## Alignment: Overall Summary

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for alignment to the Mathematics Florida Standards (MAFS). ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards.  The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor and meaningfully connecting the Standards for Mathematical Content and the Cluster Standards for Mathematical Practice (MPs).

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## Gateway 1:

### Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
22
31
38
36
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

### Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

### Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. In instances where there are inconsistencies, the material could easily be omitted or modified by the teacher. Probability, statistical distributions, similarities, transformations, and congruence do not appear in the assessments.

The series is divided into topics, and each topic has a topic assessment that can be administered online and/or in paper and pencil formats. There is a Topic Performance Task for each topic. Additional assessments include a readiness assessment found in Topic 1, four cumulative/benchmark assessments, and a cumulative end of year assessment. Assessments can be found in the Assessment Resource book or an online version is available. The materials also include an ExamView Test Generator that is able to be used.

Examples of assessments that contain grade-level content questions include the following:

• Topic 1 Assessment, Question 9 states, “Eddy’s plum weighs 3.042 ounces. Desta’s plum weighs 3.24 ounces. Whose plum weighs more? How can you tell?” (5.NBT.1.3.b)
• In the Assessment Sourcebook, Topic Assessment 2, Question 3, students find the sum of 5.92 + 3.48. Students are given a choice of four numbers, and each of the distractors represents a misconception students may have about decimals and place value. (5.NBT.2.7)
• Topics 1-4, Cumulative/Benchmark Assessment, Question 1 states, “When multiplying a number by $$10^5$$, how is the decimal point moved?” (5.NBT.1.2)
• Topic 4 Assessment, Question 16 states, “A forest preserve has an area of 1.6 square miles, and 0.3 of the forest preserve is open for hiking. Part A Shade the grid to model the multiplication. Part B How many square miles are open for hiking? Use an equation and the model to explain.” (5.NBT.2.7)
• In the Topic 7 Performance Task, students add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. (5.NF.1.1)
• Topic 8 Assessment, Question 9 states, “Complete the equation. Explain how you got your answer. $$\frac{4}{5}$$ x $$\frac{3}{7}$$ =?” (5.NF.2.4.a)
• In Topic 9 Assessment, Question 14, students are given four equations, two whole numbers divided by a unit fraction, and two whole numbers multiplied. Students write numbers in the boxes to make the equations true and then make generalizations about the equations. (5.NF.2.7.b)

### Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

### Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 12 out of 16, which is approximately 75 percent.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 87.5 out of 108, which is approximately 81 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 123 out of 148, which is approximately 83 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 81 percent of the instructional materials focus on major work of the grade.

### Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
8/8
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Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

### Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards are used to support major work of the grade and often appear in lessons with connections to the major work of the grade.

Throughout the series, supporting standards/clusters are connected to the major standards/clusters of the grade. The following are examples of the connections between supporting work and major work in the materials:

• In Lesson 10-2, students make line plots (cluster 5.MD.2.2) using the understanding of ordering fractions and decimals. (cluster 5.NF.1.2)
• In Lesson 10-3, students solve problems based on data from line plots (5.MD.2.2) using understanding of operations with fractions to solve problems. (5.NF.1.2)
• In Lesson 12-1, students convert customary units of length (5.MD.1.1) to solve problems involving multiplication and division. (5.NBT.2.5 and 5.NBT.2.6)
• In Lesson 12-5, students convert metric units of capacity (5.MD.1.1) to find patterns in multiplying and dividing a number by powers of 10. (5.NBT.1.2)
• In Lesson 12-8, students solve word problems using measurement conversions (5.MD.1.1) to solve problems involving multiplication and division of fractions. (5.NBT.2.5)

### Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades.

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 148 days.

• There are 108 content-focused lessons designed for 45 to 75 minutes including differentiation.
• There are eight 3-Act Mathematics Modeling Lessons, which are one day each.
• There is a Topic Review and Assessment for each of the 16 Topics, two days per Topic (32 days).

There are also additional resources containing more lessons to be used after the last Topic, including Math Diagnosis and Intervention System, Florida Standards Practice, and 10 Step-Up Lessons.

### Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
2/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet the expectation for being consistent with the progressions in the CCSSM. Content from prior grades is identified or connected to grade-level work, and students are given extensive work with grade-level problems.

Overall, the materials develop according to the grade-by-grade progressions in the standards. Typically, material related to prior and future grades is clearly identified or related to grade-level work. In the Teacher’s Edition Program Overview, all grade-level standards are present as noted in the section, "Correlation to Florida Grade 5 Standards."

The Teacher’s Edition contains a Topic Overview Coherence: Look Back, and a Lesson Overview Coherence: Look Back, which identify connections to content taught earlier in the grade and/or in previous grades, indicating the relevant topics and/or lessons. In the Topic Overview Coherence: Look Ahead includes connections to content taught later in the grade and/or in future grades, topics, or lessons. Though explicit connections are made to prior and future work, standards are not listed in either the "Look Back” or "Look Ahead,” and the connections are written as general statements from the standards.

For example, the Teacher’s Edition, Topic 4 Overview, Math Background: Coherence includes:

• Look Back: Grade 4 Topic 3, “Students used strategies and properties to multiply 1-digit numbers by numbers with up to 4 digits. In Topic 4, they did the same to multiply 2-digit whole numbers. Some of the whole-number strategies, such as partial products, are applied to decimals in Grade 5, Topic 4. Early in Grade 5, Lesson 3-1, students explored patterns in multiplying whole numbers by powers of 10.”
• In Topic 4 includes: "Students are multiplying decimals by powers of 10 in Lesson 4-1 and estimate products of whole numbers and decimals.
• Look Ahead: “Later in Grade 5, students will use what they learn about multiplying with decimals when they divide with decimals in Topic 6.”

The instructional materials give extensive work with grade-level problems. All Topics begin with an optional, on grade-level project, and every other Topic incorporates on grade-level 3-Act Mathematical Modeling tasks. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. The Guided Practice allows students to solve problems and check for understanding before moving on to Independent Practice. The Independent Practice provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section provides additional practice problems for each of the lessons, such as in the Student Edition, Lesson 12-3, "4 oz = ___lb.” (5.MD.1.1)

There is support in the Quick Checks for each lesson to assign additional problems to students, including, Intervention Activity, Reteach to Build Understanding, Build Mathematical Literacy, Enrichment, Activity Centers, or Additional Practice (with leveled-assignment choices provided).

### Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

​The instructional materials for enVision Florida Mathematics Grade 5 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Examples of learning objectives that are visibly shaped by CCSSM cluster headings include:

• In Lesson 5-5, the lesson objective states, “Use place value and sharing to divide by 2-digit divisors,” which is shaped by cluster 5.NBT.2, “Perform operations with multi-digit whole numbers and with decimals to the hundreths.”
• In Lesson 7-3, the lesson objective states, “Add fractions with unlike denominators using equivalent fractions with a common denominator,” which is shaped by cluster 5.NF.1, “Use equivalent fractions as a strategy to add and subtract fractions.”
• In Lesson 11-1, the lesson objective states, “Find the volume of solid figures” which is shaped by 5.MD.3, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.”

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

• Topic 3, 3-Act Math, 5.NBT.1 connects to 5.NBT.2 when students use place-value understanding to perform operations with multi-digit numbers, including those with decimals.
• Lesson 4-5, 5.NBT.1 connects to 5.NBT.2 when students use place value understanding and models to multiply a decimal.
• Lesson 15-3, 5.G.1 connects to 5.OA.2 when students analyze and graph relationships using numerical patterns.

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

​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.

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

​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.

### Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

​​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.”

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

​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?”

### Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and used to enrich mathematics content, and the instructional materials support the standards’ emphasis on mathematical reasoning.

### Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

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)

### Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 partially meet expectations for carefully attending to the full meaning of each practice standard.

The materials do not attend to the full meaning of MP.4.1 and MP.5.1. The MPs are discussed in both the topic and lesson narratives, as appropriate, when they relate to the overall work.

Examples of the materials attending to the full meaning of MPs include:

• MP.1.1: In Topic 1, 3-Act Math students make sense of the problem. Students watch a short video about 4 kids pressing buzzers at virtually the same time after 3 seconds. After the video students have a brief discussion about what they noticed about the video. Then the teacher poses the question, 'Who hit the button closest to 3 seconds?' Students have to make sense of the information they are given in order to solve the problem and then persevere in order to find the answer
• MP.2.1: In Lesson 6-6, Convince Me! states, “Reasoning: Ms. Watson is mixing 34.6 fluid ounces of red paint and 18.2 fluid ounces of yellow paint to make orange paint. How many 12-fluid ounce jars can she fill? Use reasoning to decide.” The relationships between quantities are similar to the problem prior to this one, so the bar diagrams are similar too. The connection presents the opportunity for students to reason both abstractly and quantitatively.
• MP.6.1: In Lesson 12-8, students attend to precision by considering symbols and units as they calculate conversions. Students are provided a visual of a city pool shaped into a rectangle with dimensions in yards and feet. Students are asked to find the perimeter. “If the width of the pool is increased by 3 feet, what would be a new perimeter of the pool?”
• MP.7.1: In Lesson 1-2, students use the structure of the place value system to determine the relationship between digits in multi-digit whole numbers. The text states, “The population of a city is 1,880,000. What is the value of each of the two 8’s in this number? How are the two values related?” Students use structure by utilizing the place value chart provided to analyze the relationship between the digits of a number.
• MP.8.1: In Lesson 4-4, students complete two different problems involving multiplying a whole number by a decimal. ”Place the decimal point correctly in each answer. Explain your thinking.” Students express regularity in repeated reasoning to explain the placement of the decimal points in the products.

Examples of the materials not attending to the full meaning of MP.4.1 and MP.5.1 include:

• MP.4.1: In Lesson 5-4, students find the number of rows of seats when the total number of seats and number in each row is given. “Model with Math: Why can you use division to solve this problem?” The task tells students which operation is used to model the mathematics.
• MP.5.1: Lesson 9-4, Question 15, “Use Appropriate Tools Strategically: Students will use tools such as area models and number lines to divide a whole number by a unit fraction.” The question states, “Dan has 4 cartons of juice. He pours ⅛ carton for each person on a camping trip. How many people can he serve? Draw a picture to help you answer the question.” There are 4 rectangles drawn to the side of the problem, which chooses the tool for the students.

### Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

### Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

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?”

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

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.

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

​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.

## Usability

### Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

### Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
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Indicator Rating Details

​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.

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

​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.

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

​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.

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

​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.

### Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Narrative Evidence Only
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Indicator Rating Details

​The visual design in enVision Florida Mathematics Grade 5 is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

• The printed and digital lesson materials for teachers follow a consistent format for each lesson. Lessons include sidebar links so teachers can find specific parts of the lesson in the digital format. The materials provide labels for specific parts of the lesson. Text boxes with Supports for English Language Learners are placed within the activity they support and are specific to the activity. Topic overviews follow a consistent format. The format of course overviews, topic, and individual lessons are also consistent across the Grade 5 materials.
• Student print and digital materials also follow a consistent format. Tasks within a lesson are numbered to match the teacher guidance. The print and visuals on the materials are clear without any distracting visuals.
• Student practice problem pages generally include enough space for students to write their answers and demonstrate their thinking. Each lesson and topic has a consistent layout for the teacher and student.

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, 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, a teacher edition that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

### Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

​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?”

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

​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.

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) 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.
1/2
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Indicator Rating Details

​The instructional materials for enVision Florida Mathematics Grade 5 partially meet expectations that materials contain adult-level explanations so that teachers can improve their own knowledge.

The Teacher Edition Program Overview includes resources to help teachers understand the mathematical content within each Topic and Lesson. The program Overview includes the overarching philosophy of the program, a user’s guide, and a content guide. Each Topic has a Professional Development Video that presents full adult-level explanations of the mathematics concepts in the lessons. The Professional Development Video includes examples that are clearly explained. There is also a Math Background for each Topic and Lesson that identifies the connections between previous grade, grade level, and future-grade mathematics. However, these do not support teachers to understand the underlying mathematical progressions.

The Assessment Source Book, Teacher Edition, and Mathematical Practices and Problem Solving Handbooks provide answers and sample answers to problems and exercises presented to students; however, there are no adult-level explanations to build understanding of the mathematics in the tasks.

### Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
2/2
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Indicator Rating Details

​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).

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 provide a list of concepts in the teacher edition that cross-references the standards addressed and provides an estimated instructional time for each unit and lesson.

• The Teacher Edition Program Overview provides a visual showing the number of lessons per topic by domains.
• The Teacher Edition Program Overview provides a Pacing Guide showing how many total days by topic the material will take, as well as support on what might take additional time which states, “Each Core lesson, including differentiation, takes 45-75 minutes. The pacing guide above allows for additional time to be spent on the following resources during topics and/or at the end of the year (resources are then listed).”

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Family Materials for each topic include a Home-School Connection letter to family and caregivers on what their student will be learning over the course of the topic. The Family Materials provide an overview of what the student will be learning in accessible language. For example, in Topic 1, the Home-School Connection letter states, "Dear Family, In this topic, your student will be learning how to interpret a fraction as division of the numerator by the denominator and show quotients as fractions and mixed numbers. He or she will solve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions. A fraction with a numerator of 1 is a unit fraction. Here is an activity you can use to acquaint your student with the concept of fractions as division.” In addition to the explanation of the current concepts and big ideas from the unit, there are diagrams and problems/tasks for families to discuss and solve.

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 contain explanations of the program's instructional approaches and the identification of research-based strategies.

The materials draw on research to explain and contextualize instructional routines and lesson activities. The Teacher Edition Program Overview contains specifics about the instructional approach. For example:

• Program Goals includes two sections: Section 1: Efficacy Research and Section, and Section 2: Research Principles for Teaching with Understanding. The Efficacy Research sections states, "First, the development of enVision Florida Mathematics started with a curriculum that research has shown to be highly effective.” The Research Principles for Teaching with Understanding states, “The second reason we can promise success is that the enVision Florida Mathematics fully embraces time-proven research principles for teaching mathematics with understanding. One understands an idea in mathematics when one can connect that idea to previously-learned ideas (Hiebert et al., 1997). So, understanding is based on making connections, and enVision Florida Mathematics was developed on this principle.”
• On page 25, the organization and reasoning for the structure is articulated. It states, “Our goal was to build a curriculum that achieves focus and coherence in a way that is best for developing deep understanding of the mathematical content.” More information is provided on the reasoning why the structure was chosen as well.

In the Teacher Edition Program Overview, all of the Instructional Routines are fully explained.

• The first two steps are stated with an explanation statement and further narratives to provide a deeper understanding. The Step 1 Problem-Based Learning statement says, “Introduce concepts and procedures with a problem-solving experience (with more information to follow).” The Step 2 Visual Learning statement says, “Make the important mathematics explicit with enhanced direct instruction connected to Step 1 (with more information to follow).”
• Program components are sorted by their purpose: Develop, Assess, Differentiate, Review, and Other.
• Support for how to use a lesson and each instructional routine within each lesson is provided. Tips are provided for teachers in addition to the descriptions. The 5Es of instruction are showcased. For example, “Solve & Share begins the lesson by engaging students with a problem in which new math ideas are embedded.”
• The Problem Solving lessons are outlined "Throughout enVision Florida Mathematics, the eight math practices are infused in lessons. Each Problem Solving lesson gives special focus to one of the eight math practices. Features of these lessons include the following: Solve and Share, Visual Learning Bridge, Convince Me!, Guided Practice, Independent Practice, Performance Task, and Additional Practice.” All of these have additional descriptions for each to explain the instructional routine further.
• Pick a Project part is explained.
• The 3-Act Math tasks are outlined.

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
9/10
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills, and assessments that clearly denote which standards are being emphasized.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
2/2
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Indicator Rating Details

​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.

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
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Indicator Rating Details

​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.”

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
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Indicator Rating Details

​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.

### Indicator 3p

Materials offer ongoing formative and summative assessments:

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

​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.

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 partially meet expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

• There are “scoring guidelines” to assist the teacher in interpreting student performance; however, these are provided in an answer key or in sample student answers.
• There is no rubric to interpret student-written responses.
• Topic Readiness and End of Topic Assessments have Item Analysis for Diagnosis and Intervention, which include standards being assessed and depth of knowledge levels.
• Assessments can be taken online where they are automatically scored, and students are assigned appropriate practice/enrichment/remediation based on their results.
• Teachers interpret the results on their own and determine materials for follow-up when students take print assessments.
• Teachers are prompted to complete observations and portfolios (page xi).

### Indicator 3q

Materials encourage students to monitor their own progress.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials for enVision Florida Mathematics Grades 5 do not include opportunities for students to monitor their own progress. There are no specific materials for students that will encourage them to monitor their own progress.

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
12/12
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

​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.

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
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Indicator Rating Details

​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).

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

​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.

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
2/2
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Indicator Rating Details

​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.

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
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Indicator Rating Details

​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.

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

​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.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 provide opportunities for teachers to use a variety of grouping strategies. The materials include teacher-led instruction that present limited options for whole-group, small-group, partner, and/or individual work. When suggestions are made for students to work in small groups, there are no specific roles suggested for group members, but teachers are given suggestions and questions to ask to move learning forward. Teachers are directed to “support productive struggle, observe, and if needed, ask guiding questions that elicit thinking. How can you use counters to show the prizes with 6 in each row?”

The Visual Learning Bridge Animation Plus focuses on independent work while the Pick a Project and in 3-Act Math sections have opportunities to work together in small groups or partners.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 encourage teachers to draw upon home language and culture to facilitate learning.

The Teacher Edition Program Overview includes Supporting English Language Learners, which contains ELL Instruction and Visual Learning. The Teacher Edition Program Overview states: “Levels of English language proficiency are indicated, and they align with the following level identified in WIDA (World-Class Instructional Design and Assessment): Entering, Emerging, Developing, Expanding, and Bridging.”

English Language Learners' support for each lesson is provided for the teacher throughout lessons to provide scaffolding for reading, as well as differentiated support based on student language proficiency levels (emerging, expanding, or bridging). The Home-School Connection letters for each Topic are available in both English and Spanish. There is also an English Language Learners Toolkit available that consists of many Professional Development Articles and Graphic Organizers. A few of the examples of the Professional Development Articles that can help teachers support ELL learners include: English Language Learners in the Math Classroom, Strategies for Teaching English Language Learners, Welcoming Newcomers to the Mainstream Classroom, Multilingual Thinking Words, and Teaching Math to Culturally and Linguistically Diverse Students.

### Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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Criterion Rating Details

​​The instructional materials reviewed for enVision Florida Mathematics Grade 5: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; can be easily customized for individual learners; and include or reference technology that provides opportunities for teachers and/or students to collaborate with each other.

### Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 are print and web-based (print resources are available online as Interactive Student Edition Pages, Teacher Edition eText Pages, or PDF files at PearsonRealize.com) and compatible with multiple internet browsers.

• The materials are platform-neutral (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, Safari, etc.)
• Materials are compatible with various devices including iPads, laptops, Chromebooks, and other devices that connect to the internet with an applicable browser.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Narrative Evidence Only
+
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

• enVision Florida Mathematics provides online assessments and data at PearsonRealize.com. The online assessments are in ExamView. Teachers can assign and score material and analyze assessment data through dashboards.
• There are online fluency games and games using procedural skills to solve problems.
• Virtual Nerd offers tutorials on procedural skills, but there are no assessments or opportunities to practice the procedural skills with the tutorials.
• The Skill and Remediation activities in the Topic Readiness online assessment tab include tutorials and opportunities for students to practice procedural skills using technology. There is a Remediation button to see online activities.

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Narrative Evidence Only
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Indicator Rating Details

​i. The instructional materials reviewed for enVision Florida Mathematics Grade 5 include opportunities for teachers to personalize learning for all students. Teachers can select and assign individual practice items for student remediation based on the Topic Readiness assessment. Teachers can create and assign classes online for students through the Accessible Student Edition. Closed Captioning is included in STEM and 3-Act Math videos.

ii. The instructional materials reviewed for enVision Florida Mathematics Grade 5 can be easily customized for local use. There are digital materials that provide the same lessons to draw from on a topic as the print materials. Teachers can create and upload files, attach links, and attach documents from Google Drive that can be assigned to students. Teachers can also create assessments using a bank of items or using self-written questions that can also be assigned to students.

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 incorporate technology that provides opportunities for teachers and/or students to collaborate with each other. There is “Discuss” for assigning discussion prompts or "Classes" to attach files for students.

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
Narrative Evidence Only
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Indicator Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 5 integrate technology including interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the MPs.

Teachers and students have access to tools and virtual manipulatives within a given activity or task, when appropriate. Pearson Realize provides additional components online such as games, practice, instructional videos, links to other websites, differentiation, etc. In the print Teacher Edition, there are statements in each lesson that there are more resources available online. However, the resources are not detailed, and teachers using print materials may miss them. For example, In Step 3, Assess and Differentiate, many lessons include opportunities to use the Math Tools found in the Technology Center. These embedded opportunities allow students to become more familiar with the tools available to them, so they can begin making strategic decisions about which tools to use. (MP.5.1)

There are several parts of the program that support students attending to precision.

• The Animated Glossary embedded in the program helps students internalize what the key concepts mean and, when applicable, visual models are provided.
• The Problem-Based Learning activity provides repeated opportunities to students to use precise language to explain their solutions.
• In Convince Me!, students revisit key terms or concepts and provide explicit explanations. (MP.6.1)
abc123

Report Published Date: 2019/01/15

Report Edition: 2020

Title ISBN Edition Publisher Year
Teacher Edition - Grade 5, Volume 1 9780134910598 Pearson 2020
Teacher Edition - Grade 5, Volume 2 9780134910659 Pearson 2020
Student Edition - Grade 5, Volume 1 9780134910727 Pearson 2020
Student Edition - Grade 5, Volume 2 9780134910796 Pearson 2020
Teacher Resource Master - Grade 5, Volume 1 9780134910864 Pearson 2020
Teacher Resource Master - Grade 5, Volume 2 9780134910925 Pearson 2020
Assessment Sourcebook - Grade 5 9780134910994 Pearson 2020
Teacher Edition Program Overview, Grade 5 9780134922317 Pearson 2020

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.