing numbers. Children use counters and then number sentences to represent solutions. The problem starts by asking, “I have 6 marbles. Some are red, and some are yellow. There is the same number of red marbles as yellow marbles. How many are red, and how many are yellow?” As the problem continues students explore an open-ended clue: “I have 9 marbles. Some are red and some are yellow. There are more red marbles than yellow marbles. How many red marbles, and how many yellow marbles could I have?” The students are building on 2 more closed scenarios and are invited to explore and share results and explain their reasoning on the open-ended clue.
• In Unit 4 Lesson 19 students build understanding of 10 more and 10 less. Students are given digit cards 0-9. Using these digit cards students make a number and find 10 less and 10 more. In addition to multiple solutions being possible, students are encouraged to connect this work to their work with cubes, with a 120 chart, and with drawing a picture.

The instructional materials reviewed for Ready Grade 1 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 4 Lesson 18 includes an English Language Learners Tip: “To present visual language support for children who need help distinguishing between a row and a column, provide a 120 chart labeled with the words “column” and “row.” The labels should include an arrow pointing to a column and a row.”
• Prerequisite lessons include specific ELL support as needed. For example, in Unit 5 Lesson 21 there are two prerequisite lessons. Prerequisite Lesson 21 includes an English Language Learners support that states: “Have children work with a partner to show 11 fingers, using all 10 fingers from one child and the extra on the other child’s hand.”
• A Differentiated Instruction page is included in some lessons of the Teacher Resource Book. For example, Unit 3 Lesson 15 Understand Volume 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 1 meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Materials offer the following instructional support for advanced learners:

• A Differentiated Instruction page that provides Challenge Activities is included in many lessons of the Teacher Resource Book. For example, in Unit 4 Lesson 17 students extend the concepts in the lesson by making more than 9 tens.
• Some lessons include a Concept Extension. For example, Unit 1 Lesson 1: “Build the concept of a variable. Display the box and tell children there are 5 pencils inside the box. Set 3 single pencils next to the box and ask: How many pencils do I have altogether? How can you count on to find out? Listen for counts of '5, 6, 7, 8' and ask how they knew to start with 5. Children should recognize that since they know there are 5 pencils in the box, they do not need to be counted or drawn separately. Have children record the process in a number sentence to make a symbolic connection to the problem.”

The instructional materials reviewed for Ready Grade 1 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 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.