The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

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

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where conceptual understanding for the Topic is outlined.
• Lessons are introduced with a video, “Visual Learning Animation Plus,” at PearsonRealize.com to 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, 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. For example:

• In Lesson 1-4, Do You Understand? Question 6, students use number lines and diagrams to develop the concept of division of fractions by whole numbers. “What division equation is represented by the diagram?” (6.NS.1.1)
• In Lesson 1-5, Example 2, students use bar diagrams and area models to understand the concept of dividing fractions. “How much of a $$\frac{3}{4}$$-cup serving is in the $$\frac{2}{3}$$ cup of yogurt?” (6.NS.1.1)
• Lesson 4-8 poses the essential question, “What does it mean for one variable to be dependent on another variable?” In Practice Problem 19, students solve: “The number of oranges in a bag and the cost of the bag of oranges are related. What is the independent variable in this relationship? Explain.” (6.EE.3.9)
• Lesson 4-10 relates variables to the coordinate plane. Students use tables to discover relationships between dependent and independent variables and graph them appropriately. Practice Problem 7: “Complete the table and graph to show the relationship between the variables in the equation d = 5 + 5t.” (6.EE.3.9)
• In Lesson 5-1, students analyze and use bar diagrams and double number lines to build an understanding of ratios. Example 2: “The ratio of footballs to soccer balls at a sporting goods store is 5 to 3. If the store has 100 footballs in stock, how many soccer balls does it have?” Students use a bar diagram to show the initial ratio of 5:3 and then use the same diagram to show 100 footballs to determine the correct number of soccer balls. In Example 3, students use a double number line to find, “Chen can ride his bike 3 miles in 15 minutes. At this rate, how long will it take Chen to ride his bike 18 miles?” (6.RP.1.1 and 6.RP.1.3)

Physical manipulatives are not a part of the materials. When manipulatives are to be used by teacher and students, they are referenced in digital format.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade.

The structure of the lessons includes several opportunities to develop these skills.

• In the Teacher’s Edition, every Topic begins with Math Background: Rigor, where procedural skill and fluency for the content is outlined.
• In the Student Practice problems, Do You Know How? provides students with a variety of problem types to practice procedural skill and fluency.
• Each topic ends with a fluency review puzzle.
• There is additional practice of procedural skills and fluency online.

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

• Lesson 3-3: Students use Order of Operations to evaluate numerical expressions. (6.EE.1.1) For example, Do You Know How? Question 6: “Evaluate. $$(8.2 + 5.3)\div5$$."
• Lesson 1-2: Students use the division algorithm to develop and maintain fluency in dividing whole numbers and decimals. (6.NS.2.2 and 6.NS.2.3) For example, Practice and Problem Solving question 25: “Divide. 187.2 ÷ 8."
• Lesson 1-1: Students practice fluently adding, subtracting and multiplying decimals (6.NS.2.3). For example, “Do You Know How?” Question 10. “Find the difference. 15 – 6.108.”
• Lesson 3-1: Students develop procedural skills with whole number exponents. (6.EE.1.1) For example, Do You Know How? Question 13: “Evaluate each power. $$7^3$$.”
• Lesson 3-6: Students generate equivalent expressions. (6.EE.1.4) For example, Practice and Problem Solving Question 18: “Write equivalent expressions, 2x + 4y.”
• Lesson 7-2: Students find the area of a triangle. (6.G.1.1) For example, Practice and Problem Solving Question 13: “The vertices of a triangle are A(0,0), B(3,6), and C(9,0). What is the area of the triangle?”

In addition, each cumulative assessment spirals through all previous topics, reviewing key information with a a variety of problems to reinforce skills.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that the materials are 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.

The structure of the lessons includes several opportunities for students to engage in application.

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where applications of the content are outlined.
• In the Student Practice problems, Practice & Problem Solving provides students with a variety of problem types to apply what they have learned.
• Each Topic includes a Performance Task, where students apply math of the topic in multi-step, real-world situations.
• Every topic also includes a 3-Act Mathematical Modeling application problem.
• Each topic includes a STEM project which is application; this incorporates more science or engineering.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level as well as provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. Non-routine problems are typically found in Performance Tasks and STEM activities.

• Topic 7 Performance Task Question 3: "Suppose you make dog blankets for Delia's company. Create a blanket with the following features: The finished blanket has an area of 28 inches by 18 inches; It has at least three sections of color, but no more than five; It has one section with an area of 81 square inches; It uses at least three different polygons, including a parallelogram that is not a rhombus."
• In Lesson 1-5, Practice and Problem Solving, students use models to divide fractions by fractions. (6.NS.1.1) For example, Question 26: “A large bag contains $$\frac{12}{15}$$ pound of granola. How many $$\frac{1}{3}$$-pound bags can be filled with this amount of granola? How much granola is left over?”
• In Lesson 4-3, Practice and Problem Solving, students write and solve addition and subtraction equations. (6.EE.2.7) For example, Question 17: “You have some baseball cards. You give 21 baseball cards to a friend and have nine left for yourself. How many baseball cards were in your original deck? Write and solve an equation to find t, the number of baseball cards in your original deck.”
• Topic 7, 3-Act Mathematical Modeling: That's a Wrap (6.G.1.4 and 6.EE.1.2c): Students determine how many stickers are needed to cover the surface area of a box. Question 15, "A classmate says that if all dimensions of the gift were doubled, you would need twice as many squares. Do you agree? Justify his reasoning or explain his error."

The instructional materials for enVision Florida Mathematics Grade 6 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

All three aspects of rigor are present in program materials. With few exceptions, lessons are connected to two aspects of rigor with an emphasis on application. Student practice includes all three aspects of rigor, though there are fewer questions for conceptual understanding.

There are instances where all three aspects of rigor are present independently throughout the program materials.

• Lesson 8-7, Practice and Problem Solving emphasizes application. Students use what they’ve learned about mean and median and apply it to describe the center, spread, and overall shape of data. (6.SP.1.2, 6.SP.2.5b, 6.SP.2.4, and 6.SP.2.5c) Question 10: “Describe the pattern in the dot plot. Then write about a situation that this data could represent. Explain why your situation has this pattern.”
• Lesson 1-6 emphasizes procedural skill. Students divide mixed numbers by mixed numbers and whole numbers. (6.NS.1.1) Practice and Problem Solving Question 21: “$$16\div2\frac{2}{3}$$”
• Lesson 4-6 emphasizes conceptual understanding. Students use and identify properties of equality to write equivalent equations. (6.EE.1.4) Practice and Problem Solving question 15: “This scale was balanced. Find the number to add that makes the scale become balanced again. Then complete the equation to make it true. 12 + ____ = 2 + 7 + 3 + 16.”

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

• Lessons 7-1, 7-2, 7-3, and 7-4: Students apply conceptual understandings of formulas when solving for area in real-world problems. (6.G.1) Practice and Problem Solving Question 21: Students determine if a custom truck with rectangular dimensions of 13.5 ft by 8.5 ft can fit in a parallelogram-shaped parking space with an area of 209 $$ft^2$$.
• Lesson 7-1: Find Areas of Parallelograms and Rhombuses emphasizes conceptual understanding and procedural skill. (6.G.1.1) Example 1 shows students the conceptual connection between parallelograms and rectangles. Example 2 introduces the formula for finding area. In Example 3, students practice the procedure for finding the area.
• Lesson 4-1: “Students are introduced to the concept of an equation and understanding that a solution of an equation is a value for the variable that makes the equation true.” Students also apply their understanding when they “solve one-step equations and use equations with one variable in mathematical and real-world problems.” The lesson includes two examples using a pan balance, then moves into bar diagrams. Students test solutions using substitution and begin to translate situations to equations. Practice and Problem Solving Question 21: “Gerard spent $5.12 for a drink and a sandwich. His drink cost $1.30. Did he have a ham sandwich for $3.54, a tuna sandwich for $3.82, or a turkey sandwich for $3.92? Use the equation s + 1.30 = 5.12 to justify your answer.”

For some standards that emphasize conceptual understanding, the materials do not provide students a consistent opportunity to develop understanding of the mathematical content within the standard and quickly transition to developing procedural skills around the mathematical content. An example of this includes:

• Lesson 3-7 Simplifying Algebraic Expressions  identifies a connection to 6.EE.1.3 with an emphasis on conceptual understanding: “Students use conceptual understanding when they identify like terms and equivalent expressions.” The lesson starts with an expression, x + 5 + 2x + 2, and shows steps to simplify, indicating that Alma used the commutative property and the property of multiplication. There are further examples and practice problems that are similar. Students do not have an opportunity to develop understanding of why 2x and 2 cannot be combined.

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

All eight MPs are clearly identified throughout the materials in numerous places, including:

• The Program Overview book begins by listing the eight Topics and their connections to standards and practices.
• The Table of Contents in the Program Overview book connects every lesson to standards and practices.
• The Math Practice and Problem Solving Handbook includes a list of the Mathematical Practice Standards and real-world scenarios modeled through questions and answers.  
• The online tools offer a video, “Math Practices Animation,” for each MP, with explanations of the Math Practices as well as problems that demonstrate the practice.  
• Topic Overviews contain bulleted descriptions of how MPs are addressed and what mathematically proficient students should do.
• Topic Planner Tables at the beginning of each Topic in the Teacher Edition connect standards and practices to descriptions of each lesson.
• Lesson Overviews include indications of Math Practices within a lesson. For example, in Lesson 5-2, “MP.5.1 Use Appropriate Tools Strategically: Students will use a multiplication table to generate equivalent ratios.”
• In Student Practice problems, MPs are labeled with descriptions within problems. For example, Lesson 2-5, Practice and Problem Solving Question 22, “Use Structure: Suppose a, b, and c are all negative numbers. How do you find the distance between points (a,b) and (a,c)?”

The MPs are consistently used to enrich the mathematical content. For example:

• MP.4.1 enriches the mathematical content when students use unit rates to model the relationships between quantities presented in real-world problems, as well as identifying important quantities and using them to complete a double number line diagram to model ratio relationships. Lesson 5-6 identifies MP4 as an emphasis of instruction for Ratios and Rates. Practice and Problem Solving Question 19: “Katrina and Becca exchanged 270 text messages in 45 minutes. An equal number of texts was sent each minute. The girls can send 90 more text messages before they are charged additional fees. Complete the double number line diagram. At this rate, for how many more minutes can the girls exchange texts before they are charged extra?”
• MP.5.1 is used to enrich the mathematical content by using a tool (the multiplication table) that is already familiar to the students and having students connect that to ratios. In Lesson 5-2, students use a multiplication table to generate equivalent ratios. Practice and Problem Solving Question 19, “Equivalent ratios can be found by extending pairs of rows or columns in a multiplication table. Write three ratios equivalent to ⅖ using the multiplication table.”
• MP.1.1 is embedded in the problem as students go beyond a solution and show their understanding in a picture and words. In Lesson 1-5, students work with dividing fractions and mixed numbers. Practice and Problem Solving Question 27: “Higher Order Thinking. Find $$\frac{3}{4}$$ divided by $$\frac{2}{3}$$. Then draw a picture and write an explanation describing how to get the answer.”

Because the Mathematical Practices are labeled in so many places, they are not always consistent and are often overidentified. The identification is broad, rather than targeted, with labels being most relevant at the Lesson level. For example:

• In Lesson 7-4, the Table of Contents lists MPs 1.1, 4.1, 6.1, & 7.1, with MP1.1 listed in the Lesson Overview. MP.1.1 is integrated into the lesson; however, the other MPs are not a major part of the lesson.
• All 3-Act Math lessons identify all eight MPs, and the questions within 3-Act Math lessons are identical in each topic.

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet the expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

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

• Lesson 7-2, Do You Understand? Question 3: “In example 1, if the other diagonal were used to divide the parallelogram into two triangles, would the area of each of these triangles be half the area of the parallelogram? Explain.”
• Lesson 2-2, Practice and Problem Solving, Question 28: “A classmate ordered these numbers from greatest to least: 4.4, 4.2, -4.42, -4.24. Is he correct? Construct an argument to justify your answer.”
• Lesson 3-5, Practice and Problem Solving, Question 31: “Katrina says that the expression 5,432 + 4,564 + 23,908 ÷ 61n can be evaluated by adding 5,432 + 4,564 + 13,908 and then dividing by the value of 61n. Do you agree? Explain.”
• Lesson 3-6, Explain It!: “Juwon says all three expressions are equivalent. (Graphics show three expressions Juwon has solved for A., B., and C.) Do you agree with Juwon that all three expressions are equivalent? Explain.”
• Lesson 6-1, Practice and Problem Solving, Question 22: “Kyle solved 18 of 24 puzzles in the puzzle book. He says that he can use an equivalent fraction to find the percent of puzzles in the book that he solved. How can he do that? What is the percent?”
• Lesson 2-3, Practice and Problem Solving, Question 39: “Alberto and Rebecca toss horseshoes at a stake. Whoever’s horseshoe is closer to the stake wins a point. Alberto’s horseshoe is 3 feet in front of the stake. Rebecca’s horseshoe is 2 feet past the stake. Alberto says that -3 is less than 2, so he wins a point. Is Alberto correct? Explain.”

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet the expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

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

• Solve & Discuss It! or Explain It! at the beginning of each lesson include guidance for teachers to Facilitate Meaningful Mathematical Discourse. In Lesson 6-2, the materials prompt teachers to “Ask students to share their solutions. If needed, project Francisco’s and Abby’s work and ask: 'How does Francisco’s model show that Tom’s friends ate the same amount of vegetable pizza as pepperoni pizza? How does Abby’s model show that $$\frac{2}{5}$$ = $$\frac{4}{10}$$?'”
• In the Visual Learning portion of the lesson, there are sections labeled, Elicit and Use Evidence of Student Thinking and Convince Me. In Lesson 8-5, the materials prompt teachers with, “Can the mean absolute deviation ever have a negative value? Explain.”
• The 3-Act Mathematical Modeling activities prompt the teacher to ask students about their predictions. “Ask about predictions. Why do you think your prediction is the answer to the Main Question? Who had a similar prediction? How many of you agree with that prediction? Who has a different prediction?”
• When MP.3.1 is identified as the emphasis of the lesson, teachers are provided with question prompts in the Lesson Overview and “look fors” such as: “How can you justify your answer? What mathematical language, models, or examples will help you support your answer? How could you improve this argument? How could you use counterexamples to disprove this argument? What do you think about this explanation? What question would you ask about the reasoning used?”

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet the expectations that materials use accurate mathematical terminology.

The materials use precise and accurate mathematical terminology and definitions, and support students in using them. Teacher editions, student books, and all supplemental materials explicitly attend to the specialized language of mathematics.

• Each Topic Overview lists the vocabulary being introduced for each lesson. In Topic 5 Understand and Use Ratio and Rate, the vocabulary listed for the lessons includes: ratio, terms, circumference, diameter, equivalent ratios, Pi, rate, and unit rate.   
• New vocabulary terms are highlighted in the text and definitions are provided within the sentence where each term is found. In Lesson 5-5, the terms rate and unit rate are highlighted and defined. “A rate is a special type of ratio that compares quantities with unlike units of measure.”
• A Glossary in the back of Volume 1 lists all the vocabulary terms.
• A Vocabulary Review is included in the Topic Review. Students are provided with explicit vocabulary practice. In Topic 1, students use the word bank of four terms to fill in the blanks on three items. Students also provide a mathematical example of the term used in each item. Students are to Use Vocabulary in Writing with this prompt: “Explain how to use multiplication to find the value of $$\frac{1}{3}\div\frac{9}{5}$$. Use the words multiplication, divisor, quotient, and reciprocal in your explanation.”
• Online there is an Animated Glossary and a Vocabulary Game. The video is another way to expose students to the vocabulary terms as it provides a visual and audio definition of each term.
• Teacher question prompts attend to precision using appropriate terminology. Lesson 7-5, page 414 Elicit and Use Evidence of Student Thinking: “How many bases does this solid figure have? What is the shape of the base(s)? What are the shapes of the other faces? Is this solid a prism or a pyramid?”
• Each mid-Topic checkpoint includes a vocabulary section where students demonstrate understanding of the terms.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that there is a clear distinction between problems and exercises in the materials.

There are eight Topics in each grade level. Each Topic presents lessons in a consistent structure. During the instructional sections, which include guided instruction, step-by step procedures, and problem solving, students work on examples and problems to learn new concepts.

At the end of the lesson, a variety of exercises allow students to independently show their understanding of the material. The exercises also include Higher Order Thinking, a Lesson Quiz, and Additional Practice.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that the design of assignments is intentional and not haphazard.

Lessons follow a consistent format that sequences assignments intentionally.

• In Solve and Discuss It, students are introduced to concepts and procedures through a problem-based situation.
• Visual Learning: This portion of instruction connects to the problem learned previously and is the substance of the lesson. There are three different examples explored to create student understanding.
• Do You Understand? These exercises generally promote conceptual understanding from the lesson.
• Do you Know How? These exercises generally promote procedural skill and fluency from the lesson.
• Practice and Problem Solving: These are a mix of rigorous exercises and include application problems.

Lessons are in a logical order that build coherence throughout the grade level. Exercises are intentional to encourage a progression of understanding and skills.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example:

• Lesson 1-5: Students explain the concept of dividing fractions using bar diagram and area models.
• Lesson 2-1: Students use a number line to compare integers.
• Lesson 3-5: Students defend or critique the work of others to show their understanding of Order of Operations.
• Lesson 8-2: Students explain their reasoning when using mean, median, mode, and range when describing data sets.
• Lesson 5-1: Students analyze double number lines and bar diagrams to understand ratios.

The instructional materials reviewed for enVision Florida Mathematics Grade 6 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, but the materials do not include physical manipulatives.

• Manipulatives and other mathematical representations are consistently aligned to the mathematical content in the standards, and virtual manipulatives are used for developing conceptual understanding, such as bar diagrams or geometric objects.
• The materials have manipulatives embedded within Visual Learning Animation Plus for many lessons and also within Independent Practice and Differentiated Intervention activities.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide teachers with quality questions for students.

In the Teacher Edition, facilitator notes for each activity include questions for the teacher to guide students' mathematical development and to elicit students' understanding. The materials indicate that questions provided are intended to provoke thinking and provide facilitation through the mathematical practices as well as getting the students to think through their work. For example:

• Lesson 1-1: “Why is it important to line up the digits by place value when you add decimals?”
• Topic 1 Introduction: “What picture or model could you draw to represent the problem?” and “What place value is to the right of the decimal point?”
• Lesson 2-6: “How can you find the perimeter of any polygon?” and “How are the methods used to convert between customary and metric units similar to those used to convert within one measurement system?”

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide teachers guidance for presenting the content and using embedded technology for student learning.

• The Topic Overview includes Math Background for the Topic. This provides a big picture of the learning throughout the lessons. The Math Background also looks at how Focus, Coherence, and Rigor, as well as the Mathematical Practices, are addressed within the Topic.
• Each STEM Activity provides teachers with background information on the math, science, and engineering and technology found in the activity. In addition, it gives information on how to present the topic, including discussion questions. It also gives direction on when to show the STEM video, and when the project can be launched.

In each lesson teachers are provided with the following guidance:

• Information about how to activate prior knowledge is given in the Review What You Know! section. A Vocabulary Review activity is also given, as well as instructions on preparing students for reading success.
• A Lesson Overview that includes the Objectives, Essential Understandings, descriptions of how the mathematical content builds over the grades and within the topic, and how rigor is addressed in the lesson. In addition, both the content and the practice standards addressed in the lesson are described.
• Tips on what to do before, during, and after problems are available for the teacher.
• Technology enhancement included in the online program is noted in the teacher materials, though specific games/lessons/videos/online tools must be accessed online for teachers to know what they include.  

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials explain the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Each topic opens with a Topic Overview that includes a Math Background for the Topic.
• The Coherence section has three parts: Look Back, Topic ____, and Look Ahead. Each section gives a clear, specific explanation of how the topic is connected across grades.
• Each topic includes a Review What You Know! section. The section includes a practice page for students, questions for teachers to activate prior student knowledge, and a vocabulary review.
• Teacher Edition Program Overview Materials contain an overview of mathematics for K-12.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

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

There is a Review What You Know assignment at the beginning of each Topic that helps students activate prior knowledge and prepare for the skills needed in the Topic. Each of these assignments has questioning strategies for the teacher. Each lesson also provides information for the teacher about prior and current grade levels and future math that is used.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

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

• In Lesson 7-4, Error Intervention for Item 12 is “Students may have difficulty converting square feet to square yards.”
• In Lesson 2-1, Prevent Misconceptions for Item 3 includes “Explain that numbers that are not preceded by a sign are presumed to be positive.”

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

• Each Topic includes a Review what you know/Concept and Skills Review section 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 2, 4, 6, and 8 provide review of prior topics as an assessment. An Item Analysis is provided for diagnosis and intervention. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores.
• The Math Diagnosis and Intervention System has practice pages which are specific to a skill or strategy (i.e., Markups and Markdowns and Mental Math).
• There are multiple pages of extra practice available at Pearson Realize online that give students extra opportunities to review skills assigned by the teacher. Each of these pages is able to be customized by the teacher or used as is.
• Different games online at Pearson Realize support students in practice and review of skills, as well procedural fluency.

Teacher materials in print and online complement each other in many instances; however, It is worth noting that teachers who only use the print materials will miss the extensive resources available online, as the print edition has some notes that point teachers to the digital materials but does not identify the full extent of the online resources. Digital assessments are auto-scored and generate reports that can help with grouping and differentiation.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that assessments clearly denote which standards are being emphasized.

The Item Analysis for Diagnosis and Remediation clearly denotes which standards are being assessed. This is found for all of the assessments, including the quizzes.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The Topic Overview in the Teacher Edition includes a section on Coherence which enhances the opportunity to scaffold instruction by identifying prerequisite skills that students should have.

All lessons include instructional notes and classroom strategies that provide teachers with sample questions, differentiation strategies, discussion questions, possible misconceptions, and what to look for from students, which provides structure for the teacher in making content accessible to all learners. Often, the Practice & Problem Solving section begins with scaffolded problems for students. In the Solve and Discuss It! section, teachers are given questions for before, during, and after the activity that provide scaffolding for students. For example:

• Topic 6, Lesson 6-6: Before: “What information are you given in the problem? What is the unknown in this problem situation?” During: “How does your model represent this problem?” After: “How does Adam use a double number line diagram to calculate the number of matches the soccer team played?"

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

• 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 that help students cement or extend their understanding of the concept being taught. It includes an extra problem for the teacher to use, as well as questions to help elicit meaningful responses.
• Each lesson has Differentiated Interventions for a wide-range of learners:
• Reteach to Build Understanding provides scaffolding to reteach.
• Additional Vocabulary Support helps students with key vocabulary.
• Build Mathematical Literacy provides support for struggling readers.
• Enrichment extends concepts from the lesson.
• Online Math Tools and Games build understanding and fluency.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials embed tasks with multiple entry-points.

Lessons begin with Problem-Based Learning, including Solve & Discuss It or Explore It, and can often be solved with a variety of solution strategies.  Also, 3-Act Mathematical Modeling and Performance Tasks include questions with multiple entry points that can be solved using a variety of representations.

• Lesson 7-6, Solve & Discuss It!: “Marianne orders boxes to pack gifts. When they arrive, she finds flat pieces of cardboard as shown below. Marianne needs to cover each face of the boxes with green paper. What is the least amount of paper needed to cover the box? Explain.” This is extended with “Suppose Melanie has only one large sheet of green paper that is 15 inches by 30 inches. Is the area of this sheet of paper great enough to cover all of the faces of one box? Explain.”

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials suggest support, accommodations, and modifications for English Language Learners and other special populations.

• Each lesson has support, accommodations and modifications for ELL students.
• During lessons, strategies are given for teachers to address different levels of English Language Learners such as:
• Emerging: “Ask students to identify which parts of the illustration show ‘four matches.’ Ask the students: 'What other meanings do you know for the word match? Explain. How can the illustration help you know which meaning to use?”
• Expanding: “English Language Learners may not understand the questions asked. Have students state the problem in their own words.”

An English Language Learners Toolkit suggests teaching strategies, assessment tips, vocabulary and reading strategies, and discussion and problem-solving grouping ideas.

• Two pages of multilingual thinking words include the following languages: English, Spanish, Chinese, Vietnamese, Korean, and Hmong.
• There is also a limited list of key vocabulary in the same 6 languages.
• Teaching Math to Culturally and Linguistically Diverse Students provides tips and strategies.

Each chapter has Prepare for Reading Success that gives teachers pre-reading strategies to help all students access the language of the topic. For example, one strategy is Making Predictions, where there are teacher questioning strategies, as well as work for students that involves making predictions regarding the content. It also includes an extension for all readers.

Another special population that is addressed is Early Finishers. Each lesson addresses these students' needs by asking an additional question for students to ponder that correlates with the essential question in the lesson.

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

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

• Lesson 6-6 Enrichment example 3: “Challenge advanced students to create a game in which players match problems such as 4.5% of what number is 5.4? to the correct answer, which is 120 in this case.”
• Lesson 6-6 Challenge item 12: “Have students create a real-world problem using the numbers in the exercise.”

The instructional materials for enVision Florida Mathematics Grade 6 meet the expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

For example:

• Different cultural names and situations are represented in the materials, ie., Sandra, Nadia, Nigel, Yoshi, Joaquin, Archie.
• The materials avoid pronouns, referencing a role instead, ie., the carpenter, the teacher, a plumber, the cross country team.
• There are few pictures of actual people in the Student Book, mostly objects or cartoonish drawings.