Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Agile Mind Grade 8 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 8 meet expectations for focus and coherence. The instructional materials do not assess topics beyond Grade 8, and students and teachers using the materials as designed would devote the large majority of instructional time to the major work of the grade. The instructional materials meet expectations for coherence, and they show strength in having an amount of content that is viable for one school year and fostering coherence through connections within the grade.

Criterion 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 8 meet expectations for not assessing topics before the grade-level in which the topic should be introduced. Overall, there are not assessment items that align to topics beyond Grade 8.

Indicator 1a

The instructional 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 reviewed for Agile Mind Grade 8 meet the expectations for assessing grade-level content. The majority of the Grade 8 assessment content was appropriate for the grade. There are some items in the assessments that align to standards above Grade 8 or address content not explicitly addressed in the CCSSM, but omitting or modifying these assessment items would not significantly impact the underlying structure of the Grade 8 materials.

The questions within the Practice and Assessment sections were reviewed for this indicator. The Practice sections within each topic contain multiple questions under the categories of Guided Practice and More Practice. The Assessment sections within each topic contain Automatically Scored questions and Constructed Response questions.

The questions that include content from future grades or address content not explicitly addressed in the CCSSM are as follows:

  • Topic 10 Guided Practice 14 asks students to write an exponential rule (F-LE.2): “Now, write an exponential function rule to find M, the amount of medicine left in the body t hours after the scan. Complete the process column in the table to help you find this rule.”
  • Topic 15 includes items assessing surface area of spheres, which is a topic not explicitly addressed by any standards from the CCSSM. These items are as follows:
    • Guided Practice: 3, 4, and 9
    • More Practice: 7, 8, and 9
    • Automatically scored: 2 and 4

Criterion 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
+
-
Criterion Rating Details

The instructional materials reviewed for Agile Mind Grade 8 meet the expectations for students and teachers devoting the majority of class time to the major work of the grade when materials are used as designed. Overall, the materials spend approximately 83% of class time on the major work of Grade 8.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 meet the expectations for spending the majority of class time on the major clusters of the grade. Overall, the instructional materials spend approximately 83% of class time on the major clusters of Grade 8.

For this indicator, the following were examined: all Blocks of instruction within all Topics in Course Contents, Alignment to Standards in Course Materials, the Mathematics 8 Scope & Sequence with Common Core State Standards document in Professional Support, and the Block descriptions for each Topic located within Deliver instruction under Advice for Instruction in Professional Support. There are fifteen topics divided into the following categories: Overview, Explore, Summary, Practice, and Assessment. Each Topic contains 7 to 12 Blocks of instruction, and each Block of instruction represents a 45-minute class period.

In the Block descriptions for each Topic, individual activities are not assigned specific amounts of time, or ranges of time, for the activities to be completed. Thus, when calculating the percentage of class time spent on the major cluster of the grade, two perspectives were appropriate, Topics and Blocks. For these materials, analysis by Blocks is the most appropriate because the Topics do not have an equal number of Blocks within them and the Blocks are not subdivided into smaller increments.

In addition to the Blocks directly aligned to major clusters of the grade, all Blocks aligned to supporting clusters of the grade were also examined. Those Blocks aligned to supporting clusters that were found to incorporate major work of the grade were included in the calculations below:

  • Blocks: 109 of the 132 Blocks, approximately 83%, are spent on the major clusters of the grade.
  • Topics: 14 of the 15, Topics , approximately 93%, are spent on the major clusters of the grade.

Criterion 1c - 1f

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

The instructional materials reviewed for Agile Mind Grade 8 meet the expectation for being coherent and consistent with the Standards. The instructional materials show strengths in having an amount of content that is viable for one school year but do not always make explicit connections between prior knowledge and future learning and the major work of the grade. Therefore, the progressions in the Standards are not always evident. The materials foster coherence within grade level work.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Overall, supporting content is found primarily in Topics 2, 9, and 15, and the supporting content in these Topics does enhance focus and coherence by engaging students in the major work of the grade. Examples of the connections between supporting work and major work found in these topics include the following:

  • In Topic 2 Blocks 4, 8, 10, and 11 connect major standard 8.EE.2 to supporting standards 8.NS.1 and 8.NS.2. Students are identifying irrational numbers using perfect squares and writing and solving equations to find approximate values of radicals.
  • In Topic 9 Blocks 1, 2, 4, 5, and 7 connect major standards 8.F.3 and 8.F.4 to supporting standards 8.SP.1, 8.SP.2, and 8.SP.3. As students explore bivariate data they are making scatter plots, finding the line of best fit, writing the equation of the line, and using the line of best fit to interpret additional data.
  • In Topic 15 Blocks 3 and 6 connect major standards 8.F.3 and 8.F.4 to supporting standard 8.G.9. As students explore the surface area and volume formulas for cones, cylinders, and spheres they are comparing properties of functions that are represented in different ways and looking at examples of functions that are not linear.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. The suggested pacing contains 15 Topics and 132 Blocks (days) of instruction, including assessments. According to the Agile Mind Mathematics 8 Scope and Sequence, each block is expected to last 45 minutes. Some lessons (Constructed Response, MARS tasks) may take longer than indicated.

Each Block includes the following sections: Overview, Exploring, Summary, and Assessment. The Exploring pages are categorized by math concept and can be discussed and reviewed as a class or by individuals/small groups of students.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 partially meet the expectations for being consistent with the progressions in the Standards. Overall, the materials develop according to the grade-by-grade progressions in the Standards, and they give all students extensive work with grade-level problems. However, content from prior or future grades is not always clearly identified or related to grade-level work, and the materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades.

Examples of Grade 8 materials in which off grade-level content is present and not identified as such includes the following:

  • In Topic 10 Blocks 4, 5, and 6, aligned to 8.F.3, extend above grade-level when students must write equations for nonlinear functions, especially exponential functions (F-LE.2).
  • In Topic 11 Block 4, aligned to 8.EE.7, involves solving one-step (6.EE.7) and two-step (7.EE.4) equations algebraically.

The Grade 8 materials provide extensive work with grade-level standards. All students are expected to complete the same problems, and lessons or ideas presented for differentiated instruction also include grade-level problems. The MARS tasks that are included, especially the ones in Topics 5, 7, 8, 9, and 12, are places where students are given the opportunity to engage with the grade-level standards to their full intent.

In lessons where prior knowledge is included, identification of content from prior grades is mentioned in four components of the materials, but the identification is general and not explicitly connected to a grade-level or standard. Examples from the four components are as follows:

  • In the first paragraph of the About the Course section, there is a brief, general overview of topics of which students acquired a foundation prior to Grade 8.
  • The first paragraph in Agile Mind Mathematics 8 Scope and Sequence, 2016-2017 briefly references prior work with expressions, equations/inequalities, dependent/independent variables, area, surface area, and volume and how these concepts connect to Grade 8 work.
  • The Advice for Instruction section references prior work in different places, although specific standards are not referenced. Some examples of this include:
    • In Topic 3 Topic at a glance states, “Throughout this topic, it is assumed that students have had previous exposure to the meaning of exponents.”
    • In Topic 5 the following Prerequisite skills are listed under Prepare instruction: Labeling coordinate axes, Plotting points, Reading information from graphs, Recognizing constant rates of change given a graphical representation, Representing constant rates of change given a verbal description, and Calculating unit rates. The Prerequisite skills are not explicitly connected to any previous, grade-level standards.
    • In Topic 7 the Goals and objectives start by stating, “The topic Linear patterns and functions builds on students' work in patterning in previous grades to develop the formal notion of 'function' and to begin to recognize patterns that can be modeled with linear functions.”
    • In Topic 14 Opening the lesson for Block 4 states, “Students have seen angle relationships from two intersecting lines and from two lines cut by a transversal. They have also seen how the various angle pairs they have been working with relate to each other and how they can be used to establish the fact that two lines are parallel. Now, we want to find ways to extend these geometric relationships to other shapes and situations.”
    • In Topic 15 the first Classroom strategy for Block 1 states, “This Exploring connects to students’ prior understandings of surface area of pyramids and prisms and extends that understanding to include cylinders, cones and spheres.”
  • The Overview of the student material sometimes informs students what they will learn within the Topic and occasionally gives a general connection to previous learning. For example, the Overview of Topic 2 states, “In this topic, you will learn about a set of numbers that behave quite differently from numbers you are currently familiar with. Let’s review the types of numbers that you have learned about in previous mathematics courses.”

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 meet the expectations for fostering coherence through connections at a single grade, where appropriate and when the standards require. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains when these connections are natural and important.

Some examples of Topic Headings and Goals and Objectives shaped by cluster headings include the following:

  • Topic Headings:
    • In Topic 7 “ Linear patterns and functions” is shaped by 8.F.A,B.
    • In Topic 11 “Solving Linear Equations” is shaped by 8.EE.C.
  • Goals and Objectives:
    • In Topic 2 “know that there are numbers that are not rational” is shaped by 8.NS.A.
    • In Topic 3 “generate the laws of exponents and apply them in problem solving situations” is shaped by 8.EE.A.
    • In Topic 4 “apply the Pythagorean Theorem and its converse in problem situations” is shaped by 8.G.B.
    • In Topic 7 “use variables to generalize linear patterns and represent problem situations that can be modeled by linear functions” is shaped by 8.F.B.
    • In Topic 13 “solve systems of linear equations using the substitution method” is shaped by 8.EE.C.

The following are topics that contain problems and/or activities which connect two or more clusters in a domain or two or more domains in a grade.

  • In Topic 4, 8.G.B and 8.EE.A are connected as students solve problems involving the Pythagorean Theorem by applying knowledge of square roots.
  • In Topic 7, 8.F.A and 8.F.B are connected as students define, evaluate, and compare functions along with using functions to model relationships between quantities.
  • In Topic 8, 8.F.A and 8.EE.B are connected as students connect various representations of a function by writing equations, making graphs and tables, and interpreting values within these representations.
  • In Topic 10, 8.F.A and 8.F.B are connected as students explore nonlinear relationships by examining examples of functions that are not linear and by qualitatively describing the relationship between two quantities that are not linear.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

+
-
Gateway Two Details

The instructional materials reviewed for Agile Mind Grade 8 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
+
-
Criterion Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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 8.EE.B addresses understanding the connections between proportional relationships, lines, and linear equations, and standards 8.F.2,3 address comparing and defining functions.

  • In Topic 8 students are given opportunities to connect verbal descriptions of situations to graphs and write situations that can be represented by a specific graph. The MARS task “Vacations” gives students the opportunity to compare slopes on two different graphs. Students also use proportional and nonproportional reasoning to derive a two-variable equation representing a situation. Overall, students are responsible for interpreting the given real-world situation and representing it in multiple ways, i.e. tables, graphs, verbal descriptions, and equations.

Standard 8.F.1 addresses understanding that a function is a rule that assigns to each input exactly one output.

  • In Topic 7 the definition of a function is developed in multiple ways. Students understand functions through the use of verbal description, input-output machines, real-world situations, graphs, and mappings.

Cluster 8.G.A addresses understanding congruence and similarity through different tools.

  • In Topic 1 students are given multiple opportunities to describe the effects of a transformation of a shape on the coordinate plane. Students demonstrate understanding by moving points on the coordinate plane given a specific transformation and by describing the movement of a point algebraically. Although there are a few opportunities to describe a sequence of transformations and to explain the effects of change on the figure as a whole, greater focus is placed on individual ordered pairs. In this topic, angle measures and side lengths are referenced in dilations.
  • In Topic 14 students further develop their understanding of how angle relationships are affected by transformations through the use of verbal descriptions, animations, real-world examples with maps, and the use of geometric tools.

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 8 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skills. Overall, students are given opportunities to develop procedural skills within clusters 8.EE.C and 8.G.C.

Cluster 8.EE.C addresses students developing procedural skills with analyzing and solving linear equations and pairs of linear equations in one variable.

  • In Topic 11 students have opportunities to practice solving multi-step equations in one variable using the Distributive Property and combining like terms through the Practice and Assessment sections, along with the Student Activity Sheets. Also, within this topic there are opportunities to develop procedural skills with solving equations resulting in infinitely many or no solutions.
  • In Topic 12 students have opportunities to solve systems of equations both graphically and algebraically. Also, within this Topic there are opportunities to develop procedural skills with solving systems of linear equations resulting in infinitely many or no solutions.

Cluster 8.G.C addresses developing procedural skills with the formulas for the volume of cylinders, cones, and spheres.

  • In Topic 15, 3-dimensional animations are provided as assistance for students in understanding the development of the volume formulas. There is limited practice in using the formulas to find the volume of cones, cylinders, and spheres. There are problems within the Practice and Assessment questions, which are multiple choice, that involve finding the volume of cones, cylinders, and spheres, and there are three Constructed Response items that involve these formulas as well.

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 8 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 8.EE.8c addresses students solving real-world and mathematical problems leading to two linear equations in two variables.

  • In Topic 12 Constructed Response 1 students are given tables of data for two students walking in front of a motion detector. The tables include the distances in feet from the motion detector after different amounts of time in seconds. Students are ultimately asked to interpret the point of intersection for the graphs of the two sets of data. Students are provided with scaffolded steps in this problem that lead them to interpreting the point of intersection.
  • Topic 12 Constructed Response 2 is a scaffolded problem that leads students through the steps of creating a solution that contains a certain percentage of pure acid.
  • In Topic 12 Constructed Response 3 students are presented a problem that has them create a solution containing a certain percentage of pure acid, just as in Constructed Response 2 of Topic 12, but the problem does not provide them any scaffolded questions to help them obtain the answer.
  • In Topic 12 the MARS task, Pathways, allows students to write and solve a system of equations that will yield the appropriate dimensions of a paving stone based on a desired design design of the pathway. This problem does not include any questions or prompts for scaffolding, and the context is unique to the topic, which makes the problem non-routine.
  • In Topic 13 Constructed Response 1 students write and solve a system of equations that will result in the dimensions of three horse pens. This problem does not include any questions or prompts for scaffolding, and the context is unique to the topic, which makes the problem non-routine. Furthermore, students must alter the equations and recompute the dimensions based on a change in feet of fencing used.

Cluster 8.F.B addresses students being able to use functions to model relationships between quantities.

  • In Topic 5 Constructed Response 2 students are given a graph that shows the volume of four different gas tanks and how much time is needed for each gas tank to become empty. Students have to answer different questions using the graph, and the questions involve analyzing the volumes of the tanks, the time needed to empty the tanks, distance traveled, and gas mileage. There are no questions or prompts that provide scaffolding to lead students toward the answers, and although the context is similar to one students encountered during the Topic, the use of four gas tanks as opposed to one gives students the opportunity to apply their mathematical knowledge in a non-routine way.
  • In Topic 6 Constructed Response 1 students are presented with a graph that shows distance traveled from a motion detector over time. Students are expected to answer different questions about the graph, but the context used is exactly the same as the context used with many other problems throughout the Topic. Also, the questions used in this problem are the same in wording and structure as other questions posed in the Topic.
  • In Topic 7 Constructed Response 2 students are presented with the first three steps of a tile pattern and must answer questions about different steps in the pattern. Students are provided with some scaffolding during the problem as they are instructed to include a general function rule and a description of what is constant and what changes in the tile pattern as they respond. The context of tiles is unique for this problem in comparison to the other contexts used in the Topic.

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 8 meet the expectations for balance. Overall, the three aspects of rigor are not always treated together and are not always treated separately. Most Topics 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 Topic 4 when students apply and extend previous understanding of the Pythagorean Theorem as they complete an activity. Balance is further evidenced in Topic 11 where students conceptually solve linear equations using different models.

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 8 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 8 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 six 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 8 Block 8 the teacher leads the class through the “Connecting Representations” pages. With the use of teacher questioning and activities found in the Deliver Instruction teacher material, the teacher helps the students understand that relationships can be expressed abstractly and quantitatively. Throughout this lesson, the students are engaging in MP2.
    • Topic 12 Block 6 Deliver Instruction suggests teachers tell students to make sense of the problem by explaining it to their partner. By doing this, students are engaging in MP1; however, that is not noted within the teacher information.

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 8 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 7 during the MARS Task “Squares and Circles” the teacher is directed to “observe how students are modeling with mathematics” by noting different representations that the students pick/create in order to model a context. In this task, most of the models are provided for the students, and students are not defining quantities for themselves or needing to revise their initial choices. In Topic 8 there are different opportunities for students to engage with this MP, but the problems do not allow for students to define their own quantities, and most of the models are provided for the students. There are some opportunities for students to revisit their initial calculations, but this is due to new information being introduced into the problem and not because there could be other solutions that are more optimal. In Topic 13 students create a system of equations to solve a real-world problem, but the quantities needed are defined for the students and revisions to the initial calculations are due to new information being introduced into the problem.
  • 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 1 Block 1 teachers are given assistance for discussing the full meaning of MP5 with students, but the students are not engaged with using appropriate tools strategically at this time as the tools for the activity are given to them. Also in Topic 1, students are told to use patty paper as their tool in Block 2, and teachers are directed to tell students that they will have dilations as a new tool to use in problems in Block 9. In Topic 4 during Block 3, students are told to use patty paper, a ruler, and a pencil as they work on a proof related to the Pythagorean Theorem. In Topic 11 during Blocks 2 and 3 students are lead through using a graphing calculator to solve an equation with both tables and graphs. In Block 4 this MP is identified, but students are shown how to use algebra tiles to solve an equation.

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 8 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 for students to analyze the arguments of others.

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

  • In Topic 4 Block 4 the class is investigating the converse of the Pythagorean Theorem and must answer, “What do the conclusions you have reached so far tell you about the triangles and ∠?????”
  • In Topic 5 during the MARS task “Graphs” students are told to “Explain how you made your choices” after matching several equations and graphs.
  • In Topic 8 Block 4 students compare data in a table during a class discussion and must answer, “Which amount grows at a faster rate—the amount paid or the amount collected? How do you know?”
  • In Topic 14 Block 2 the class is introduced to parallel lines cut by a transversal and the related angles. The class is asked “Use what you have learned about parallel lines, supplementary angles and corresponding angles to explain why ????∠2 = ????∠7.”

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

  • In Topic 2 Constructed Response 3 students create a cube out of modeling clay that has a volume of 20 cubic centimeters. In the last part of the problem, students are instructed to “Compare your group's estimates and results with another group by reading your written responses to another group. Did your methods differ for finding an approximation for the edge length? Did your explanations differ? Revise your writing after reflection and feedback from the other group.”

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 8 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 2 after the students complete Constructed Response 1, there is a class discussion and the teacher is instructed, “The debrief of this task provides an opportunity for students to construct viable arguments and critique the reasoning of others. As students are explaining their solution methods, they should also attend to precision. Encourage the audience members to ask questions of the presenters if information is not clear, either in vocabulary or logic. Push students to clarify their thinking and to use precise vocabulary when explaining their solution method(s).”
  • In Topic 3 Block 1 Professional Support Deliver Instruction, teachers are guided to listen for misconceptions related to exponents, use questions as needed that specifically ask students to analyze why or how a hypothetical person thinks about an answer or gets an answer, and identify whether the person correctly interpreted the meaning of the mathematics in the problem. The intent of these questions is to help students analyze the arguments presented by others and determine how those arguments support the mathematics in this specific problem.
  • In Topic 4 Block 3 students watch animations to help them understand the Pythagorean Theorem, and the teacher is instructed to pose these questions: “Consider one of the right triangles on your Patty Paper. What is the base of the triangle? What is the height of the triangle? Do all four right triangles have the same area? How do you know?” These questions assist teachers in engaging students in constructing viable arguments.
  • In Topic 4 Block 4 students investigate the converse of the Pythagorean Theorem. Teachers are provided with the following assistance, “This may be the first time students have been pushed to make precise mathematical arguments about a geometric relationship. ... Give students the opportunity to make their own arguments before showing the final Check button. Then let students compare their arguments with the one shown online. Discuss the precision of the language and the logical reasoning used. The intent of this page is not for students in this course to develop strict mathematical proofs, but instead to expose students to the reasoning and language used in such arguments.” This assistance is specific in that teachers can draw students’ attention to specific aspects of the solutions provided, which helps in constructing an argument. Also, students can use the correct solutions as a way to analyze their own arguments and improve them as needed.
  • In Topic 5 of the MARS Task “Graphs” teachers are provided with the following assistance, “As the majority of students seem to be finishing the task, put students into pairs and assign one of the four graphs to the each pair of students by counting off student pairs by four. ... This can help students grow in their ability to construct sound arguments and provide meaningful critiques of others’ arguments.”
  • In Topic 5 as the students work on Constructed Response 1, the teacher is instructed to have “students verify their graphs and written responses with a partner. Provide students an opportunity to revise their work as needed but ask that they note any modifications and justification for changes.”
  • In Topic 5 as the students work on Constructed Response 2, the teacher is given the following Classroom Strategy: “Divide the class into two “teams.” Then have each team come to a consensus on their responses for each part. Have team leaders present their team’s answers. Allow time for the other team to ask for clarifications. This will provide students with an opportunity to practice constructing viable arguments and critiquing the reasoning of others as they justify their conclusions, communicate them to others, and respond to the arguments of others.” The assistance provided for the teacher helps create an environment where MP3 can occur.
  • In Topic 14 Block 2 students construct an argument to show that the measures of two angles are equal. The assistance provided to the teacher is as follows: “Encourage students to begin their proving process by measuring or tracing angles. They can write algebraic equations using the variables labeling each angle. Students may need to state their reasons verbally before recording their ideas on paper. These are a great opportunity to promote the mathematical practice of constructing viable arguments and critiquing the reasoning of others. Engage students in each others' arguments by asking them to restate key arguments in their own words or describe how those arguments are related to angles within each image.” This assistance gives teachers specific strategies for helping students construct a viable argument, and it also provides specific ways in which students can begin to analyze the arguments of others.
  • In Topic 14 Constructed Response 1 students construct an argument to prove that two rays are parallel. The assistance that is provided to teachers with this problem is to “Ask a few students to share their explanation. Again, encourage students to critique the reasoning of the students, in a respectful way, and come to a class consensus on a strong explanation."

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 8 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 2: “Discuss the term corresponding points. Make sure students understand this, as it is part of all three transformations.”
  • Topic 3 Block 2: “...encourage them to use technical vocabulary to describe what is happening: base, exponent, and sum.”
  • Topic 11 Block 1: “Language strategy. Students may have trouble at first telling the difference between a function and an equation, and may need to review some core vocabulary from previous topics: function rule, function, equation, input, output, domain, and range may need further review before, during, and after the lessons. Stress the relationship between a function, which describes the relationship between two varying quantities, and an equation, which represents a specific instance of the functional relationship.”

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 8 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
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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 8 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, solving systems of linear equations in Topic 12 incorporates and builds upon solving individual linear equations from Topic 11.
  • 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 8 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 8 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 15 Exploring Volume, students use physical geometric models to explore finding the volumes of various solids along with having interactive, virtual models of the same shapes.

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 8 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 8 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 8 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 12 Block 3 the Framing Questions are: “What do we mean by a 'solution' to a system of equations? How would solve these systems?” 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 12 Block 5 “Could we have solved the two equations modeling the tickets in terms of d? What would the equations have been? If so, what would the solution have looked like?”

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 8 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 3 Block 4 teachers are directed to, “Show students the animation on page 7 that combines multiplication and division with different bases in the same problem. [SAS, question 7] Next, have students work on finding the solution for the expression on page 8. [SAS, question 8]”

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 8 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 8 materials also contain a section of interactive essays entitled “Going beyond Grade 8”. 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 8th grade students; rather, they are designed to provide you with important connections and background that will support you as you help your students master 8th grade content.” The topics for these three essays are are Rate of Change, Finding the Line of Best Fit, and Trigonometric Ratios. 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 9, the essay Finding the Line of Best Fit is referenced for teachers in Block 1 on pages 1-2 of Exploring Trend Lines, and in Topic 1, Trigonometric Ratios is referenced in Block 9 on page 12. The three essays connect the Grade 8 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 8 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 1 the Prerequisite Skills include “Using operations with integers; Creating ratios; Using operations with fractions; Knowledge of the coordinate plane; and Identifying lines of symmetry.” 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 1 “This topic, Transformational geometry and similarity, explores congruence transformations and dilations. These transformations are fun for students and most students have an intuitive understanding of what 'looks right' when performing the transformations. However, students need to have a deeper understanding of what's happening algebraically, as these principles will be applied in later math. These transformations are the basis for how the coordinate plane will be used.”

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 8 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 8 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 8 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 8 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 8 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 8 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 15 two of the Prerequisite Skills are: “Area and circumference of circles and Surface area and volume of prisms and pyramids.” Then, in the Lesson Activities for the Overview, teachers are told, “This Exploring connects to students’ prior understandings of surface area of pyramids and prisms and extends that understanding to include cylinders, cones and spheres. The formulas for surface area and volume are developed from physical models so that students are able to see and make strong connections.”

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 8 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 7 Block 5 teachers are told, “A common misunderstanding that students make when working with this task (MARS Task: Squares and CIrcles) is that they graph points incorrectly, or forget to graph the points, in questions 1 and 2. If this misunderstandings occurs, ask students to re-read both parts of each prompt or ask them to explain how they determined the coordinates or location of the point they graphed.”

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 8 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 8 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 8 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 8 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
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-
Criterion Rating Details

The instructional materials for Agile Mind Grade 8 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 8 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 8 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 5 Block 1 the Deliver Instruction states “Give students the situation, either the verbal description or the graph, and give them time to see what information they can pull from it. Then, give them additional time to present that information in the opposing format. Students can usually catch on to analyzing graphs quickly, when given sufficient time initially to process important data from the graph. Ask students smaller, more specific questions about parts of a graph or situation before tackling the entire problem.”

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 8 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 14 Constructed Response 2 students complete a geometry puzzle called an angle network. Students are given information about a picture containing three parallel lines intersected by two transversals, and they have choices as to which information to use first and how to proceed in determining the angles measures for the angles in the puzzle. Another example is in Topic 13 Student Activity Sheet 6 Problem 11. Students create one system of linear equations for each of the following three conditions: a system with one solution, a system with many solutions, and a system with no solutions.

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
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Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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 6, Block 3 is “Use a think-write-pair-share strategy to help ELL and those with other learning differences process the given information and the framing questions. Give time for students to individually think about the questions and time to write a response. Then pair a non-native English speaker with a native English speaker and have each student share his or her responses.” An example of a strategy for other special populations from Topic 2, Block 2, Pages 3-4 is “Classroom strategy. Students may not be familiar with bar notation used to represent repeating decimals. Take time now to review this notation. The use of technology in this case is especially important for those students with certain learning differences; it can remove barriers and allow them to access the content they need to learn.”

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 8 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 14 Block 2 teachers are given the following assistance, "The animation shows only one case, so you may prefer to ask the students to conduct a further exploration in the following way: Give each group of students three pieces of spaghetti and a different angle measure to explore. Ask each group to use spaghetti to construct lines cut by a transversal in such a way that one pair of corresponding angles has the measure assigned to the group. Ask the group to measure the distance between the two parallel‐line candidates. Then, ask the group to try to keep the angles congruent but make the parallel lines not be parallel. Then ask the group to shift the position of the transversal and redo the process."

Indicator 3w

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

The instructional materials reviewed for Agile Mind Grade 8 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
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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 7 Block 7 teachers are told to “have each student in a group present one part of the problem.”

Indicator 3y

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

The instructional materials reviewed for Agile Mind Grade 8 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
+
-
Criterion Rating Details

The instructional materials for Agile Mind Grade 8 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
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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 8 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 8 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
+
-
Indicator Rating Details

The instructional materials reviewed for Agile Mind Grade 8 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 8 Student Activity Book 978-1-943460-82-3 Agile Mind 2016
Mathematics 8 Advice for Instruction 978-1-943460-83-0 Agile Mind 2016

About Publishers Responses

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Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

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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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