8th Grade - Gateway 1
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Focus & Coherence
| Score | |
|---|---|
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 reviewed for Agile Mind Grade 8 meet expectations for focus and coherence. The instructional materials do not assess topics beyond Grade 8, and students and teachers using the materials as designed would devote the large majority of instructional time to the major work of the grade. The instructional materials meet expectations for coherence, and they show strength in having an amount of content that is viable for one school year and fostering coherence through connections within the grade.
Criterion 1.1: Focus
The instructional materials reviewed for Agile Mind Grade 8 meet expectations for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are not assessment items that align to topics beyond Grade 8.
Indicator 1a
The instructional materials reviewed for Agile Mind Grade 8 meet the expectations for assessing grade-level content. The majority of the Grade 8 assessment content was appropriate for the grade. There are some items in the assessments that align to standards above Grade 8 or address content not explicitly addressed in the CCSSM, but omitting or modifying these assessment items would not significantly impact the underlying structure of the Grade 8 materials.
The questions within the Practice and Assessment sections were reviewed for this indicator. The Practice sections within each topic contain multiple questions under the categories of Guided Practice and More Practice. The Assessment sections within each topic contain Automatically Scored questions and Constructed Response questions.
The questions that include content from future grades or address content not explicitly addressed in the CCSSM are as follows:
Topic 10 Guided Practice 14 asks students to write an exponential rule (F-LE.2): “Now, write an exponential function rule to find M, the amount of medicine left in the body t hours after the scan. Complete the process column in the table to help you find this rule.”
Topic 15 includes items assessing surface area of spheres, which is a topic not explicitly addressed by any standards from the CCSSM. These items are as follows:
Guided Practice: 3, 4, and 9
More Practice: 7, 8, and 9
Automatically scored: 2 and 4
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 reviewed for Agile Mind Grade 8 meet the expectations for students and teachers devoting the majority of class time to the major work of the grade when materials are used as designed. Overall, the materials spend approximately 83% of class time on the major work of Grade 8.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Agile Mind Grade 8 meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, the instructional materials spend approximately 83% of class time on the major clusters of Grade 8.
For this indicator, the following were examined: all Blocks of instruction within all Topics in Course Contents, Alignment to Standards in Course Materials, the Mathematics 8 Scope & Sequence with Common Core State Standards document in Professional Support, and the Block descriptions for each Topic located within Deliver instruction under Advice for Instruction in Professional Support. There are fifteen topics divided into the following categories: Overview, Explore, Summary, Practice, and Assessment. Each Topic contains 7 to 12 Blocks of instruction, and each Block of instruction represents a 45-minute class period.
In the Block descriptions for each Topic, individual activities are not assigned specific amounts of time, or ranges of time, for the activities to be completed. Thus, when calculating the percentage of class time spent on the major cluster of the grade, two perspectives were appropriate, Topics and Blocks. For these materials, analysis by Blocks is the most appropriate because the Topics do not have an equal number of Blocks within them and the Blocks are not subdivided into smaller increments.
In addition to the Blocks directly aligned to major clusters of the grade, all Blocks aligned to supporting clusters of the grade were also examined. Those Blocks aligned to supporting clusters that were found to incorporate major work of the grade were included in the calculations below:
Blocks: 109 of the 132 Blocks, approximately 83%, are spent on the major clusters of the grade.
Topics: 14 of the 15, Topics , approximately 93%, are spent on the major clusters of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Agile Mind Grade 8 meet the expectation for being coherent and consistent with the Standards. The instructional materials show strengths in having an amount of content that is viable for one school year but do not always make explicit connections between prior knowledge and future learning and the major work of the grade. Therefore, the progressions in the Standards are not always evident. The materials foster coherence within grade level work.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Agile Mind Grade 8 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Overall, supporting content is found primarily in Topics 2, 9, and 15, and the supporting content in these Topics does enhance focus and coherence by engaging students in the major work of the grade. Examples of the connections between supporting work and major work found in these topics include the following:
In Topic 2 Blocks 4, 8, 10, and 11 connect major standard 8.EE.2 to supporting standards 8.NS.1 and 8.NS.2. Students are identifying irrational numbers using perfect squares and writing and solving equations to find approximate values of radicals.
In Topic 9 Blocks 1, 2, 4, 5, and 7 connect major standards 8.F.3 and 8.F.4 to supporting standards 8.SP.1, 8.SP.2, and 8.SP.3. As students explore bivariate data they are making scatter plots, finding the line of best fit, writing the equation of the line, and using the line of best fit to interpret additional data.
In Topic 15 Blocks 3 and 6 connect major standards 8.F.3 and 8.F.4 to supporting standard 8.G.9. As students explore the surface area and volume formulas for cones, cylinders, and spheres they are comparing properties of functions that are represented in different ways and looking at examples of functions that are not linear.
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 reviewed for Agile Mind Grade 8 meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. The suggested pacing contains 15 Topics and 132 Blocks (days) of instruction, including assessments. According to the Agile Mind Mathematics 8 Scope and Sequence, each block is expected to last 45 minutes. Some lessons (Constructed Response, MARS tasks) may take longer than indicated.
Each Block includes the following sections: Overview, Exploring, Summary, and Assessment. The Exploring pages are categorized by math concept and can be discussed and reviewed as a class or by individuals/small groups of students.
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 reviewed for Agile Mind Grade 8 partially meet the expectations for being consistent with the progressions in the Standards. Overall, the materials develop according to the grade-by-grade progressions in the Standards, and they give all students extensive work with grade-level problems. However, content from prior or future grades is not always clearly identified or related to grade-level work, and the materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades.
Examples of Grade 8 materials in which off grade-level content is present and not identified as such includes the following:
In Topic 10 Blocks 4, 5, and 6, aligned to 8.F.3, extend above grade-level when students must write equations for nonlinear functions, especially exponential functions (F-LE.2).
In Topic 11 Block 4, aligned to 8.EE.7, involves solving one-step (6.EE.7) and two-step (7.EE.4) equations algebraically.
The Grade 8 materials provide extensive work with grade-level standards. All students are expected to complete the same problems, and lessons or ideas presented for differentiated instruction also include grade-level problems. The MARS tasks that are included, especially the ones in Topics 5, 7, 8, 9, and 12, are places where students are given the opportunity to engage with the grade-level standards to their full intent.
In lessons where prior knowledge is included, identification of content from prior grades is mentioned in four components of the materials, but the identification is general and not explicitly connected to a grade-level or standard. Examples from the four components are as follows:
In the first paragraph of the About the Course section, there is a brief, general overview of topics of which students acquired a foundation prior to Grade 8.
The first paragraph in Agile Mind Mathematics 8 Scope and Sequence, 2016-2017 briefly references prior work with expressions, equations/inequalities, dependent/independent variables, area, surface area, and volume and how these concepts connect to Grade 8 work.
The Advice for Instruction section references prior work in different places, although specific standards are not referenced. Some examples of this include:
In Topic 3 Topic at a glance states, “Throughout this topic, it is assumed that students have had previous exposure to the meaning of exponents.”
In Topic 5 the following Prerequisite skills are listed under Prepare instruction: Labeling coordinate axes, Plotting points, Reading information from graphs, Recognizing constant rates of change given a graphical representation, Representing constant rates of change given a verbal description, and Calculating unit rates. The Prerequisite skills are not explicitly connected to any previous, grade-level standards.
In Topic 7 the Goals and objectives start by stating, “The topic Linear patterns and functions builds on students' work in patterning in previous grades to develop the formal notion of 'function' and to begin to recognize patterns that can be modeled with linear functions.”
In Topic 14 Opening the lesson for Block 4 states, “Students have seen angle relationships from two intersecting lines and from two lines cut by a transversal. They have also seen how the various angle pairs they have been working with relate to each other and how they can be used to establish the fact that two lines are parallel. Now, we want to find ways to extend these geometric relationships to other shapes and situations.”
In Topic 15 the first Classroom strategy for Block 1 states, “This Exploring connects to students’ prior understandings of surface area of pyramids and prisms and extends that understanding to include cylinders, cones and spheres.”
The Overview of the student material sometimes informs students what they will learn within the Topic and occasionally gives a general connection to previous learning. For example, the Overview of Topic 2 states, “In this topic, you will learn about a set of numbers that behave quite differently from numbers you are currently familiar with. Let’s review the types of numbers that you have learned about in previous mathematics courses.”
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 reviewed for Agile Mind Grade 8 meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.
Some examples of Topic Headings and Goals and Objectives shaped by cluster headings include the following:
Topic Headings:
In Topic 7 “ Linear patterns and functions” is shaped by 8.F.A,B.
In Topic 11 “Solving Linear Equations” is shaped by 8.EE.C.
Goals and Objectives:
In Topic 2 “know that there are numbers that are not rational” is shaped by 8.NS.A.
In Topic 3 “generate the laws of exponents and apply them in problem solving situations” is shaped by 8.EE.A.
In Topic 4 “apply the Pythagorean Theorem and its converse in problem situations” is shaped by 8.G.B.
In Topic 7 “use variables to generalize linear patterns and represent problem situations that can be modeled by linear functions” is shaped by 8.F.B.
In Topic 13 “solve systems of linear equations using the substitution method” is shaped by 8.EE.C.
The following are topics that contain problems and/or activities which connect two or more clusters in a domain or two or more domains in a grade.
In Topic 4, 8.G.B and 8.EE.A are connected as students solve problems involving the Pythagorean Theorem by applying knowledge of square roots.
In Topic 7, 8.F.A and 8.F.B are connected as students define, evaluate, and compare functions along with using functions to model relationships between quantities.
In Topic 8, 8.F.A and 8.EE.B are connected as students connect various representations of a function by writing equations, making graphs and tables, and interpreting values within these representations.
In Topic 10, 8.F.A and 8.F.B are connected as students explore nonlinear relationships by examining examples of functions that are not linear and by qualitatively describing the relationship between two quantities that are not linear.