6th Grade - Gateway 1

The instructional materials reviewed for Grade 6 meet the expectation for assessing the grade-level content and, if applicable, content from earlier grades. The Sample Unit Quizzes and Tests included in the Teacher Resources Part 1 Section I and Teacher Resources Part 2 Section U, along with the answer keys and "Scoring Guides and Rubrics," were reviewed for this indicator. Examples of Unit Tests that include great-level assessment items include the following:

• In Teacher Resources Part 1, the Unit 5 Test that addresses standards from 6.RP has students complete ratio tables, find the percent of a quantity, answer word problems using equivalent ratios, and represent different relationships with ratios.
• In Teacher Resources Part 2, the Unit 3 Test that addresses standards from 6.EE.A,B has students writing and evaluating numerical expressions with whole-number exponents, writing algebraic expressions, and solving word problems by writing and solving one variable equations of the form x + p = q or px = q.

The instructional materials reviewed for Grade 6 meet the expectations for spending the majority of class time on the major clusters of each grade. Overall, approximately 65 percent of class time is devoted to major work of the grade.

The materials for Grade 6 include 15 Units. In the materials, there are 171 lessons, and of those, 28 are Bridging lessons. According to the materials, Bridging lessons should not be “counted as part of the work of the year” (page A-56), so the number of lessons examined for this indicator is 143 lessons. The supporting clusters were also reviewed to determine if they could be factored in due to how strongly they support major work of the grade. There were connections found between supporting clusters and major clusters, and due to the strength of the connections found, the number of lessons addressing major work was increased from the approximately 84 lessons addressing major work as indicated by the materials themselves to 92.5 lessons.

Three perspectives were considered: 1) the number of units devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of instructional days devoted to major work including days for unit assessments.

The percentages for each of the three perspectives follow:

• Units– Approximately 67 percent, 10 out of 15;
• Lessons– Approximately 65 percent, 92.5 out of 143; and
• Days– Approximately 65 percent, 102.5 out of 158.

The number of instructional days, approximately 65 percent, devoted to major work is the most reflective for this indicator because it represents the total amount of class time that addresses major work.

The instructional materials reviewed for Grade 6 meet the expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. When appropriate, the supporting work enhances and supports the major work of the grade-level.

Examples where connections are present include the following:

• In Lesson 4 of Unit 6 in Teacher Resources Part 1 and Lesson 25 of Unit 5 in Teacher Resources Part 2, the materials connect 6.NS.C with 6.G.3 as students graph points in the coordinate plane in order to solve mathematical problems about polygons.
• In Lessons 12 and 13 of Unit 6 in Teacher Resources Part 1, the materials connect 6.EE.7 with 6.G.1 as students are expected to solve real-world and mathematical problems by writing and solving equations that arise from finding the area of triangles, parallelograms, and trapezoids.
• In Lessons 33 and 41 of Unit 8 in Teacher Resources Part 2, the materials connect 6.EE.7 with 6.G.2 as students are expected to solve real-world and mathematical problems by writing and solving equations that arise from finding the volume of a right rectangular prism.

The instructional materials reviewed meet the expectations for having an amount of content designated for one grade-level that is viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is approximately 158 days which is appropriate for a school year of approximately 140-190 days.

• The materials are written with 15 units containing a total of 171 lessons.
• Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 171 lessons, and of those, 28 are Bridging lessons. Twenty-eight Bridging lessons have been removed from the count because the Teacher's Edition states that they are not counted as part of the work for the year, so the number of lessons examined for this indicator is 143 lessons.
• There are 15 unit tests which are counted as 15 extra days of instruction.
• There is a short quiz every 3-5 lessons. Materials expect these quizzes to take no more than 10 minutes, so they are not counted as extra days of instruction.

The instructional materials reviewed for Grade 6 meet the expectation for being consistent with the progressions in the Standards. Overall, the materials address the standards for this grade-level and provide all students with extensive work on grade-level problems. The materials make connections to content in future grades, and they explicitly relate grade-level concepts to prior knowledge from earlier grades.

The materials develop according to the grade-by-grade progressions in the Standards, and content from prior or future grades is clearly identified and related to grade-level work. The Teacher Resources contain sections that highlight the development of the grade-by-grade progressions in the materials, identify content from prior or future grades, and state the relationship to grade-level work.

• At the beginning of each unit, "This Unit in Context" provides a description of prior concepts and standards students have encountered during the grade levels before this one. The end of this section also makes connections to concepts that will occur in future grade-levels. For example, "This Unit in Context" from Unit 5, Geometry: Coordinate Grids, of Teacher Resources Part 2 describes the geometric topics students encountered in Grade 5, specifically graphing in the first quadrant of the coordinate plane, the work students will encounter graphing and solving problems in all four quadrants of the coordinate plane, and how the work of this unit will build to transformations and the Pythagorean Theorem in Grade 8.

There are some lesson that are not labeled Bridging Lessons that contain off, grade-level material, but these lessons are labeled as “preparation for” and can be connected to grade-level work. For example, Lesson 31 of Unit 4 in Teacher Resources Part 1 addresses multi-digit addition with positive integers, and the lesson is labeled as "preparation for 6.NS.3."

The materials give all students extensive work with grade-level problems. The lessons also include "Extensions," and the problems in these sections are on grade-level.

• Whole class instruction is used in the lessons, and all students are expected to do the same work throughout the lesson. Individual, small-group, or whole-class instruction occurs in the lessons.
• The problems in the Assessment & Practice books align to the content of the lessons, and they provide on grade-level problems that "were designed to help students develop confidence, fluency, and practice." (page A-51, Teacher Resources)
• In the Advanced Lessons, students get the opportunity to engage with more difficult problems, but the problems are still aligned to grade-level standards. For example, the problems in Lesson 28 of Unit 5 in Teacher Resources Part 2 engage students in reflecting points across one axis and then the other, but these problems still align to 6.NS.6. Also, the problems in Lesson 41 of Unit 8 in Teacher Resources Part 2 that have students solving problems involving volume and surface area of prisms and pyramids align to standards from 6.NS, 6.EE, and 6.G.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of these explicit connections include:

• Every lesson identifies "Prior Knowledge Required" even though the prior knowledge identified is not aligned to any grade-level standards. For example, Lesson 9 of Unit 3 in Teacher Resources Part 2 identifies knowing addition and subtraction, along with multiplication and division, as inverse operations in order for students to accomplish the goal of the lesson, which is solving one-step equations using logic and the concept of operations.
• There are 28 lessons identified as Bridging Lessons, and most of these lessons are aligned to standards from prior grades and also state for which grade-level standards they are preparation. Lesson 2 of Unit 3 in Teacher Resources Part 1, which has students write and solve addition equations, is aligned to 4.OA.3 and is in preparation for 6.EE.2 and 6.EE.5. Also, Lessons 1 and 3 of Unit 6 in Teacher Resources Part 1, which have students identify right angles, parallel lines and perpendicular lines, are aligned to 4.G.1 and 4.G.2 and are in preparation for 6.G.3.

The instructional materials reviewed for Grade 6 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings and make connections within and across domains.

In the materials, the units are organized by domains and are clearly labeled. For example, Teacher Resources Part 1 Unit 3 is entitled Expressions and Equations: Variables and Equations, and Teacher Resources Part 2 Unit 9 is entitled Statistics and Probability: Distribution. Within the units, there are goals for each lesson, and the language of the goals is visibly shaped by the CCSSM cluster headings. For example, in Unit 8 of Teacher Resources Part 2, the goal for Lesson 41 states "Students will solve problems involving the surface area of rectangular and triangular pyramids and prisms and the volume of rectangular prisms." The language of this goal is visibly shaped by 6.G.A, "Solve real-world and mathematical problems involving area, surface area, and volume."

The instructional materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. Examples of these connections include the following:

• In Lesson 36 of Unit 4 in Teacher Resources Part 1 and Lessons 23 and 24 of Unit 5 in Part 2, the materials connect 6.NS.B with 6.NS.C as students compute fluently with multi-digit numbers and order rational numbers.
• In Lessons 10 and 11 of Unit 6 in Teacher Resources Part 1, the materials connect 6.EE.A with 6.EE.B as students evaluate expressions at specific values of their variables and solve real-world and mathematical problems by writing and solving equations.
• In Lessons 5 through 9 of Unit 9 in Teacher Resources Part 2, the materials connect 6.SP.A with 6.SP.B as students develop an understanding of statistical variability and summarize and describe distributions.
• In Lesson 5 of Unit 6 in Teacher Resources Part 1, the materials connect 6.NS with 6.EE as students solve real-world and mathematical problems by graphing points and writing and solving equations.
• In Lessons 39 and 40 of Unit 8 in Teacher Resources Part 2, the materials connect 6.G with 6.NS as students represent three-dimensional figures using nets made up of rectangles and triangles, use the nets to find the surface area of these figures, and compute fluently with multi-digit numbers.