6th Grade - Gateway 1

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet the expectations for focus within assessment.

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

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

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

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

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

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6.5 out of 8, which is approximately 81 percent.
• The number of lessons (Content-focused lessons, 3-Act Mathematical Modeling, and STEM Projects, Topic Review, and Assessment) devoted to major work of the grade (including supporting work connected to the major work) is 73 out of 93, which is approximately 78 percent.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 161 out of 194, which is approximately 83 percent.

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

The instructional materials reviewed for enVision Florida Mathematics Grade 6 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

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

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

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

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

Instructional materials for enVision Florida Mathematics Grade 6 meet expectations that the amount of content designated for one grade-level is viable for one year.

As designed, the instructional materials can be completed in 194 days. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. Though this is slightly above the suggested range, several days are included in the course that can be used flexibly.

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

• There are 61 Content-focused Lessons, two days per lesson, for a total of 122 days.
• There is one 3-Act Mathematical Modeling Lesson for each of the eight Topics, two days per Topic, for a total of 16 days.
• There is one STEM Project per Topic, for a total of eight days.
• There is one Topic Review and one Assessment per Topic, one day each for a total of 16 days.
• There are four additional days per Topic for remediation, fluency practice, differentiation, and other assessment, for a total of 32 days.

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

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

• Each Topic begins with “Get Ready! Review What You Know!” This section includes below grade-level work that is clearly identified and connected to the topic being introduced.
• Each Topic has a Topic Overview for the teacher that includes “Math Background Coherence.” This shows progression of a concept across grade levels: Look Back shows how the topic connects to what students learned earlier; Look Ahead shows how the Topic connects to what students will learn later.
• In Topic 5, Understand and Use Ratio and Rate: Look Back recalls that, in Grade 5, students learned to use the four operations with fractions, converted measurement units, and graphed points on a coordinate plane (5.NF.1, 5.MD.1, 5.G.1). Earlier learning in Grade 6 includes computing with rational numbers, finding common factors and multiples, and solving one-step equations with rational numbers (6.NS.2, 6.EE.2). Look Ahead states that later in Grade 6, students will use percent (6.RP.3c), and in Grade 7,  they will learn unit rates of fractions, $$\pi$$, and proportions.

At the beginning of each lesson there is “Focus, Coherence, and Rigor” for the teacher to connect prior and future learning with the lesson being taught. Lesson 2-4, Integers and Rational Numbers: “In Grade 5, students represented real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane. In this lesson, students extend their knowledge to plot-ordered pairs with integer and rational coordinates in all four quadrants of a coordinate plane and to reflect points across both axes. Later in this Topic, students will use what they learn to find distances between two points on a coordinate plane."

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

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

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

The instructional materials for enVision Florida Mathematics Grade 6 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards.

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

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

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

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