## enVision Florida Mathematics

##### v1
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Our Review Process

Title ISBN Edition Publisher Year
Student Edition - Grade 7, Volume 1 9780134912707 Pearson 2020
Teacher Edition - Grade 7, Volume 1 9780134912769 Pearson 2020
Teacher Edition - Grade 7, Volume 2 9780134912837 Pearson 2020
Teacher Resource Master - Grade 7, Volume 1 9780134912868 Pearson 2020
Assessment Resource Book - Grade 7 9780134912899 Pearson 2020
Teacher Edition Program Overview - Grade 7 9780134912950 Pearson 2020
Student Edition - Grade 7, Volume 2 9780134913223 Pearson 2020
Teacher Resource Master - Grade 7, Volume 2 9780134913278 Pearson 2020
Teacher Edition - Grade 5, Volume 1 9780134910598 Pearson 2020
Teacher Edition - Grade 5, Volume 2 9780134910659 Pearson 2020
Student Edition - Grade 5, Volume 1 9780134910727 Pearson 2020
Student Edition - Grade 5, Volume 2 9780134910796 Pearson 2020
Teacher Resource Master - Grade 5, Volume 1 9780134910864 Pearson 2020
Teacher Resource Master - Grade 5, Volume 2 9780134910925 Pearson 2020
Assessment Sourcebook - Grade 5 9780134910994 Pearson 2020
Teacher Edition Program Overview, Grade 5 9780134922317 Pearson 2020
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
Student Edition - Grade 6, Volume 2 9780134913216 Pearson 2020
Teacher Resource Master - Grade 6, Volume 2 9780134913292 Pearson 2020
Teacher Edition - Grade 1, Volume 1 9780134910550 Pearson 2020
Teacher Edition - Grade 1, Volume 2 9780134910611 Pearson 2020
Student Edition - Grade 1, Volume 1 9780134910673 Pearson 2020
Student Edition - Grade 1, Volume 2 9780134910741 Pearson 2020
Teacher Resource Master - Grade 1, Volume 1 9780134910819 Pearson 2020
Teacher Resource Master - Grade 1, Volume 2 9780134910888 Pearson 2020
Assessment Sourcebook - Grade 1 9780134910956 Pearson 2020
Teacher Edition Program Overview, Grade 1 9780134922270 Pearson 2020
Teacher Edition - Grade 2, Volume 1 9780134910567 Pearson 2020
Teacher Edition - Grade 2, Volume 2 9780134910628 Pearson 2020
Student Edition - Grade 2, Volume 1 9780134910680 Pearson 2020
Student Edition - Grade 2, Volume 2 9780134910758 Pearson 2020
Teacher Resource Master - Grade 2, Volume 1 9780134910826 Pearson 2020
Teacher Resource Master - Grade 2, Volume 2 9780134910895 Pearson 2020
Assessment Sourcebook - Grade 2 9780134910963 Pearson 2020
Teacher Edition Program Overview, Grade 2 9780134922287 Pearson 2020
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
Teacher Edition - Grade 4, Volume 1 9780134910581 Pearson 2020
Teacher Edition - Grade 4, Volume 2 9780134910642 Pearson 2020
Student Edition - Grade 4, Volume 1 9780134910710 Pearson 2020
Student Edition - Grade 4, Volume 2 9780134910789 Pearson 2020
Teacher Resource Master - Grade 4, Volume 1 9780134910840 Pearson 2020
Teacher Resource Master - Grade 4, Volume 2 9780134910918 Pearson 2020
Assessment Sourcebook - Grade 4 9780134910987 Pearson 2020
Teacher Edition Program Overview, Grade 4 9780134922300 Pearson 2020
Teacher Edition - Grade 3, Volume 1 9780134910574 Pearson 2020
Teacher Edition - Grade 3, Volume 2 9780134910635 Pearson 2020
Student Edition - Grade 3, Volume 1 9780134910703 Pearson 2020
Student Edition - Grade 3, Volume 2 9780134910765 Pearson 2020
Teacher Resource Master - Grade 3, Volume 1 9780134910833 Pearson 2020
Teacher Resource Master - Grade 3, Volume 2 9780134910901 Pearson 2020
Assessment Sourcebook - Grade 3 9780134910970 Pearson 2020
Teacher Edition Program Overview, Grade 3 9780134922294 Pearson 2020
Teacher Edition - Grade K, Volume 1 9780134910543 Pearson 2020
Teacher Edition - Grade K, Volume 2 9780134910604 Pearson 2020
Student Edition - Grade K, Volume 1 9780134910666 Pearson 2020
Student Edition - Grade K, Volume 2 9780134910734 Pearson 2020
Teacher Resource Master - Grade K, Volume 1 9780134910802 Pearson 2020
Teacher Resource Master - Grade K, Volume 2 9780134910871 Pearson 2020
Assessment Sourcebook - Grade K 9780134910949 Pearson 2020
Teacher Edition Program Overview, Grade K 9780134922263 Pearson 2020
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### Overall Summary

The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for alignment to the Mathematics Florida Standards (MAFS). ​The instructional materials meet expectations for Gateway 1, focus and coherence, by focusing on the major work of the grade and being coherent and consistent with the Standards.  The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor and meaningfully connecting the Standards for Mathematical Content and the Cluster Standards for Mathematical Practice (MPs).

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

### Focus & Coherence

​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 7 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' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet the expectations for focus within assessment.

According to the Assessment Guide, enVision Florida contains four categories for assessment: 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 2 Assessment: Analyze and Use Proportional Relationships Question 3: Given a graph to examine, students answer, “Part A: What is the constant of proportionality, and what does it mean in this situation? Part B: Choose one ordered pair on the graph. What does it represent in this situation?” (7.RP.1.2b)
• Topic 1 Assessment: Integers and Rational Numbers, Form A, Question 2  “Four out of nine dogs weigh less than 20 pounds. What is the decimal equivalent for the number of dogs weighing under 20 pounds? A) 0.$$\overline{2}$$; B) 0.24; C) 0.$$\overline{4}$$; D) 0.49” (7.NS.1.2d)
• Topic 3 Performance Task: Analyze and Solve Percent Problems, Form A, Question 6: “The sanctuary takes out a $12,500 loan to renovate its gift shop. At 5% simple interest, how much would the sanctuary need to pay back in total after 10 years?” (7.RP.1.3) • Topics 1-4 Cumulative/Benchmark Assessment Question 10: Given a linear graph of earnings vs. time, students answer, “The graph represents the amount of money Sal earns for babysitting. Part A: What does the ordered pair (2.5, 20) represent in the situation? Part B: Does the graph represent a proportional relationship? Explain. Part C: What is the linear equation represented by the graph?” (7.RP.1.2a,c,d) #### Criterion 1.2: Coherence Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade. ​The instructional materials reviewed for enVision Florida Mathematics Grade 7 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' | indicatorName}} Instructional material spends the majority of class time on the major cluster of each grade. The instructional materials reviewed for enVision Florida Mathematics Grade 7 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 5.5 out of 8, which is approximately 69 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 67 out of 89, which is approximately 75 percent. • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 144 out of 186, which is approximately 77 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 75 percent of the instructional materials focus on major work of the grade. #### Criterion 1.3: Coherence Coherence: Each grade's instructional materials are coherent and consistent with the Standards. The instructional materials reviewed for enVision Florida Mathematics Grade 7 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' | indicatorName}} Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. The instructional materials reviewed for enVision Florida Mathematics Grade 7 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: • 7.G.1 supports 7.RP.1 in Lesson 8-1, students use proportional reasoning when they analyze scale drawings. • 7.SP.3 supports 7.RP.1 in Lessons 7-3 and 7-4, students use proportional reasoning when they extrapolate from random samples and use probability. • 7.SP.3.5 supports 7.EE.2.3 in Lesson 7-1, Cross-Cluster Connection: “Calculating the probability of a chance event connects to applying properties of operations to solve real-life and mathematical problems.” • 7.G.2.4 supports 7.EE.2.4a in Lesson 8-5: Calculating the diameter of a circle connects to solving word problems using equations. Students use the circumference in an equation to solve for diameter. • 7.SP.2 supports 7.EE.2 in Lesson 6-4: “Finding the measure of center and variation of random sample to make inferences about populations connects to applying properties of operations to solve multi-step real-life problems.” • 7.SP.1 supports 7.RP.1 in Lesson 6-2: students “make comparative inferences about a population based on random samples connecting to solving multi-step problems using ratios and percents.” • 7.G.2.5 supports 7.RP.1.2 in Lesson 8-4, students connect finding the unknown angle measurement to using proportional relationships. ##### Indicator {{'1d' | indicatorName}} The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. Instructional materials for enVision Florida Mathematics Grade 7 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 186 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 57 Content-focused Lessons, two days per lesson, for a total of 114 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 for each, or 16 days total. • There are four additional days per Topic for remediation, fluency practice, differentiation, and other assessment, for a total of 32 days. ##### Indicator {{'1e' | indicatorName}} Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades. The instructional materials for enVision Florida Mathematics Grade 7 meet expectations for the materials being consistent with the progressions in the standards. The Grade 7 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. For example: • In Topic 3, Analyze and Solve Percent Problems, the Look Back recalls that in Grade 6, “Students learned about ratio reasoning using equivalent ratios and tables of equivalent ratios and used their understanding to work with percents.” (6.RP.1) Earlier in Grade 7, “Students made connections between ratios, rate, and unit rate and ratios with fractions.” They also learned about proportional relationships, how to write equations that describe proportional relationships, how to graph proportional relationships and use this to solve multi-step problems. (7.RP.1) • The Look Ahead states that later in Grade 7, students will learn to write expressions, use properties of operations, and expand expressions with rational coefficients. They will solve equations using tables, graphs, and diagrams. (7.EE.1, 7.EE.2) In Grade 8 students will continue to use connections with proportional relationships to work with scale factor in percent form, in scale drawings, and to differentiate between reduction and enlargement (8.EE.3). Students will also use similar triangles to investigate slope and develop equations (8.EE.2) 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, Understand Proportional Relationships: Equivalent Ratios, “In Grade 6, students found equivalent ratios and used ratio and rate reasoning to solve real-world problems. In this lesson, students look for equivalent ratios to identify proportional relationships and use proportions to solve problems. Later in this Topic, students will use the constant of proportionality to write equations for proportional relationships and graph a line through the origin, deciding whether they can use proportional reasoning to solve given problems. Off grade-level work, if present, 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. 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. For example, in Topic 3: • Analyze and Solve Percent Problems, students analyze percents between 1-100, greater than 100, and less than 1 to make a connection between percent and proportion. They use real-life situations to deepen understanding by solving problems that involve markups, markdowns, and taxes. They learn interest terminology and the formula for simple interest. (7.RP.1.3) • Reteach to Build Understanding, defines population and representative sample at the top of the page, then scaffolds the following question: “Walter wants to learn more about the preferred salad ingredients of students in his school. He surveys all students in his math class and finds that 4 prefer tomatoes, 14 prefer carrots, and 9 prefer cucumbers. What is the population and the sample? Is the sample a representative same? Explain." 1. The population is the entire group of people that Walter is studying. What is the population Walter wants to study? 2. Add the number of responses to determine the sample. The sample is ____ + ____ + ____ = ____ students in Walter’s math class. 3. Think about whether Walter’s sample accurately reflects the entire population. Is Walter’s example representative? Explain. “ (7.SP.1) • Enrichment 3-6, “A bank offers three different savings accounts.” A table shows the account types, minimum initial deposit, and annual simple interest rate. “Make a graph that shows the annual balance of a Super Savings account opened with an initial deposit of$500, assuming no additional deposits or withdrawals are made. How would the graph be different for an initial deposit greater than $500? How would the graph be different for a Basic Savings account? Explain.” (7.RP.1.3) ##### Indicator {{'1f' | indicatorName}} Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. The instructional materials for enVision Florida Mathematics Grade 7 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 Lesson 7-4, Develop a probability model to evaluate a situation and Make an estimate, is shaped by 7.SP.3, Investigate chance processes and develop, use, and evaluate probability models. • The objectives for Lesson 1-3, Add positive and negative integers and Model integer addition in real-life applications, are shaped by 7.NS.1, Apply and extend previous understandings of operations with fractions. • The objectives for Lesson 4-8, write equivalent expressions by combining like terms, using the distributive property, and performing other mathematical operations, is shaped by 7.EE.1, Use properties of operations to generate equivalent expressions. • The objective for Lesson 8-5, Calculate the circumference, radius, or diameter of a circle is shaped by 7.G.2, Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 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. • 7.NS.1 and 7.EE.2 are connected in Lesson 4-2, when students use algebraic expressions and equations that include rational numbers. • 7.RP.1 and 7.EE.2 are connected in Lesson 3-3, when students use their understanding of proportional relationships and equations with percentages. • 7.EE.1 and 7.RP.1 are connected in Lesson 2-1, when solving multi-step problems using ratios, rates, and unit rates is connected to using numerical and algebraic expressions and equations. • 7.EE.1 and 7.NS.1 are connected in Topic 4, 3-Act Mathematical Modeling, when simplifying algebraic expressions connects to adding, subtracting, multiplying, and dividing rational numbers. • 7.SP.2 and 7.SP.1 are connected in Lesson 7-5, when representing sample spaces for compound events connects to generating a random sample that is representative of a population. ###### Overview of Gateway 2 ### Rigor & Mathematical Practices ​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for Gateway 2, rigor and balance and practice-content connections. The instructional materials meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor, and they meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). ##### Gateway 2 Meets Expectations #### Criterion 2.1: Rigor Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. ​The instructional materials reviewed for enVision Florida Mathematics Grade 7 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' | indicatorName}} Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The instructional materials for enVision Florida Mathematics Grade 7 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, students use number lines to build their understanding by writing matching equations. In Example 2, “Ian’s football team lost two yards on a running play. Then they received a 5-yard penalty. What is the team’s total change in yards? Write a subtraction expression to represent the change in yards. Write an equivalent addition expression.” This example also shows the problem using a number line. (7.NS.1.1c and 7.NS.1.1d) • Lesson 1-6, Example 2, “Why is it easier to show three groups of -500 on the number line than -500 groups of 3?” (7.NS.1.2a and 7.NS.1.2c) • In Lesson 4-3, students simplify expressions by combining like terms with both integer and rational coefficients, as well as with two variables. (7.EE.1.1) Do You Understand? Question 1, “How are properties of operations used to simplify expressions?” Practice and Problem Solving Question 17, “Explain whether 11t - 4t is equivalent to 4t - 11t. Support your answer by evaluating the expression for t = 2.” • In Lesson 1-1, students are shown how positive and negative numbers relate to zero on a number line by combining opposite quantities. Problems include determining the change in a temperature drop and the end height of a car on a roller coaster after dropping and rising. (7.NS.1.1a) 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' | indicatorName}} Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The instructional materials for enVision Florida Mathematics Grade 7 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 1-5, students use the same procedure for adding and subtracting signed rational numbers as they do when adding and subtracting integers. (7.NS.1.1b and c) For example, Practice and Problem Solving, Question 11: “Simplify each expression. a) $$50\frac{1}{2}+(-12.3)$$ b) $$-50\frac{1}{2}+(-12.3)$$ c) $$-50\frac{1}{2}+12.3$$.” • In Lesson 5-3, students use the distributive property to organize information in word problems in order to write and solve equations. (7.EE.2.3 and 7.EE.2.4a) For example, Do You Know How? Question 4: “A family of 7 bought tickets to the circus. Each family member also bought a souvenir that cost$6. The total amount they spent was $147. How much did one ticket cost?” • In Lesson 1-9, students divide rational numbers. (7.NS.1.2b) For example, Practice and Problem Solving, question 15: “Find the quotient. Express your answer as a simplified fraction. $$\frac{3}{8}\div3.8$$” • In Lesson 7-1, students use probability to describe chance, likelihood, and fairness. (7.SP.3.5) For example, Practice and Problem Solving, question 8: “A spinner has 8 equal-sized sections. Six of the sections are green. A) What is the probability that the spinner will land on green? ____ out of 8, or ____/4, or ____%. B) Use words to describe the probability. It is ____ that the spinner will land on green.” In addition, each cumulative assessment spirals through all previous topics, reviewing key information with a variety of problems to reinforce skills. ##### Indicator {{'2c' | indicatorName}} Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade The instructional materials for enVision Florida Mathematics Grade 7 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 demonstrate the use of mathematics flexibly and independently in a variety of contexts. Non-routine problems are typically found in Performance Tasks and STEM activities. • In Lesson 2-1, Practice and Problem Solving, students apply knowledge of solving multi-step problems with rational numbers to solving problems with ratios, rates, and unit rates. (7.RP.1.1 and 7.RP.1.3) Question 9: Given 3 bags of rice, “Which package has the lowest cost per ounce of rice?” • In Lesson 1-10, Do You Know How?, students solve problems using rational numbers operations. (7.NS.1.3) Question 6, page 66: “The temperature of a cup of coffee changed by -54$$\degree$$F over $$22\frac{1}{2}$$ minutes. What was the change in temperature each minute?” In Practice and Problem Solving, Question 11, page 67: “Brianna works as a customer service representative. She knows that the amount of her yearly bonus is$155, but $2.50 is taken away for each customer complaint about her during the year. What is her bonus if there are 12 complaints about her in a year?” • In Topic 5 STEM Project (7.EE.2.3 and 7.EE.2.4), students research filtration systems, decide which one they would purchase, and plan a fundraiser. Part of planning is writing an equation to represent the amount of money they will earn from a fundraiser to purchase the filtration system. • In Topic 2 3-Act Mathematical Modeling: Mixin' It Up (7.RP.1.1 and 7.RP.1.2a), students attempt to make liquid in a water glass have the same flavor as that of a large water cooler. Question 15, "A classmate usually adds six drops to 16 ounces of water. Use your updated model to predict the number she would use for the large container." ##### Indicator {{'2d' | indicatorName}} Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. The instructional materials for enVision Florida Mathematics Grade 7 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 8-1: Students build conceptual knowledge of scale using scale drawings to find actual lengths and widths of things like a kitchen island, flooring needed in a living room, and the dimensions of a tennis court. Students use the scale to write proportions in order to solve for actual measurements. • Lesson 5-3: Students learn and practice procedural skills using the distributive property to solve for problems that include a negative number. • Lesson 7-3: Students apply the concepts of experimental and theoretical probability by comparing them: “Hakeem randomly draws equal-sized cards labeled with letters A, B, C, D, and F from a hat and records the results in the table. Compare the theoretical and experimental probabilities of randomly drawing a card that is labeled with the letter C.” Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. • In Lesson 6-2, students build conceptual understanding of using random samples to make and compare inferences about populations and determine if the inferences are valid. In Lesson 6-3, students practice procedures to compare two populations using measures of center and variability. In Lesson 6-4, students apply their knowledge of measures of center and variability and make inference about two populations. • Lesson 1-3: Students build conceptual understanding of adding integers and apply this in real-world problems. Students start by analyzing the level of water in a pool. All of the examples in the lesson utilize a number line and students are prompted in the exercises to use a number line. Finally they apply it in situations such as Practice & Problem Solving question 13, “A submarine traveling 200 meters below the surface of the ocean increases its depth by 45 meters. Adam says that the new location of the submarine is -155 meters. Describe an error Adam could have made that would result in the answer he gave.” 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 4-2 Simplifying Expressions identifies a connection to 7.EE.1.1 with an emphasis on conceptual understanding. “Students develop a deeper understanding of the Associative and Commutative Properties and become fluent in simplifying expressions by combining like terms.” The lesson starts with students looking at how Marco and Andrea sorted a pile of number tiles that included variables: Marco did it by variable, Andrea used coefficients. Next, example 1 uses pictures of algebra tiles to simplify “-2c + 3c - 5 - 4c + 7.” Example 2 is “-3 + $$\frac{1}{3}$$x + (-4.5) - $$\frac{1}{5}$$x” and uses properties of operations to solve. The rest of the lesson and practice uses procedural steps. Students do not have an opportunity to develop understanding of like terms. #### Criterion 2.2: Math Practices Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice ​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). The MPs are identified and used to enrich mathematics content, and the instructional materials support the standards’ emphasis on mathematical reasoning. ##### Indicator {{'2e' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. The instructional materials reviewed for enVision Florida Mathematics Grade 7 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 1-5, page 31A states, “MP.8.1 Express Regularity in Repeated Reasoning: Students will generalize about the solutions of equations of the form $$x^2=p$$, where p is a positive rational number and of the form $$x^3=p$$.” • In Student Practice problems, MPs are labeled with descriptions within problems. For example, Lesson 3-1, Practice and Problem Solving Question 17, “Make Sense and Persevere: 153 is 0.9% of what number? Tell which equivalent ratios you used to find the solution.” The MPs are consistently used to enrich the mathematical content. • MP.2.1 enriches the mathematical content when students interpret and compare statistical measures and reason about data sets in both qualitative and quantitative forms. Lesson 6-3 Do You Understand? Question 5 says, “The box plots describe the heights of flowers selected randomly from two gardens. Use the box plots to answer 4 and 5. Make a comparative inference about the flowers in the two gardens.” Practice and Problem Solving, Question 9 says, “A family is comparing home prices in towns where they would like to live. The family learns that the median home price in Hometown is equal to the median home price in Plainfield and concludes that the homes in Hometown and Plainfield are similarly priced. what is another statistical measure that the family might consider when deciding where to purchase a home?” • MP.1.1 enriches the mathematical content when students examine the relationships between the quantities and solve for the whole. Lesson 3-2, Question 11: “A restaurant customer left$3.50 as a tip. The tax on the meal was 7% and the tip was 20% of the cost including tax. What was the total bill?”
• MP.4.1 enriches the mathematical content when students use a table as a mathematical model to represent a real-world situation. They use the quantities in the table to write expressions that represent relationships in the context of the situation. Lesson 1-10, Model with Math, Solve & Discuss It!: “Stefan estimates the income and expenses for renting a phone accessory store in the mall. He enters the amounts in the table below. Should Stefan rent a phone accessory store? Explain.”

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 2-4, the Table of Contents lists MPs 2.1, 3.1, 4.1, & 7.1, but only MPs 2.1 and 7.1 are listed in the Lesson Overview. MPs 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' | indicatorName}}
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for enVision Florida Mathematics Grade 7 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 1-4, students use number lines to represent subtraction of two integers to explore the idea that subtraction of a number is the same as adding its opposite. In Lesson 3-2, students make sense of givens, constraints, and relationships by solving multi-step problems in real-world situations involving percent.
• MP.2.1: In Lesson 8-4, Explore It!, students reason about angle quantities and their relationships in a problem situation related to folding chairs. In Lesson 6-2, students make inferences about two sets of data and determine if either set is valid or not. Students demonstrate understanding that not all subsets of a population are necessarily representative of the sample.
• MP.6.1: In Lesson 8-7, students describe cross sections in clear mathematical language, giving precise measurements of their dimensions. In Lesson 5-4, students find the error by correctly using the appropriate property to solve the inequality.
• MP.7.1: In Lesson 6-6, students “analyze relationships between values in double number line diagrams to solve percent problems.” In Lesson 4-3, students use structure when identifying which terms in an algebraic expression are like terms.
• MP.8.1: In Lesson 2-4, students recognize that all proportional relationships can be represented by equations of the form y = kx, where k is the constant of the proportionality. In Lesson 5-4, students “use tables and graphs to model and solve real-world problems.” In Lesson 6-1, students “use hundredths grids and number lines to represent the percent of the whole.”
##### Indicator {{'2g' | indicatorName}}
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
##### Indicator {{'2g.i' | indicatorName}}
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for enVision Florida Mathematics Grade 7 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 7-7, Practice and Problem Solving: “Construct Arguments: How is the difference between the simulated probability and the theoretical probability of an actual event related to the number of simulated trials conducted?”
• Lesson 5-3, Explain It!: “Six friends go jet skiing. The total cost for the adventure is $683.88, including a$12 fee per person to rent flotation vests. Marcella says they can use the equation 6r + 12 = 683.88 to find the jet ski rental cost, r, per person. Julia says they need to use the equation 6(r + 12) = 638.88. A) Whose equation accurately represents the situation? Construct an argument to support your response. B) What error in thinking might explain the inaccurate equation?”
• Lesson 5-5, Practice and Problem Solving, Question 2: “Why is -x <3 equivalent to x> -3? Provide a convincing argument.”
• Lesson 4-5, Practice and Problem Solving, Question 17: “Ryan says the expression 3 + 5y cannot be factored using GCF. Is he correct? Explain why or why not.”
• Lesson 2-1, Explain It?: “In a basketball contest, Elizabeth made 9 out of 25 free throw attempts. Alex made 8 out of 20 free throws attempts. Janie said that Elizabeth had a better free-throw record because she made more free throws than Alex. A) Do you agree with Janie’s reasoning? B) Decide who had the better free-throw record. Justify your reasoning using mathematical arguments.”
• Lesson 8-5, Do You Understand?: “Are there any circles for which the relationship between the diameter and the circumference cannot be represented by pi? Explain.”
##### Indicator {{'2g.ii' | indicatorName}}
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for enVision Florida Mathematics Grade 7 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 Anna’s and Armando’s work and ask: 'How are Anna’s and Armando’s approach similar? How are they different?'” In Lesson 2-1, Explain It!, “How does Janie’s statement compare with Kyle’s argument to oppose it? What additional reasoning does Kyle use to oppose Janie’s statement?”
• In the Visual Learning portion of the lesson, there are sections labeled, Elicit and Use Evidence of Student Thinking and Convince Me. In Lesson 7-3, the materials prompt teachers with, “Is it possible for the theoretical probability to be $$\frac{1}{2}$$ while the experimental probability is 1? Give an example.”
• 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?”
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for enVision Florida Mathematics Grade 7 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 7 Probability, the vocabulary listed for the lessons includes: outcomes, probability, event, theoretical probability, experimental probability, relative frequency, sample space, probability model, compound event, and simulation.
• New vocabulary terms are highlighted in the text and definitions are provided within the sentence where each term is found. In Lesson 7-3, the terms relative frequency and experimental probability are highlighted and definitions provided within the sentence each term is found. “The relative frequency is the ratio of the number of times an event occurs to the total number of trials.”
• 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 7, Use Vocabulary in Writing: “A restaurant serves either skim milk or whole milk in glasses that are small, medium, or large. Use vocabulary words to explain how you cold determine all the possible outcomes of milk choices at the restaurant. Use vocabulary words 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. In Lesson 3-2, Pose Purposeful Questions, “Multiply the numerator and denominator of $$\frac{20}{100}$$ by an integer to get an equivalent fraction with a numerator of 260. What is the multiplier? What is the equivalent fraction?”
• Each mid-Topic checkpoint includes a vocabulary section where students demonstrate understanding of the terms.

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for being well-designed and taking into account effective lesson structure and pacing. The instructional materials include an underlying design that distinguishes between problems and exercises, assignments that are not haphazard with exercises given in intentional sequences, variety in what students are asked to produce, and manipulatives that are faithful representations of the mathematical objects they represent.

##### Indicator {{'3a' | indicatorName}}
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials for enVision Florida Mathematics Grade 7 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example:

• Lesson 1-3: Students use number lines to add integers and look for patterns and opposites.
• Lesson 3-1: Students use bar diagrams and fraction representations to explain proportional relationships with a percent equations.
• Lesson 6-2: Students construct arguments and use reasoning to determine if an inference is valid.
• Lesson 2-1: Students compare the free throw records of two players and construct a mathematical argument to justify which player has a better record.
• Lesson 1-4: Students use number lines and write equations to show their understanding of adding and subtracting integers.
• Lesson 7-5: Students use tree diagrams and tables to demonstrate the outcomes of a compound event.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for enVision Florida Mathematics Grade 7 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' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials for enVision Florida Mathematics Grade 7 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 3.2: Teacher Planning

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for supporting teacher learning and understanding of the CCSSM. The instructional materials include: quality questions to support teachers in planning and providing effective learning experiences, a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials, a teacher edition that partially contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons, and explanations of the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials for enVision Florida Mathematics Grade 7 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: “What do negative numbers and positive numbers represent in this problem?”
• Topic 1, 3-Act Mathematical Modeling Lesson: “Why do you think your prediction is the answer to the Main Question?”
• Lesson 2-2: “What are two different ways to solve this problem?”
• Lesson 6-4: “Why is it important to use statistical measures to compare populations?”
##### Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials for enVision Florida Mathematics Grade 7 cross-reference standards and provide a pacing guide.

The Teacher Edition Program Overview includes a Pacing Guide, which 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' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials for enVision Florida Mathematics Grade 7 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 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' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials for enVision Florida Mathematics Grade 7 use research-based instructional practices.

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 3.3: Assessment

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge, strategies for teachers to identify and address common student errors and misconceptions, opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills, and assessments that clearly denote which standards are being emphasized.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials for enVision Florida Mathematics Grade 7 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

• Lesson 5-2, Prevent Misconceptions Item 4: “Remind students to write each number as a fraction before multiplying.”
• Lesson 5-3, Error Intervention Item 6: “Students may need help drawing a conclusion from the data.”
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for enVision Florida Mathematics Grade 7 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.

##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials encourage students to monitor their own progress.

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 3.4: Differentiation

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 7 meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations, and they provide opportunities for advanced students to investigate mathematics content at greater depth. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials for enVision Florida Mathematics Grade 7 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 3, Lesson 3-1: Before: “How would you find the total cost of a bill plus a 15% tip?” During: “How do you find an equal share among four people?” After: “What did Caleb assume about the amount each person would pay? Did Caleb and Jackie use the same steps to find one share with a 15% tip? Explain.”
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials for enVision Florida Mathematics Grade 7 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.

• Topic 1, 3-Act Mathematical Modeling: Students are shown a video and then are encouraged to consider the situation and ask any questions that come to mind. Teachers are given the Main Question which students will be tasked with answering: “Who will win the game? What is the final score?”Teachers are given questions and tips to facilitate discussion about the 3-Act Mathematical Modeling activities.
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials for enVision Florida Mathematics Grade 7 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 8-9 Enrichment Example 3: “Challenge advanced students to find the volume of the shed by thinking of it as a prism with a pentagon for a base.”
• Lesson 8-3 Challenge Item 7: “Reinforce the students’ understanding of the classification of triangles by angle measures and side lengths.”
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for enVision Florida Mathematics Grade 7 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' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

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' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

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 3.5: Technology

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 7: integrate technology in ways that engage students in the Mathematical Practices; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; can be easily customized for individual learners; and include or reference technology that provides opportunities for teachers and/or students to collaborate with each other.

##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

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

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' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

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.).

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

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.

## Report Overview

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

#### Math K-2

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

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

#### Math 3-5

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

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

#### Math 6-8

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

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

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### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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