Alignment: Overall Summary

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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).


See Rating Scale
Understanding Gateways

Alignment

|

Meets Expectations

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

Usability

|

Meets Expectations

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

+
-
Gateway One Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

The instructional materials reviewed for enVision Florida Mathematics Grade 6 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:

  • Lesson 6-1 Quiz: Understand and Use Percent, Question 3: “Peter babysits his sister on Monday and Friday. He babysits for his neighbor 40% of the days Monday through Friday. On the weekend, Peter babysits 50% of the days. How many days does Peter babysit each week?” (6.RP.1.3c)
  • Topic 7 Assessment : Solve Area, Surface Area, and Volume Problems, Question 7: “What is the surface area of the triangular prism shown?” (6.G.1.4) Question 8: “The net below represents a container. What solid figure does it show?” (6.G.1.4)
  • Topics 1-6 Cumulative /Benchmark Assessment, Question 5: “Last month, Tara worked 16.5 hours the first week, 19 hours the second week, 23 hours the third week, and 15.75 hours the fourth week. She plans to work more hours this month than last month. Write an inequality to represent the number of hours, h, Tara plans to work this month.” (6.EE.2.8, 6.NS.2.3)
  • Topic 1 Assessment: Use Positive Rational Numbers Form A, Question 6: “Raven is making pillows. Each pillow requires $$\frac{3}{5}$$ yard of fabric. Raven has 6$$\frac{2}{3}$$ yards of fabric. Find the number of pillows Raven can make.  A. 11 pillows; B. 10 pillows; C. 5 pillows; D. 4 pillows.” (6.NS.1.1)

There are above grade-level assessment items that could be modified or omitted without impact on the underlying structure of the instructional materials. These items include:

  • Topic 5 Assessment: Understand and Use Ratio and Rate, Question 10: discuss properties of circles (7.G.2.4).
  • Lesson 4-10 Quiz:  Represent and Solve Equations and Inequalities, Question 6: "Stacy has 3 collector’s cards. She receives 2 more cards each week that she volunteers at the student center. Let = the number of weeks. Let y = the number of collector’s cards. Which equation represents the amount of cards Stacy has? A) y = 3x; B) y = 2x+3; C) y = 3x+2; D) y = x/2 + 2."  (7.EE.2.4a)

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
+
-
Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

The instructional materials reviewed for enVision Florida Mathematics Grade 6 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 6.5 out of 8, which is approximately 81 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 73 out of 93, which is approximately 78 percent.
  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 161 out of 194, which is approximately 83 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 78 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
+
-
Criterion Rating Details

The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

The instructional materials reviewed for enVision Florida Mathematics Grade 6 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:

  • 6.NS.2 supports 6.EE.1 in Lesson 3-2, Cross-Cluster Connection: “Finding common factors and multiples of two whole numbers connects to using the properties of operations, such as the Distributive Property, to generate equivalent algebraic expressions. "In the Student Edition, page 125, Example 3 directly connects GCF and the Distributive Property: “Use the GCF and the Distributive Property to find the sum of 18 and 24.”
  • 6.G.1 supports 6.EE.2 in Lessons 7-1, and 7-6, Cross-Cluster Connection: "Applying understanding and knowledge of numerical and algebraic expressions and how they work connects to using formulas when solving real-world and mathematical problems involving area, surface area, and volume." (6.G.1)
  • 6.G.1 supports 6.NS.3 in Lesson 2-3: Finding absolute value on a number line is connected to drawing polygons on a coordinate plane.
  • 6.G.1 supports 6.NS.3 in Lesson 2-6: Students use their understanding of integers to represent polygons on the coordinate plane.
  • 6.G.1 supports 6.EE.2 in Lesson 7-2: Students connect finding the area of triangles to writing and solving equations.

There was an instance where the teacher materials stated a connection; however, that was not supported in the student work:

  • Lesson 8-1, Cross-Cluster Connection: “Recognizing a statistical question and understanding statistical variability (6.SP.1) connects to recognizing and analyzing quantitative relationships between dependent and independent variables." (6.EE.3) The student work in this chapter does not include discussion of independent/dependent variables, nor are they mentioned in problems.

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
+
-
Indicator Rating Details

Instructional materials for enVision Florida Mathematics Grade 6 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 194 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. Though this is slightly above the suggested range, 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 61 Content-focused Lessons, two days per lesson, for a total of 122 days.
  • There is one 3-Act Mathematical Modeling Lesson for each of the eight Topics, two days per Topic, for a total of 16 days.
  • There is one STEM Project per Topic, for a total of eight days.
  • There is one Topic Review and one Assessment per Topic, one day each for a total of 16 days.
  • There are four additional days per Topic 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
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 meet expectations for the materials being consistent with the progressions in the standards.

The Grade 6 materials develop according to the grade-by-grade progressions with content from prior or future grades clearly identified and related to grade-level work. Prior knowledge from earlier grades is explicitly related to grade-level concepts.

  • 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 grade 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.
  • In Topic 5, Understand and Use Ratio and Rate: Look Back recalls that, in Grade 5, students learned to use the four operations with fractions, converted measurement units, and graphed points on a coordinate plane (5.NF.1, 5.MD.1, 5.G.1). Earlier learning in Grade 6 includes computing with rational numbers, finding common factors and multiples, and solving one-step equations with rational numbers (6.NS.2, 6.EE.2). Look Ahead states that later in Grade 6, students will use percent (6.RP.3c), and in Grade 7,  they will learn unit rates of fractions, $$\pi$$, and proportions.

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 2-4, Integers and Rational Numbers: “In Grade 5, students represented real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane. In this lesson, students extend their knowledge to plot-ordered pairs with integer and rational coordinates in all four quadrants of a coordinate plane and to reflect points across both axes. Later in this Topic, students will use what they learn to find distances between two points on a coordinate plane."

Off grade-level work, when present, is preparation for Grade 6 work and is identified as such. In Lesson 1-3, Multiply Fractions addresses 5.NF.4. The Teacher Edition states that this lesson “prepares for 6.NS.1.”

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The Additional Practice Workbook and Reteach to Build Understanding worksheets, found in The Teacher’s Resource Masters, 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 5, Understand and Use Ratio and Rate, students work with ratio reasoning and graph ratios, use tables to create equivalent rates, and convert measurement within and between measurement systems. (6.RP.1)
  • Reteach to Build Understanding, page R3-4 reviews definitions for variable, algebraic expression, term, and coefficient at the top of the page, then scaffolds the following question: “Luca works at the grocery store on the weekends. He earns $8.50 an hour. Choose a variable to represent the number of hours Luca works. Write an algebraic expression to represent the total amount Luca earns from working at the grocery store." (6.EE.2)
  • Enrichment 8-1, page E8-1 leads students through a mini-research study. (6.SP.1.1, 6.SP.2.4, and 6.SP.2.5) “Follow the steps to complete a mini-research study. (1) Write a statistical question. (2) Identify the target audience. (3) Ask at least 15 people from your target audience the statistical question from Step 1. (4) Create a dot plot to display the data collected in step 3. (5) Summarize the data displayed in Step 4.”

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
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 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:

  • Objectives for Lesson 3-1, Evaluate expressions with whole-number exponents and 3-6, Identify and write equivalent expressions are shaped by 6.EE.1, Apply and extend previous understandings of arithmetic to algebraic expressions.
  • The objective for Lesson 5-8, Use ratio reasoning and conversion factors to convert customary units of measure, is shaped by 6.RP.1, Understand ratio concepts and use ratio reasoning to solve problems.
  • The objective for Lesson 8-2, Determine the measures of center of a data set, is shaped by 6.SP.1, Develop understanding of statistical variability.

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.

  • 6.RP.1 and 6.NS.3 are connected in Lesson 5-4, when students plot rational numbers in the coordinate plane as they analyze proportional relationships.
  • 6.EE.1 and 6.RP.1 are connected in Lesson 4-3, when writing subtraction and addition equations is connected to understanding ratio concepts in bar diagrams.
  • 6.RP.1 and 6.EE.1 are connected in Lesson 6-5, when finding the percent connects to real-world problems involving one variable.
  • 6.RP.1 and 6.EE.3 are connected in Lesson 5-4, when students interpret a graph showing the relationship between two quantities to make a prediction about the variables.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

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.

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
+
-
Indicator Rating Details

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.

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
+
-
Indicator Rating Details

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."

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
+
-
Indicator Rating Details

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.

Criterion 2e - 2g.iii

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

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.

Indicator 2f

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

The instructional materials reviewed for enVision Florida Mathematics Grade 6 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 5-5, students look for entry points to a problem when they determine how they can use a table to make sense of the quantities in the problem.
  • MP.2.1: In Lesson 4-8, students use reasoning to explain how the size and contents of a box may affect its weight. In Lesson 6-2, students write both quantities and compare them in a written explanation: “Write the part of the grid that is shaded yellow as a decimal and a percent. How are the decimal and the percent alike, and how are they different?”
  • MP.6.1: In Lesson 3-7, students use precision as they communicate clearly when identifying and describing equivalent expressions. In Lesson 5-6, students express numerical answers with a degree of precision appropriate to the context of problem using the correct symbols: “Explain how to decide which is the better value. 4 greeting cards for $10 or 6 greeting cards for $14.”
  • MP.7.1: In Lesson 2-3, students use structure of number lines to analyze, compare and order rational numbers. In Lesson 1-5, students “use patterns to apply the algorithm for dividing with fractions.”
  • MP.8.1: In Lesson 2-6, students generalize when they apply formulas for finding the perimeter of polygons to finding the perimeter of polygons on the coordinate plane. In Lesson 7-2, students generalize when they analyze/look for repeated reasoning in the rule for finding the area of any triangle. In Lesson 6-6, students generalize about percents of a number as they evaluate whether results are reasonable.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

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
+
-
Indicator Rating Details

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.”

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 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?”

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 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.

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 6 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 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.

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 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.

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 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.

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 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.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 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 6 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 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?”

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 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.  

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 6 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 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.

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).
0/0
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 cross-reference standards and provide a pacing guide.

The Teacher Edition Program Overview includes a Pacing Guide. 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.
0/0
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 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. For example, in Topic 4:

  • 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 for $80. 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.
0/0
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 use 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
+
-
Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

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.

Indicator 3n

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

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.”

Indicator 3o

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

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.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

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.

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
+
-
Indicator Rating Details

The instructional materials for enVision Florida Mathematics Grade 6 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, page xi.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
+
-
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
+
-
Criterion Rating Details

​The instructional materials reviewed for enVision Florida Mathematics Grade 6 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
+
-
Indicator Rating Details

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?"

Indicator 3s

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

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.

Indicator 3t

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

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.”

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
+
-
Indicator Rating Details

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.

Indicator 3v

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

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.”

Indicator 3w

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

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.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
+
-
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.
0/0
+
-
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 3z - 3ad

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 6: 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 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.
0/0
+
-
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. These are not detailed in the print materials, and teachers see statements in each lesson that there are more resources online.
  • 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. 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.  

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.
0/0
+
-
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.
0/0
+
-
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.
0/0
+
-
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 to assign to students.

Indicator 3ad

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.).
0/0
+
-
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 no evidence for multiple students to collaborate with the teacher or each other.

Additional Publication Details

Report Published Date: 01/15/2019

Report Edition: 2020

Title ISBN Edition Publisher Year
Student Edition - Grade 6, Volume 1 9780134912691 Pearson 2020
Teacher Edition - Grade 6, Volume 1 9780134912752 Pearson 2020
Teacher Edition - Grade 6, Volume 2 9780134912844 Pearson 2020
Assessment Resource Book - Grade 6 9780134912875 Pearson 2020
Teacher Edition Program Overview - Grade 6 9780134912936 Pearson 2020
Teacher Resource Master - Grade 6, Volume 1 9780134912998 Pearson 2020
Additional Practice Workbook - Grade 6 9780134913049 Pearson 2020
Student Edition - Grade 6, Volume 2 9780134913216 Pearson 2020
Teacher Resource Master - Grade 6, Volume 2 9780134913292 Pearson 2020

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

The publisher has not submitted a response.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. 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).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, 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.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric 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 rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric 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.

X