​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.

​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.

​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.”

​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.”

​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.

​​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?”

​​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?”

​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.

​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.

​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.

​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.

​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.

​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?”

​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.

​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).

​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.

​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.”

​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.

​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.

​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.

​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).

​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.

​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.

​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.

​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.