​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The structure of the lessons include several opportunities that address conceptual understanding.

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where conceptual understanding for the topic is outlined.
• Lessons are introduced via video, Visual Learning Animation Plus, at PearsonRealize.com building on conceptual understanding.
• Each Lesson Overview includes Rigor highlighting how conceptual understanding is incorporated into the lesson.
• Each lesson includes Solve and Share where students are able to build and demonstrate conceptual understanding.

Materials include problems and questions developing conceptual understanding throughout the grade-level and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade.

• In Lesson 2-1, students “understand what it means to describe quantities as being equal as they compare groups of objects.” In Solve and Share, students “explain how they know if two given groups of objects are the same in number.” (K.CC.3.6)
• In Lesson 5-3, students “analyze data in a new way as they compare numbers in each category.” In Solve and Share, students “sort objects into two categories, then count and compare the numbers in each category.” Students determine, “What do you need to know first before you can compare? How can you find this? How can you compare the numbers in each category? How have you compared numbers before?” (K.MD.2.3)
• In Lesson 6-1, students utilize multiple representations to “conceptualize addition problems in order to solve them.” In Solve and Share, students “determine the number of flowers in all and represent the total in different ways,” using counters, showing with their fingers, or counting on. Multiple representations are also present in Visual Learning Animation Plus, where students are presented with blocks, fingers, and a student’s thinking process in order to show how to solve a problem. (K.OA.1.1)  
• In Topic 6, Lesson 6-5, students “build upon their understanding of addition as they work more closely with interpreting, representing, and solving addition word problems.” In Solve and Share, students “show ways to add to solve a word problem.” (K.OA.1.2)
• In Lesson 7-2, students “continue to explore subtraction with the idea that a whole can be separated into parts.” In Visual Learning Animation Plus, students are provided with the visual of pears, apples, and peaches to take apart. (K.OA.1.1)
• In Lesson 11-2, students further their “understanding of counting with both tens and ones... The continued use of a number chart allows students to see the relationships between the numbers they count and encourages the application of previously learned patterns, including consideration of tens and ones digits.” (K.CC.1.1)
• In Lesson 11-3, students “use the decade numbers to count by tens to 100. Counting to 100 in this way gives students an understanding of the structure of numbers greater than those they have encountered so far. Recognizing patterns within this sequence and having experience with the hundred chart will allow students to generalize about counting later as they apply what they know to other numbers. This lays the foundation for counting within 100 in different ways.” In Solve and Share, students “identify decade numbers and count by tens to 100.” (K.CC.1.1)

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade-level.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where procedural skill and fluency for the topic is outlined for teachers. The structure of the lessons include several opportunities to develop procedural skill and fluency, including:

• Activity Centers
• Reteach to Build Understanding
• Build Mathematical Literacy
• Enrichment

Later Topics include Additional Practice and Fluency worksheets, Math Diagnosis and Intervention Systems, and My Fluency Progress Forms. Additional practice is located online at PearsonRealize.com.

Materials include problems and questions intended to develop procedural skill and fluency throughout the grade-level and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade.

• In Lesson 6-2, students “count on from a number to find the total.” In Visual Learning Animation Plus, students “use connecting cubes to model adding to the group when more boats come, and then write and addition sentence to hell how many in all.” Independent Practice and Additional Practice sections provide opportunities for students to independently demonstrate procedural skill and fluency. (K.OA.1.1, K.CC.1.3, and K.OA.1.2)
• In Lesson 6-7, students “solve addition equations without corresponding pictures or number stories (and) follow the procedure of filling in parts of an addition equation...The strategy of using patterns to solve addition problems should help students increase both the speed in which they solve the problems and the accuracy of their answers.” Independent Practice, Build Mathematical Literacy, Additional Practice, and Enrichment include opportunities for students to develop procedural skill and fluency in addition by using patterns to complete number sentences, fact families, and equations. (K.OA.1.5 and K.OA.1.1)
• In Lesson 8-1, students “work on the procedural skill of showing parts of a number and representing those parts in an equation as they solve word problems.”  Visual Animation Plus, Guided Practice, Independent Practice, Reteach to Build Understanding, Build Mathematical Literacy, and Enrichment provide opportunities for students to solve word problems in different ways, with both addends unknown. (K.OA.1)
• In Lesson 8-4, students “find different ways to solve equations within 5.” In Independent Practice, “students solve the equation any way they choose, and then tell how they solved the problem.” Reteach to Build Understanding, Build Mathematical Literacy, and Enrichment sections provide additional opportunities for students to solve equations within 5. (K.OA.1.5 and K.OA.1.1)

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for teachers and students spending sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where applications for the topic are outlined for teachers. Each Topic also includes:

• Topic Opener, containing a contextual STEM problem designed to spark interest in the content of the topic,
• Topic Centers with application problems,
• 3-Act Math activities where students engage in application problems, and
• Performance Tasks, where students apply mathematics of the topic in multi-step, real-world situations.

The structure of the lessons includes several opportunities for students to engage in routine and non-routine application problems. Practice & Problem Solving sections provide students with a variety of problem types to apply what they have learned. The way in which application is incorporated into specific lessons is stated in the Rigor section of the Lesson Overview of those lessons.

Examples of opportunities for students to engage in routine and non-routine application problems include:

• In Topic 2, Topic Centers, students apply comparing numbers 0-5, including writing numbers sequences in the correct order, numbering plants, counting the number of sprouts and seeds in each cup, and walking on a taped line taking no more than 5 steps.
• In Topic 2, Performance Task, students “count the large puzzles and cars that David can see in the toy chest, and then write the numbers to tell how many of each toy. Then have them draw a circle around the number that is greater than the other number and mark an X on the number that is less than the other number.” (K.CC.1.3 and K.CC.3.6).
• In Topic 5, STEM Project, students classify animals by attributes, such as color, count the animals by each color, and create a poster after researching the animal. (K.MD.2, K.CC.2)
• In Topic 5, 3-Act Math, students create mathematical models representing a situation by tallying, drawing tens frames, counting in order to classify, or counting data. (K.MD.2.3, K.OA.1.1, K.CC.1.2, and K.CC.2.5)
• In Lesson 14-6, Lesson Overview, Rigor, the materials state, “mathematics instruction calls for the selection, use, and management of problem-solving methods. Use the Thinking Habits shown in the Solve & Share task to help focus thinking on precision in the lesson.” Students are asked to compare the length of a piece of ribbon to a 3 cubed train. (K.MD.1.2)

​The instructional materials for enVision Florida Mathematics Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Each Topic Overview contains Math Background: Rigor, where the components of Rigor are addressed. Every lesson within a topic contains opportunities for students to build conceptual understanding, procedural skill and fluency, and/or application. During Solve and Share and Guided Practice, students explore alternative solution pathways to master procedural fluency and develop conceptual understanding. During Independent Practice, students apply the content in real-world applications, use procedural skills and/or conceptual understanding to solve problems with multiple solutions, and explain/compare their solutions.

In some instances, the three aspects of Rigor are present independently throughout the instructional materials. For example:

• Lesson 3-7 emphasizes Conceptual Understanding, “Students deepen their basic understanding of the counting sequence as they count to find a quantity that is 1 less than or 1 greater than a given number.” (K.CC.1.2)
• Lesson 9-7 emphasizes Application, “mathematics instruction calls for the selection, use, and management of multiple problem-solving methods. Use the Thinking Habits shown in the Solve & Share task to help focus thinking in the lesson on explaining why answers work with the criteria and identifying why there is more than one correct answer.” (K.CC.1.2 and K.CC.2.5)
• Topic 12, Fluency Practice Activity, students “practice fluently adding and subtracting within 5 during a partner activity.” (K.OA.1.5)

Multiple aspects of Rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• In Lesson 4-1, Lesson Overview, Conceptual Understanding and Procedural Skill are the focus of the lesson. “Conceptual Understanding: Students further their understanding of comparison as they compare larger groups to determine which is greater or less in number. Procedural Skill: Students use a 1-to-1 matching strategy to compare groups.” Students demonstrate both aspects of Rigor in the Solve and Share, where they “draw cubes from a bag, sort by color, and make drawings to compare groups.” (K.CC.3.6 and K.CC.2.5)
• In Lesson 8-8, Lesson Overview, Conceptual Understanding and Application are emphasized. “Conceptual Understanding: Students continue to develop their understanding of addition situations as they work with problems involving sums of 10. Application: Students show parts of a number and represent those parts in an equation as they solve real-life word problems.” Students demonstrate both aspects of rigor in the Solve and Share, when “students use counters and an equation to model a way to solve a word problem where only the total is known.” (K.OA.1.a and K.OA.1.1)

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade-level.

The MPs are used to enrich the mathematical content and are not treated separately. MPs are highlighted and discussed throughout Topic Planners, Topic Overviews, 3-Act Math Tasks, and identified within each lesson of every topic. Additionally, the Math Practice and Problem Solving Handbook includes a list of the MPs and real-world scenarios modeled through questions and answers. The online tools offer a Math Practices Animation video that explains the MPs and offers problems that demonstrate each one.

Examples of the MPs identified within individual lessons:

• In Lesson 3-8, MP.7.1, “Students use a pattern to show all the ways to make a number. Students make the pattern both with colors and numbers to help them visualize and keep track of the ways they have found.”
• In Lesson 5-1, MP.6.1, “Students classify objects into two categories, analyzing to find those which have a given attribute and those which do not.”
• In Lesson 9-7, MP.2.1, “Students identify possible answers to word problems that have more than one potential answer.”
• In Lesson 14-4, MP.5.1, “Students see that objects can be described by more than one measurable attribute, and consider the appropriate tool to measure.”

Examples of where MPs are identified and used to enrich the content:

• In Topic 6, the Topic Overview states, “math practices are highlighted in all lessons and are given special emphasis in lessons that focus on problem solving.” MP.1.1: Make sense of problems and persevere in solving them. Students make sense of word problems with two addends, and they use drawings and addition equations to represent the problems (e.g., [Lesson 6-5], Solve and Share).”
• In Topic 7, 3-Act Math Task (Fruit Salad), “As students carry out mathematical modeling, they engage in sense-making (MP.1.1), abstract and quantitative reasoning (MP.2.1), and mathematical communication and argumentation (MP.3.1). They use appropriate tools to develop their models (MP.5.1). In testing and validating their models, students attend to precision (MP.6.1) and look for patterns in the structure of their models (MP.7.1 and MP.8.1)."

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Several structures exist within the Kindergarten materials prompting students to construct viable arguments such as:

• In Convince Me!, students answer open-ended questions to demonstrate how they know the answer.
• In the 3-Act Math activities, Critique Reasoning, students share solutions and analyze the work of others that allows students to construct viable arguments.
• In most lessons, Construct Arguments, students answer open-ended questions to construct viable arguments.
• In Solve and Share, there is an opportunity for students to critique the reasoning of others and construct viable arguments.
• In Visual Learning Bridge, there is an opportunity for students to construct viable arguments.

Student materials consistently prompt students to both construct viable arguments and analyze the arguments of others.

• In Lesson 1-10, students “focus on explaining solutions to problems where they have to count. They draw on the concepts learned previously in this topic to clearly communicate their understanding in different ways.”
• In Lesson 5-4, students “tell whether a given statement makes sense and provide reasons for their choice using numbers, pictures, or words to explain.”
• In Lesson 8-4, Critique Reasoning, students answer, “Daniel says 2 - 1= 3 because he starts with 2 counters, add 1 more, and has 3 in all. Is he correct? Explain.”
• In Lesson 11-3, Solve and Share, students answer, “Alan says he knows which numbers to count because they are the only numbers that have a zero in them. Is Alan correct? Why does Alan not put an X on 10 or 20?”

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking.

• At the beginning of each lesson the Solve and Share contains After: Discuss Solution Strategies and Key Ideas.
• Each lesson has Convince Me! in the Visual Learning Bridge where teachers are provided with prompts to assist students in constructing viable arguments.
• The 3-Act Math Activity has Construct Arguments with prompts for the teacher to use during the activity.
• The Math Practices and Problem Solving Handbook for each grade level identifies the lessons for each grade level focusing on constructing viable arguments and critiquing the reasoning of others (Lessons 1-10 and 5-4).

Teacher materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others frequently throughout the program:

• In Lesson 1-10, Solve and Share, Discuss Solution Strategies and Key Ideas, “Based on your observations, choose which solutions to have students share and in what order. Focus on the explanations of ways to tell there are 5. If needed, show and discuss the student work at the right.”
• In Lesson 3-3, Visual Learning Bridge, Classroom Conversation, Construct Arguments, “How can you find out how many counters there are? Does it matter which counter you count first? Why are there 9 counters? How many counters should you color?”
• In Lesson 5-4, Visual Learning Bridge, Classroom Conversation, Critique Reasoning, “What do you see? Tucker and Olivia counted 6 cars and 5 vehicles that are not cars. How can you check whether their answers make sense?” In Convince Me, Critique Reasoning, “Emily says the number of cars is equal to the number of vehicles that are not cars. Does this make sense?”
• In Lesson 10-1, Solve and Share, “Based on your observations, choose which solutions to have students share and in what order.  Focus on how students knew how the equation should be written. If needed, show and discuss the students work at the right.”

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for explicitly attending to the specialized language of mathematics.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them.

• The Teacher Edition Topic Overview: Build Mathematical Literacy outlines multiple ways the materials address mathematics vocabulary. These components can be found in every topic under Build Mathematical Literacy:
• Build math vocabulary: “using the vocabulary cards, vocabulary activities, vocabulary review, and glossary plus the online glossary and vocabulary game.”
• My Word Cards: “Vocabulary cards for a topic are provided online at PearsonRealize.com. Students use the example on the front of the card to complete the definition on the back.”
• Vocabulary Activities: “The Teacher Edition provides vocabulary activities at the start of topics. These include activities for vocabulary in My Word Cards or activities for vocabulary in Review What You Know.”
• Vocabulary Review: “A page of vocabulary review is provided at the end of each topic. It reviews vocabulary used in the topic.”
• Glossary: “A glossary is provided at the back of Volume 1 of the Students’ Edition.”
• Animated Glossary: “An online, bilingual, animated glossary uses motion and sound to build understanding of math vocabulary.”
• Online Vocabulary Game: “An online vocabulary game is available in the Game Center.”
• Lesson-specific vocabulary can be found in each Topic Planner. For example, in the Teacher Edition, Topic 5, Lesson 5-1: category, classify; Lesson 5-2: chart, tally mark; and so on. The same vocabulary words are listed in the Lesson Overview under Lesson Resources.
• A Glossary is provided in the back of the Student Edition.
• Both the topic and the lesson narratives contain specific guidance for the teacher to support students to communicate mathematically. Within the lesson narratives, new terms are highlighted in yellow and explained as related to the context of the material.
• Topic 1, Vocabulary Review, “Have students 1. draw a circle around the number, 2. write the number that means none, 3. Draw a circle around the number four, 4. mark an X on the one red cube and draw a circle around all five cubes in the group.” The vocabulary listed for this topic include: number, none, four, one, and five.
• Topic 11, Vocabulary Review, “Understand vocabulary: Have students 1-draw a circle around the part of the number in the orange column that is 3 ones 2-draw a circle around the part of the number in the blue column that shows the pattern of 8 ones 3-color the decade numbers red.” The vocabulary listed for the topic includes: ones, pattern, and decade.

No examples of incorrect use of vocabulary, symbols, or numbers were found within the materials.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson. It is clear when the students are solving problems to learn and when they are completing exercises to apply what they have learned.

Lessons include: Solve & Share, Look Back, Visual Learning Bridge, Convince Me!, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice. Additional Practice is in a separate section of the instructional materials, distinguishing between problems students complete and exercises in the lessons. The Solve and Share section serves to either connect prior learning or engage students with a problem in which new math ideas are embedded. Students learn and practice new mathematics in Guided Practice.

In the Independent Practice and Problem Solving sections, students have opportunities to build on their understanding of the new concept. Each activity lesson ends with an Assessment Practice in which students have opportunities to apply what they have learned from the activities in the lesson and can be used to help differentiate instruction.

Additional Practice problems are consistently found in the Additional Practice Workbook accompanying each lesson. These sets of problems include problems that support students in developing mastery of the current lesson and topic concepts.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for not being haphazard; exercises are given in intentional sequences.

Overall, activities within lessons within topics are intentionally sequenced. Students have the opportunity to develop understanding leading to mastery of the content. The structure of a lesson provides students with the opportunity to activate prior learning and build procedural skill and fluency. Students also engage with multiple activities that are sequenced from concrete to abstract and increase in complexity.

Students are introduced to concepts and procedures through a problem-based situation in the Solve and Share, and then connect that problem to the content of the lesson during the Visual Learning Bridge. The Convince Me! portion of the lesson serves to solidify understanding of mathematical concepts through the MPs, followed by teachers and students working together through Guided Practice. Students engage in problems independently in the Independent Practice section. Lessons close with Problem Solving, where students apply learning from the lesson, and Assessment Practice, where students engage with two questions aligned to the daily lesson objective.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for having variety in what students are asked to produce.

The instructional materials prompt students to produce written answers and solutions within Solve & Share, Guided Practice, Independent Practice, Problem Solving, and 3-Act Math. Students produce oral arguments and explanations through discussions that occur in whole group, small group, or partner settings. Students also produce written critiques of fictional students’ work including models, drawings, and calculations.

In the materials, students use a digital platform (Visual Learning Animation Plus) and paper-pencil activities to conduct and present their work. The materials prompt students to use appropriate mathematical language in their written and oral responses, and students frequently use various mathematical representations in their work even though the representation is often provided for students. For example:

• In Lesson 1-1, students circle and count boxes to show their knowledge.
• In Lesson 2-1, students solve using counters to show work and critical reasoning skills to describe the answer.
• In Lesson 7-1, students listen to the story, and then complete all of the following to find how many are left: give an explanation of the mental image, use objects to act it out, and hold up fingers.
• In Lesson 10-1, students work in pairs and use their fingers to represent situations presented in the word problems.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

There are few hands-on manipulatives used in the materials. In general, the manipulatives are visual manipulatives printed in the materials or virtual manipulatives found in the online materials. Occasionally, students will be prompted to use tools such as, “Teaching Tools,” including: counters, cubes, place value blocks, ten frames, ruler, protractor, or grid paper. When they are used, they are used appropriately. If manipulatives are used in lessons, students are usually directed as to when and which manipulatives to use.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains a narrative for the teacher including the Lesson Overview, suggested questions for discussion, and guiding questions designed to increase classroom discourse, support the teacher in knowing what to look for, and ensure understanding of the concepts. For example:

• In Lesson 1-5, Visual Learning, Model with Math, students answer, “How does this picture go with the bees? Why are all the boxes covered with counters?”
• In Lesson 3-5, Visual Learning, Convince Me!, students answer, “How can you use a ten-frame and counters to count 10 objects? What is another tool you can use?”
• In Lesson 8-1, Visual Learning, Use Structure, students answer, “What whole do you see? What parts do you see? How does the five-frame help show the whole?”

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet the expectation for containing 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 also include teacher guidance on the use of embedded technology to support and enhance student learning.

• Each Topic has a Topic Planner that gives an overview of every lesson, the Objective of the lesson, Essential Understanding, Vocabulary, Materials needed, Technology and Activity Centers, along with the Standards.
• The Topic Planner also includes Lesson Resources such as the Digital Student Edition, Additional Practice Workbook, print material available, and what can be found in the Digital Lesson Courseware and Lesson Support for teachers.
• Each lesson opens with a Lesson Overview including: an Objective, an Essential Understanding, Look Back, Look Ahead, Cross-Cluster Connections, aspect(s) of rigor addressed, support for English Language Learners, and any possible Daily Review pages with Today’s Challenge to be implemented. Within the lesson, technology resources or places to print PDF work pages are embedded.
• Lessons include detailed guidance for teachers for the Warm-Up, Activities and the Lesson Synthesis.
• Each lesson activity contains an overview, guidance for teachers and student facing materials, anticipated misconceptions, extensions, differentiation support based on formative assessments called “Quick Checks,” and opportunities for further practice in the online materials. Included within the lessons are guiding questions and additional supports for students.
• The teacher materials that correspond to the student lessons provide annotations and suggestions on how to present the content within the lesson structure: Step 1 (Engage and Explore), Step 2 (Explain, Elaborate, and Evaluate) and Step 3 (Assess and Differentiate). A “Launch” section follows which explains how to set up the activity and what to tell students. During the Visual Learning Bridge in Step 2, supporting questions and narratives for students are provided.
• The materials are available in both print and digital forms. Additional online resources support the material. These opportunities are noted within the lessons. For example, each lesson has an Interactive Practice Buddy noted in Step 2 and Step 3, as well as Another Look Video found in Step 3.

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Each topic opens with a Topic Overview including a Math Background for the Topic.
• The Coherence section has three parts: Look Back, Topic, and Look Ahead. Each section gives a clear, specific explanation of how the topic is connected across grades.
• Each topic includes an Objective, Essential Understanding, (critical area for grade level), Look Back, This Lesson, Look Ahead, Cross-Cluster Connection, Conceptual Understanding, Procedural Skill, and Lesson Resources.
• The Teacher Edition Program Overview Materials contain an overview of mathematics for K-12.

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations for providing strategies to gather information about students’ prior knowledge within and across grade levels.

The Assessment Sourcebook and the Teacher’s Program Overview provide information about the use of assessments to gather information about students’ prior knowledge. Every grade level includes a Grade-Level Readiness test. The Topic Readiness Assessment in each Topic helps teachers gather information about students’ prior knowledge within and across grade levels. Topic Readiness assessments can also be taken online, where it is auto-scored and interventions are auto-assigned.

The Topic Opener assignment located at the beginning of each Topic helps students activate prior knowledge and prepare for the skills needed in the Topic. Each of these assignments has questioning strategies for the teacher. Each lesson also provides information for the teacher about prior, current grade level, and future math that is used.

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

Each lesson identifies common errors and misconceptions for the teacher to address in the Independent Practice. The misconception/error is followed with prompts that the teacher can ask to help students understand their mistakes.

• In Lesson 2-5, Error Intervention, “If students are unsure how to solve the problem, then refer them to the cube trains. Remind students that the number of cubes in the shorter cube train is less in number than the other cube train.”
• In Lesson 9-1, Error Intervention Item 2, “If students have difficulty writing the number 12, then have them practice by using a finger to trace over the numbers on their number cards or in the air.”
• In Lesson 12-1, Error Intervention Item 1, “If students identify the circle or triangle as solid, then discuss the examples in the Visual Learning Bridge again. Read the words flat and solid and ask students where the circle and triangle fit.”
• In Lesson 14-6, Error Intervention Item 2, “If students’ comparisons are incorrect, then help them use the dashed lines as guides to compare the ends of the pictured object.”

​The instructional materials for enVision Florida Mathematics for Kindergarten meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure, consisting of Solve and Share, Visual Learning Bridge, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice, provide students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently, with partners and in groups where review, practice, and feedback are embedded into the instructional routine. In addition, practice problems for each lesson activity reinforce learning concepts and skills and enable them to engage with the content and receive timely feedback. Discussion prompts in the Teacher Guide provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

Each Topic includes a “Review what you know/Concept and Skills Review” containing a vocabulary review and practice problems. This section also includes review and practice on concepts related to the new Topic.

The Cumulative/Benchmark Assessments found at the end of Topics 4, 8, 11, and 14 provide review of prior topics as an assessment. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores.

Different games online at Pearson Realize support students in practice and review of procedural skills and fluency.

​The instructional materials for enVision Florida Mathematics for Kindergarten meet the expectations for assessments clearly denoting which standards are being emphasized.

Assessments are located in a separate book, or the online portion of the program, and can be accessed at any time. For each topic a Practice Assessment, an End-Unit Assessment, and a Performance task are included. Assessments in the Teacher Edition provide a scoring guide and standards alignment for each question.

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

The materials include a detailed Scope and Sequence of the course, including pacing. The Topic Overview in the Teacher Edition includes Coherence which enhances scaffolding instruction by identifying prerequisite skills that students should have. Each lesson is designed with a Daily Review and a Solve & Share Activity reviewing prior knowledge and/or preparing all students for the following activities.

In lessons, the following explicit instructional supports are available for sequencing and scaffolding: the Lesson Overview, questions and extensions for the Solve & Share, Prevent Misconceptions in Visual Learning Bridge, Revisit the Essential Question in Convince Me!, Error Intervention during Guided Practice, and item-related support during Independent Practice and Problem Solving. This information assists the teacher in making the content accessible to all learners.

Lesson narratives often include guidance on where to focus questions in all lesson activities, sample student work, and guidance on what to look for. Optional activities are often included in Step 3 (Assess and Differentiate) and can be used for additional practice or support before moving on to the next activity or lesson.

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• The Additional Practice Materials include a lesson for each topic including specific questions for the leveled assignment for all learning ranges. These three levels of problems are I (Intervention), O (On-Level), and A (Advanced) and include verbal, visual, and symbolic representations.
• Response to Intervention strategies are included in each lesson. Teachers identify “Look Fors” and suggestions to address the needs of students who are struggling. Questions for the teacher to ask are also included.
• Each lesson has at least one Additional Example. These help students cement or extend their understanding of the concept being taught. It includes an extra problem for the teacher to use.
• Each lesson has Differentiated Interventions for a wide-range of learners, which include Reteach to Build Understanding (provides scaffolding to reteach) and Enrichment (extends concepts from the lesson).

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for embedding tasks with multiple entry­-points that can be solved using a variety of solution strategies or representations.

The Solve & Share, Explore It, Visual Learning Bridge, Guided and Independent Practice, 3-Act Math Tasks, and Quick Check/Assessment Practice provide opportunities for students to apply mathematics from multiple entry-points. Though there may be times when the material asks a student to use a specific strategy, there are still questions within the same lesson that allow for students to use a variety of strategies.

The lesson and task narratives provided for teachers offer possible solution paths and presentation strategies from various levels. For example:

• In Lesson 6-1, Solve & Share, “Students determine the number of flowers in all and represent the total in different ways.” The Student Work examples show students using counters, fingers, and numbers to represent the groupings of flowers.
• In Lesson 11-1, Solve & Share, “Count forward from 1 to 30. Count aloud and point to each numbers as you say it. What patterns do you see or hear when you count to 30 using the numbers on the chart? Color the boxes that show a pattern you find.” The example shows the different patterns in which the students heard and colored.

​The instructional materials reviewed for enVision Florida Mathematics Kindergarten meet expectations for suggesting support, accommodations, and modifications for English Language Learners (ELL) and other special populations that will support their regular and active participation in learning mathematics.

The ELL Design is highlighted in the Teacher Edition Program Overview and describes support based on the student’s level of language proficiency. An ELL Toolkit provides additional support for English Language Learners.

Two ELL suggestions are provided for every lesson, one in Solve & Share and another in Visual Learning Bridge. Also, Visual Learning support is embedded in every lesson to support ELL learners. This includes a Visual Learning Animation Plus online, Visual Learning Bridge for each lesson, and the Animated Glossary. These use motion and sound to reduce language barriers. Questions are read aloud, visual models are provided, and motion and sound definitions of mathematical terms are provided.

Additionally, a multilingual handbook is included with a mathematics glossary in multiple languages, and an English Language Learners Toolkit is a resource providing professional development and resources for supporting English Language Learners.

An example of ELL supports within the instructional materials:

• In Lesson 12-1, Lesson Overview, English Language Learners, Teachers are asked to use with the Solve & Share in Student Edition. “Speaking: Write and read different.  Remind students they have used this work before. Ask students to tell you what they think the work different means. Show a square and a cube. Say: These are both shapes. Rotate the shapes so that students can see the dimensions. Ask: How are these shapes different? Entering: Have students tell what is different with one or two words. Show another 2-D shape and another 3-D shape and repeat. Developing: Have students explain with the sentence stem: “The shapes are different because ____.” Show another 2-D shape and another 3-D shape and repeat. Expanding: Have students explain the difference in their own words. Show another 2-D shape and another 3-D shape and repeat.”

Support for other special populations noted in the Teacher Edition Program Overview include:

• Resources are provided on for Ongoing Intervention (during a lesson), Strategic Information (at the end of the lesson), and Intensive Intervention (as needed anytime).
• The Math Diagnosis and Intervention System (MDIS) supports teachers in diagnosing students needs and providing more effective instruction for on- or below-grade-level students. Diagnosis, Intervention Lessons, and Teacher Support is provided through teachers notes to conduct a short lesson where vocabulary, concept development, and practice can be supported.
• Online Auto Design Differentiation is included, and the supports within this part of the program include: Differentiation After a Lesson (based on an Online Quick Check where the Interactive Practice Buddy can be utilized), Differentiation after a Topic (based on the online topic assessments where Visual Learning Animations Plus are then assigned), and Differentiation after a Group of Topics (based on the online cumulative benchmark assessments where students can then receive remediation or enrichment). The teacher can track progress using Assignment Reports and analyze Usage Data.

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Each lesson offers differentiated instruction to extend the concepts in the lesson and provides opportunities to challenge advanced students:

• Extensions are found at the end of every Solve & Share;
• Higher Order Thinking items within the Independent Practice and Problem Solving section;
• Enrichment pages as a result of the Quick Checks in every lesson;
• Opportunities to engage in STEM activities during the activity centers;
• Noted advanced problems to complete during the Additional Practice portions of each lesson; and 
• Differentiation after a group of Topics based on the online cumulative benchmark assessments where students can then receive enrichment.

​The instructional materials for enVision Florida Mathematics Kindergarten meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• The lessons contain tasks including various demographic and personal characteristics. All names and wording are chosen with diversity in mind and the materials do not contain gender biases.
• The materials mostly contain pictures of objects or cartoonish drawings instead of photos or drawings of people.
• The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
• The materials include a set number of names used throughout the problems and examples (e.g., Carlos, Jada, Martha, Carl, Benito, Drake, Daniel, Yasmin, Jonathan). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity.