Kindergarten - Gateway 3

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for distinguishing between problems and exercises. 

There are several practice pages provided with each lesson. After receiving guidance from the teacher in the Try It section of each lesson, students can demonstrate their understanding in a variety of ways. Students solve problems to learn new mathematics in the Explore sessions of each lesson. These ideas are further developed in Develop sessions, where students solve problems in the Try It and Connect It sections. In the Refine session, students complete exercises where they apply their learning. For example:

• In Kindergarten, Lesson 16, Session 1, Explore, students explore the meaning of addition using the word “and” as a word for joining numbers in the problem, “Have 3 children come to the front of the classroom. How many children are at the front of the classroom? What can I do to make 5?” In Session 2, students practice the skill by finding things they can add together to represent 2 + 1. In Sessions 3 and 4, students use connecting cubes to find various addition equations.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for designing assignments not being haphazard and exercises given in intentional sequences. 

The sequence of lessons in each topic is designed to move from concrete and pictorial representation toward abstract work with numbers. Each unit has a Unit Flow and Progressions Video that highlights the work of the unit and how it fits in the progression of mathematics across grade levels. 

Each unit also has a Learning Progression Chart that shows which lessons are building upon and which lessons students are preparing for within the unit. Each lesson has learning progression information which highlights work done in previous grade levels, as well as the work to be done in this lesson and subsequent lessons.

Each lesson has a consistent structure that builds towards independence. For example, 

• In Kindergarten, Lesson 26, Session 1 Explore, Try It, the teacher is provided with guiding questions to develop understanding that correspond to the first page of the Student Worktext. Some of these questions state, “Explore the numbers on the page. What do you see? What do you already know?” The following Teacher Page provides guidance to the partner section (Connect it). Partners are working together in the following way: “Give each pair of children some number of counters between 11 and 19. Have children fill the 10-frame on the Student Worktext page and place the leftover counters below the 10-frame.” Lastly, children complete solution and practice pages followed by an Exit Ticket to independently show their understanding. 

Lessons within units build upon each other. For example: 

• In Kindergarten, Unit 3 includes the following lessons and topics: Lesson 12: Name Shapes, Lesson 13: See Position and Shape, Lesson 14: Compare Shapes, and Lesson 15: Build Shapes

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for having a variety in what students are asked to produce. 

Students are expected to respond to problems in a variety of ways, including produce answers, use models, drawings, and equations to support their explanations. Students are asked to justify their solutions with a partner and participate in discussions with Discuss It and Pair/Share prompts. Students respond to different problem types in the Refine section of the lessons, including short answer explanations, multiple choice, fill in the blank, and drawings. For example:

• In Kindergarten, Lesson 18, Session 2, Develop, students demonstrate their understanding of subtraction by drawing, sharing, discussing, marking, and giving examples. Directions on the Student Worktext pages state, “Ask children to draw a picture that could show 3 take away 1. For example, they might draw 3 books with 1 book crossed out. Have children share and discuss their drawings, using the terms take away, minus, and subtract. Have children describe each set of pictures. Remind children that the apples marked with an X are being taken away. Have children draw lines from the pictures to match the expressions.”

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for manipulatives being faithful representations of the mathematical objects they represent.

There are a variety of manipulatives in the Math Tool Kit available during lessons, and students are introduced to these in appropriate contexts for the concept being developed. 

• In Kindergarten, Lesson 10, Session 1, Explore, students use two different color connecting cubes to make 10.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for providing teachers with questions that are designed to elicit students’ mathematical understanding and thinking. 

• In Kindergarten, Lesson 1, Session 1, Explore, questions are posed for the teacher to ask the students. Under the Try It and Connect It sections of the sessions, the questions are in italics and easy for the teacher to see. The materials state, “In this session, children explore why people might count and identify items to count in pictures.” While children are looking at page 5 of their Student Worktext, teachers are prompted, “Ask: What are some objects in the picture that you might count?” “Did anyone circle the pencil? Can you count the pencil? Why or Why not? Tell children that they are going to be explorers and explore things that people count. Lead the class on a walk around the classroom. Encourage children to think about what happens in each area and what people might count. Ask: When might you or an adult need to count in this area? Why might it be important to count?”

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meets expectations for including ample notes and useful annotations and suggestions on how to present the content in the student edition. 

The Program Implementation tab includes a “Digital Math Tools - Support Videos” section. This section includes support videos for counters and connecting cubes, base ten introduction, base ten: add and subtract, number line, multiplication models, perimeter and area, fraction models: add and subtract, and fraction models: compare and multiply.

In Classroom Resources, guidance for teachers supports the delivery of the content, as well as information on student responses for each section of the lesson. For example: 

• In Kindergarten, Lesson 4, Session 3, Develop, a common misconception is available for teachers to review. The materials state, “Common Misconception If the children correctly count the dots but cannot determine a group of counters that is more or a group of counters that is fewer, then have them think about the next numbers in the counting sequence and the numbers that come before.” This session also includes Deepen Understanding notes, additional common misconception notes, and notes for a hands-on activity if students are struggling. 

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

In Classroom Resources at the beginning of each unit, Learning Progressions, Math Background, and Unit Flow and Progression Videos provide information for teachers on mathematics and models. For example: 

• In Kindergarten, Lesson 10, the Learning Progression deepens teachers' understanding of how content progresses within and across grades. 

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for containing a teacher’s edition that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for Kindergarten through Grade 12.  

The Ready Classroom Mathematics materials include a “Learning Progression,” section in the teacher edition for each lesson that describes how the grade-level appropriate standard is developed in previous grades as well as how it will extend in the next grade. For example:

• In Kindergarten, Lesson 4, Standards K.CC.3 and K.CC.6 are listed and defined.  Under the Learning Progression section on the same page, which describes the progression students will learn about counting and cardinality, it starts with In Kindergarten and moves to In This Lesson, In Later Lessons, and In Grade 1.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. 

The materials in Ready Classroom Mathematics list prerequisite skills for each lesson in the Lesson overview. Prerequisite Lessons are provided with each lesson to review concepts or to provide students with instruction in areas that may be gaps in their learning. For example:

• In Kindergarten, there are activities at the beginning of each session to activate prior knowledge and review content from earlier in the grade. For example, Lesson 28, Prerequisite Skills include “Understand teen numbers as 10 and some more. Count 11-19 objects. Match a teen number to a quantity.” 

In addition to identifying prerequisite skills for each lesson, Explore, at the beginning of each lesson, connects students’ prior knowledge with the content of the lesson. In some Warm-up questions there is a tag “Prerequisite” noting that the question is assessing prior knowledge.  

The instructional materials include adaptive Diagnostic Assessments with Prerequisite  Reports found in i-Ready, Reports.

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

The Ready Classroom Mathematics materials provide strategies for teachers to identify and address common student errors and misconceptions. For example,

• In Kindergarten, Lesson 19, Session 3, Develop, the Common Misconception states, “If children are unable to create a story about a subtraction situation, then give them a context to work with, such as giving away crayons or markers.”  

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. 

Over the course of a lesson, which includes multiple sessions, materials engage students with multiple activities to review, practice, and independently demonstrate the grade-level mathematical concepts and skills. 

Feedback is provided to students as they progress through the Sessions. Frequent feedback opportunities to address skills and concepts are provided in the Classroom Resources tab, within each lesson and its sessions. The Reteach - Tools for Instruction within each lesson provides teachers with sample errors and remediation strategies to address those errors. In addition, throughout the lesson sessions, potential misconceptions are highlighted with guidance for teachers to provide feedback and new opportunities for practice. For example: 

• In Kindergarten, Lesson 23, Reteach - Tools for Instruction, Subtract Within 10,  Check for Understanding states, “If you observe, that the student identifies an incorrect difference; the student may, be miscounting while subtracting; then try, asking the student to move the counters away from the group while saying the numbers aloud.”

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for offering ongoing formative and summative assessments that clearly denote which standard is being emphasized.

• Standards are clearly noted within the assessments found at the end of each lesson. Standards are provided alongside the questions as well as the Depth of Knowledge level. Unit Assessment Correlations are available with the question number, DOK, Standard, and Lesson. 
• A Mid-Unit Assessment is provided for longer units. Mid-Unit Assessments also provide standards correlations for each item. These can be found in the Classroom Resources tab, End of Unit, Assess, Lesson Quizzes, and Unit Assessments. 
• Formative assessments are also available:
• Lesson quizzes, exit tickets, and quick checks are provided for most lessons. These quizzes assess the specific standard(s) being taught in the lesson.
• Within the sessions are Check For Understanding supports that include a statement as to why the check is being done. The why relates back to the standard being taught in the activities for that session.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for including aligned rubrics and scoring guidelines to support teachers in interpreting student performance and sometimes provide for follow-up instruction. 

Rubrics are provided for Mid-Unit Assessments, Unit Assessments, Unit Performance Tasks, Lesson Quizzes, and Math in Action. (grade 2 and above) The rubrics and scoring guidelines support teachers to interpret student performance. Assessment answer keys are provided alongside the questions along with the DOK level for the item. For multiple choice answers, the correct answer and explanations for incorrect choices are given, including the most common misconceptions.  

Reports from i-Ready diagnostic assessments and comprehension checks assist teachers in providing follow-up instruction for misconceptions and mathematical errors. The electronic reports also include links to assist in reteaching items missed. Within lessons, rubrics and scoring guidelines provide guidance for teachers to follow-up and, throughout Ready Classroom Mathematics, there is guidance for teachers on behaviors to look for, error alerts, and Common Misconceptions. 

• Unit Assessments include a Unit Assessment Teacher Guide that provides instructors with solutions, points possible, the exact standard covered, and the depth of knowledge (DOK) level for each item.
• The Scoring Guide for the problems in the scoring table include: DOK, points of scoring, standard addressed, and lesson assessed by each problem.
• The Scoring Rubrics includes points and expectations for short response, multiple select, choice matrix, extended response, and fill-in-the-blank items.
• Assessment Practice provides some support for follow-up by identifying standards that need further study and reinforcement. Assessment Practice Answer Key and Correlations identify the standard which each question has been designed to evaluate.

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

The sessions within a lesson follow the sequence of Explore, Develop, and Refine. Within a session, there is a sequence of Start, followed by Try It, Model It, or Apply It; Discuss; Connect; and Close.

• Start is designed to build fluency or connect to prior knowledge. 
• Try It is designed to give students an opportunity to explore the concept on their own.
• Model It is designed to allow students the opportunity to explore the concept through manipulatives or drawings. 
• Apply It is designed to give students an opportunity to practice the skill on their own. 
• Discuss is designed to allow students to talk to other students about the concept and compare what they did with each other. 
• Connect It is designed to help students connect the concept to real-life. 
• Close is designed to solidify the learning for the day and to check for understanding through the use of an exit ticket. 

Each lesson includes a Differentiated Instruction Teacher Toolbox that includes Reteach (Tools for Instruction), Reinforce (Math Center Activities), and Extend (Enrichment Activities). For example, the Lesson 1 Overview states: 

• Reteach- “Children who require additional support for prerequisite or on-level skills will benefit from activities that provide targeted skills instruction.”
• Reinforce- “Children who require additional practice to reinforce concepts and skills and deepen understanding will benefit from small group collaborative games and activities.” This is available in three versions: on-level, below-level, and above-level.
• Extend- “Children who have achieved proficiency with concepts and skills are ready for additional challenges will benefit from group collaborative games and activities to extend understanding.” 

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for providing teachers with strategies to meet the needs of a range of learners. 

Each lesson provides opportunity for differentiation in small group lessons, interactive digital tutorials, support for teachers to address common misconceptions at different points throughout lessons. For example:

• The Differentiated Instruction opportunities provide support to reteach students who need additional support, reinforce learning for students who need additional practice, and extend learning for students who have achieved proficiency and are ready for further challenges.
• The Language Development sections for English Language Learners provides even more differentiated support for students who are at different levels of English proficiency.
• Community and Cultural Responsiveness activities build bridges between the mathematics students are learning to investigations of authentic contexts and issues. For example, students apply mathematics they have learned to objects and activities found in parks.

The materials also support learning with a variety of different experiences to develop connections in each lesson. For example:

• Lessons use manipulative objects such as counters and connecting cubes for hands-on experiences where students are actively applying and representing mathematics with hands-on objects.
• Partner and Whole group discussion are incorporated in all sessions to provide dialogue surrounding the mathematics being done.
• Visual representations and physical representations using mathematics manipulatives are used throughout each session.

The instructional materials reviewed for Ready Classroom Mathematics Grade 1 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations. 

The materials present word problems at the beginning of most lessons in the Try It part of the session, which provides multiple points of entry for students. During Model It, students can model the problem in whichever way they like. Examples of problems that provide multiple entry points, different representations, and/or solution pathways include: 

• In Kindergarten, Lesson 7, Student Worktext, Session 2, Explore, Model It states, “How can you show 1 more than 5?” 

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations to engage students in regular and active participation in learning mathematics.

In Program Implementation, Implementation Support there are resources, including:

• A Multilingual Glossary
• A Bilingual Glossary
• An Academic Vocabulary Glossary
• WIDA PRIME V2 Correlation
• Try-Discuss-Connect Routine Resources

In Classroom Resources, Teachers Edition, Language Development is identified for each lesson. This differentiated instruction chart provides guidance for teachers at three levels of differentiation that identifies specific strategies (e.g., Speaking/Writing, Reading/Writing) directly connected to lesson sessions and activities. During sessions, specific strategies target additional supports for students to support engagement in lesson activities. For example:

• Prerequisite lessons are identified for most lessons and include specific supports for ELLs.
• Develop Language includes Why (rationale for the suggestions) and How (strategies and guidance on how to engage students) sections, along with explanations as needed.  
• Discuss It provides supports for all students to engage in mathematical discourse.
• Differentiated Instruction is included for most lessons and includes activities for intervention, on-level, and challenge.
• Math Center activities provide multiple levels of content. 
• Math in Action lessons in Grade 2 and higher build background in a variety of contexts to ensure access for all.

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for providing opportunities for proficient and advanced students to participate in enrichment activities for a deeper challenge. 

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Classroom Resources, Teacher, Lesson Pacing Guide includes Small Group Differentiation Activities, and highlights Extend, Enrichment Activity. These Enrichment Activities can be found during the Refine session in the lesson, and include a Challenge Activity related to the content of the lesson. For example: 

• In Kindergarten, Lesson 16, Extend states, “Invite children to put together tangram shapes on paper to make a picture. You may also wish to show a tangram puzzle. Encourage children to use all 7 tangram shapes to make their picture.”

The instructional materials reviewed for Ready Classroom Mathematics Kindergarten meet expectations for providing a balanced portrayal of demographic and personal characteristics representing a variety of backgrounds. 

In the Program Implementation tab, a multilingual, bilingual, and academic glossary are provided. Throughout the materials there are examples of animated pictures of children that have varied skin tone, features, hair color, and hair types such as pictures of children with brown skin and black hair, light skin and blond hair, and brown skin and brown hair. Pictures with more than one child show interactions between children with varied skin and hair colors such as one with light brown skin and black hair and the other with dark brown skin and black hair. The pictures of objects included are pencils, cars, soccer balls, footballs, apples, bananas, crayons, goldfish, rocks, flowers and other objects commonly known to most students. A variety of names representing different ethnic and cultural backgrounds are used, including:  Rosa and Ryan, Nick and Nora, Dave and Ari, Roberto and Rena, Fran and Pete, Gabe and Rose, Darious, Sam, Lexi, Paco, Julija, Lana, and Kyle.