6th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials for Ready Grade 6 meet the expectation for focusing on the major work of the grade and having a sequence of topics that is consistent with the logical structure of mathematics. The materials do not assess topics before the grade level indicated and are coherent and consistent with the standards, and the materials spend approximately 65 percent of class time on the major clusters of the grade.
Criterion 1.1: Focus
The instructional materials for Ready Grade 6 meet the expectations for not assessing topics before the grade level in which the topic should be introduced. Overall, the materials assess grade-level content and, if applicable, content from earlier grades.
Indicator 1a
The instructional materials reviewed for Ready Grade 6 meet the expectations for assessing grade-level content. The program provides two versions (Form A and Form B) of Mid-Unit assessments, Interim assessments, and End of Unit assessments for each unit. The assessments are available online and in print format.
In general, assessments contain grade-level content questions. Examples of questions include the following:
- In Unit 1, Mid-Unit Assessment Form B, Question 5, students represent a ratio as a picture or diagram, and write the ratio in three ways. (6.RP.A)
- In Unit 4, Unit Assessment Form B, Question 5, students find the area of a triangle from a diagram in a real-world context. (6.G.1)
However, Unit 3 Ratio and Proportionality assessments contain problems that align to above grade-level standards. The following assessment items could be modified or omitted without a significant impact on the instructional flow of the unit:
- The Performance Task on the Interim Assessment and Questions 1 and 4 on both forms of the End of Unit Assessment have students write, interpret, and solve equations of the form r = px + q. (7.RP.2c, 7.EE.4a)
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 for Ready Grade 6 meet the expectations for devoting the majority of class time to the major work of the grade. Overall, the instructional materials spend approximately 65 percent of class time on the major clusters of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Ready Grade 6 meet expectations for spending a majority of instructional time on major work of the grade. To determine focus on major work, three perspectives were evaluated: the number of units devoted to major work, the number of lessons devoted to major work, and the number of instructional days devoted to major work. Of the three perspectives, the number of instructional days is most representative and was used to determine the score for this indicator.
- Grade 6 instruction is divided into five units. Unit 1 addresses 6.RP, Unit 2 addresses 6.NS, and Unit 3 addresses 6.EE. Therefore, three out of five units, approximately 60 percent, focus on major work of the grade.
- Grade 6 instruction is divided into 29 lessons. Nineteen out of 29 lessons, approximately 65 percent, focus on major work of the grade or supporting work connected to major work.
- Grade 6 instruction consists of approximately 129 instructional days including quizzes, with an additional two days per unit for games, performance tasks, and unit or interim assessments. In total, there are 139 days of instruction, of which 90 days, approximately 65 percent, focus on major work of the grade or supporting work connected to major work.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials for Ready Grade 6 meet the expectation for being coherent and consistent with the CCSSM Standards. Overall, the instructional materials have supporting content that enhances focus and coherence, are consistent with the progressions in the standards, and foster coherence through connections at a single grade, where appropriate and required by the standards.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Ready 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 are connected to the major standards/clusters of the grade.
Examples of the connections between supporting work and major work include the following:
- Unit 4, Lesson 22, Area of Polygons (6.G.A) is connected to the major work of expressions, equations, and inequalities (6.EE.A and 6.EE.B). Students evaluate expressions at specific values. Students use formulas to find the volume of polygons.
- Unit 1, Lesson 4, Solve Problems with Unit Rate (6.RP.3) is tied to supporting standards 6.NS.2,3 as students are solving equivalent ratio problems involving the division of multi-digit numbers and the four operations with multi-digit decimals.
- In Unit 2, Lesson 11, Common Factors and Multiples (6.NS.4), students use common factors to rewrite a numerical expression using the distributive property (6.EE.3).
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials for Ready 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 approximately 145 days with 15 additional days for assessment and diagnostics, for a total of 160 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. According to the Teacher Guide page A44, each lesson is expected to last between 45 and 60 minutes. Other lesson resources include Fluency Skills Practice, Practice and Problem Solving, Unit Opener Lessons, and Classroom Routine Lessons for the first 5 days, which is included in the total number of days for this program.
Indicator 1e
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 Ready Grade 6 partially meet expectations for the materials being consistent with the progressions in the Standards.
The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each unit begins with a Unit Opener progression overview chart. The Learning Progressions set a context for the standards of the lessons based on how the standard builds on prior knowledge, particularly from the previous grades, and how it leads to expectations for the next grade. Additionally, prerequisite skills are connected to new skills and concepts in the Lesson Overview document with Small Group Differentiation and Personalized Learning Lessons. For example, Unit 2, Lesson 7 Overview, the Learning Progression states, “In Grade 5 students learn to understand fractions as division and to divide whole numbers by unit fractions. Earlier in Grade 6 students built upon the understanding from Grade 5 using models to show division of fractions.” Furthermore, the introduction of each lesson presents an opportunity to connect students’ prior knowledge to what they are going to learn. For example, in Unit 3 Lesson 15, the Use What You Know section reminds students: "You already know that multiplication is a shorter way to write repeated addition. You use exponents to write repeated multiplication in a shorter way.”
The instructional materials do not make clear connections across the domains Expressions and Equations (Unit 3) and Ratios and Proportional Relationships (Unit 1). In Grade 6, students work with equations of the form of q=px (6.EE.7). Students work with equations in the form of q=px in Unit 3, Lesson 19, and as inequalities in the form q and q>px in Unit 3, Lesson 20. In Unit 3, Lesson 21, students work with equations in the form of px+q=r where $$q\neq0$$ (7.EE.4a). In addition, there is no connection in Unit 3 Lessons 19 and 21 to the underlying mathematics of equations in the form of q=px where p is defined as a unit ratio, and that in Grade 7 p is defined as a proportional relationship. Furthermore, these connections between ratio and proportionality, and linear equations are the critical foundation for the study of functions in Grade 8 and High School. The removal of above grade level Lesson 21 does not impact the learning progression of Unit 3 for Grade 6, however, the removal of Lesson 21 means that there are no lessons that address Standard 6.EE.9.
Students also engage with grade-level problems in the Practice and Problem Solving Book as well as Additional Fluency Practice section of the teacher website. However, there are some standards where students do not have sufficient opportunities to practice a grade level standard. For example, In Unit 4 Lesson 25, there is not enough practice with finding the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths in order to meet the full intent of the volume standard 6.G.2.
Indicator 1f
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 Ready Grade 6 meet expectations that materials foster 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 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.
Instructional materials are clearly shaped by the CCSSM cluster headings. The units are divided into grade-level domains. Grade 6 standards are clearly identified in the Table of Contents and in the Ready Mathematics Standards Correlations pages, which identify the lessons that address specific standards. Instructional materials shaped by cluster headings include the following examples:
- Unit 2, Lesson 7, Divide with Fractions is shaped by 6.NS.A, apply and extend previous understandings of multiplication and division to divide fractions by fractions.
- Unit 2, Lesson 12, Understand Positive and Negative Numbers is shaped by 6.NS.C, apply and extend previous understandings of numbers to the system of rational numbers.
- Unit 4, Lesson 25, Volume is shaped by 6.EE.A and 6.G.A, apply and extend previous understandings of arithmetic to algebraic expressions and solve real-world and mathematical problems involving area, surface area, and volume.
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, in cases where the connections are natural and important. At the end of every unit there is a Performance Task and/or Interim Assessment that connects two or more clusters in a domain. For example:
- The Unit 2 Performance Task connects 6.RP.A, understand ratio concepts and use ratio reasoning to solve problems, with 6.NS.B, compute fluently with multidigit numbers and find common factors and multiples.
- Unit 3, Lesson 16 Algebraic Expressions connects 6.EE.A, apply and extend previous understandings of arithmetic to algebraic expressions, to 6.EE.B, reason about and solve one-variable equations and inequalities.
- The Unit 4 Interim Assessment connects 6.NS.B, compute fluently with multidigit numbers and find common factors and multiples, with 6.G.A, solve real-world and mathematical problems involving area, surface area, and volume, and 6.RP.A, understand ratio concepts and use ratio reasoning to solve problems.