## Alignment: Overall Summary

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for alignment to the Mathematics Florida Standards (MAFS). ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards.  The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor and meaningfully connecting the Standards for Mathematical Content and the Cluster Standards for Mathematical Practice (MPs).

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## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

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

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## Gateway 3:

### Usability

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

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

### Criterion 1a

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for not assessing topics before the grade level in which the topic should be introduced. The materials assess grade-level content and, if applicable, content from earlier grades.

### Indicator 1a

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet the expectations for focus within assessment.

According to the Assessment Guide, enVision Florida contains four categories for assessment (page vii): Progress Monitoring, Diagnostic, Formative, and Summative. All assessments are available as both print and digital resources.

The Summative Topic Assessments, Performance Tasks, and Cumulative Assessments were examined for this indicator. The assessments are aligned to grade-level standards. For example:

• Topic 3 Performance Task: Use Functions to Model Relationships Form A, Question 3: Given a non-linear graph showing height vs. distance for the Motion of the Shot Put, students answer, “Hector makes a graph to show the height of a shot put after it is thrown. Describe the behavior of the shot put based on the graph.” (8.F.1.5)
• Topics 1-4 Cumulative/Benchmark Assessment Question 15: “Students at a community college were asked a survey question. The two-way frequency table shows the responses from full-time students and part-time students. Is there evidence that responding yes was related to attending the college full-time or part-time? Explain.” (8.SP.1.4)
• Lesson 6-7 Quiz: Congruency and Similarity Question 4: Given a coordinate grid showing the image and pre-image, “Triangle DEF is congruent to triangle ABC. What is the sequence of transformations that maps triangle ABC to triangle DEF?” (8.G.1.4)
• Topic 3 Assessment: Use Functions to Model Relationships Question 3: Given Function A in a table and Function B as an equation, students answer, “Which function has a greater rate of change?” (8.F.1.2)
• Topics 1-8, Cumulative/Benchmark Assessment Question 9: “Jennie has 177 more songs downloaded on her mp3 player than Diamond. Together, they have 895 songs downloaded. Part A: What systems of equations could be used to determine how many songs each girl has downloaded? Part B: How many songs does each girl have?” (8.EE.3.8c)

### Criterion 1b

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade.

### Indicator 1b

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 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 6 out of 8, which is approximately 75 percent.
• The number of lessons (Content-focused lessons, 3-Act Mathematical Modeling, and STEM Projects, Topic Review, and Assessment) devoted to major work of the grade (including supporting work connected to the major work) is 71 out of 84, which is approximately 85 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 152 out of 176, which is approximately 86 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 85 percent of the instructional materials focus on major work of the grade.

### Criterion 1c - 1f

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

### Indicator 1c

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Supporting standards/clusters connected to the major standards/clusters of the grade include:

• 8.SP.1 supports 8.EE.2 and 8.F.2 in Lesson 4-3, students write the equation for a trend line of a scatter plot and use it to make a prediction.
• 8.SP.1 supports 8.F.2 in Lesson 4-2, using a trend line to determine linear association, non-linear association, or no association is connected to graphing linear functions.
• 8.NS.1 supports 8.EE.1 in Lesson 1-7, students connect properties of exponents to irrational numbers.
• 8.G.3 supports 8.EE.2 in Lesson 8-2, using the formula for the volume of cylinders connects to solving equations of the form “$$x^2=p$$”.
• 8.G.3 supports 8.NS.1 in Lesson 8-1, using the formula for surface area of a cylinder requires students to estimate $$\pi$$.

### Indicator 1d

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

Instructional materials for enVision Florida Mathematics Grade 8 meet expectations that the amount of content designated for one grade level is viable for one year.

As designed, the instructional materials can be completed in 176 days. 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. Several days are included in the course that can be used flexibly.

There are eight Topics in the course. Each Topic is broken down into three instructional activities: Content-focused Lessons, 3-Act Mathematical Modeling Lessons, and an enVision Stem Project. The Program Overview notes that “All three of these instructional activities are integral to helping students achieve success.” Each Topic also includes assessment.

• There are 52 Content-focused lessons, two days per lesson, for a total of 104 days.
• There is one 3-Act Mathematical Modeling Lesson per topic, two days each, or 16 days total.
• There is one STEM Project per topic, one day each,  or eight days total.
• There are a Topic Review and Assessment for each topic, one day each, or 16 days total.
• There are four additional per Topic days for remediation, fluency practice, differentiation, and other assessment, for a total of 32 days.

### Indicator 1e

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

The instructional materials for enVision Florida Mathematics Grade 8 meet expectations for the materials being consistent with the progressions in the Standards.

• Each Topic begins with Get Ready! Review What You Know! This section includes below grade-level work that is clearly identified and connected to the topic being introduced.
• Each topic has a Topic Overview for the teacher that includes Math Background Coherence. This shows progression of a concept across grades levels: Look Back shows how the topic connects to what students learned earlier; Look Ahead shows how the topic connects to what students will learn later.
• Topic 2, Analyze and Solve Linear Equations, page 80C: Look Back reminds that in Grade 7, students analyze and write equivalent expressions, and solve multi-step equations using the distributive property (7.NS.1, 7.EE.1). Students also applied proportional reasoning to solve problems, compare ratios in fraction form and tables, and compute unit rates to determine whether two properties have a proportional relationship. (7.RP.1) Look Ahead states that later in Grade 8, “Students will construct functions to model linear relationships. (8.F.1) They will also solve systems of linear equations by graphing, substitution, and elimination. (8.EE.3) In Grade 9, students will solve problems by manipulating complex equations into simpler equations. (A-SSE.2) They will interpret functions in real-world contexts and build new functions from existing functions." (F-IF.3)
• At the beginning of each lesson there is “Focus, Coherence, and Rigor” for the teacher to connect prior and future learning with the lesson being taught.
• Lesson 2-7 - Analyze Linear Equations: y = mx, “In Grade 7, students: recognized the graph of a proportional relationship as a line through the origin and interpreted points on a graph of a proportional relationship and determined the constant of proportionality. In this lesson, students: write a linear equation to describe a proportional relationship and graph a linear equation that describes a proportional relationship. Later in this topic, students will: understand the y-intercept of a line and analyze linear equations of the form y = mx + b.”
• Off grade-level work, if present, it is in the readiness or review portion of the Topics.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. In the Teacher's Resource Masters  additional Practice Workbook and Reteach to Build Understanding worksheets include grade level problems with scaffolding for differentiation. The Teacher’s Resource Masters also include Enrichment problems that address grade level concepts. Each lesson contains ample problems for students to work with grade-level problems. There are additional problems for teachers to use with students noted in each lesson at PearsonRealize.com. Reteach, additional vocabulary support, build mathematical literacy, enrichment and math tools and games are all on grade level to support all students.

• In Topic 2, Analyze and Solve Linear Equations, students manipulate equations that include like terms on both sides of equation, the distributive property, and inverse operations. They determine how many solutions an equation might have, use understanding of proportional relationships to expand and make connections between proportional relationships and finding slope,  connect the slope of a line with unit rate, and write and graph linear equations to describe proportional relationships. Students learn to graph a line in an equation in the form y = mx + b and interpret the meaning of m and b. (8.EE.2,3)
• Enrichment 5-3, “Sometimes solving a system of equations requires substituting more than once. (3) The sum of the reciprocals of two numbers is 2. One of the reciprocals is $$\frac{1}{2}$$ greater than the other reciprocal. What are the two numbers?” (8.EE.3.8b,c)

### Indicator 1f

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

The instructional materials for enVision Florida Mathematics Grade 8 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:

• The objectives for Lessons 1-6, Generate equivalent expressions with exponents, and 1-9, Students use scientific notation to write very large or very small quantities, are shaped by 8.EE.1, Work with radicals and integer exponents.
• The objective for Lesson 5-4, Understand how the process of elimination can be used to solve a system of linear equations with no solution, one solution, or infinitely many, is shaped by 8.EE.3, Analyze and solve linear equations and pairs of simultaneous linear equations.
• The objective for Lesson 8-4, Recognize the relationship between the formulas for volume of cones and spheres, is shaped by 8.G.3, Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
• The objective for Lesson 3-4, Write an equation in the form y = mx + b to describe a linear function, is shaped by 8.F.2, Use functions to model relationships between quantities.
• The objectives for Lesson 6-3, Identify and perform a rotation, Describe a rotation, and Determine how a rotation affects a two-dimensional figure, are shaped by 8.G.1, Understand congruence and similarity using physical models, transparencies, or geometry software.

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.

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

### Criterion 2a - 2d

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications. The instructional materials also do not always treat the aspects of rigor separately or together.

### Indicator 2a

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

The instructional materials do provide students opportunities to demonstrate conceptual understanding independently throughout the grade. For example:

• Lesson 6-2, Do You Understand?, “What do you notice about the corresponding coordinates of the pre-image and image after a reflection across the x-axis?” (8.G.1.1a, b, c and 8.G.1.3)
• Lesson 3-2, Do You Understand? Question 2, “How can you use a graph to determine that a relationship is NOT a function?” (8.F.1.1)
• Lesson 3-3, Practice and Problem Solving Question 11, “Justin opens a savings account with $4. He saves$2 each week. Does a linear function or a nonlinear function represent this situation? Explain.” (8.F.1.2 and 8.F.1.3)
• Lesson 6-1, Do You Understand? Question 2, “Triangle L’M’N’ is the image of triangle LMN after a translation. How are the side lengths and angle measures of the triangles related? Explain.” (8.G.1.1a,b,c, and 8.G.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.

### Indicator 2b

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

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency.

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

• In the Teacher Edition, every Topic begins with Math Background: Rigor, where procedural skills for the content is outlined.
• In the Student Practice problems, Do You Know How? is the second section, which provides students with a variety of problem types to practice procedural skills.
• There is additional practice of procedural skills 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.

• In Lesson 2-3, students solve multi-step equations using the distributive property. (8.EE.3.7b) For example, Do You Know How? Question 5: “Solve the equation -3(x-1) + 7x = 27.” Practice and Problem Solving Question 12, “What is the solution of the equation 3(x + 2) = 2(x + 5)?”
• In Lesson 5-4, students solve systems of equations using elimination. (8.EE.3.8b) For example, Practice and Problem Solving, Question 8: “Solve the system of equations using elimination: 2y - 5x = -2; 3y + 2x = 35.”
• Lesson 6-4, students describe a sequence of transformations involving floor plans using a coordinate plane. (8.G.1.3) For example, Try It!: “Ava decided to move the cabinet to the opposite wall. What sequence of transformations moves the cabinet to its new position?”

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

### Indicator 2c

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

• In Topic 2 STEM Project (8.EE.2.6), students use linear equations to explore demography, connecting linear equations to predictions of population growth. "Develop a linear equation to represent population growth after x years.”
• Topic 3 Performance Task, Form A (8.F.1 and 8.F.2): “Sofia and Hector are captains of their track and field teams. As captains, they help their teammates train for the different events.” The following questions provide different information in graph and table form and five different questions about this scenario.

### Indicator 2d

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

The instructional materials for enVision Florida Mathematics Grade 8 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 4-1: Students develop conceptual understanding about constructing scatter plots to interpret the relationship of paired data.
• Lesson 2-3: Students develop procedural skills using the distributive property to solve multi-step equations.
• Lesson 1-10: Students apply scientific notation using operations: “The total consumption of fruit juice in a particular country in 2006 was about 2.28 x $$10^9$$ gallons. The population of that country that year was 3 x $$10^8$$. What was the average number of gallons consumed per person in that country in 2006?”

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

• In Lesson 7-2, students build conceptual understanding about using of the Converse of the Pythagorean Theorem to identify right angles. In Lesson 7-3, students use the Pythagorean Theorem and its converse in real-world problems like solving for the longest poster to fit in a given box and whether the angle of a ramp meets recommendations of horizontal distance for every foot of vertical rise.
• Throughout Topic 3, conceptual understanding about functions is developed and applied using real-world problems. Lesson 3-1 Question 11: Students identify if a relation is a function. “Taylor has tracked the number of students in his grade since third grade. He records his data in the table below. Is the relation a function? Explain.” Lesson 3-3, Question 1: Students compare linear and nonlinear functions. “Justin opens a savings account with $4. He saves$2 each week. Does a linear function or a nonlinear function represent this situation? Explain.” Lesson 3-5, Question 2: Students investigate intervals of increase and decrease. “How would knowing the slope of a linear function help determine whether a function is increasing or decreasing?” Lesson 3-6, Question 9: Students sketch functions from verbal descriptions: “Melody starts at her house and rides her bike for 10 minutes to a friend’s house. She stays at her friend’s house for 60 minutes. Sketch a graph that represents this description.”

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 7-1 Understand the Pythagorean Theorem has an emphasis on conceptual understanding and procedural fluency: “Students learn and understand the Pythagorean Theorem.” The lesson starts with: “Kelly drew a right triangle on graph paper. Kelly says that the sum of the areas of squares with side lengths a and b is the same as the area of the square with side length c. Do you agree with Kelly? Explain.” Example 1 shows pictures that develop the proof of the theorem and includes $$a^2+b^2=c^2$$. Example 2 immediately moves into Use the Pythagorean Theorem. The rest of the lesson and practice uses procedural steps.

### Criterion 2e - 2g.iii

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and used to enrich mathematics content, and the instructional materials support the standards’ emphasis on mathematical reasoning.

### Indicator 2e

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 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 TE connect standards and practices to descriptions of each lesson.
• Lesson Overviews include indications of Math Practices within a lesson. For example, in Lesson 6-2, states, “MP.2.1 Reason Abstractly and Quantitatively: Students will analyze the relationship between random samples and populations to make inferences about populations. They will compare different samples from the same populations.”
• In Student Practice problems, MPs are labeled with descriptions within problems. For example, Lesson 7-3 Do you Understand, question 2 says, “Look for Structure: How is using the Pythagorean Theorem in a rectangular prism similar to using it in a rectangle?”

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

• MP.7.1 enriches the mathematical content when students justify that a relationship is proportional when represented as a graph and then flexibly use graphs to describe proportional relationships. Lesson 2-6 identifies MP7.1 as an emphasis for students to analyze and solve Linear Equations. Do You Understand? For example, Question 3 “Why is the slope between any two points on a straight line always the same?” Practice and Problem Solving Question 9 says, “The points (2.1, -4.2) and (2.5, -5) form a proportional relationship. What is the slope of the line that passes through these two points?”
• MP.2.1 enriches the mathematical content as students expand their knowledge about rational numbers and the relationships with decimals and fractions when explaining their answer. Lesson 1-1, Question 16: ”When writing a repeating decimal as a fraction, why does the fraction always have only 9s or 9s and 0s as digits in the denominator?”
• MP.8.1 enriches the mathematical content when students recognize the mistake as using a + b = c instead of $$a^2+b^2=c^2$$, demonstrating that they’ve practiced using the equation $$a^2+b^2=c^2$$ and see the patterns of the equation in similar situations. Lesson 7-2, Question 13: “Three students draw triangles with the side lengths shown. All three say their triangle is a right triangle. Which students are incorrect? Which mistake might they have made?”

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 1-5, the Table of Contents lists MPs 2.1, 3.1, 4.1, 7.1, & 8.1, but MPs 2.1 and 7.1 are listed in the Lesson Overview. MP.2.1 and 7.1 are 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.
• Multiple MPs are identified for every lesson.

### Indicator 2f

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 partially meet expectations for carefully attending to the full meaning of each practice standard.

The materials do not attend to the full meaning of MPs 4.1 and 5.1, and examples of this include:

• MP.4.1: In each 3-Act Mathematical Modeling lesson, there is a problem labeled, Model with Math, and the directions for this problem state, “Represent the situation using the mathematical content, concepts, and skills from this topic. Use your representation to answer the Main Question.” By telling students to use the content, concepts, and skills from the topic, students do not engage in the full meaning of MP.4.1 as the mathematics has been identified.
• MP.5.1: In each 3-Act Mathematical Modeling lesson, there is a problem labeled, Use Appropriate Tools, and the directions for this problem state, “What tools can you use to get the information you need? Record the information as you find it.” Students and teachers can access a video which contains all the information needed to solve the problem. Students do not engage in the full meaning of MP.5.1 because they are not choosing and using appropriate tools strategically in order to gather information for solving the problem.

The instructional materials attend to the full meaning of the following Practice Standards:

• MP.1.1: In Lesson 7-6, students “analyze multi-step problems involving surface area of prisms and consider different ways to find solutions.” In Lesson 4-5, students “organize data into two-way relative frequency tables and interpret relationships between the data using rows and columns.” In Lesson 8-3, students “examine the mathematical relationship between the volumes of a cone and a cylinder.”
• MP.2.1: In Lesson 2-4, students solve an equation and use the resulting statement to identify the number of solutions for the equations. In Lesson 5-2, students “interpret graphs of linear systems of equations and make meaning by understanding that the solution is the intersection point(s).”
• MP.6.1: In Lesson 6-1, students describe how they know the lengths and sides of two trapezoids on a coordinate plane are equal. Students show understanding of translations when they pay attention to details of measurements of the lengths and sides. In Lesson 1-10, students “perform calculations with numbers in scientific notation to solve real-world problems.” In Lesson 5-3, students “communicate the specific steps needed to solve a system of equations by substitution.”
• MP.7.1: In Lesson 1-8, students use the structure of place-value systems to correctly make estimates of very large and very small quantities using powers of 10. Students determine that very large numbers can be represented as a power of 10 with a positive exponent and that positive numbers less than one can be represented as a power of 10 with a negative exponent. In Lesson 7-3, students demonstrate understanding of structure as they explain how using the Pythagorean Theorem is similar to using it in a triangle. In Lesson 8-1, students use their understanding of the overall structure of the formulas to solve for surface area of a cone and surface area of a sphere. In Lesson 1-2, students “learn the characteristics of rational and irrational numbers and use this structure to analyze, describe, and make classifications.” In Lesson 5-4, students look for patterns and structures to either find or make opposite terms in order to use [the] elimination method. They interpret whether the system has a unique solution, no solution, or infinitely many solutions.
• MP.8.1: In Lesson 6-6, students explain patterns, discuss methods and solution strategies, and evaluate the result of a dilation given a scale factor and a fixed center. In Lesson 3-1, students use reasoning to generalize whether a relation is a function. They understand when a relation is a function by recognizing that each input value has a unique output value.

### Indicator 2g

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

### Indicator 2g.i

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 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 3-4, Practice and Problem Solving, Construct Arguments: “Suppose another store sells a similar package, modeled by a linear function with initial value 7.99. Which store has the better deal? Explain.” • Lesson 1-2, Explain It!: “Sofia wrote a decimal as a fraction. Her classmate Nora says that her method and answer are not correct. Sofia disagrees and says that this is the method she learned (graphic shown). Is Nora or Sofia correct?” • Lesson 3-1, Practice and Problem Solving, Question 10: “During a chemistry experiment, Sam records how the temperature changes over time using ordered pairs (time in minutes, temperature in ℃). Is the relation a function? Explain.” • Lesson 3-6, Explain It!: “The Environmental Club is learning about oil consumption and energy conservation around the world. Jack says oil consumption in the United States has dropped a lot. Ashley says oil consumption in China is the biggest problem facing the world environment. A) Do you agree or disagree with Jack’s statement? Construct an argument based on the graph to support your position. B) Do you agree or disagree with Ashley’s statement? Construct an argument based on the graph to support your position.” • Lesson 1-2, Practice and Problem Solving, Question 13: “Deena says that 9.565565556… is a rational number because it has a repeating pattern. Do you agree? Explain.” • Lesson 2-1, Practice and Problem Solving, Question 14 page 109: “Your friend solved the equation 4x + 12x - 6 = 4(4x + 7) and got x = 34. What error did your friend make? What is the correct solution?” • Lesson 4-2, Practice and Problem Solving, question 3 page 220: “How does the scatter plot of a nonlinear association differ from that of a linear association?” ### Indicator 2g.ii Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. 2/2 + - Indicator Rating Details The instructional materials reviewed for enVision Florida Mathematics Grade 8 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 6-7 Solve and Discuss It!, the materials prompt teachers to “Ask students to share their solutions. If needed, project Melanie’s and Nick’s work and ask: 'How does Nick’s observation differ from Melanie’s? Do you think Melanie’s Answer or Nick’s answer is more complete? Explain.'” • In the Visual Learning portion of the lesson, there are sections labeled, Elicit and Use Evidence of Student Thinking and Convince Me. In Lesson 8-4, the materials prompt teachers with, “A cone and a sphere have the same radius and height. Which will make the cone have the same volume as the sphere, doubling the radius of the cone or doubling the height of the cone? Explain.” • The 3-Act Mathematical Modeling activities prompt teachers 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?” In Lesson 1-1, the materials prompt teachers with, “As students work through the Explain It, listen and look for different ways in which students analyze Sofia’s work. Incorporate their critiques into the classroom discussion.” ### Indicator 2g.iii Materials explicitly attend to the specialized language of mathematics. 2/2 + - Indicator Rating Details The instructional materials reviewed for enVision Florida Mathematics Grade 8 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 2 Analyze and Solve Linear Equations, the vocabulary listed for the lessons includes: slope, y-intercept, and slope-intercept form. • New vocabulary terms are highlighted in the text and definitions are provided within the sentence where each term is found. In Lesson 2-8, the term y-intercept is highlighted, and the definition is provided within the sentence. “The y-coordinate of the point where the line crosses the y-axis is the y-intercept.” • 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 4 Review, page 247, Use Vocabulary in Writing: “Describe the scatter plot at the right. Use vocabulary terms in your description.” ### Gateway Three ## Usability #### Meets Expectations ### Criterion 3a - 3e Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing. 8/8 + - Criterion Rating Details ​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent. ### Indicator 3a The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose. 2/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 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. ### Indicator 3b Design of assignments is not haphazard: exercises are given in intentional sequences. 2/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 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. ### Indicator 3c There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc. 2/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example: • Lesson 3-1: Students identify functions using arrow diagrams and ordered pairs. • Lesson 1-6: Students use a table or the Quotient of Powers Property to explain expressions with negative and zero exponents. • Lesson 7-2: Students construct arguments and justify their reasoning concerning the Converse of the Pythagorean Theorem. • Lesson 1-2: Students construct an argument and justify reasoning about another student’s response to a number being rational or not. • Lesson 2-2: Students build a model for a problem by using diagrams and equations. • Lesson 3-2: Students use a diagram and a coordinate plane to represent a linear equation. ### Indicator 3d Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods. 2/2 + - Indicator Rating Details The instructional materials reviewed for enVision Florida Mathematics Grade 8 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. ### Indicator 3e The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject. Narrative Evidence Only + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 are not distracting or chaotic and support students in engaging thoughtfully with the subject. The page layout in the materials is user-friendly, and the pages are not overcrowded or hard to read. Graphics promote understanding of the mathematics being learned. The digital format is easy to navigate and is engaging. There is ample white space for students to write answers in the student book. ### Criterion 3f - 3l Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards. 7/8 + - Criterion Rating Details ​The instructional materials reviewed for enVision Florida Mathematics Grade 8 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 Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. 2/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 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 1-4: “Of all the possible floor dimensions, which floor dimension has the greatest perimeter? The least?” • Lesson 2-8: “If you created a graph with Alex’s age on the x-axis, what number might you count by? Explain.” • Lesson 3-6: “How many intervals does the sketch show? Explain.” • Topic 7, STEM: “What criteria might you consider when designing your slanted roof system to collect rainwater?” ### Indicator 3g Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning. 2/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 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. ### Indicator 3h Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary. 1/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 partially meet the 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 a topic and a lesson. The Program Overview includes the overarching philosophy of the program, a user’s guide, and a content guide. Each Topic has a Professional Development Video that presents full adult-level explanations of the mathematics concepts in the lessons. The Professional Development Video includes examples that are clearly explained. There is also a Math Background for each Topic and lesson that identifies the connections between previous grade, grade level, and future grade mathematics; however, these do not support teachers to understand the underlying mathematical progressions. The Assessment Source Book, Teacher Edition, and Mathematical Practices and Problem Solving Handbooks provide answers and sample answers to problems and exercises presented to students; however, there are no adult-level explanations to build understanding of the mathematics in the tasks. ### Indicator 3i Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve. 2/2 + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 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. ### Indicator 3j Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide). Narrative Evidence Only + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials cross-reference standards and provide a pacing guide. The Teacher Edition Program Overview includes a Pacing Guide, page 16. The Pacing Guide does not reference the standards covered but does provide an overview of the number of days expected per Topic. The standards are cross-referenced in multiple places including a Topic Planner at the beginning of each topic that shows the lesson names, vocabulary, objectives, standards, mathematical practices, and essential understandings for the Topic. The Topic Planner includes a suggested pacing for each lesson. ### Indicator 3k Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. Narrative Evidence Only + - Indicator Rating Details The instructional materials for enVision Florida Mathematics Grade 8 include strategies for parents to support their students' progress. The Teacher Resource Masters have Home School Connection Letters in English and Spanish for each Topic. The letters include information on the mathematical content, activities that parents could use with their child, and the Mathematical Practices section that encourages parents to support their child with the math presented in each Topic. In Grade 6 Topic 4, for example: • Sample Family Letter Intro: “Dear Family, Your child is learning how to write and solve algebraic equations involving addition, subtraction, multiplication, and division, and how to write and solve one-step inequalities. He or she will learn to use variables to represent numbers when solving real-world and mathematical problems. You child will also learn…..” • Sample Family Letter Activity: “How Much Is That? Look in newspapers for ads that give prices of groceries, electronics, toys, sporting goods, and other items that are of interest to your child. Use the ads to have your child write an equation. Suppose an ad shows a bicycle on sale for80. Examples of equations are shown below….”
• Sample Family Letter Focus on Mathematical Practices: “Observe Your Child: Use appropriate tools strategically. Help your child become proficient with this Mathematical Practice. A number line is an appropriate tool to use to describe the possible solutions of an inequality. Ask your child to represent the inequality from the activity above on a number line. Ask him or her to explain…..”

### Indicator 3l

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

The instructional materials for enVision Florida Mathematics Grade 8 include instructional practices that are research-based.

The Teacher Edition Program Overview describes the organization of the curriculum and why the structure was chosen. The core instructional model for enVision Florida is a two-step approach including Problem Based Learning and Visual Learning. The two steps are described, with references in the teacher materials.

### Criterion 3m - 3q

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills, and assessments that clearly denote which standards are being emphasized.

### Indicator 3m

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

### Indicator 3n

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

The instructional materials for enVision Florida Mathematics Grade 8 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

• Lesson 3-6, Error Intervention Item 12: “If students confuse the input and output, review how to label the axes correctly.”
• Lesson 1-2, Prevent Misconceptions Item 5: “Students may have trouble identifying 2,500 as a perfect square. Look at the first two digits in 2,500. Is 25 a perfect square? What is its square root? 2,500 is equal to 25 times 100. Is 100 a perfect square? What is the square root of 100?”

### Indicator 3o

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

The instructional materials for enVision Florida Mathematics Grade 8 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 (page viii) and generate reports that can help with grouping and differentiation (page xii)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, page viii, and generate reports that can help with grouping and differentiation, page xii.

### Indicator 3p

Materials offer ongoing formative and summative assessments:

### Indicator 3p.i

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

### Indicator 3p.ii

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

The instructional materials for enVision Florida Mathematics Grade 8 partially meet the 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 answer keys and/or sample student answers, however, scoring guidelines to assist the teacher in interpreting student performance are absent.
• There is no rubric to interpret student-written responses.
• Topic Readiness Assessments, as well as End of Topic Assessments have an Item Analysis for Diagnosis and Remediation. These items include the standard being assessed as well as a depth of knowledge level.
• 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.
• In addition, Item Analysis Charts identify the Depth of Knowledge level for each question, page viii. Teachers are also prompted to do observation and portfolios.

### Indicator 3q

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

The instructional materials for enVision Florida Mathematics Grade 8 include Mid-Topic Checkpoints that students fill in with a three-star self-rating question. It asks them to reflect on how well they did on the Mid-Topic assessment; the question doesn’t require writing, just filling in the stars. There are no other specific materials for students to monitor their own progress.

### Criterion 3r - 3y

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

### Indicator 3r

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

The instructional materials for enVision Florida Mathematics Grade 8 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 8, Lesson 8-1: Before: “What everyday objects are cylinders?” During: "When you take the top off a can what is its shape? If you break apart the rest of a can and flatten it out, what are the rest of the shapes?” After: "Is Ky correct when he writes that the longest side of the rectangle is equal to the circumference of the circle?”

### Indicator 3s

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

The instructional materials for enVision Florida Mathematics Grade 8 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. These 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.

### Indicator 3t

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

• Explore It! “Calvin and Mike do sit-ups when they work out. They start with 64 sit-ups for the first set and do half as many each subsequent set.  A) What representation can you use to show the relationship between the set number and the number of sit-ups? B) What conclusion can you make about the relationship between the number of sit-ups in each set?” Sample answers show two entry points to answering part B.

### Indicator 3u

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

### Indicator 3v

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

The instructional materials for enVision Florida Mathematics Grade 8 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 5-1 Enrichment Example 1: “Challenge students to complete the table showing the characteristics and number of solutions for different possibilities of two lines.”
• Lesson 5-1 Challenge Item 15: “Challenge students to change this system of equations so it has a different solution.”

### Indicator 3w

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

The instructional materials for enVision Florida Mathematics Grade 8 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.

### Indicator 3x

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

Materials provide opportunities for teachers to use a variety of grouping strategies.

Each lesson begins with whole-class instruction, then breaks into small groups to accomplish the lesson content, then comes back to whole class to discuss their learning before moving to independent practice. Beyond the format of the lesson, there are no specific grouping strategies suggested. If the digital materials are used for assessments, there are some reports that could help teachers group students with similar needs.

### Indicator 3y

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

Materials encourage teachers to draw upon home language and culture to facilitate learning.

• There is an English Language Learners Toolkit which provides many resources, including a limited list of key vocabulary in six languages.
• The digital materials include a Spanish-English glossary.
• Each Topic has a Home-School Connection letter that explains the contents of the topic in Spanish.
• The online Intervention Lessons/Remediation Lessons include a button for text in Spanish. It opens in a text box hovering over the problem on the screen.

The Publisher noted that Spanish resources are being planned for implementation in Fall 2019, including a complete student eText, the Additional Practice workbook, Assessment masters, and online interactive lessons; however, these components were not reviewed.

### Criterion 3aa - 3z

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 8: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; can be easily customized for individual learners; and include or reference technology that provides opportunities for teachers and/or students to collaborate with each other.

### Indicator 3aa

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

Digital materials, included as part of the core materials, are web-­based and compatible with multiple internet browsers, e.g., Internet Explorer, Firefox, Google Chrome, Safari, 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. Materials allow for the use of tablets and mobile devices including iPads, laptops, Chromebooks, MacBooks, and other devices that connect to the internet with an applicable browser.

### Indicator 3ab

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

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

• There are online games that enhance fluency as well as games where students use procedural skills to solve problems.
• Virtual Nerd offers tutorials on procedural skills, but no assessment or opportunity to practice the procedures is included with the tutorials.
• The online Readiness Assessment tab for each topic includes a Remediation link that has tutorials and opportunities for students to practice procedural skills using technology.

### Indicator 3ac

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

Materials can be easily customized for individual learners.

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

• 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.
• There is an online Accessible Student Edition that can be assigned to students.
• Closed Captioning is included in STEM and 3-Act videos.
• There are no adaptive technologies.

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

• Digital materials provide the same lessons to draw from on a topic as the print materials.
• Teachers can create and assign classes online for students.
• Teachers can create and upload files, attach links, and attach docs from Google Drive. These can be assigned to students.
• Teachers can create assessments using a bank of items or using self-written questions and assign to students.

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

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.

• There is a Discuss tab to assign discussion prompts to students in the Classes tab. A file can be attached.
• There is not an obvious way for multiple students to discuss with the teacher and one another.

### Indicator 3z

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

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

• Pearson Realize provides additional components online such as games, practice, instructional videos, links to other websites, differentiation, etc. Unfortunately, these are not detailed in the print materials. Teachers simply see statements on each lesson that there is more online; they may miss the depth of resources available.
• For each Mathematical Practice, there is a detailed interactive video included in the online materials.
• There are online tools and virtual manipulatives to use with the materials. However, in the teacher print materials, online resources are referenced generically without specific guidance. On the website, there is not an explicit link to activity directions for the online tools; they are not clearly labeled or connected to specific lessons. Opening a tool from the Math Tools icon menu is not helpful without the directions as the tools are not intuitive for students to use without guidance.
abc123

Report Published Date: 2019/01/15

Report Edition: 2020

Title ISBN Edition Publisher Year
Student Edition - Grade 8, Volume 1 9780134912721 Pearson 2020
Teacher Edition - Grade 8, Volume 1 9780134912776 Pearson 2020
Teacher Edition - Grade 8, Volume 2 9780134912851 Pearson 2020
Assessment Resource Book - Grade 8 9780134912929 Pearson 2020
Teacher Edition Program Overview - Grade 8 9780134912974 Pearson 2020
Teacher Resource Master - Grade 8, Volume 1 9780134913018 Pearson 2020
Student Edition - Grade 8, Volume 2 9780134913247 Pearson 2020
Teacher Resource Master - Grade 8, Volume 2 9780134913308 Pearson 2020

## Math K-8 Review Tool

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

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

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

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

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

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

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

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

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

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

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

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

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