Kindergarten - Gateway 3

The instructional materials reviewed for Ready Kindergarten 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 12 students compare two written numbers from 1 to 10. In the Lesson 12 Introduction the teacher is instructed to give one student six crayons and another seven. The teacher asks: “Who has more crayons? How do you know?” Students then work in pairs to compare six and seven counters to find out which has more. During Practice Together students use 10-frames to compare which number is less in a given pair of numbers. During the Practice by Myself Independent Practice Hands-On Activity “Make sets with more, less, and the same,” students are given thirty counters, 10-frame cards, and cards with six, seven, eight, or nine dots. Students engage with problems requiring them to choose a card and use counters to show more than that number. They continue using counters to show less than the number and the same as the number represented on their cards. In the Practice and Problem Solving Books, teachers are guided to have students complete more practice with ten frames and counters to compare different numbers within 10.

The instructional materials reviewed for Ready Kindergarten 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 how what students learn in Kindergarten 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 students are learning in Kindergarten and what will happen in the next grade.

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, Unit 1 Counting and Cardinality Numbers 1-5 is followed by Unit 2 Counting and Cardinality, Numbers 6 - 9. The Unit 2 sequence of lessons is as follows: Lesson 7 Count 6 and 7; Lesson 8 Make 6 and 7; Lesson 9 Count 8 and 9; Lesson 10 Make 8 and 9. In Unit 3 Counting and Cardinality, Numbers to 10 the sequence of lessons continues from Unit 2. Lesson 11 Count 10 is followed by Lesson 12 Compare Within 10. Lesson 13 Make 10 completes this sequence of lessons.

The instructional materials reviewed for Ready Kindergarten meet 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. Problem, Talk About 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, 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 11 students explain orally how to count sets of ten objects in different arrangements, represent a set of ten objects using counters in different arrangements, use numerals for 10 to show the total number of objects represented, and finally shade ten objects.

The instructional materials reviewed for Ready Kindergarten 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 two-color counters, bear counters, cubes, attribute blocks, geometric solids, ten-frame representations, 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 15 students use red and yellow counters and a five frame to create an addition equation.

Throughout the materials, various manipulatives are introduced and used in lessons. Their use is appropriate for the mathematics content represented. For example, in Lesson 30 students sort two-dimensional and three-dimensional shape cards onto a mat. During the Hands-on Activity, pairs of students are given either a geometric solid (i.e. sphere, cube, cylinder, or cone), or a an attribute block (i.e. circle, rectangle, square, triangle, or hexagon). Students search for similar shapes in the classroom and share their shape name and the classroom object that has the same shape.

The instructional materials reviewed for Ready Kindergarten 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 11 teachers are prompted to: “Discuss other size groups as well and note number pairs for 10...Ask: 'How many blue fish are there? (9) How many more will make 10? (1) Do you see one object you could add to the group to make 10?' (the seahorse or the snail)”
• The Mathematical Discourse section in each lesson includes questions to engage students and advance their mathematical understanding. For example, Lesson 5 Mathematical Discourse Talk About It states: “When children have completed this page, say: 'Work with a partner. Was it easier for you to compare the plates and cups or to compare the dots? Why?'” There are also examples of possible responses for the teacher.

The instructional materials reviewed for Ready Kindergarten 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 Kindergarten 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 14 the SMP TIP for MP2 states: “Telling a story with numbers allows children to make sense of quantities and understand how these quantities relate to real-world situations.”
• In Unit 4 Lesson 15 Independent Practice Talk About It teachers receive the following information: “Responses should accurately reflect the addends and total in each problem. Discuss both add-to and put-together problems.” This guidance helps teachers to understand the types of operation problems within the lesson and to make connections to CCSSM Table 1 Common Addition and Subtraction Situations.

Throughout Ready Kindergarten 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 Kindergarten 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 lists lessons that students are preparing for in future grades. For example, Unit 1 Lesson 5 is preparing students for Grade 1 Lesson 22 and Grade 2 Lesson 12.

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

The instructional materials reviewed for Ready Kindergarten 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 22 the teacher direction states, “Watch for children who have difficulty starting with 10 and counting on. Find opportunities to practice counting with these children, counting on from 10 as well as from other starting points. Help them see that 1 more than 10 is always 11, 1 more than that is 12, and so forth.”

The instructional materials reviewed for Ready Kindergarten 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 Kindergarten 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 Kindergarten 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 Quick Check and Remediation Activity, Hands-On 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 Kindergarten 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: Teacher-led Activities and Student-Led Activities. 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 Kindergarten 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.

• Unit 2 Lesson 7 Problem Solving Connection Problem 3, “There are 7 people wearing hats. How many people can wear blue hats, and how many people can wear red hats?” Students work on the problem independently and share their answers with the class.
• Unit 6 Lesson 26 Problem Solving Connection Problem 2, “There are 6 flowers. Some are tall. The rest are short. How many can be tall, and how many can be short?” Teachers are encouraged through the Step by Step instructions to read the problem and give students time to work independently to solve the problem. Students are also asked to share answers and discuss as a class. “Encourage children to explain how their answers are alike and how they are different. Ask if anyone got a different answer, to assess understanding and help children avoid common errors.”
• Unit 1 Lesson 4 the Explore Together section notes: “Encourage children to describe the groups of objects they see in the picture.” The focus of the lesson is counting 5. The students have an opportunity to notice, count, and share with the class. Because students may notice different aspects of the image, the work is more open ended.
• Unit 3 Lesson 11 the Mathematical Discourse section notes: “Erica was absent when her class learned about the number 10. What should her friends tell her to help her catch up on what she missed?” This section allows students to approach problems in multiple ways and to discuss their approach to the questions. The materials offer multiple examples of how students may describe 10.

The instructional materials reviewed for Ready Kindergarten 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 3 Lesson 13 includes an English Language Learners Tip: “Guide children to look at the bats at the bottom of the page. Ask children to tell the numbers that describe the two groups that make the 10 bats.”
• A Differentiated Instruction page is included in some lessons of the Teacher Resource Book. For example, Unit 7 Lesson 31 Compare Shapes includes an Quick Check and Remediation, Hands-On Activity, and a Challenge Activity.
• Math Center Activities are provided On Level, Below Level, and Above Level.

The instructional materials reviewed for Ready Kindergarten 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 5 Lesson 22 students extend the concepts in the lesson by building numbers 11-15 using 2 groups of dots. For an additional challenge, teachers are instructed to remove the dot card for 10 from children’s sets.
• Some lessons include a Concept Extension. For example, in Unit 4 Lesson 16: “Connect subtraction and addition. Write '2+1=3' on the board. Describe a real-world situation and have 3 children act it out. Say: 'There are 2 boys at a table. One girl joins them, and now there are 3 children at the table. Then have the girl walk away.' Ask: 'How many children are left after the girl leaves the table? (2) What number sentence shows how many children are left?' Write '3-1=2' on the board and say: 'Three take away 1 is 2.'”

The instructional materials reviewed for Ready Kindergarten 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.