## enVision Florida Mathematics

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Our Review Process

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### Overall Summary

The instructional materials reviewed for enVision Florida Mathematics Grade 3 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).

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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.

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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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. In instances where there are above grade-level questions, 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 available online and/or in paper and pencil format. The series also includes a Topic Performance Task for each Topic. Additional assessments include a Grade 3 Readiness Test and four Cumulative/Benchmark Assessments that address Topics 1-4, 1-8, 1-12, and 1-16. Assessments can be found in the Assessment Resource Book in print or online. The materials also include an ExamView Test Generator.

Assessments contain grade-level content questions. Examples of questions include the following:

• Topic 3, Topic Assessment, Question 4 states, “Jamal broke up a large array into a 3x6 array and a 4x6 array. What was the large array?” (3.OA.2.5)
• In Topic 4, Topic Assessment, Question 7, students match each expression on the left with the equivalent expression. (3.OA.3.7) Expressions on the left include $$0\div8$$, $$36\div6$$, $$4\div4$$, $$35\div5$$. Expressions on the right include: $$8\div8$$, 6 x 0, 7 x 1, 1 x 6.
• Topics 1-8, Cumulative Assessment, Question 12 states, “Louise made the shape from tiles. What is the area of the shape. Explain.” The shape has 4 whole squares and 6 diagonal halves of squares around the outside. (3.MD.3.6)
• In the Topic 12, Performance Task students represent fractions on a number line (3.NF.2) and partition whole numbers into equal parts using a number line.
• In Topic 13, Topic Assessment, Problem 8, students compare equivalent fractions by filling them in on a double number line and has the number line missing $$\frac{1}{4}$$, $$\frac{2}{4}$$, and $$\frac{3}{4}$$, and its equivalent $$\frac{2}{8}$$, $$\frac{4}{8}$$, and $$\frac{6}{8}$$. (3.NF.1.3)

Questions that are above grade level could be omitted or modified. The following questions align to 4.NBT.2.6 as they include a remainder in the solution:

• In Topic 2, Performance Task, Question 6 states, “Carlos reads 10 pages every day. The book he is reading has 46 pages. How many days will it take him to finish his book? Complete the chart and explain your answer.”
• In Topic 4, Assessment, Question 10A states, “Jerome divided his baseball card collection into 2 equal groups. There was 1 baseball card left over. Describe the number of baseball cards Jerome has.”
• In Topics 1-4, Cumulative/Benchmark Assessment, Question 13, students answer a question that involves leftovers/remainders.

#### Criterion 1.2: Coherence

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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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.

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Instructional material spends the majority of class time on the major cluster of each grade.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 86 out of 104, which is approximately 83 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 115 out of 144, which is approximately 80 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 83 percent of the instructional materials focus on major work of the grade.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for enVision Florida Mathematics Grade 3 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.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 Lessons 7-1 through 7-4, students interpret data in scaled picture graphs and bar graphs (cluster 3.MD.2.3) and connect it to solving problems with equal groups, multiplication and division, and solving one- and two-step word problems involving multiplication and division. (clusters 3.OA.1.3 and 3.OA.4.8)
• In Lesson 10-2, students use place-value understanding and properties of operations (3.NBT.1.3) with the properties of multiplication. (3.OA.1.3)
• In Lesson 15-1, students describe quadrilaterals using the understanding of a fraction as the quantity formed when a whole is partitioned into equal parts. This connects the supporting work of (3.G.1.1) to the major work of (3.NF.1.1).
• In Lesson 15-4, students work with attributes of shapes (3.G.1.1) to answer problems about the area of shapes. (3.MD.3.7.b)
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The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 144 days.

• There are 104 content-focused lessons designed for 45 to 75 minutes including differentiation.
• There are eight 3-Act Math Lessons, 1 day each .
• There is a Topic Review and Assessment for each of the 16 Topics, 2 days per Topic.

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' | indicatorName}}
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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 meet the expectation for being consistent with the progressions in the standards. Content from prior grades is identified and 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 Edition Program Overview, all grade-level standards are present as noted in the section, "Correlation to Florida Grade 3 Standards."

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

For example, the Teacher Edition, Topic 5 Overview, Math Background: Coherence includes:

• Look Back: Grade 2: "In Topic 2, students began to work in equal groups of objects arranged in arrays. They learned to find the total number of objects by writing equations using rows or columns.” Earlier in Grade 3: "Understand Multiplication and Division Situations" and "Multiplication Facts" reference content from Topics 1 and 2 respectively.
• Topic 5 describes how the content is connected within the topic, including "Multiplication Tables," Use of  Strategies," and "Connecting Stories and Equations."
• Look Ahead: Later in Grade 3, "Fact Fluency" (Throughout the grade) and "Apply Multiplication and Division Facts" (Topic 6). In Grade 4, this topic is connected to "Whole Number Multiplication and Division" (Topics 3, 4, and 7) and "Extend Multiplication Concepts" (Topic 10).

The instructional materials give extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling task. 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. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to Independent Practice. During Independent Practice students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example, in the Student Edition, Lesson 16-3, “These plane figures each have equal sides that are whole numbers. One figure has a perimeter of 25 inches. Which could it be? Explain.” (3.MD.4.8)

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).

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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.

​The instructional materials for enVision Florida Mathematics Grade 3 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 1-4, the lesson objective states, “Use sharing to separate equal groups and to think about division,” which is shaped by 3.OA.1, “Represent and solve problems involving multiplication and division.”
• In Lesson 13-2, the lesson objective states, “Represent equivalent fractions on the number line,” which is shaped by 3.NF.1, “Develop understanding of fractions as numbers.”
• In Lesson 14-2, the lesson objective states, “Tell and write time to the nearest minute and measure time intervals in minutes,” which is shaped by 3.MD.1, “Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.”

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.

• In Lesson 2-1, 3.OA.1 connects to 3.OA.4 when students represent and solve problems involving multiplication and division while solving problems involving the four operations that include identifying and explaining patterns in arithmetic.
• In Lesson 14-5, 3.MD.1 connects to cluster 3.NF.1 when students connect solving problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects to developing an understanding of fractions as numbers.
• In Lesson 6-4, page 221A, 3.MD.3 connects to 3.OA.1 when students write an area equation for a rectangle with an unknown dimension.
• In Lesson 11-2, page 413A, 3.OA.4 connects to 3.OA.3 when students solve two-step word problems to develop fluency in multiplication and division facts.

### Rigor & Mathematical Practices

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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.

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

​The instructional materials for enVision Florida Mathematics Grade 3 meet expectations for developing 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 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.

• In Lesson 12-1, the Visual Learning Animation Plus states, “How Can You Name the Equal Parts of a Whole?” The scenario begins by having students divide sections of green wholes into four equal parts. The visual shows correct ways, as students fold their paper, along with incorrect ways, and the animation discusses ¼ as a unit fraction that represents one of the equal parts.
• The Topic 1 Overview, Conceptual Understanding states, “Throughout Topic 1, students build their conceptual understanding of how multiplication and division relate to equal-group situations. They come to understand that equal-group situations can be represented using multiplication or division depending on what information is known and what is unknown. Bar diagrams help students understand and explain how the numbers are related.” In Lesson 1-3, students use counters to build groups and evaluate multiplication problems. Students draw arrays to show equal groups.
• The Topic 6 Overview, Conceptual Understanding states, “Understand area as covering with unit squares.” In Lessons 6-1, 6-2, and 6-3, students count unit squares, both nonstandard and standard, to find the area of figures. This explicit focus on area as covering with unit squares helps students develop conceptual understanding of area.
• The Lesson 13-7 Lesson Overview, Conceptual Understanding states, “Students use the knowledge they have gained about fraction strips, number lines, and equivalencies to find fraction names for whole numbers.” By emphasizing that whole numbers have many fractions names, the lesson reinforces the understanding of fractions as numbers.
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Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

​The instructional materials for enVision Florida Mathematics Grade 3 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 5 Overview, Procedural Skill and Fluency states, “Fluency with multiplication and division within 100 is an expectation in this topic.” Students are provided opportunities to interpret multiplication tables and use other strategies to multiply and divide.
• 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 for students to  demonstrate procedural skill and fluency independently throughout the grade level.

• In Lesson 5-2, Independent Practice, students find the missing factors and products in a table.
• In Lesson 5-3, Independent Practice, students use strategies to find the products.
• In Lesson 16-2, Visual Learning Bridge, Convince Me!, Guided Practice, and Independent Practice sections of the lesson students use multiplication within 100 to find the perimeter of common shapes.

The instructional materials provide regular opportunities for students to attend to the Standard 3.NBT.1.2, adding and subtracting within 1,000 and to the Standard 3.OA.3.7, multiplying and dividing within 100.

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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

​The instructional materials for enVision Florida Mathematics Grade 3 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 2 Overview, Math Background: Rigor states, “Students solve a variety of real-world problems involving equal groups and arrays. These situations allow students to apply multiplication facts to their understanding of multiplication.”

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 Topic 1, 3-Act Math, students solve multiplication and division problems in the context of a story problem. Students complete the three acts to solve the main question, “How many packs of pencils will it take to fill 3 cups?” In Act 1: THE HOOK, students watch an informational video, brainstorm questions, and predict reasonable answers to the main question. In Act 2: THE MODEL, students identify and reveal information as well as develop a model. In Act 3: THE SOLUTION, students reveal an answer and reflect to validate conclusions, revise their models, discuss math practices, and revisit brainstorming.
• In Lesson 2-6 Problem Solving Performance Task, students solve multiplication and division problems in the context of a story problem. “David and Jon are placing coffee orders for their friends. David orders 10 large cups of coffee. Jon orders 4 fewer large cups than David. Jon pays for his orders with a $50 dollar bill. Jon wants to know how much he spent on coffee.” Students are provided with information on the cost of different sizes of coffee cups. • In Lesson 5-4 Problem Solving, students solve multiplication and division problems in the context of a story problem. “Jodie has 24 flowers in her garden. She wants to give an equal number of flowers to 4 families in her neighborhood. How many flowers will each family get? Complete the bar diagram and write an equation to help solve this problem." • In the Topic 11 Performance Task, students solve two-step word problems using the four operations in the context of a story problem. “Mrs. Radner and Mr. Yu teach filmmaking at a summer camp. The students work in crews to make movies. The summer ends with the crew and actors watching all the movies.” Class detail information is provided, along with two tables (Film Types and Film Lengths). Students use this information to answer 5 problems. • In Lesson 11-4 Problem Solving Performance Task, students solve two-step word problems using the four operations in the context of a story problem. “A Grade 3 class is going to buy buttons like the ones shown. Each package costs$8. Each package is 40 cm long. They need to know if $50 is enough money to buy 200 buttons.” ##### Indicator {{'2d' | indicatorName}} 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. ​The instructional materials for enVision Florida Mathematics Grade 3 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 Lesson 3-2, students develop conceptual understanding by using visual models such as pictures, drawings, and counters to show multiplication. • In Lesson 2-2, students practice the procedural skill of multiplying by 1 and 0 using patterns to gain fluency in the products for multiplication with 0 and 1. “Kira has 8 plates with 1 orange on each plate. How many oranges does Kira have?” • In Lesson 11-1, students apply knowledge of addition and subtraction by using bar diagrams, equations, and information from a table to solve a two-step problem and determine how they relate. “Write equations to find how many more tickets were sold for the roller coaster on Saturday than for the swings on both days combined. Use letters to represent the unknown quantities.” Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. • In Lesson 13-8, Independent Practice, students develop conceptual understanding of fractions through drawing diagrams and shading the fraction, then applying this information to solve, “Reyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long. She uses $$\frac{2}{c}$$ of the red ribbon and $$\frac{2}{4}$$ of the blue ribbon. Conjecture: Reyna uses the same amount of red and blue ribbon.” #### Criterion 2.2: Math Practices Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice ​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. ​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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, the Overview identifies MP.1.1. “Students make sense of problems and use counters, bar diagrams, drawings, or equations to represent their work.” • In Topic 4, the Overview identifies MP.7.1. “Students analyze the relationship between multiplication and division by solving division facts using related multiplication facts.” 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 15-1 Convince Me, MP.1.1 is identified. “Students draw a quadrilateral that is an example of one of the shapes listed in Box B and then name the shape. They also draw a quadrilateral that is not an example of a shape listed in Box B. Check students’ drawings to make sure that they understand the attributes of different quadrilaterals.” • In Lesson 4-4, problem 19, MP.2.1 is identified. “What other equations are in the same fact family as $$18\div9$$ = 2? After students have listed the facts in the fact family, have them explain why the facts are a fact family.” • In Lesson 7-5, problem 7, MP.6.1 is identified. “Use precise math language and symbols. Students accurately explain how Marta can buy 12 sketches for$50 or less. Ask students if they could have solved the problem another way.”
• The Topic 13, 3-Act Math Task identifies MP.4.1 as the primary Math Practice but connects to other MPs: “As students carryout mathematical modeling, they will also engage in sense-making (MP.1.1), abstract quantitative reasoning (MP.2.1), and mathematical communication and argumentation (MP.3.1). In testing and validating their models, students look for patterns in the structure of their models." (MP.7.1, MP.8.1)

The MPs are identified within a lesson in the Lesson Overview, and the lesson narratives highlight when a 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 2-6, Problem Solving, MP.4.1 is identified. “Students use number lines as another way to represent the problem. On the top number line, students can show the addition of 2 + 6, and on the bottom number line, they can show multiplication by skip counting by 2's eight times.”
• In Lesson 6-6, MP.7.1 is identified. “Students find the relationship between the area of a decomposed shape and the area of the irregular shape.”
• In Lesson 3-7, Problem Solving: Repeated Reasoning Guided Practice, MP.8.1 is identified. “Listen and look for these behaviors as evidence that students are exhibiting proficiency with this practice: Notice and describe when certain calculations or steps in a procedure are repeated, generalize from examples or repeated observations, recognize and understand appropriate shortcuts, and evaluate the reasonableness of intermediate result.
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Materials carefully attend to the full meaning of each practice standard

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 a boy opening packages of pencils and putting them into a cup. After the video students have a brief discussion about what they noticed about the video. Then the teacher poses the question, “How many packs of pencils will it take to fill 3 cups?” 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 solution.
• MP.2.1: In Lesson 2-2, students solve problems with information from a table. For example, “The library is having a used book sale. How much do 4 hardcover books cost? Draw a number line to show the answer.” Through teacher questioning, students reason quantitatively about the information in the table and then what the number line would look like.
• MP.7.1: In Lesson 3-2, Convince Me! states, “Use structure: Suppose there were 7 canoes in each of 3 rows. How can 2 x 7 help you find the total number of canoes?” Students are provided opportunities to explain how they can use known facts to find the total number of canoes.
• MP.8.1: In Lesson 3-6, Convince Me! states, “Generalize: Use the Associative Property of Multiplication to show two different ways to find 5 x 2 x 3. Did you get the same answer both ways? What can you generalize?” Students express regularity in the repeated reasoning of the problems they solved to come to the generalization of the Associative Property for Multiplication.

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

• MP.4.1: Lesson 8-4, Question 17 states, “Model with Math: Jessica has an array with 9 columns. There are 36 counters in the array. How many rows does her array have? Show how to represent the problem and find the answer.” The model is provided for students, and the teacher’s note says to remind students that when they know the total amount as well as the number of groups, they should use division.
• MP.5.1: In Lesson 9-2, the Solve and Share question states, “Suppose a bus travels 276 miles on Monday and 248 miles on Tuesday. How many miles does the bus travel?” There is an added note in the material with this problem on the student page that states, “You can use appropriate tools, such as place-value blocks, to add larger numbers. What other strategies can you use to solve this problem?”
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

​​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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:

• In Lesson 1-6, Problem Solving, Question 10: "Critique Reasoning: Kerry says she can use a tens rod to represent the array. Do you agree? Explain.” Students have to use their understanding of arrays to critique Kerry’s reasoning.
• Lesson 2-5, Problem Solving, Question 27: “Abdi says that 9 x 6 is less than 10 x 4 because 9 is less than 10. Do you agree with Abdi’s reasoning? Explain why or why not.”
• In Topic 4, Topic Assessment, Question 11: “Mandy is trying to find 6 0. She says the answer is 6 because 6 x 0 = 6. Is Mandy correct? Explain.”
• In Lesson 8-3, Problem Solving, Question 16: “Critique Reasoning: Bill added 438 + 107. He recorded his reasoning below. Critique Bill’s reasoning. Are there any errors? If so, explain the errors. Find 438 + 107. I’ll think of 7 as 2 and 5. 438 +2 = 440, 440 + 7=447, 447 + 100= 547, so, 438 + 107 is 547.”

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

• In Lesson 4-7, Convince Me, students construct arguments to explain the relationship between multiplication and division equations, finding that both belong to the same fact family. “Why can both $$28\div7$$ = ? and ? x 7 = 28 be used to solve the problem above?” Students can use the argument of the relationship between multiplication and division to solve this problem.
• In Lesson 5-6, Problem Solving, Question 9, “Construct Arguments: Compare the costs of buying the $4 packages to the$6 packages. Which package type costs less if Trina wants to buy 24 necklaces? Explain how to solve without computing.”
• In Lesson 9-7, students use the digits 0, 1, 2, 3, 4, and 5 once to make two 3-digit addends with the greatest sum. “How do you know you have made the greatest sum?”
##### Indicator {{'2g.ii' | indicatorName}}
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.

​​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 1-3, Visual Learning Bridge Classroom Conversation, Part B: “You can use addition or skip counting to find the total. The teacher asks students, “Why do you add 5 four times? How would the addition change if the array had another row?”
• In Lesson 2-5, Critique Reasoning prompts the teacher to ask questions related to the mistakes a student makes when estimating a product.
• In Topic 3, 3-Act Math, Critique Reasoning states, “Have students share their solution methods." Let students ask questions about others' solutions.
• In Lesson 9-7, Solve and Share prompts teachers with the following questions to assist students in constructing viable arguments for their work: “What are you asked to do?; What information will you use?; How might you use place value to help solve this problem?; “What is the value of the greatest place value in the boxes?; What is the sum of the two greatest numbers in the group of six numbers?”
• In Lesson 10-3, Construct Arguments (in the margin), students answer questions and construct arguments about why 4 x 20 could be grouped as 4 x (2 x 10).
• In Lesson 11-4, Visual Learning Bridge Classroom Conversation, teachers have the following questions to assist students in analyzing the arguments of others: “What is the main question you need to answer to check Danielle’s reasoning?; What is the hidden question?; What strategy did Danelle use?; What calculations of Danielle’s do you need to check?”
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 3 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, in the Teacher Edition, Lesson 13-1, the following words are listed: equivalent fractions. These same words are listed in the Lesson Overview.
• Lesson 2-3 introduces the Identity (One) Property of Multiplication and Zero Property of Multiplication. Within the Visual Learning Bridge, students work with equal groups. The definition of the Identity (One) Property of Multiplication is developed and applied as students place 8 groups with 1 in each group using correct language. For example, “The Identity (One) Property of Multiplication, when you multiply a number by 1, the product is that number, 1 plate with 8 oranges also equals 8 oranges.” Within the Convince Me! Activity, students use counters to show 7 x 1 using the Identity Property of Multiplication. The Classroom Conversation provides further practice and discussion questions for the teacher that will solidify the concept of the Identity (One) Property of Multiplication. “How could you use counters to show the number of oranges on this plate? What property lets you know that 8 x 1 = 1 x 8? Can you show 0 x 4 with counters? What property lets you know that 0 x 4 = 0?”
• In Lesson 6-1, students interpret square units by using estimation. Students use the context to build proper mathematical vocabulary.
• Lesson 9-2 introduces regrouping to the students. The Visual Learning Bridge includes 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 1: “When you add 3-digit numbers, how do you know if you need to regroup?” A sample answer is provided to support teachers using precise vocabulary language with students.

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

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 accompanies each lesson. These sets of problems include problems that support students in developing mastery of the current lesson and topic concepts.

##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 14-4, students use 1-liter bottles, large bowls, and assorted containers when estimating liquid volumes. Animated versions of the task are also provided as an option.
• The materials provide digital manipulatives for developing conceptual understanding, such as fraction strips or rulers. When physical, pictorial, or virtual manipulatives are used, they are aligned to the mathematical concepts they represent. Topic 6 includes color tiles and centimeter grid paper to support work with area, to ensure the use of mathematical vocabulary, and to connect covering regions with squares to find area with the formula for finding area.
• 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 1-4, teachers give 50 two-color counters to each group of students. Students use these counters to show how six friends picked 48 grapefruits, by showing equal parts.

Examples of manipulatives for Grade 3 include:

• Two-colored counters, number lines, cubes, place-value blocks, multiplication table, and fraction strips.
• Geometry toolkits contain tracing paper, 1-centimeter and 1-inch grid paper, colored pencils, scissors, index card, rulers, blank clock faces, 1-liter bottles, large bowls, marked 1-liter beaker, assorted containers, soup can, large pot, pan balance, weights, shapes.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

​The visual design in enVision Florida Mathematics Grade 3 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 3 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 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 partially 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' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains a narrative for the teacher 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 2-1 Visual Learning Bridge and Classroom Conversation, the following questions are included: "Why do you use doubling to solve this problem? What other operations or strategies could you use to solve the problem?” In Lesson 8-5 Solve & Share, the following questions are included: “Do you need to find exactly how many stickers Derek has? How does a number line help you round numbers?”

##### Indicator {{'3g' | indicatorName}}
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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 meet the expectation for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning.

• Each Topic has a Topic Planner that gives an overview of every lesson, the Objective of the lesson, Essential Understanding, Vocabulary, Materials needed, Technology and Activity Centers, along with the Math Standards.
• 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' | indicatorName}}
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.

​The instructional materials for enVision Florida Mathematics Grade 3 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' | indicatorName}}
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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 4 Overview of Math Background: Coherence states that the work in this topic relates to using related facts and even/odd numbers from Grade 2, meanings of multiplication and division and multiplication facts from earlier in Grade 3, fact fluency, two-step problems and measurement problems later in Grade 3, and division with greater numbers in Grade 4.

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' | indicatorName}}
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).

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 on pages 6-7.
• The Teacher Edition Program Overview provides a Pacing Guide on page 23A 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' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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, Your child is learning how to multiply. Help him or her think of multiplication as joining equal groups. For example, 5 × 2 is 5 groups of 2. So, 5 × 2 = 10. Your child is also learning how to divide. Help him or her think of division as sharing equally. For example, $$42\div7$$ can be thought of as 42 crayons and 7 boxes. Each box has an equal number of crayons. There are 6 crayons in each box. Do the activities below with your child to help him or her learn multiplication and division concepts and facts.” 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' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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:

• On page 24, the Program Goals and Organization are outlined. Under Program Goals, there are 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.

• On pages 26 and 27, the instructional model is 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).”
• On pages 42-43, the program components are sorted by their purpose: Develop, Assess, Differentiate, Review, and Other.
• On pages 44-55, 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, on page 47, it explains the Solve & Share by saying, “Solve & Share begins the lesson by engaging students with a problem in which new math ideas are embedded.”
• The Problem Solving lessons are outlined on pages 58-59, stating, “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.
• On pages 68-69, the material's Pick a Project part is explained.
• On pages 70-71, the 3-Act Math tasks are outlined.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 students' 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' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 4-6, the Error Intervention gives the following guidance: “If students are unsure of the quotient when dividing zero by a number, then go over the rule with them again. Zero divided by any other number (except 0) is 0. Show several models of zero objects divided into any number of groups (except 0). The result is 0 objects per group.”

##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials encourage students to monitor their own progress.

​The instructional materials for enVision Florida Mathematics Grades 3 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 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 1-3 Solve & Share, students represent an array with an equal number of cards in rows. 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 multiplication using factors.
• In Lesson 2-5 Convince Me!, students use data from a previous problem to answer a question about how many points were scored from an arrow that hit a yellow ring. Students determine this information by using a chart, bar diagram, skip counting using a number line, or another strategy of their own. The teacher is encouraged to look for multiple strategies such as patterns to solve multiplication problems when the factor is 10.
• In Lesson 5-1 Question 9, students create multiplication equations given when asked, “How many arms do 9 starfish have if…” Multiple strategies can be provided as this question is considered a quick-check question for prescribing differentiation.
• In Lesson 14-1, students are given clocks that show different times, and they are asked to use any counting method to find the time on each. 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.
##### Indicator {{'3u' | indicatorName}}
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).

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 on pages 82-83 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:

• Lesson 3-4 includes English Language Learners' Tips for Emerging: “Ask students to complete the sentences and read them to their partner: There are ____ rows of prizes. There are ____ prizes in each row;” Developing: “Ask students to write 8 x 6 = 48 and explain to their partners which numbers are the factors and which number is the product;” Bridging: “Ask partners to explain the information given in the problem to each other and explain their answers.”
• In each Topic Opener, there is information provided to include specific ELL supports as needed. For example, in Topic 3, 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 includes:

• 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' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 3 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 4-6, questions 19-22, Addie, Marty, and Fiona are hiking on trails. Addie and Marty hike on the same trails. Fiona hiked the trails on different days. There is no differentiation of what roles the characters take when hiking that suggests a gender, racial, or ethnic bias.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 3.5: Technology

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 3: 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' | indicatorName}}
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.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
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.

​i. The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 3 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.).

The instructional materials reviewed for enVision Florida Mathematics Grade 3 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' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

​The instructional materials reviewed for enVision Florida Mathematics Grade 3 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 for 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)

## Report Overview

### Summary of Alignment & Usability for enVision Florida Mathematics | Math

#### Math K-2

​​The instructional materials reviewed for enVision Florida Mathematics Kindergarten-Grade 2 meet expectations for alignment to the Standards and usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

​The instructional materials reviewed for enVision Florida Mathematics Grades 3-5 meet expectations for alignment to the Standards and usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 6-8

​The instructional materials reviewed for enVision Florida Mathematics Grades 6-8 meet expectations for alignment to the Standards and usability. The instructional materials meet expectations for Gateway 1, focus and coherence, Gateway 2, rigor and balance and practice-content connections, and Gateway 3, instructional supports and usability indicators.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

###### Alignment
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###### Usability
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