Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Agile Mind Grade 6 Agile meet the expectations for alignment to the CCSSM. The materials meet the expectations for focus and coherence in Gateway 1, and they meet the expectations for rigor and the mathematical practices in Gateway 2.

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
31
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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-
Gateway One Details

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 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

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 material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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-
Indicator Rating Details

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 1b

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.
4/4
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-
Criterion Rating Details

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.
4/4
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Indicator Rating Details

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 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
+
-
Criterion Rating Details

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.
2/2
+
-
Indicator Rating Details

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.
2/2
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Indicator Rating Details

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.
1/2
+
-
Indicator Rating Details

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.
2/2
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Indicator Rating Details

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.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for rigor and the mathematical practices. The materials meets the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and applications. The materials also meet the expectations for mathematical practices. Overall, the materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialized language of mathematics.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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-
Criterion Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and application with a balance in all three.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Multiple opportunities exist for students to work with standards that specifically call for conceptual understanding and include the use of visual representations, interactive examples, and different strategies.

Cluster 6.RP.A addresses understanding ratio concepts and using ratio reasoning to solve problems.

  • In Topic 2 “Understanding Ratio and Proportion” and Topic 3 “Introduction to Rates” students develop their understanding of ratios and rates through real-world, interactive examples. Students represent ratios and rates in various forms, including ratio tables, bar models, equivalent fractions, and points on a line or coordinate plane. Students are also given opportunities to solve problems using these concepts in multiple topics within the materials.
  • In Topic 4 students understand the connections between fractions, decimals, and percents, and during the topic, they are reminded that each of these forms represent ratios of rational numbers.

Cluster 6.NS.C calls for applying and extending previous understandings of numbers to the system of rational numbers.

  • In Topic 8 “Extending the Number System” students are introduced to rational numbers, integers, absolute value, and opposites. The animations allow students to develop an understanding of these terms visually, and many of the animations include the use of number lines and a coordinate grid. Through the topic, students have the opportunity to understand that the absolute value of a number is its distance from 0 on a number line. Students also have an opportunity to explore rational numbers in real-world contexts such as banking, sea level, and traveling distances. One aspect of 6.NS.C for which students are given limited opportunities to develop an understanding is that the opposite of the opposite of a number is the number itself.

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, there are opportunities for students to practice dividing multi-digit numbers using the standard algorithm, and students are given opportunities to develop fluency with decimal operations.

Standard 6.NS.2 addresses students being able to fluently divide multi-digit numbers using the standard algorithm.

  • In Topic 1 Blocks 1-3 there are multiple opportunities for students to engage with dividing multi-digit numbers within the Practice section, along with more problems in the Assessment section and Student Activity Sheets.

Standard 6.NS.3 addresses students being able to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

  • In Topic 5 there are multiple opportunities for students to develop fluency with adding and subtracting decimals within the Practice section, along with more problems in the Assessment section and Student Activity Sheets.
  • In Topic 6 there are multiple opportunities for students to develop fluency with multiplying and dividing decimals within the Practice section, along with more problems in the Assessment section and Student Activity Sheets.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
2/2
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Indicator Rating Details

The materials reviewed for Agile Mind Grade 6 meet the expectation for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade. Overall, students are given opportunities to solve application problems that include multiple steps, real-world contexts, and are non-routine.

Application problems allowing students to make their own assumptions in order to apply their mathematical knowledge can be found in different parts of the materials, including MARS Tasks, Constructed Response items and occasionally within the Student Activity Sheets (SAS).

Standard 6.RP.3 addresses using ratio and rate reasoning to solve real-world and mathematical problems.

  • In Topic 2 Constructed Response 1 students are expected to use rate reasoning to determine the number of candles in boxes of different sizes or the price of boxes of different sizes. This problem does not include any questions or prompts for scaffolding, and the context is unique when compared to other contexts used in the Topic.
  • In Topic 7 Constructed Response 2 students determine how long it will take for two people to paint a wall when they work together. Students calculate the area of the wall and then calculate how much of the wall each person paints per minute.

Standards 6.EE.7 and 6.EE.9 address students writing and solving linear equations in order to solve real-world and mathematical problems.

  • In Topic 9 Constructed Response 1 students write linear equations, along with tables and graphs for the equations, in order to answer questions about the type of growth for two different plants. The context is unique for this Topic.
  • In Topic 11 Constructed Response 1 students write linear equations in order to answer questions about how much time is needed to save a certain amount of money or how much money needs to be saved if there is only a certain amount of time. This context is the same as one that is used in the Topic, and there are scaffolded questions that let students know how to define the variables and how many equations they need to write.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for balance. Overall, the three aspects of rigor are not always treated together and are not always treated separately. Most Topics attempt to provide opportunities through lessons and assessments for students to connect conceptual understanding, procedural skill and fluency, and application when appropriate or engage with them separately as needed.

Balance is displayed in Topics 14 and 15. In Topic 14 students begin to understand how statistical questions involve variability, and they also begin to develop procedural skills with creating different plots that represent data distributions. In Topic 15 students further their understanding of statistical variability as they summarize and describe data distributions with measures of center and measures of spread, and they also explain which measures best represent the distributions. These understandings and skills are developed in conjunction with sets of data that allow students to apply them in real-world contexts.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for practice–content connections. Overall, the materials show strengths in identifying and using the MPs to enrich the content along with attending to the specialized language of mathematics. However, the materials do not attend to the full meaning of MPs 4 and 5, and there are few opportunities for students to choose their own models or tools when solving problems.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for the Standards for Mathematical Practices (MPs) being identified and used to enrich the mathematics content within and throughout the grade. The instructional materials for the teacher identify the MPs, and students using the materials as intended will engage in the MPs along with the content standards for the grade.

  • The Practice Standards Connections are found within the Professional Support section for the teacher. The eight MPs are listed with four to ten examples for each. According to the Practice Standards Connections, “each citation is intended to show how the materials provide students with ongoing opportunities to develop and demonstrate proficiency with the Standards for Mathematical Practice.”
  • Deliver Instruction is located within Advice for Instruction under Professional Support in the teacher material. Occasionally, there will be information within the Deliver Instruction section giving some guidance on how to implement the MP within the task/activity.
    • In Topic 7 Block 5 while students are working individually on Constructed Response 1, the teacher is asked to encourage the practice of modeling (MP4) and sense‐making with mathematics (MP1) by helping students make connections between what they are exploring about rates in graphs with questions such as: “How is this situation similar to the ones we have been studying?; What information do you need in order to determine a rate?; and What operations help you determine a unit rate?”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectations for carefully attending to the full meaning of each practice standard (MP). Overall, the materials attend to the full meaning of most of the MPs, but there are two MPs for which the full meaning is not addressed.

The instructional materials do not attend to the full meaning of MPs 4 and 5.

  • MP4: This MP is integrated several times throughout the materials, but the full meaning of the MP is not developed through these different parts of the materials. In Topic 3 during Introduction to rates and the constructed response items, students answer questions about different contexts where quantities are defined for them and models are provided for them as well. There are also no opportunities for students to revise initial assumptions or models once calculations have been made. In Topic 8 during the Overview and Constructed Response 3, students focus on how a number line or coordinate grid can be used as a model for rational numbers, but other aspects of MP4 are not attended to during this Topic. In Topic 12 during Covering the Pedestal, students engage in a problem in which they are led through some aspects of MP4- defining quantities, creating a model, and making calculations, but in this problem, the students do not get the opportunity to engage in any of these aspects on their own.
  • MP5: This MP is integrated at different points in the materials, but the full meaning of the MP is not developed through these different parts of the materials. In Topic 8 during Rational numbers in the coordinate plane, teachers are told to promote this MP “by using masking tape to create a coordinate grid on the floor,” but students are not getting to choose any tools as they use the grid to practice plotting points. In Topic 8 there is a problem where students are directed to use a coordinate plane and patty paper to help them plot points and reflect them, but the students are not given a choice as to what to tools they might use. In Topic 12 there are multiple places where this MP is referenced, but in each of these places, students are told to measure with a ruler/yardstick and what units to use when measuring or are provided pictures on pre-labeled grids.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectations for prompting students to construct viable arguments and analyze the arguments of others. Overall, the materials prompt students to construct viable arguments and present opportunities to analyze the arguments of others.

The instructional materials provide opportunities for students to construct viable arguments.

  • In Topic 3 Block 2 students are matching dimensions of photographs to the corresponding coordinate on a graphical representation. The Student Activity Sheet asks the student to explain the process used to match the name with the picture.
  • In Topic 12 Block 12 students are given the coordinates of a parallelogram and are asked to determine whether statements are true or false and record their reasoning.
  • In Topic 15 Block 5 during the MARS Task “Suzi’s Company,” students are given a table depicting jobs and annual salaries of fifteen people in a small company. Students connect their understanding of measures of center as they explain their solution to several questions.

The instructional materials provide opportunities for students to analyze the arguments of others.

  • In Topic 1 Block 8 Constructed Response 2 students engage in analyzing the arguments of fictitious students. Even though students are told in which step the error occurs, this is an opportunity for students to analyze the mathematical arguments that are presented to them and justify their suggested corrections.
  • In Topic 15 Block 5 one part of the MARS Task “Suzi’s Company” asks students to analyze the statement made by a person in the problem, identify the mistake that was made, and present the correct mode for the problem.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. In Deliver Instruction, classroom strategies and question prompts are provided to assist teachers in engaging students to construct viable arguments or analyzing the arguments of others.

The following are examples of assistance provided to the teachers to promote the construction of viable arguments and analysis of other’s thinking, including prompts, sample questions to ask, and guidance for discussions.

  • In Topic 1 Block 5 students are determining all possible dimensions for a 225 square-foot school banner. The teacher is instructed as follows: “As pairs work to find all the possible dimensions for this banner, they will develop the practice of constructing viable arguments and critiquing the reasoning of the members of their group. Encourage students to justify the reasoning they used to decide when they found all possible dimensions.”
  • In Topic 1 Block 8 Constructed Response 2 teachers are told that two parts of the problem “provide an opportunity to promote the practice of constructing arguments and responding to the ideas of others.”
  • In Topic 3 Block 5 students are analyzing batting averages of two softball games at a family reunion. The teacher is instructed to “Promote the habit of communicating mathematical ideas by critiquing the reasoning of others with this activity. Allow students plenty of time to engage with each written argument and discuss their ideas with a partner.”
  • In Topic 12 Block 1 teachers are assisted with “as they share strategies, ask students to consider which strategies may be more or less accurate and have them justify their responses. This discussion promotes the mathematical practice of constructing viable arguments and critiquing the reasoning of others.”
  • In Topic 12 Block 6 students are finding the area of an irregular shape, a map of the United States. The teacher is instructed as follows: “As students share and discuss their strategies for finding the area of the unusual shape, promote the mathematical practice of constructing viable arguments and critiquing the reasoning of others. You may need to model this strategy to get the discussion started, “Who agrees with Monique’s strategy? Tell us why her strategy is effective.”
  • In Topic 15 Block 11 in the MARS Task “TV Hours” teachers are given the following assistance: “Encourage students to be active listeners during the debriefing of this task. For example, after a student has shared her strategy summarizing the results of Mrs. Campbell’s letters you can engage students by saying; “Raise your hand if you understand Sarah’s conclusion.” Then call on one or more of those students to restate the first student’s conclusion in their own words. ... As students or pairs of students are sharing their answers and strategies with the rest of the class, encourage students to critique each other’s reasoning and to compare the various strategies.”

In the Advice for Instruction there is a missed opportunity to provide support for teachers that explains and identifies where and when problems, tasks, examples, and situations lend themselves to these types of questions. Additional guidance is needed to broaden the application of these questions throughout the course so that students routinely construct viable arguments and analyze the arguments of others.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for explicitly attending to the specialized language of mathematics. Overall, the materials appropriately use the specialized language of mathematics and expect students and teachers to use it appropriately as well.

Occasionally, there are suggestions within Deliver Instruction as to how teachers can reinforce mathematical language during instruction.

  • Topic 1 Block 7: "Reinforce the use of precise mathematical language as you introduce the Distributive Property. Most students are familiar with the words product, addend, factor, and sum. However, this is a new context and application for those words. Provide additional number sentences with which to identify factors, addends, products and sums (with and without common factors).”
  • Topic 9 Block 2: “Students at this grade level may have had very few experiences with using variables to write equations or expressions. Pause with each panel to clarify for students how the variables, x and y, are being used to take the place of the numbers.”

In the student materials, vocabulary terms can be found in bold print within the lesson pages, and these terms are used in context during instruction, practice, and assessment. Vocabulary terms are also available to the students at all time through My Glossary within the materials. For teachers, vocabulary terms for each Topic can be found under Language Support, which is within Advice for Instruction. Both core vocabulary and reinforced vocabulary are listed for each unit.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet expectations that the materials are well designed and take into account effective lesson structure and pacing. Overall, materials are well-designed, and lessons are intentionally sequenced. Students learn new mathematics in the Exploring section of each Topic as they apply the mathematics and work toward mastery. Students produce a variety of types of answers including both verbal and written answers. The Overview for the Topic introduces the mathematical concepts, and the Summary highlights connections within and between the concepts of the Topic. Manipulatives such as algebra tiles and virtual algebra tiles are used throughout the instructional materials as mathematical representations and to build conceptual understanding.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for having an underlying design that distinguishes between problems and exercises.

  • Each Topic includes three sections: Overview, Exploring, and Summary. The Overview section introduces the mathematical concepts that will be addressed in the Topic. The Exploring section includes two to four explorations where students learn the mathematical concepts of the Topic through problems that include technology-enhanced animations and full-class activities. The Summary section highlights the most important concepts from the Topic and gives students another opportunity to connect these concepts with each other.
  • Each Topic also includes three additional sections: Practice, Assessment, and Activity Sheets. The Practice section includes Guided Practice and More Practice. Guided Practice consists of exercises that students complete during class periods and give opportunities for students to apply the concepts learned during the explorations. More Practice contains exercises that are completed as homework assignments. The Assessment section includes Automatically Scored and Constructed Response items. These items are exercises to be completed during class periods or as part of homework assignments. They provide more opportunities for students to apply the concepts learned during the explorations. The Activity Sheets also contain exercises, which can be completed during class periods or as part of homework assignments, that are opportunities for students to apply the concepts learned during the explorations.
  • Some Topics also include MARS Tasks, which are exercises that present students with opportunities to apply concepts they have learned from the Topic in which the MARS Task resides or to apply and connect concepts from multiple Topics.

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for having a design of assignments that is not haphazard with problems and exercises given in intentional sequences.

The sequencing of Topics, and explorations within the Exploring section for each Topic, develops in a way that helps to build students’ mathematical foundations.

  • The Topics are comprised of similar content.
  • Within the explorations for each Topic, problems generally develop from more simple to more complex problems and incorporate knowledge from prior problems or Topics, which offers students opportunities to make connections among mathematical concepts. For example, using equations and inequalities to solve problems in Topic 11 builds upon writing algebraic expressions, equations, and inequalities from Topics 9 and 10.
  • As students progress through the Overview, Exploring, and Summary sections, the Practice (Guided and More), Assessment (Automatically Scored and Constructed Response), and Activity Sheets sections are placed intentionally in the sequencing of the materials to help students build their knowledge and understanding of the mathematical concepts addressed in the Topic.
  • The MARS Tasks are also placed intentionally in the sequencing of the materials to support the development of the students’ knowledge and understanding of the mathematical concepts that are addressed by the tasks.

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for having a variety in what students are asked to produce.

Throughout a Topic, students are asked to produce answers and solutions as well as explain their work, justify their reasoning, and use appropriate models. The Practice section and Automatically Scored items include questions in the following formats: fill-in-the-blank, multiple choice with a single correct answer, and multiple choice with more than one correct answer. Constructed Response items include a variety of ways in which students might respond, i.e. multiple representations of a situation, modeling, or explanation of a process. Also, the types of responses required vary in intentional ways. For example, concrete models or visual representations are expected when a concept is introduced, but as students progress in their knowledge, students are expected to transition to more efficient solution strategies or representations.

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written models. The materials include a variety of virtual manipulatives, as well as integrate hands-on activities that allow the use of physical manipulatives.

Most of the physical manipulatives used in Agile Mind are commonly available: ruler, patty paper, graph paper, algebra tiles, and graphing calculators. Due to the digital format of the materials, students also have the opportunity to represent equations or functions virtually with tables and graphs. Each Topic has a Prepare Instruction section that lists the materials needed for the Topic. Manipulatives accurately represent the related mathematics. For example, Topic 13, Surface Area and Volume, students work with physical unit cubes and a cardboard box, along with having virtual representations of them, in order to expand their understanding of volume to include rectangular prisms whose edge lengths are not whole numbers.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 have a visual design that is not distracting or chaotic but supports students in engaging thoughtfully with the subject. The student materials are clear and consistent between Topics within a grade-level as well as across grade-levels. Each piece of a Topic is clearly labeled, and the explorations include Page numbers for easy reference. Problems and Exercises from the Practice, Assessment, and Activity Sheets are also clearly labeled and consistently numbered for easy reference by the students. There are no distracting or extraneous pictures, captions, or "facts" within the materials.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet expectations that materials support teacher learning and understanding of the standards. The instructional materials provide Framing Questions and Further Questions that support teachers in delivering quality instruction, and the teacher’s edition is easy to use and consistently organized and annotated. The materials provide full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject. Although each Topic contains a list of Prerequisite Skills, this list does not connect any of the skills to specific standards from previous grade levels, so the instructional materials partially meet the expectation for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials reviewed for Grade 6 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development. The Deliver Instruction section for each Block of a Topic includes Framing Questions for the start of each lesson. For example, in Topic 8 Block 4 the Framing Question is: “Have you ever used a map that had a grid system for naming points?” During the lesson the Deliver Instruction section includes multiple questions that teachers can ask while students are completing the activities. At the end of each lesson, Deliver Instruction includes Further Questions. For example, in Topic 8 Block 4 “If both coordinates are positive, what does that tell you about the location of a point? If both coordinates are negative, what does that tell you about the location of a point? If one coordinate is positive and the other is negative, what does that tell you about the location of the point?”

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for containing a teachers edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Also, where applicable, the materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The materials contain Professional Support which includes a Plan the Course section and a Scope and Sequence document. The Plan the Course section includes Suggested Lesson-planning Strategies and Planning Resources. Each Topic contains an Advice for Instruction section that is divided into Prepare Instruction and Deliver Instruction. For each Topic, Prepare Instruction includes Goals and Objectives, Topic at a Glance, Prerequisite Skills, Resources, and Language Support, and for each Block within a Topic, Deliver Instruction includes Agile Mind Materials, Opening the Lesson, Framing Questions, Lesson Activities, and Suggested Assignment. In Lesson Activities, teachers are given ample annotations and suggestions as to what parts of the materials should be used when and Classroom Strategies that include questions to ask, connections to mathematical practices, or statements that suggest when to introduce certain mathematical terms or concepts.

Where applicable, the materials include teacher guidance for the use of embedded technology to support and enhance student learning. For example, in Topic 7 Block 2 teachers are directed to, “Use the interactive animation to explore a distance vs. time graph. Use these questions to guide student discussions during the activity: When you drag Terrence away from the motion detector, what does the graph look like? Why? [When you drag him away, his distance from the motion detector increases. Since the graph measures Terrence's distance from the motion detector at any given time, this causes the graph to rise, or get farther away from the x-axis, as you move from left to right on the graph.]; How does dragging him back toward the motion detector affect the graph? Why? [When you drag him toward the motion detector, his distance from the motion detector decreases. Since the graph measures Terrence's distance from the motion detector at any given time, this causes the graph to fall, or get closer to the x-axis, as you move from left to right on the graph.]; What does the graph look like when you drag him at a fairly slow, steady rate away from the motion detector? [The graph will be a line that rises from left to right, but will not be very steep.] What if you drag him away from the motion detector faster, but still at a steady rate? [The graph will still be a line that rises from left to right, but it will be steeper than the first line.]; and When Terrence stops during his skate, what does the graph do? Why? [The graph will be a horizontal line. This happens because when Terrence is not moving, his distance from the motion detector is not changing, but time continues to pass.]”

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for containing full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

In Professional Support, Professional Learning, there are four interactive essays entitled “Developing concepts across grades”. There is an Overview that explains the purpose of the four essays, and the topics for these four essays are Functions, Volume, Rate, and Proportionality. Each essay is accessible to teachers and not students, and the Overview states “these essays are available for educators to illustrate connections and deepen understanding around what students may have already learned, and where they are headed on their journey.” Each essay examines the progression of the concept from Grades 6-8 through Algebra I, Geometry, Algebra II, and beyond. By examining the progressions of the concepts beyond Algebra II, teachers have the opportunity to improve their own knowledge of more advanced mathematics concepts that build upon grade-level standards. For example, in Volume, teachers progress from packing a right, rectangular prism with unit cubes to developing the formulas for the volume of cylinders and cones to finding the volume of a figure generated by rotating a two-dimensional shape around a horizontal axis. Also, in Proportionality, teachers explore how proportional relationships are part of the following mathematical concepts: scaling images, linear functions, trigonometric ratios, rational functions, and the derivative.

In addition to “Developing concepts across grades”, the Grade 6 materials also contain a section of interactive essays entitled “Going beyond Grade 6”. There is an Overview that explains the purpose of the three essays, and the Overview states, “These essays are not intended for use with your 6th grade students; rather, they are designed to provide you with important connections and background that will support you as you help your students master 6th grade content.” The topics for these three essays are Rate of Change, Understanding Area of Irregular Shapes, and Calculating Outliers. Along with having their own section in Professional learning, each of these essays are also referenced in Deliver Instruction for the Blocks where they are appropriate under the title of Teacher Corner. For example, in Topic 3, the essay Rate of Change is referenced for teachers in Block 1 as part of the Overview, and in Topic 12, Understanding Area of Irregular Shapes is referenced in Block 5 on page 4. The three essays connect the Grade 6 content to advanced mathematical concepts through multiple grades and courses.

In Professional Support, there is a section of Professional Essays which are in either Print or Video format. The Print essays are divided as either Curriculum or Course Management Topics, and although some of the Curriculum Essays are content specific, they do not address mathematical concepts that extend beyond the current grade. The Video Essays - categorized into Teaching with Agile Mind, More Teaching with Agile Mind, and Dimensions of Mathematics Instruction - do not directly provide adult-level explanations or examples of advanced mathematics concepts.

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectation for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum.

The Prepare Instruction section for each Topic contains a list of Prerequisite Skills, but this list does not connect any of the skills to specific standards from previous grade levels. For example, in Topic 6 the Prerequisite Skills include “Multiples of a given whole number; Rational numbers in equivalent forms; and Operations with whole numbers.” In Prepare Instruction the Topic at a Glance occasionally provides general references to how concepts will be used in future courses. For example, in Topic 6 “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. Throughout the topic, students build and apply fluency with these operations. They will continue to build and demonstrate fluency in future topics. The activities in this topic are outlined in ten 45-minute instructional blocks and assessment.”

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 provide a list of lessons in the teacher's edition, cross­‐referencing the standards covered and providing an estimated instructional time for Topics and Blocks. The materials provide a Mathematics 6 Scope and Sequence document which includes the number of Blocks of instruction for the duration of the year, time in minutes that each Block should take, and the number of Blocks needed to complete each Topic. The Scope and Sequence document lists the CCSSM addressed in each Topic, but there is no part of the materials that aligns Blocks to specific content standards. The materials also provide Alignment to Standards in the Course Materials which allows users to see the alignment of Topics to the CCSSM or the alignment of the CCCSM to the Topics. The Deliver Instruction section contains the Blocks for each Topic. The Practice Standards Connections, found in Professional Support, gives examples of places in the materials where each MP is identified.

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 do not contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 do not contain explanations of the instructional approaches of the program and identification of the research-based strategies within the teaching materials. There is a Professional Essays section which addresses a broad overview of mathematics in grades 6-8 as discussed in indicator 3h.

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
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-
Criterion Rating Details

The instructional materials for Agile Mind Grade 6 partially meet exceptions that materials offer teachers resources and tools to collect ongoing data about students progress on the Standards. Opportunities for ongoing review and practice, and feedback occur in various forms. Standards are identified that align to the Topic; however, there is no mapping of Standards to items. There are limited opportunities for students to monitor their own progress, and there are no assessments that explicitly identify prior knowledge within and across grade levels. The materials include few opportunities to identify common misconceptions, and strategies to address common errors and misconceptions are only found in a few Deliver Instruction topics.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels. The materials do not provide any assessments that are specifically designed for the purpose of gathering information about students’ prior knowledge, but the materials do provide indirect ways for teachers to gather information about students’ prior knowledge if teachers decide to use them that way.

In Prepare Instruction for each Topic, there is a set of Prerequisite Skills needed for the Topic, and the Overview for each Topic provides teachers with an opportunity to informally assess students prior knowledge of the Prerequisite Skills. For example, in Topic 4 the Prerequisite Skills are: “Writing equivalent fractions and Multiplication and division of whole numbers.” Then, in the Lesson Activities for Page 1 of Block 2, teachers are told, “Use this page to connect with students' prior understanding and begin developing an understanding of what a rational number is.”

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions. There is not an explicit way in which the materials help teachers identify and address common student errors and misconceptions, but there are a few instances in the Deliver Instruction where common errors and misconceptions are identified and suggestions are given for how to address them. For example, in Topic 6 Block 3 teachers are told, “There may be some misunderstanding when using both a linear and area model for multiplication of rational numbers. Take time to distinguish the differences by using manipulatives where needed.”

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The materials provide opportunities for ongoing review and practice, and feedback occurs in various forms. Within interactive animations, students submit answers to questions or problems, and feedback is provided by the materials. Practice problems and Automatically Scored Assessment items are submitted by the students. Immediate feedback is provided letting students know whether or not they are correct, and if incorrect, suggestions are given as to how the answer can be improved. The Lesson Activities in Deliver Instruction provide some suggestions for feedback that teachers can give while students are completing the lessons.

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectation for assessments clearly denoting which standards are being emphasized. The items provided in the Assessment section align to the standards addressed by the Topic, but the individual items are not clearly aligned to particular standards. The set of standards being addressed by a Topic can be found in the Scope and Sequence document or in Course Materials through Alignment to Standards. The MARS Tasks also do not clearly denote which standards are being emphasized.

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectation for assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. The MARS Tasks that are included in the materials are accompanied by rubrics aligned to the task that show the total points possible for the task and exactly what students need to do in order to earn each of those points. The Constructed Response items are accompanied by complete solutions, but rubrics aligned to the Constructed Response items are not included. For both the MARS Tasks and the Constructed Response items, alternate solutions are provided when appropriate, but sufficient guidance to teachers for interpreting student performance and suggestions for follow-up are not provided with either the MARS Tasks or the Constructed Response items.

Indicator 3q

Materials encourage students to monitor their own progress.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 offer few opportunities for students to monitor their own progress. Throughout the Exploring, Practice, and Automatically Scored Assessment sections, students get feedback once they submit an answer, and in that moment, they can adjust their thinking or strategy. Goals and Objectives for each Topic are not provided directly to students, but they are given to teachers in Prepare Instruction. There is not a systematic way for students to monitor their own progress on assignments or the Goals and Objectives for each Topic.

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
10/12
+
-
Criterion Rating Details

The instructional materials for Agile Mind Grade 6 meet expectations that materials support teachers in differentiating instruction for diverse learners within and across grades. Activities provide students with multiple entry points and a variety of solution strategies and representations. The materials provide strategies for ELLs and other special populations, but the materials do not always challenge advanced students to deepen their understanding of the mathematics. Grouping strategies are designed to ensure roles for each group member.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

Each Topic consists of three main sections- Overview, Exploring, and Summary, and these three sections are divided into Blocks. Each Block contains lesson activities including Practice, Assessment, and Activity Sheets, along with any MARS Tasks in the Topic. In each Topic, the Blocks are sequenced for the teachers, and the lesson activities within the Blocks are sequenced for the teachers. In the Advice for Instruction for each Topic, Deliver Instruction for each Block contains instructional notes and classroom strategies that provide teachers with key math concepts to develop, sample questions to ask, ways in which to share student answers, and other similar instructional supports.

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners. Overall, the instructional materials embed multiple and/or visual representations of mathematical concepts where appropriate, include audio recordings with many explorations, and give students opportunities to engage physically with the mathematical concepts. However, the instructional notes provided to teachers do not consistently highlight these strategies that can be used to meet the needs of a range of learners. When instructional notes are provided to teachers, they are general in nature and are intended for all students in the class, and they do not explicitly address the possible range of needs for learners. For example, in Topic 3 Block 7 the Deliver Instruction states “As students are working, listen for unique strategies that students use to approach this problem that you can highlight in your debrief of the problem. Encourage students to provide strong mathematical evidence for their claims. If students are not sure, encourage them to sketch and shade tape diagrams on the Student Activity Sheet. Remind students to find and use familiar percents if needed, such as 10%, 50%, and 25% in order to label their tape diagrams.”

In some explorations, teachers are provided with questions that can be used to extend the tasks students are completing, which are beneficial to excelling students. For struggling students, teachers are occasionally provided with strategies or questions they can use to help move a student’s learning forward. The Summary for each Topic does not provide any strategies or resources for either excelling or struggling students to help with their understanding of the mathematical concepts in the Topic.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation that materials embed tasks with multiple entry­-points that can be solved using a variety of solution strategies or representations. Overall, tasks that meet the expectations for this indicator are found in some of the Constructed Response Assessment items and Student Activity Sheets that are a part of all Topics. MARS Tasks embedded in some Topics have multiple entry-points and can be solved using a variety of solution strategies or representations. For example, in Topic 8 Constructed Response 1 students are instructed to "Describe four more possible events in the life of Andre or his family. For each event describe when it happened. Then graph and label the rational number representing that event. Use at least one negative rational number, at least one whole number, and at least two fractions or decimals." Another example is in Topic 12 Constructed Response 2. Students are asked to find the area and/or perimeter of different figures that are superimposed on a grid. Students are given the scale for the grid.

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation that the materials suggest accommodations and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

The materials provide suggestions for English Language Learners and other special populations in regards to vocabulary and instructional practices. In Prepare Instruction for Topic 1, Teaching Special Populations of Students refers teachers to the Print Essay entitled “Teaching English Language Learners” in Professional Support, which describes general strategies that are used across the series such as a vocabulary notebook, word walls, and concept maps. Teaching Special Populations of Students also describes general strategies that are used across the series for other special populations, including progressing from concrete stage to representational stage to abstract stage and explicitly teaching metacognitive strategies through think alouds, graphic organizers, and other visual representations of concepts and problems.

In addition to the general strategies mentioned in Teaching Special Populations of Students, there are also many specific strategies listed across each course of the series in Deliver Instruction. In Deliver Instruction, Support for ELL/other special populations includes strategies that can be used with both English Language Learners and students from other special populations. Strategies specific to other special populations can also be found in Classroom strategy or Language strategy. An example of Support for ELL/other special populations from Topic 1, Block 4, Page 5 is “Provide students who have handwriting challenges or other language challenges with index cards that contain the 4 rules of the Order of Operations. Having the text already written will allow these students to focus on understanding the meaning of each rule instead of transcribing the words. While the rest of the class is writing the rules, encourage these students to write an example next to each rule to help them process the meaning. Have them circle each rule in a different color. Then have them write the expression from the animation and color code each step in the expression with the color of the appropriate rule.” An example of a strategy for other special populations from Topic 8, Block 1, Page 1 of Exploring Positive and Negative Rational Numbers is “Classroom strategy. Bank balances will use negative numbers, but when we talk about those balances using the word “debt” we use the absolute value. We say, “I have a debt of $15,” rather than, “I have a debt of $-15.” Or, stated another way, “I have a balance of $-15, so my debt is $15.” This is a subtle distinction, especially for students at this age, and complete mastery of this concept is not expected on this page. Throughout the topic, as students are discussing debt, continue to reinforce the notion that the greatest debt is the balance with the least value, or the negative number furthest from zero. Be aware that some students with learning differences may continue to need more explicit instructions and repetition.”

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. Overall, all of the problems provided in the materials are on grade level, and the materials are designed so that all of the problems are assigned to all students over the course of the school year. There are opportunities for advanced students to investigate mathematics at a greater depth in some of the Topics through notes given to teachers in the Advice for Instruction. For example, in Topic 13 Block 2 teachers are told, "Students can also do the following activity for further exploration. Give groups a set number of cubes and ask them to build a rectangular prism. Give them some numbers that will make a cube (27), some that will make several prisms (24), and some that will make only one (17; 1 x 1 x 17). This is a nice activity for spatial visualization but also for number sense."

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 meet the expectation for providing a balanced portrayal of various demographic and personal characteristics. The activities are diverse, meeting the interests of a demographically, diverse student population. The names, contexts, videos, and images presented display a balanced portrayal of various demographic and personal characteristics.

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 provide opportunities for teachers to use a variety of grouping strategies in the Deliver Instruction Lesson Activities including when students work individually, in pairs, or in small groups. When suggestions are made for students to work in small groups, there are no specific roles suggested for group members, but teachers are given suggestions to ensure the involvement of each group member. For example, Topic 1 Block 4 teachers are told to “have students work independently or with a partner to solve the problem. Ask groups to share how they used the Order of Operations. Review the importance of the Order of Operations.”

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 do not encourage teachers to draw upon home language and culture to facilitate learning. Questions and contexts are provided for teachers in the materials, and there are no opportunities for teachers to adjust the questions or contexts in order to integrate the home language and culture of students into the materials to facilitate learning.

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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-
Criterion Rating Details

The instructional materials for Agile Mind Grade 6 are web-based and platform neutral but do not include the ability to view the teacher and student editions simultaneously. The materials embed technology enhanced, interactive virtual tools, and dynamic software that engage students with the mathematics. Opportunities to assess students through technology are embedded. The technology provides opportunities to personalize instruction; however, these are limited to the assignment of problems and exercises. The materials cannot be customized for local use. The technology is not used to foster communications between students, with the teacher, or for teachers to collaborate with one another.

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 are web-based and compatible with multiple internet browsers (Chrome, Firefox, and Internet Explorer). In addition, the materials are “platform neutral” and allow the use of tablets with ChromeOS, Android, or iOS operating systems, but they do not support the use of mobile devices. However, the transition between student and teacher materials is not fluid. There are no direct links between the student and teacher materials, and the student and teacher materials cannot be viewed simultaneously.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology. All Practice and Automatically Scored Assessment questions are designed to be completed using technology. These items cannot be edited or customized.

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 include few opportunities for teachers to personalize learning for all students. Within the Practice and Assessment sections, the teacher can choose which problems and exercises to assign students, but these problems and exercises cannot be modified for content or wording from the way in which they are given. Other than being able to switch between English and Spanish in My Glossary, there are no other adaptive or technological innovations that allow teachers to personalize learning for all students.

The instructional materials reviewed for Grade 6 cannot be easily customized for local use. Within My Courses, there are not any options for modifying the sequence or structure of the Topics or any of the sections within the Topics.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 provide few opportunities for teachers and/or students to collaborate with each other. Under My Agile Mind, teachers can communicate with students through the Calendar and Score and Review. There are no opportunities for teachers to be able to collaborate with other teachers.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 6 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices. Given the digital platform of the materials, the inclusion of interactive tools and virtual manipulatives/objects helps to engage students in the MPs in all of the Topics, and the use of animations in all of the Topics provides examples as to how the interactive tools and virtual manipulatives can be used.

Additional Publication Details

Report Published Date: Thu Jun 08 00:00:00 UTC 2017

Report Edition: 2016

Title ISBN Edition Publisher Year
Mathematics 6 Student Activity Book 978-1-943460-78-6 Agile Mind 2016
Mathematics 6 Advice for Instruction 978-1-943460-79-3 Agile Mind 2016

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Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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