8th Grade - Gateway 1

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

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

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

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

The instructional materials reviewed for enVision Florida Mathematics Grade 8 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 8, which is approximately 75 percent.
• The number of lessons (Content-focused lessons, 3-Act Mathematical Modeling, and STEM Projects, Topic Review, and Assessment) devoted to major work of the grade (including supporting work connected to the major work) is 71 out of 84, which is approximately 85 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 152 out of 176, which is approximately 86 percent.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 85 percent of the instructional materials focus on major work of the grade.

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

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

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

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

As designed, the instructional materials can be completed in 176 days. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. Several days are included in the course that can be used flexibly.

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

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

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

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

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

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

The instructional materials for enVision Florida Mathematics Grade 8 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

Examples of learning objectives that are visibly shaped by CCSSM cluster headings include:

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

Materials include problems and activities that connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.