7th Grade - Gateway 1

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)

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.

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.
  

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.
  

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)
  

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.