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 reviewed for Agile Mind Grade 6 meet expectations for focus and coherence. The instructional materials do not assess topics beyond Grade 6, and students and teachers using the materials as designed devote the large majority of instructional time to the major work of the grade. The instructional materials meet the expectations for coherence, and they show strengths 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 6 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 6.
Indicator 1a
The instructional materials for Agile Mind Grade 6 meet the expectations for assessing grade-level content. The majority of the Grade 6 assessment content was appropriate for the grade, but there are some items in the assessments that align to standards above Grade 6. The assessment items that align to standards above Grade 6 could be modified/omitted without effecting the underlying structure of the materials or are mathematically reasonable in relationship to the Grade 6 standards.
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 assessment items that are above Grade 6 but are mathematically reasonable in relationship to the Grade 6 standards are as follows:
- In Topic 2 Automatically Scored 3, Guided Practice 13 and More Practice 12 ask students to identify different ways to write a given proportion (7.RP.2).
- In Topic 2 Constructed Response 2a has students describe how proportions can be used to show that three photos are proportional (7.RP.2).
- In Topic 2 Guided Practice 14 asks students to determine if one figure is proportional to another one, and More Practice 8 and 9 have students analyze the outcome of specified enlargements to photographs to determine if the result is proportional to the original (7.RP.2a).
- In Topic 2 Constructed Response 3, parts c and d ask students to determine the scale factor needed to create one geometric figure from another and to determine the area of a figure created with a given scale factor (7.G.1).
The assessment items that include content from future grades and could be modified/omitted without effecting the underlying structure of the materials are as follows:
- In Topic 7 Automatically Scored 9 and Constructed Responses 1 and 3 have students qualitatively describe a relationship between two variables by analyzing distance-time graphs (8.F.5).
- In Topic 11 More Practice 26, 27, and 29 have students write equations and inequalities of the form y = mx + b (7.EE.4).
- In Topic 12 Automatically Scored 1 students use square root to find the length of one side of a square (8.EE.2).
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 6 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 65% of class time on the major work of Grade 6.
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 6 meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, the instructional materials spend approximately 65% of class time on the major clusters of Grade 6.
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 6 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 6 to 14 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.
There are 141 Blocks in Grade 6 Agile Mind.
- All Blocks in Topics 2, 3, 4, 7, 8, 9, 10, and 11 aligned to major work of the grade. In addition, three Blocks in Topic 6 were also aligned to major work of the grade. Thus, 73 of 141 Blocks, approximately 52%, aligned to major clusters of Grade 6.
- A review of Topics and Blocks aligned to supporting clusters in Grade 6 demonstrated that in 19 of these Blocks, the supporting clusters connected to major clusters as well. Thus 19 of 141 Blocks connected supporting clusters of the grade to major clusters of Grade 6.
Overall, 92 out of 141 Blocks, approximately 65%, connected or aligned to major work 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 6 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 6 meet the 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 5-7 and 9-15, and the supporting content 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 include the following:
- In Topic 1 Block 4 major standards 6.EE.1,2 are tied to supporting standard 6.NS.2 as students divide multi-digit numbers when evaluating numerical expressions.
- In Topic 1 Block 7 major standard 6.EE.3 is tied to supporting standard 6.NS.4 as students find the area of a segmented banner using the distributive property.
- In Topic 7 Blocks 1-8 major standard 6.RP.3 is tied to supporting standards 6.NS.2,3 as students are solving various rate and measurement problems involving the division of multi-digit numbers and the four operations with multi-digit decimals.
- In Topic 11 major cluster 6.EE.B is tied to supporting standards 6.NS.2,3 as students are writing and solving equations and inequalities with a variety of rational numbers.
- In Topic 12 Block 4 major standard 6.RP.3 is tied to supporting standard 6.G.1 as students find the percentage of areas in the MARS Task: Flag.
- In Topics 12 and 13 supporting cluster 6.G.A is connected to major cluster 6.EE.B as students occasionally write the expressions and equations needed to calculate areas, surface areas, and volumes.
- In Topic 14 Block 4 major standard 6.RP.3 is tied to supporting standard 6.SP.4 as students use percentages to display and describe numerical data in a circle graph.
- In Topic 15 Block 2 major standard 6.EE.1 is tied to supporting standard 6.SP.3 as students write expressions that are evaluated to find the mean of a set of data.
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 6 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 138-141 Blocks (days) of instruction, including assessments. According to the Agile Mind Mathematics 6 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. The Scope and Sequence suggests that Block 6: Metric Conversion in Topic 7: Rates and Measurement can be used as extension content. In addition, Blocks 7-8: Representing 3-Dimensional Shapes in Topic 13: Surface Area and Volume can also be used as an extension activity related to different views of 3-dimensional shapes.
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 6 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 6 materials in which off grade-level content is present and not identified as such includes the following:
- Topics 2 and 3 address scale factor and 3-D representations (7.G.A).
- In Topic 5 Blocks 1, 2, 4, and 6 and Constructed Response 2, identified as 6.NS.B, focus on addition and subtraction of fractions, 5.NF.1,2.
- In Topic 6 Blocks 1-4 and Constructed Response 1, identified as 6.NS.B, focus on multiplication of fractions, 5.NF.4-6.
The Grade 6 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 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 6.
- The first paragraph in Agile Mind Mathematics 6 Scope and Sequence, 2016-2017 briefly references prior work in numbers and operations, geometry, measurement, data, and equivalent fractions and how these concepts connect to Grade 6 work.
- The Advice for Instruction section references prior work in different places, although specific standards are not referenced. Some examples of this include:
- Topic 1 Block 1 states “Use page 5 to remind students that they have used these operations with whole numbers in their previous math classes. The intent of this topic is to develop fluency and extend that work to some other ways to represent numbers, including factors, multiples, and exponents.”
- In Topic 6, Topic at at glance states, “This topic is intended to help students make sense of and formalize processes for operating with positive rational numbers. Once students understand how to operate with fractions, they can use that knowledge to learn how to operate with decimals. Students will learn through the topic that fractions and decimals are more similar than different.”
- In Topic 6 the first Classroom Strategy in Block 3 references both prior and future work as it connects a lesson on multiplying and dividing rational numbers to the base‐10 area model of multiplying multi‐digit whole number and the later use of algebra tiles for multiplying polynomials. The connection to prior work does not explicitly connect to a previous, grade-level standard.
- In Topic 9 the following Prerequisite skills are listed under Prepare instruction: write equivalent numerical expressions, such as 16 + 2 = 20 — 2; construct tables and graphs in the first quadrant; apply the Distributive Property in numerical contexts; and apply order of operations. The Prerequisite skills are not explicitly connected to any previous, grade-level standards.
- In Topic 12 Block 1 a Classroom strategy states, “The formulas presented on this page were introduced in earlier grades. Depending on your students’ prior experiences, they may not recall them or how to apply them. Use this page to connect to prior learning by engaging students in these formulas.”
- 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 end of the Overview of Topic 4 states, “In this topic, you will further explore the meaning of these different forms of numbers and learn how to convert from one form to another. Once you are able to do that, you will be able to compare and order them.”
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 6 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. 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 6 "Multiplying and Dividing Rational Numbers" is shaped by 6.NSA.
- In Topic 8,"Extending the Number System" is shaped by 6.NS.C.
- Goals and Objectives:
- In Topic 2 “understand ratio concepts and apply ratio and proportional reasoning in problem situations” is shaped by 6.RP.A.
- In Topics 3 and 7, “understand ratio and rate concepts…” and “apply ratio and rate reasoning…” are also shaped by 6.RP.A.
- In Topic 5 “compute fluently with multi‐digit numbers” is shaped by 6.NS.B.
- In Topics 9, 10, and 11, “apply and extend previous understandings of arithmetic to algebraic expressions” is shaped by 6.EE.A.
- In Topics 12 and 13 “solve real‐world and mathematical problems involving area and surface area” are shaped by 6.G.A.
- In Topic 14 “develop an initial understanding of statistical variability” is shaped by 6.SP.A.
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 2, 6.NS.C and 6.RP.A are connected as students plot pairs of numbers from a ratio table on the coordinate plane, identifying the graph as a line as long as the ratios are equivalent.
- In Topic 3, 6.NS.C and 6.RP.A are connected as students are comparing rates of two or more quantities using the position of the rate on the coordinate plane in which the x- and y-axes represent the labels of the rate.
- In Topic 9, 6.EE.B and 6.EE.C are connected as students write and solve one-variable equations in order to represent and analyze quantitative relationships between dependent and independent variables.
- In Topic 10, 6.EE.B and 6.NS.C are connected as students begin writing inequalities and relating them to number lines.
- In Topic 12, 6.G.A and 6.RP.A are connected as students convert measurement units for the area of rectangles.
- In Topic 13, 6.G.A and 6.NS.B are connected as students calculate volume of prisms with fractional/decimal edge lengths.
- In Topic 14, 6.SP.B and 6.NS.B are connected as students perform numerical calculations to describe data.
- In Topic 15, 6.SP.A and 6.SP.B are connected as students develop an understanding of statistical variability along with summarizing and describing distributions.