​The instructional materials for enVision Florida Mathematics Grade 5 meet 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 includes several opportunities to develop conceptual understanding.

• In the Teacher’s Edition, every Topic begins with “Math Background: Rigor,” where conceptual understanding for the topic is outlined.
• Lessons are introduced with a video, "Visual Learning Animation Plus,” at PearsonRealize.com; these often build conceptual understanding.
• Links within the digital program to outside resources, such as Virtual Nerd, include videos for students that introduce concepts.
• In the student practice problems, the section “Do You Understand” reviews conceptual understanding.

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

• The Topic 1 Overview, Conceptual Understanding states, "Understand Exponents. In Lesson 1-1, students are introduced to exponents. They learn that the exponent in a power of 10 tells the number of times 10 is used as a factor. When multiplying by a power of 10, they recognize the connection between the exponent in the power of 10 and the number of zeros in the product."
• The Lesson 2-3 Lesson Overview, Rigor states, “Conceptual Understanding. Students shade grids divided into hundredths to show how parts of the whole written in decimal form can be combined. They use shading to show part of a whole and crossing out to show the parts that are taken away." Students are provided opportunities to explain and use grids and place value blocks to model and regroup.
• In Lesson 11-1, students draw or construct models to find the number of cubes that make up a rectangular prism. Students do this work by determining the number of cubes in the bottom layer of a rectangular prism as they draw or get unit cubes to create the bottom layer of a prism using measurements of the length and width. They continue adding layers to the prism and find its height.

​The instructional materials for enVision Florida Mathematics Grade 5 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

Examples of the the instructional materials developing procedural skills and fluencies throughout the grade level include:

• Procedural skills and fluencies integrate with conceptual understanding and the work students completed with operations from prior grades. Opportunities to practice procedural skills are found throughout practice problem sets that follow the units and include opportunities to use fluencies in the context of solving problems.
• The Teacher Edition Program Overview articulates, “Steps to Fluency Success.” The six steps are: Step 1: Fluency Development with Understanding, Step 2: Ongoing Assessment of Fluency Subskills, Step 3: Fluency Intervention, Step 4: Practice on Fluency Subskills, Step 5: Fluency Maintenance, and Step 6: Summative Fluency Assessment. Fluency Expectations for Grades K-5 are also listed. The Teacher Edition Topic Overview explains the six steps and foundations for fluency. In each Topic Overview, Math Background: Rigor, there is a section explaining how the material builds Procedural Skill and Fluency. The Topic 3 Overview, Procedural Skill and Fluency identifies the procedural skill for understanding of multi-digit multiplication using the standard multiplication algorithm for whole numbers.
• Within each lesson, the Visual Learning Bridge integrates conceptual understanding with procedural skills. Additional Fluency and Practice pages are in the Teacher Edition and Ancillary Books as well as online with the Practice Buddy Additional Practice. The online component also contains a game center where students continue to develop procedural skills and fluencies. Each topic ends with Fluency Practice/Assessment Worksheets.

The instructional materials provide opportunities to demonstrate procedural skill and fluency independently throughout the grade level.

• In Lesson 3-1, students evaluate two-digit whole numbers multiplied by 10.
• In Lesson 3-3, students multiply multi-digit whole numbers using the standard algorithm.
• In Lesson 3-6, students multiply three-digit numbers by two-digit numbers using the standard algorithm.
• In Lesson 8-5, Problem 15, students multiply two fractions such as $$\frac{2}{3}$$ x $$\frac{7}{8}$$.

The instructional materials provide regular opportunities for students to attend to Standard 5.NBT.2.5, multiplying multi-digit whole numbers using the standard algorithm.

​​The instructional materials for enVision Florida Mathematics Grade 5 meet expectations for being designed so that teachers and students spend 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.

Work with applications of mathematics occurs throughout the materials. In each Topic Overview, Math Background: Rigor explains how the materials utilize applications. For example, the Topic 8 Overview, Math Background: Rigor, Application states, “Throughout Topic 8, there are real-world problems involving the computations being developed. In Lesson 8-9, students make sense and persevere in solving real-world problems involving multiplication of fractions and mixed numbers.”

Following the Topic Overview, the Topic Opener includes an enVision STEM Project where application activities are provided and can be revisited throughout the topic. In each topic, Pick A Project allows students to explore areas of interests and to complete projects that apply the mathematics of the topic. Every other topic contains 3-Act MATH where students engage in mathematical modeling.

At the end of each topic, the Performance Task provides opportunities for students to apply the content of the topic. Additional application tasks are in Additional Practice pages in the Teacher Edition, Ancillary Books, and online.

Examples of opportunities for students to engage in routine and non-routine application of mathematical skills independently and to  demonstrate the use of mathematics flexibly in a variety of contexts include:

• In the Lesson 7-12, Problem Solving Performance Task, students answer questions about camp activities where information is presented in a chart. "During the 6-hour session at day camp, Roland participated in boating, hiking, and lunch. The rest of the session was free time. How much time did Roland spend on the three activities? How much free time did he have?”
• In Lesson 8-7, Problem Solving, Question 23 states, “The city plans to extend the Wildflower Trailer 2$$\frac{1}{2}$$ times its current length in the next 5 years. How long will the Wildflower Trail be at the end of 5 years?” In this question, students solve real-world problems that involve multiplication of fractions and mixed numbers.
• In Lesson 9-5, page 404, Question 19 states, “Five friends equally share half of one large pizza and $$\frac{1}{4}$$ of another large pizza. What fraction of each pizza did each friend get? How do the two amounts compare to each other?”
• In Topic 9, Performance Task, Question 2 states, “Julie and Erin have 6$$\frac{1}{3}$$ yards of red checked cloth. After making dresses for 4 dolls, they use the remaining cloth to make bows for the dolls’ hair. They need 8 bows for 4 dolls. Part A How much cloth do Julie and Erin have for each bow? Explain. Part B. Julie wrote the equations below. What is the pattern in her equations? Explain how to use the pattern to find the quotient you found in Part A.”

​The instructional materials for enVision Florida Mathematics Grade 5 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. The instructional materials address specific aspects of rigor, and the materials integrate aspects of rigor.

Each lesson contains opportunities for students to build conceptual understanding, procedural skills, and fluency, and to apply their learning in real-world problems. 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 and use procedural skills and/or conceptual understanding to solve problems with multiple solutions and explain/compare their solutions.

All three aspects of rigor are present independently throughout the program materials.

• In Lessons 1-1 through 1-3, students develop conceptual understanding of place value by using place value charts and place value blocks when they transition from whole number place value to decimal place value to thousandths.
• In Lesson 8-9, students apply knowledge of multiplication of fractions and mixed numbers to solve real-world problems. Students solve problems where they determine the total cost of framing a painting given the dimensions of 10$$\frac{1}{4}$$ in. and 6$$\frac{1}{4}$$ in. and the framing cost $.040 per inch of framing. Students answer questions relating to the problem-solving steps: "What is the first step you need to do? What is the answer to the first step? Write an equation to show your work.”

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

• In Lesson 3-4, Question 16, students develop understanding of calculating partial products and practice procedural skills by multiplying and calculating each partial product. Students are given partial products in an array drawn on a grid, find the partial products, and calculate the final product. Students write the multiplication equation from the illustration to show the partial products.
• In Lessons 1-5 and 1-6, students apply their procedural skills to problems with various constraints and use their conceptual understanding of decimal order and place value to explain how their solutions represent the given situation. Students are shown models of number lines, inequality statements, and how to line up decimal points vertically, using these same models to determine how best to round numbers and to what value.
• In Lesson 3-4, students practice the procedural skill of multiplying two-digit by two-digit whole numbers using the standard algorithm while applying it in a real-world scenario. First, students solve a problem by multiplying two 2-digit numbers, using any strategy they choose in the Solve and Share section. In the Visual Learning Bridge section, students evaluate the standard algorithm of multiplying multi-digit whole numbers by answering questions such as, “A ferry carried 37 cars per trip on the weekend. If the ferry made 11 trips on Saturday and 13 on Sunday, how many cars did it carry on the weekend?”

The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade level.

Examples of the MPs being identified at the topic level include:

• In Topic 1 Overview, MP.1.1 is identified. “Students persevere as they try to understand problems involving place value, plan how to solve them, and determine if their solution makes sense.”
• In Lesson 8 Topic Overview, MP.7.1 is identified. “Students use quantitative reasoning as they interpret the remainders in a division problem.”

The MPs are used to enrich the mathematical content and are not treated separately. MPs are highlighted and discussed throughout the lesson narratives, and along with the lessons, the MPs are evident in the the 3-Act Math Tasks that are included in every other chapter. The MPs are listed in the student materials, and the Math Practice Handbook is available online for teachers to make available to students.

• In Lesson 4-1, MP.7.1 is identified. “Students analyze their answers in the chart to look for a pattern they can use when multiplying numbers by powers of 10.”
• In Lesson 9-2, Problem Solving, Problem 19, MP.6.1 is identified. "Tammi has 4 pounds of gala apples and 3$$\frac{1}{2}$$ pounds of red delicious apples. If she uses 1$$\frac{3}{4}$$ pounds of gala apples in a recipe, how many pounds of apples does she have left? Ask students to think about what the numbers in the problem mean and write an expression to represent the problem.”
• In Lesson 5-6, Problem Solving, Problem 15, MP.2.1 is identified. “A delivery to the flower shop is recorded at the right. The shop owner makes centerpiece arrangements using 36 flowers that are all the same type. Will they be able to make at least 10 arrangements using each type of flower? At least 100 arrangements? Explain. Encourage students to use estimation either before or after multiplying.”

The MPs are identified within a lesson in the Lesson Overview, and lesson narratives highlight when an MP is particularly important for a concept or when a task may exemplify the identified Practice. The lessons that end each Topic specifically focus on at least one MP. For example:

• In Lesson 6-6, MP.2.1 is identified. “Students extend their understanding of how to use reasoning and Thinking Habits as they solve a multi-step problem that includes dividing a decimal by a two-digit whole number.”
• In Lesson 2-6, MP.4.1 is identified. “Students will use bar diagrams to solve multi-step problems involving the addition and subtraction of decimals.”
• In Lesson 8-9, Elaborate, MP.1.1 is identified. “Listen and look for these behaviors as evidence that students are exhibiting proficiency with this practice: Chooses a strategy or strategies to use to solve problems, identifies the quantities in a problem, the data given, and if present, the question to be answered, thinks of similar problems or uses a simpler form of the problem, if needed, organizes data or uses representations to help make sense of the problem, identifies likely strategies for solving the problem, pauses when solving problems to make sure that the work being done makes sense, and makes sure the answer makes sense before stopping work."
• In Topic 7, 3-Act Math task, MP.4.1 Model with Mathematics is connected to additional MPs. “As students carry out mathematical modeling, they will also engage in sense-making (MP.1.1), abstract and quantitative reasoning (MP.2.1), and mathematical communication and argumentation (MP.3.1). In testing and validating their models, students look for patterns in the structure of their models." (MP.7.1, MP.8.1)

The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Student materials consistently prompt students to construct viable arguments and analyze the arguments of others. The Solve and Share Activities, Visual Learning Bridge Problems, Problem Sets, 3-Act Math, Problem Solving: Critique Reasoning problems, and Assessments provide opportunities throughout the year for students to construct viable arguments and analyze the arguments of others.

Examples of the instructional materials supporting students to analyze the arguments of others include:

• Lesson 2-4, Problem Solving: Critique Reasoning, Question 17: “Juan adds 3.8 + 4.6 and gets a sum of 84. Is his answer correct?”
• Topic 6, Topic Assessment, Question 20: “June says that there should be a decimal point in the quotient below after the 4. Is she correct? Use number sense to explain your answer. $$43.92\div5.2$$ = 845.”
• Lesson 11-4, Question 9: “Critique Reasoning: Does it make sense for Angelica to find the combined area of the bedroom floor and closet before finding the total volume?  Explain your thinking.” Students have to work through the previous problem in order to critique Angelica’s thinking.

Examples of the instructional materials prompting students to construct viable arguments include:

• Lesson 2-1, Question 14: “Construct Arguments: Use compensation to find each difference mentally. Explain how you found each difference. A. 67.9 - 29.9  B. 456 - 198.”
• Lesson 3-1, Question 21: “Without multiplying, tell which expression is greater, 93 x $$10^3$$ or 11 x $$10^4$$? How do you know?” Students use number sense to explain that a two-digit number multiplied by $$10^4$$ will be greater  than any two-digit number multiplied by $$10^3$$.
• In Lesson 3-5, students construct arguments by using estimation. “Is 300 x 10 a good estimate for the number of bagels sold at the bakery? Explain.”
• In Lesson 8-8, students construct a mathematical argument to compare pairs of factors to determine which is the greatest. “How is $$\frac{3}{3}$$ x 2 like 1 x 2?”
  

The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher materials assist teachers in engaging students in constructing viable arguments and/or analyzing the arguments of others throughout the program. Many of the activities are designed for students to work with partners or small groups where they collaborate and explain their reasoning to each other.

• In Lesson 1-5, Critique Reasoning (in the margin) provides the teacher with a question pertaining to a fictional student’s reasoning on a problem.
• In Lesson 1-7, “After Whole Class” provides teachers with opportunities to have students analyze the work of others: “Discuss Solution Strategies and Key Ideas: Based on your observations, choose which solutions to have students share and in what order. Focus on the strategies and structure they used to solve the problem. If needed, show and discuss the provided student work at the right.” There are also prompting questions to support teachers as they have the students analyze the provided student work.
• In Lesson 2-3, Critique Reasoning (in the margin), provides teachers with questions that pertain to how students can tell, without adding, that an answer does not make sense.
• In Lesson 4-8, Construct Arguments (in the margin), provides teachers with questions that pertain to students explaining if the product should be less than or greater than the decimal factors.
• In Lesson 11-1, “After Whole Class” provides teachers with opportunities to have students analyze the work of others: “Discuss Solution Strategies and Key Ideas: Based on your observations, choose which solutions to have students share and in what order. Focus on how students represented the prism and solved the problem. If needed, show and discuss the (provided student) work at the right.” There are also questions to support teachers as they have the students analyze the provided student work.
  

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 Grade 5 Glossary is located in the Teacher Edition Program Overview, and the Glossary is also present at the back of Volume 1 of the Student Edition.
• Lesson-specific vocabulary can be found at the beginning of each lesson, under the Lesson Overview, with words highlighted in yellow used within the lesson, and a vocabulary review is provided at the end of each topic.
• There is a bilingual animated glossary available online that uses motion and sound to build understanding of math vocabulary and an online vocabulary game in the game center.
• 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.
• The Teacher Edition Program Overview, “Building Mathematical Literacy,” outlines the many ways the materials address mathematics vocabulary, including: My Word Cards, Vocabulary Activities at the Beginning of Each Topic, Vocabulary Reteach to Build Understanding, Vocabulary and Writing in Lessons (where new words introduced in a lesson are highlighted in yellow in the Visual Learning Bridge and lesson practice includes questions to reinforce understanding of the vocabulary used), Vocabulary Review at the back of each topic, an Animated Glossary where students can hear the word and the definition, and Vocabulary Games Online. There is also Build Mathematical Literacy within each Topic Overview that outlines support for English Language Learners, Mathematics Vocabulary, and Math and Reading within the topic.
• In Topic Planner, there is a vocabulary column that lists the words addressed within each lesson in the topic. For example, Lesson 16-2 lists the following words: trapezoid, parallelogram, rectangle, rhombus, and square. These same words are listed in the Lesson Overview.
• In Lesson 7-2, students interpret equivalent fractions and common denominators. Students use the context to build proper mathematical vocabulary.
• Lesson 11-1 introduces volume, cubic unit, cube, rectangular prism, and unit cube to the students. The Visual Learning Bridge provides definitions and models/diagrams using this new vocabulary. In Guided Practice, students are provided questions within the context of the lesson to answer using vocabulary. For example, Question 2 states, “Vocabulary: What is the difference between a unit cube and a cubic unit?” A sample answer is provided to support teachers using precise vocabulary language and definitions with students.

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 either to connect prior learning or to 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 that accompany 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 Grade 5 meet expectations for not being haphazard; exercises are given in intentional sequences.

Overall, activities within lessons within the topics are intentionally sequenced, so 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 to build procedural skill and fluency. Students also engage with multiple activities that are sequenced from concrete to abstract and increase in complexity. Lessons close with Problem Solving, which typically has students apply learning from the lesson, and Assessment Practice, which is typically two questions aligned to the daily lesson objective.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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, and 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 that include models, drawings, and calculation.

In the materials, students use a digital platform (Visual Learning Animation Plus and Practice Buddy) 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 use various mathematical representations frequently in their work, even though the representation is often provided for students.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of virtual manipulatives and integrates hands-on activities that allow the use of physical manipulatives. For example:

• Manipulatives and other mathematical representations are aligned consistently to the expectations and concepts in the standards. The majority of manipulatives used are measurement and geometry tools that are commonly accessible. In Lesson 9-6, students use fraction strips and number lines when dividing whole numbers and unit fractions. In Lesson 11-2, students use cubes to derive a formula to find the volume of a rectangular prism. Animated versions of the task are also provided as an option.
• The materials have manipulatives embedded within the Visual Learning Bridge, Visual Learning Bridge Animation, and Independent Practice activities to represent ideas and build conceptual understanding. For example, in Lesson 3-1, students use place-value blocks to find the product of whole numbers and powers of 10 using patterns and mental math.

Examples of manipulatives for Grade 5 include:

• Counters, number lines, place-value blocks, bills and coins, pattern blocks, circle fraction models, decimal models, and fraction strips.
• Geometry toolkits containing tracing paper, colored pencils, scissors, index card, unit cube, centimeter ruler, inch ruler, yardstick, meter stick, and coordinate grids/paper.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations 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 that includes Lesson Overviews, 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 2-5 Solve & Share, the following questions are included: “In which place does 15.33 have a digit that 32.7 does not? What can you do to make the number of digits to the right of the decimal point match?” In Lesson 12-2 Visual Learning Bridge and Classroom Conversation, the following questions are included: “Why might you want to change from one unit of capacity to another? Will the number of fluid ounces be less than or greater than 8? How do you know?”

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations 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 givens an overview of every lesson, the Objective of the lesson, Essential Understanding, Vocabulary, Materials needed, Technology and Activity Centers, along with the CCSSM.
• The Topic Planner also includes Lesson Resources such as the Digital Student Edition, Additional Practice Workbook, Print material available, as well as what can be found in the Digital Lesson Courseware and Lesson Support for Teachers.
• Each lesson opens with a Lesson Overview including an Objective and an Essential Understanding, “I can” learning target statements written in student language, CCSSM that are either being “built upon” or “addressed” for the lesson, Cross-Cluster Connections, the 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. Guiding questions and additional supports for students are included within the lessons.
• 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, there are supporting questions and narratives for students.
• The materials are available in both print and digital forms. There are additional online resources that support the material. These opportunities are noted within the lessons. For example, each lesson has an Interactive Practice Buddy that is noted in Step 2 and Step 3, as well as Another Look Videos found in Step 3.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

The Teacher Edition explains how mathematical concepts are built from previous grade levels or topics and lessons as well as how the grade-level concepts fit into future grade-level work.

For example, Topic 7 Overview of Math Background: Coherence states that the work in this topic relates to factors/multiples, finding equivalent fractions,  decomposing mixed numbers, adding and subtracting fractions and mixed numbers with like denominators in Grade 4, solving problems using data from line plots and involving measurements later in Grade 5, and expressions and equations with fractions in Grade 6.

There is also an individual coherence section within each lesson with the sections Look Back, This Lesson, Look Ahead, and Cross-Cluster Connections (where applicable).

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels.

• In the Online Teacher Edition, Program Overview, Assessment Resources provides information about the use of assessments to gather information about student’s prior knowledge.
• Each grade level includes a Grade Level Readiness assessment that is to be given at the start of the year. This Readiness Test can be printed or distributed digitally. In this assessment, prerequisite skills from the prior grade necessary for understanding the grade-level mathematics are assessed.
• The Daily Review is designed to engage students in thinking about the upcoming lesson and/or to revisit previous grades' concepts or skills.
• Prior knowledge is gathered about students through Review What You Know assessments found in the Topic Opener. Each assessment has an Item Analysis for Diagnosis and Intervention. In these assessments, prerequisite skills necessary for understanding the topics in the unit are assessed and aligned to standards so the teacher can re-teach if needed.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

Lessons include Error Intervention that identifies where students may make a mistake or have misconceptions. There are questions for the teacher to ask along with what to assign for reteaching the concept or skill. For example, in Lesson 11-1, the Error Intervention gives the following guidance: “If students struggle to make a model, then demonstrate how to make the first layer. To work on the bottom layer, make three rows with three cubes each. This layer is three cubes long by three cubes wide. Have students work on the second layer.”

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet 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 & Share, Visual Learning Bridge, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice, provides 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 students to engage with the content and receive timely feedback. Discussion prompts in the Teacher Edition 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” that includes a Vocabulary review and Practice problems. This section includes review and practice on concepts that are related to the new Topic.

The Cumulative/Benchmark Assessments found at the end of Topics 4, 8, 12 and 16 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 reviewed for enVision Florida Mathematics Grade 5 meet 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 there is a Practice Assessment, an End-Unit Assessment, and a Performance task. Assessments in the Teacher Edition provide a scoring guide and standards alignment for each question.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 and Share Activity that reviews prior knowledge and/or prepares all students for the activities that follow.

In lessons, there are the following explicit instructional supports 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 a 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) that can be used for additional practice or support before moving on to the next activity or lesson.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The lesson structure of Step 1 (Problem-Based Learning), Step 2 (Visual Learning), and Step 3 (Assess and Differentiate) includes guidance for the teacher on the mathematics of the lesson, possible misconceptions, and specific strategies to address the needs of a range of learners. Embedded supports include:

• The Additional Practice Materials include a lesson for each topic that includes 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.
• There are Response to Intervention strategies in each lesson. These sections give teachers “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 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 Grade 5 meet expectations for embedding tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Solve & Share, Visual Learning Bridge, Guided and Independent Practice, 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 1-4 Solve & Share, students use place value to show how time is written as a decimal. Students may represent this scenario any way they choose allowing for all students to participate in the task while also focusing instruction on the mathematical concept of place value.
• In Lesson 2-5 Convince Me!, students discuss different strategies for subtracting decimals. Students can represent this in different ways, by using a standard algorithm, number lines, estimation, or using place value knowledge. The teacher is encouraged to look for multiple strategies as students use precision.
• In Lesson 4-1, students solve a story problem where they can apply their knowledge of multiplying decimals by powers of 10. The teacher is encouraged to look for multiple solution paths, and examples of different solution paths or student explanations for counting methods are provided to help the teacher anticipate student solution strategies.
• In Lesson 4-5, Question 17, students use multiplication equations to represent decimal models. Multiple strategies can be provided as this question is considered a quick-check question for prescribing differentiation.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 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 ELL Design is highlighted in the Teacher Edition Program Overview and describes support based on the student’s level of language proficiency: emerging, expanding, or bridging, as identified in the WIDA (World-Class Instructional Design and Assessment) assessment. An ELL Toolkit provides additional support for English Language Learners.

Two ELL suggestions are provided for every lesson, one in Solve and Share and another in Visual Learning Bridge. Also, Visual Learning support is embedded in every lesson to support ELL learners. Examples include:

• In Lesson 2-1 includes English Language Learners' Tips for Emerging: "Read the problem to students. Ask students to identify the cost of the three pieces of software. Ask which operation is needed to find the total cost of the software;” Expanding: “Reread the problem with students. Ask students which words indicate which operation is use to find the total cost of the software;” and Bridging: “Ask students to reread the problem with a partner. Have them find the total cost and explain their method.”
• In each topic opener, there is information provided to include specific ELL supports as needed. For example, in Topic 6, the materials provide ELL support using Visual Learning through the program, ELL instruction in lessons, a Multilingual Handbook, and an ELL Toolkit.
• Visual learning infused throughout the program provides support for English Language Learners. This includes 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.
• The Multilingual Handbook is included with a Mathematics Glossary in multiple languages.
• An English Language Learners Toolkit is a resource that provides professional development and resources for supporting English Language Learners.
• For Visual Learning in Lesson Practice, Pictures With a Purpose appear in Lesson Practice to provide information that is related to math concepts or real world problems to support student understanding.

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

• Resources and a key 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 analyzing Usage Data.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. All students complete the same lessons and activities; however, there are some optional lessons and activities that a teacher may choose to implement with students.

Opportunities to engage in the content at a greater depth include:

• Extensions found at the end of every Solve and 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.
• Differentiation after a Group of Topics based on the online cumulative benchmark assessments where students can then receive enrichment.

It should be noted that there is no guidance for teachers on engaging advanced students in these activities.

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet 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 Grade 5 materials include a set number of names used throughout the problems and examples (e.g., Jessie, Salvatore, Clara, Liza, Delbert, Ramon, Li, Yolanda, Hakeem, Jerome, Chico, June). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity.
• Characters are often presented in pairs with different solution strategies. There is not a pattern in one character using more/less sophisticated strategies.
• When multiple characters are involved in a scenario they are often doing similar tasks or jobs in ways that do not express gender, race, or ethnic bias. For example, in Lesson 5-4, Question 20 states, “Model with Math: Peter is driving 992 miles from Chicago to Dallas. His sister Anna is driving 1,068 miles from Phoenix to Dallas. Write and solve an equation to find how much farther Anna drives than Peter drives.” There is no differentiation of what roles the characters take that suggests a gender, racial, or ethnic bias.