## Agile Mind Integrated Mathematics

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
Integrated Mathematics I Student Activity Book 978-1-949175-50-9 Agile Mind 2018
Integrated Mathematics I Advice for Instruction (Teacher Edition) 978-1-949175-51-6 Agile Mind 2018
Integrated Mathematics II Student Activity Book 978-1-949175-52-3 Agile Mind 2018
Integrated Mathematics II Advice for Instruction (Teacher Edition) 978-1-949175-53-0 Agile Mind 2018
Integrated Mathematics III Student Activity Book 978-1-949175-54-7 Agile Mind 2018
Integrated Mathematics III Advice for Instruction (Teacher Edition) 978-1-949175-55-4 Agile Mind 2018
Integrated Mathematics I Online Course - Teacher 978-1-949175-71-4 Agile Mind 2018
Integrated Mathematics I Online Course - Student 978-1-949175-72-1 Agile Mind 2018
Integrated Mathematics II Online Course - Teacher 978-1-949175-73-8 Agile Mind 2018
Integrated Mathematics II Online Course - Student 978-1-949175-74-5 Agile Mind 2018
Integrated Mathematics III Online Course - Teacher 978-1-949175-75-2 Agile Mind 2018
Integrated Mathematics III Online Course - Student 978-1-949175-76-9 Agile Mind 2018
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## Report for High School

### Overall Summary

The instructional materials reviewed for the Agile Mind Integrated series meet expectations for alignment to the CCSSM for high school, Gateways 1 and 2. In Gateway 1, the instructional materials attend to the full intent of the non-plus standards and allow students to fully learn each non-plus standard, but they do not attend to the full intent of the modeling process when applied to the modeling standards. The materials have students engage in mathematics at a level of sophistication appropriate to high school and foster coherence through meaningful connections in a single course and throughout the series, but the materials do not explicitly identify knowledge from Grades 6-8. The instructional materials spend a majority of time on the widely applicable prerequisites from the CCSSM. In Gateway 2, the instructional materials meet the expectation that materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials reviewed meet the expectations for making sense of problems and persevering in solving them as well as attending to precision; reasoning and explaining; seeing structure and generalizing; and modeling and using tools.

##### High School
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus & Coherence

Focus and Coherence: The instructional materials are coherent and consistent with "the high school standards that specify the mathematics which all students should study in order to be college and career ready" (p. 57 of CCSSM).

The instructional materials reviewed for the Agile Mind Integrated series meet the expectation for focusing on the non-plus standards of the CCSSM and exhibiting coherence within and across courses that is consistent with a logical structure of mathematics. Overall, the instructional materials attend to the full intent of the non-plus standards and allow students to fully learn each non-plus standard, but they do not attend to the full intent of the modeling process when applied to the modeling standards. The materials have students engage in mathematics at a level of sophistication appropriate to high school and foster coherence through meaningful connections in a single course and throughout the series, but the materials do not explicitly identify knowledge from Grades 6-8. The instructional materials spend a majority of time on the widely applicable prerequisites from the CCSSM.

##### Indicator {{'1a' | indicatorName}}
The materials focus on the high school standards.*
##### Indicator {{'1a.i' | indicatorName}}
The materials attend to the full intent of the mathematical content contained in the high school standards for all students.

The instructional materials reviewed for Agile Mind Integrated series meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. Overall, the materials address all aspects of the non-plus standards.

Examples of standards that are addressed include:

• A-SSE.2: Students use structure to rewrite equations. The materials emphasize factoring with area models in Mathematics II, Topic 3, Student Activity Sheet 4. In Mathematics III, Topic 6, Student Activity Sheet 2, students identify the structure of quadratic equations through several guided problems. In Mathematics III, Topic 6, Student Activity Sheet 4, students factor with area models and grouping, and students choose their strategy for factoring to solve equations.
• F-TF.1: In Mathematics III, Topic 16, Exploring, students understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. Students define radians and use radians in multiple real-world application problems.
• G-CO.10: In the materials, students encounter several theorems about triangles in a variety of formats. In Mathematics II, Topic 10, Student Activity Sheet 4, students examine a flowchart proof of the Triangle Sum Theorem, a two-column proof that two angles in a right triangle are complementary, and a paragraph proof of the Exterior Angle Theorem.
• G-CO.12: Students explore geometric constructions with a variety of tools and methods. The materials demonstrate straightedge and compass constructions in Mathematics I, Topic 18, and patty paper constructions in Mathematics I, Topic 15. In Mathematics I, Topic 18, Student Activity Sheet 1, students consider the differences between a drawing and a construction.
• N-RN.2: Students rewrite expressions involving radicals and rational exponents using the properties of exponents in Mathematics II, Topic 16, Student Activity Sheets 1-3.

The following standard is partially addressed:

• G-C.5: The formula for the arc length of a sector is stated in Mathematics II, Topic 24, Exploring Areas of Sectors and Segments, but never derived.
##### Indicator {{'1a.ii' | indicatorName}}
The materials attend to the full intent of the modeling process when applied to the modeling standards.

The instructional materials reviewed for Agile Mind Integrated series partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. The instructional materials include aspects of the modeling process in isolation or combinations, however, opportunities to engage in the full modeling process are absent across the courses of the series.

In topics indicated as containing modeling there are many real world problems, however students are given much of the information and the lessons are scaffolded with prompts that lead the student to the solution rather than providing the opportunity to reason through the problem and to apply their own approach, assumptions, and way to solve the problem that allows one to fully engage in the modeling process.

The following examples allow students to engage in aspects, but not all, of the modeling process:

• In Mathematics I, Topic 2 Assessment, students determine the amount of fencing needed. The assessment provides multiple prompts which guide students through the problem. Students do not determine important information, identify assumptions, or make predictions.
• In Mathematics I, Topic 3, Exploring Modeling with Functions, students investigate the cost of purchasing roses through different flower shops for a fundraiser. The problem includes a list of factors for students to consider, but students do not make their own assumptions as part of the modeling process because of the provided list of factors. The materials provide students with a specific method for solving the problem, and an equation is given to the students rather than allowing students to make sense of the relationship between the variables.
• In Mathematics II, Topic 4, Exploring, students find the dimensions of a garden, but students do not formulate a model. The variables are explicitly stated in the activity and the problem has a single solution method with a single correct answer. Students do not interpret or validate their results.
• In Mathematics II, Topic 6, Student Activity Sheet 3, problems 2-6, students explore a real-world scenario through a series of specific questions that leads to a solution. Students do not make assumptions, interpret their model, or determine the reasonableness of their results.
• In Mathematics II, Topic 7, Assessment, students write an equation to represent the shape of the Gateway Arch in St. Louis. Students do not determine their own way to model the arch or make assumptions, as those are stated in the problem.
• In Mathematics III, Topic 6, Assessment, Constructed Response, students model when two water tanks hold the same amount of water. The questions guide students on how to solve the problem and the specific information they need to determine the solution. Students do not validate the accuracy of their model.
• In Mathematics III, Topic 10, Constructed Response, page 1, students find the domain and range of a given function and relate them to the context (wind speed) in which the function is presented. Students answer other questions using the function, but students do not develop the model.
##### Indicator {{'1b' | indicatorName}}
The materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.
##### Indicator {{'1b.i' | indicatorName}}
The materials, when used as designed, allow students to spend the majority of their time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers.

The instructional materials reviewed for Agile Mind Integrated series meet expectations for, when used as designed, spending the majority of time on the content from CCSSM widely applicable as prerequisites for a range of college majors, postsecondary programs, and careers (WAPs). (Those standards that were not fully attended to by the materials, as noted in indicator 1a.i, are not mentioned here.)

Within Mathematics I, Mathematics II, and Mathematics III, students spend the majority of their time engaging with the WAPs from N-RN, N-Q, A-CED, A-SSE, F-BF, F-IF, F-LE, G-CO, G-SRT, S-ID, and S-IC. Examples of students engaging with the WAPs across the series include:

• Mathematics I: In Topic 5, students explore linear functions through multiple representations (F-IF, F-BF, F-LE, and S-ID). In Topic 7, students explore measures of central tendency and bivariate categorical data (S-ID and S-IC). In Topic 12, students explore exponential growth and decay, compare linear and exponential functions, and create multiple representations of exponential functions (A-CED, A-SSE, F-IF, and F-BF). In Topic 15, students explore rigid transformations and applications of rigid transformations (G-CO and G-SRT).
• Mathematics II: In Topic 1, students explore multiple representations of and solving problems with absolute value and piecewise functions such as the problem of representing shipping charges as a function of the order total (A-CED and F-IF). In Topic 6, students explore real world scenarios leading to quadratic functions, and they solve problems using quadratic equations such as determining how long it will take for a tomato to hit the ground (F-BF and F-LE). In Topic 13, students explore dilations and applications of dilations within the coordinate plane and problems related to enlarging photos. The topic also has students explore how they can prove triangles are similar (G-CO and G-SRT). In Topic 18, students explore regression, modeling exponential growth and decay, and quadratic relationships in real-world scenarios, such as school enrollment and throwing a basketball (N-Q, F-LE, and S-ID).
• Mathematics III: In Topic 1, students explore the similarities and differences between arithmetic, geometric, and infinite series and apply this understanding to problems of a growing triangle pattern or tiling around a fish pond. (A-SSE , F-BF, and F-LE). In Topics 2 and 3, students use probability to make predictions and understand the likelihood of real world events. Students examine different types of statistical studies and the conclusions one can draw from those studies (S-IC). In Topic 10, students examine square and cube root functions, their inverses, and multiple representations of these functions (A-CED and F-IF). In Topic 12, students explore many different real world scenarios of exponential growth and decay and solve problems using equations, graphing, and fitting a function to given data such as the population of fire ants (F-IF and F-LE).
##### Indicator {{'1b.ii' | indicatorName}}
The materials, when used as designed, allow students to fully learn each standard.

The instructional materials reviewed for Agile Mind Integrated series, when used as designed, meet the expectation for allowing students to fully learn each non-plus standard. Overall, there are multiple opportunities for students to fully learn the non-plus standards by engaging with all aspects of the standards and not distracting students with prerequisite or additional topics.

Examples of the standards where students have multiple opportunities to fully learn the standards include, but are not limited to:

• F-BF.3: Students work with linear functions to identify the effects of transformations in Mathematics I, Topic 6, Student Activity Sheet 4. Students identify the effects of transformations on exponential functions in Mathematics I, Topic 12, Student Activity Sheet 3. Later, students identify the effects of transformation on quadratic and cubic functions in Mathematics III, Topic 4 and rational functions in Mathematics III, Topic 8.
• A-SSE.3a: In Mathematics III, Topic 6, Exploring Quadratics, and in Mathematics II, Topic 4, students factor a quadratic expression to reveal the zeros of the function.
• G-GMD.3: Students use volume formulas to solve problems involving prisms and cylinders in the context of sugar cubes in Mathematics II, Topic 25. In the same topic, students complete a MARS Task related to the volume of a swimming pool. In Mathematics II, Topic 26, students use volume formulas for pyramids and cones in real-world application problems. In Mathematics II, Topic 27, students apply volume formulas to real-world application problems for spherical objects.
• S-ID.1: In Mathematics I, Topic 7, Student Activity Sheet 1, students compare a bar graph and a histogram. Later in the worksheet, students construct a graphical representation of their choice to represent data. In Student Activity Sheet 3 of the same topic, students construct two histograms.

Examples of where the materials do not enable students to fully learn the non-plus standards are:

• F-IF.8b: The materials include exponential growth and decay in Mathematics II, Topic 18, Exploring Modeling Growth and Exploring Modeling Decay. Exponential functions are also addressed in Mathematics III, Topic 12. Students interpret expressions for exponential functions in a limited number of problems.
• F-IF.9: Students compare different functions throughout the materials (e.g. Mathematics II, Topic 2, MARS task: Graphs), but these comparisons include two functions expressed in similar forms (e.g. algebraically, graphically, numerically in tables, etc.). The materials provide a limited number of problems in which students compare functions which are expressed in different forms.
• G-GPE.2: The materials give a geometric definition of a parabola in Mathematics III, Topic 21, Exploring Defining Hyperbolas and Parabolas. The focus and directrix are defined, but the relationship between the focus, directrix, and equation for the parabola is not derived by the students.
• S-IC.6: The materials address reporting conclusions in Mathematics III, Topic 3, Exploring Experiments, but students do not read reports and evaluate them.
• S-CP.4: Students use two-way frequency tables in a variety of problems in Mathematics II, Topic 31, Exploring Conditional Probability, but they do not construct two-way frequency tables.

##### Indicator {{'1c' | indicatorName}}
The materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The instructional materials reviewed for Agile Mind Integrated series meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The materials regularly use age-appropriate contexts, apply key takeaways from Grades 6-8, and vary the types of real numbers being used.

The materials use age appropriate and relevant contexts throughout the series. The following examples illustrate appropriate contexts for high school students:

• In Mathematics I, Topic I, students construct graphs related to a student and his teammates ordering pizza.
• In Mathematics I, Topic 5, students explore the relationship between the depth of gas and number of gallons in a gas tank.
• In Mathematics I, Topic 8, students relate how many snacks you buy with the cost of the snacks at a movie theater.
• In Mathematics II, Topic 19, students model the spread of a flu virus with exponential tables and graphs.
• In Mathematics III, Topic 7, students examine a band selling candy as a fundraiser.

The following problems represent the application of key takeaways from Grades 6-8:

• In Mathematics I, Topic 6, Exploring Transformations, students make connections between geometric transformations and linear equations.
• In Mathematics I, Topic 8, students extend solving linear equations to generate formulas for linear functions and solve linear inequalities.
• In Mathematics I, Topic 9, students use their knowledge of linear functions to build absolute value functions.
• In Mathematics II, Topic 14, students apply proportional reasoning to dilations with a scale factor.

Examples of the materials varying the types of real numbers used across the courses of the series include:

• In Mathematics I, Topic 6, Exploring “Rate of Change”, students perform calculations with decimals as they analyze data from a simulation of Hooke’s Law to create a linear model for the data.
• In Mathematics I, Topic 19, Constructed responses 1 and 2, students perform calculations with decimals as they use geometry to model and solve real-world problems.
• In Mathematics II, Topic 15, Student Activity Sheet 2, Problems 8, 9, 14, 23, and 25, students operate on fractions as they apply laws of exponents to simplify expressions involving rational exponents.
• In Mathematics II, Topic 24, Guided practice, Page 9, work with irrational numbers to solve an area problem.
• In Mathematics III, Topic 1, two problems in the More and Guided Practice sections use a fractional difference in a geometric series.
• In Mathematics III, Topic 7, More practice, Pages 9 and 10, students solve problems about joint variation involving mixed numbers and decimals.
##### Indicator {{'1d' | indicatorName}}
The materials are mathematically coherent and make meaningful connections in a single course and throughout the series, where appropriate and where required by the Standards.

The instructional materials reviewed for the Agile Mind Integrated series meet the expectation for fostering coherence through meaningful connections in a single course and throughout the series. Overall, connections between and across multiple standards are made in meaningful ways. Each topic provides a Prerequisite Skills list and an overview of the topic in Topic at a Glance. The Topic at a Glance provides generic connections within each course and throughout the series.

Examples where the materials foster coherence within courses include the following:

• In Mathematics I, students explore linear equations (F-BF.1), graphs, tables, stories, rates of change (F-LE.1b), and key features of the equations and graphs (F-IF.9) in Topics 2-5. In Topic 6, students build on that understanding by modeling linear data with trend lines (S-ID.7), scatterplots, and lines of best fit (S-ID.6a,b,c).
• In Mathematics III, Topic 12, students model data with exponential functions (F-IF.B) and then build on that understanding to construct the concepts of inverse functions and logarithms in Topics 13-15.
• In Mathematics II, Topic 13, Dilations and Similarity begins by connecting the idea of transformations (G-CO.2) to deciding if two triangles are similar (G-SRT.2). This topic uses the properties of similarity to prove AA congruence (G-SRT.2) as well as congruence and similarity criteria to solve problems (G-SRT.5). At the end of this topic, students also prove that all circles are similar (G-C.1).

Examples where the materials foster coherence between the courses include the following:

• In Mathematics I, Topic 13, students explore and create arithmetic and geometric sequences (F-BF.1,2). In Mathematics III, Topic 1, students review arithmetic and geometric sequences to connect this knowledge to arithmetic, geometric, and infinite series (F-IF.3).
• The F-LE standards are connected throughout the series. In Mathematics I, students compare linear growth and exponential growth in a number of topics (Topics 5, 6, and 12). Students use the idea of linear growth in Mathematics II, Topic 10 to find lines that are parallel. In Mathematics III, Topic 14, students use concepts from Mathematics I to work with logarithms using prerequisite knowledge of exponential functions.
• In Mathematics II, Topics 4, 5, and 6, students work with quadratic equations (A-REI.4). Students fit quadratic functions to models in Topic 6 (F-IF.4). Students use their knowledge of quadratic equations from Mathematics II, to explore, factor, and solve polynomial equations in Mathematics III, Topic 6 (A-APR.B).
##### Indicator {{'1e' | indicatorName}}
The materials explicitly identify and build on knowledge from Grades 6--8 to the High School Standards.

The instructional materials reviewed for Agile Mind Integrated series partially meet expectations for explicitly identifying and building on knowledge from Grades 6-8 to the High School Standards. The instructional materials do not explicitly identify content from Grades 6-8 in either the teacher or student materials.

The following are examples of where the materials build on, but do not explicitly identify, standards from Grades 6-8:

• In Mathematics I, Topic 4, Exploring, Constant Rates, students use derived units (e.g. gallons/hour, dollars/cap, bad jeans/total jeans) while building on ratios (6.RP.1).
• In Mathematics I, Topic 15, Exploring, Applications of rigid transformations, students formalize that rotations produce congruent figures. This builds on their understanding of congruence (8.G.2).
• In Mathematics II, Topic 5, Exploring, Complex Numbers, students build on their understanding of the real number system (8.NS.1) to develop an understanding of complex numbers.
• In Mathematics II, Topic 13, Exploring, Dilations, students explore the ratios of side lengths on dilated triangles building on their understanding of similarity (8.G.4).
• In Mathematics II, Topic 19, Exploring, Trigonometric Ratios, the materials develop the trigonometric ratios from proportional reasoning (7.RP.2).
• In Mathematics III, Topic 16, Exploring, Sine and Cosine, students explore “an interesting relationship between cos and sin and use the animation to relate the Pythagorean Theorem to sin and cos to this right triangle.” Students develop the Pythagorean identity from the Pythagorean theorem (8.G.B).
• In Mathematics III, Topic 2, Exploring, Normal Distribution, students learn about the normal distribution by extending their understanding of center and spread (6.SP.2).
##### Indicator {{'1f' | indicatorName}}
The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.

The plus (+) standards, when included, are explicitly identified and coherently support the mathematics which all students should study in order to be college and career ready.

The instructional materials address the following plus standards: N-CN.8,9; N-VM.12; A-APR.5,7; F-IF.7d; F-BF.4b,4c,4d; F-BF.5; G-SRT.9-11; G-C.4; G-GMD.2; G-GPE.3; S-CP.8,9; and S-MD.6,7. In general, the instructional materials treat these standards as additional content that extends or enriches non-plus standards within the courses and would not interrupt the sequence of the topics if removed.

The following are examples of components of the materials that address the plus standards:

• In Mathematics I, Topic 16, Exploring Using Matrices to Describe Transformations, students use matrices to complete transformations of two-dimensional figures on a coordinate plane. (N-VM.12)
• In Mathematics III, Topic 5, Student Activity Sheet 5, students expand binomials and find the values for rows of Pascal’s Triangle using binomial expansions. (A-APR.5)
• In Mathematics III, Topic 8, Exploring Graphing Rational Functions, students use an applet to determine how different parts of rational functions change the graph of a rational function (transformations). Students are also provided opportunities to graph rational functions on the student activity sheets for the topic (F-IF.7d)
• In Mathematics II, Topic 5, Student Activity Sheet 5, students are expected to “State the Fundamental Theorem of Algebra in [their] own words…” Later in the worksheet, students use division to find the remainder and “Consider the polynomial function $$p(x)=x^3+8x^2+cx+10$$, where c is an unknown real number.  If x+10 is a factor of this polynomial, what is the value of c?” (N-CN.9)
• In Mathematics III, Topic 8, Student Activity Sheet 2, students are provided with multiple opportunities to add, subtract, multiply, and divide rational expressions. In Student Activity Sheet 5, students show that an expression is undefined when the denominator is zero. Materials do not address whether rational expressions are closed operations under addition, subtraction, multiplication, and division. (A-APR.7)
• In Mathematics II, Topic 29, Exploring Permutations and Combinations, students use combinations to determine the number of possible jury members for a trial. (S-CP.9)

### Rigor & Mathematical Practices

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: The instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by giving appropriate attention to: developing students' conceptual understanding; procedural skill and fluency; and engaging applications.

The instructional materials reviewed for the Agile Mind Integrated series meet the expectation that the three aspects of rigor are not always treated together and are not always treated separately. Overall, all three elements of rigor are thoroughly attended to and interwoven in a way that focuses on the needs of a specific standard as well as balancing procedural skill and fluency, application and conceptual understanding.

##### Indicator {{'2a' | indicatorName}}
Attention to Conceptual Understanding: The materials support the intentional development of students' conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

The instructional materials reviewed for Agile Mind Integrated series meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. There are instances in the materials where students are prompted to use multiple representations to further develop conceptual understanding. In addition, throughout the materials, real-world contexts provide “concreteness” for abstract concepts, especially when introducing a new topic.

Examples of the development of conceptual understanding related to specific standards are shown below:

• N-Q.1: In Mathematics I, Topic 2, Student Activity Sheet 1, Problem 5, students use a “different type of representation to solve the problem.” Joachim states, “For every 2 yards of flowerbed, you can plant 3 peonies.” Students “describe how [they] can use Joachim’s representation to solve the problem.” Students use multiple representations to demonstrate the meaning of the problem and make connections among the representations.
• F-BF.1a: In Mathematics I, Topic 13, Student Activity Sheets 1, Problem 6, students use geometric patterns in mosaics to make connections between geometric and algebraic representations. Students build conceptual understanding by connecting a real world situation, a pattern, and a sequence. Finally, students consider, “How many tiles will be in the tenth mosaic? How do you know?” Students draw out mosaics, use manipulatives, and apply the sequence to connect the different representations of the pattern.
• G-SRT.4: In Mathematics II, Topic 14, Student Activity Sheet 2, Problem 7, students prove the Triangle Proportionality Theorem. Students demonstrate their understanding of various parts of the proof and of the purpose of the proof in more than one way. In Problem 8, students connect their proof to “parallel lines that cut two transversals.”
• S-ID.9: In Mathematics I, Topic 6, Student Activity Sheet 3, Problem 25, students examine a scatterplot showing a positive association between the number of ice cream cones sold and the number of shark attacks. Students consider, “Based on this scatterplot, could you make a reasonable prediction of the number of shark attacks if you knew the number of ice cream cones sold,” and, “Does this mean that eating ice cream causes sharks to attack?” Students differentiate between correlation and causation by considering the similarities and differences between the two questions.
##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: The materials provide intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.

The instructional materials reviewed for Agile Mind Integrated series meet expectations for providing intentional opportunities for students to develop procedural skills, especially where called for in specific content standards or clusters. Within the lessons, students are provided with opportunities to develop procedural skills for solving problems. Guided Practice and More Practice sections are included within each lesson. These practice sections often contain problems with no context and provide students the opportunity to practice procedural skills when called for by the standards.

Examples of the development of procedural skills related to specific standards include:

• A-APR.1: In Mathematics II, Topic 3, students perform operations on polynomials. Students use area models and algebra tiles in the Exploring section and then practice polynomial multiplication in the Guided Practice, More Practice, and Student Activity Sheet sections.
• A-REI.2: In Mathematics III, Topic 9, Exploring, Solution methods #1-11, students solve rational equations. Students independently practice in Guided Practice #11, More Practice #1-12, and Student Activity Sheet 2.
• A-REI.7: In Mathematics II, Topic 7, Student Activity Sheet 4 #11, students algebraically solve a system of equations with three variables. Students consider connections to the geometric representations of the system.
• A-SSE.3: In Mathematics II, Topic 4, MARS Task, students develop procedural fluency by determining whether statements about quadratics are true or false. Students demonstrate algebraic skills in several ways: graphing, factoring, completing the square, and through transformations.
• F-IF.7b: In Mathematics I, Topic 9, Student Activity Sheet 1, students consider a scenario about a skater’s distance from a cone as he skates by at a constant speed.  Students sketch a graph showing the skater’s distance from the cone versus time and use the graph to determine its algebraic representation.
• G-SRT.6: In Mathematics III, Topic 18, Student Activity Sheet 1, students practice using trigonometry ratios to solve problems involving a waterslide.
• S-ID.7: In Mathematics I, Topic 6, Student Activity Sheet 2, students find the equation of the graph of a line. Later in the worksheet, students create equations to determine the equation for a trend line.
##### Indicator {{'2c' | indicatorName}}
Attention to Applications: The materials support the intentional development of students' ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.

The instructional materials reviewed for Agile Mind Integrated series meet expectations for supporting the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters. Within every topic, the Overview introduces the topic content with a real-world scenario and problems that are based on these real-world scenarios. Students begin each topic with a context to understand the mathematical idea.

Examples of students utilizing mathematical concepts and skills in engaging applications include:

• A-SSE.3: In Mathematics 2, Topic 5, Student Activity Sheet 2, students find different forms of a quadratic to answer questions about a dog kennel. Students interpret key features of a graph to determine the maximum area possible.
• A-REI.6: In Mathematics I, Topic 10, Student Activity Sheet 2, students use data to create a set of equations and then interpret the data based on whether the mowing season is almost over or has just begun.  Students consider, “It would be useful to know how many weeks it would take for the two options to result in the same total cost. How can Desmond figure that out?” Students also determine at what point advertising pays for itself.
• A-REI.10: In Mathematics I, Topic 3, More Practice, students independently construct a graph from a routine context. Students also engage in a non-routine problem to construct a general rule.
• F-IF.B: In Mathematics I, Topic 4, students engage in different real-world scenarios involving rates of change: elevators, draining a pool, and selling baseball caps. Students make predictions and compare different rates in graphs and tables.  Students build understanding from different contexts and different representations. In Student Activity Sheet 2, students interpret a graph in the context of a descending and ascending elevator.
• G-CO.2: In Mathematics II, Topic 28, Student Activity Sheet 3, students compare the volumes of two triangular prisms with congruent bases but different heights.
• G-SRT.6: In Mathematics II, Topic 19, More Practice, students independently apply prior knowledge from isosceles triangles and the Pythagorean theorem to new applications.
##### Indicator {{'2d' | indicatorName}}
Balance: The three aspects of rigor are not always treated together and are not always treated separately. The three aspects are balanced with respect to the standards being addressed.

The instructional materials reviewed for Agile Mind Integrated series meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

Each topic includes Overview, Exploring, Practice, Assessment, and Student Activity Sheets.

• The Topic Overviews provide a focal point for students to begin thinking about the topic. Materials allow for students to relate the topic to a real-world application and/or prior knowledge. This gives students an opportunity to develop conceptual understanding through applications and/or prior knowledge. For example, in Mathematics I, Topic 6, students interpret a scatter plot relating height and shoe size.  Students consider positive and negative correlation and a trend line. The teacher is then presented with several framing questions “Does the size of Tommy's shoes surprise you? Why or why not? How would you expect a shorter person's shoe size to compare to Tommy's shoe size? What would you expect to be true about a person with a shoe size that is larger than size 14? How could you confirm your predictions?”
• The Exploring section focuses on developing conceptual understanding, in context and/or by using applets. Students are given the tools to build their procedural skills throughout as algorithmic steps are connected to the concepts in this section.
• The Practice section includes Guided Practice and More Practice for students. There are a variety of types of problems (multiple choice, multiple select, true or false, etc.) with a focus on conceptual understanding and procedural skills. Students can get hints and immediate feedback if their answer is correct. If it is incorrect, students receive a statement/question to help direct their thinking.
• Assessment has two parts, Automatically Scored and Constructed Response. Automatically Scored includes Multiple Choice and Short Answer. This section has questions that require conceptual knowledge, procedural skills, and application of the topic.
• Student Activity Sheets follow the online instruction but include additional procedural skill and application problems.

In addition to this, there are MARS tasks throughout that focus on conceptual understanding and application.

The following are examples of balancing the three aspects of rigor in the instructional materials:

• A-REI.3: In Mathematics II, Topic 8, Exploring, students draw from prior conceptual understanding of linear functions to solve linear equations and systems of linear equations.  Students engage in interactive visual models to solve equations that supports the conceptual aspect of solving linear equations while gaining procedural fluency with algebra.
• F-IF.5: In Mathematics I, Topic 3, Student Activity Sheet 2, students use a function for the number of 1-square foot tiles in the border of a square pool to consider whether “the relationship between the length of the pool and the number of tiles in the border is a function?”  Students then interpret the meaning of f(10) in the context of the application to build conceptual understanding of a function. Later, in Student Activity Sheet 3, students determine the cost of roses ordered from several shops (procedural fluency) in order to recommend which shop a soccer team should use as their supplier (application).
• F-IF.6: In Mathematics I, Topic 4, Exploring, Constant Rates, students develop a conceptual understanding of constant rates through real-world scenarios and interactive lessons by sketching graphs and making predictions. Later, students develop procedural fluency by writing and calculating rates.
• S-ID.6a: In Mathematics II, Topic 18, students start with regression and move into exponential functions while building on their prior knowledge about linear functions.  In Student Activity Sheet 3, students examine flu data to determine a rule and construct a scatterplot. Students complete a table of the flu infection rates (procedural fluency). Later, students extrapolate values for the future of the flu epidemic (application).

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for the Agile Mind Integrated series meet the expectation that materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials reviewed meet the expectations for making sense of problems and persevering in solving them as well as attending to precision; reasoning and explaining; modeling and using tools; and seeing structure and generalizing.

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The materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Agile Mind Integrated series meet expectations that the materials support the intentional development of overarching, mathematical practices (MPs 1 and 6), in connection to the high school content standards.

Examples where students make sense of problems and persevere in solving them include:

• In Mathematics II, Topic 6, Overview, students examine different rectangular dog kennels with equivalent perimeters. The teacher facilitates the task by having students draw one rectangular kennel that meets the requirements. The students then decide whether other solutions exist and persevere in finding them. The teacher aggregates the solutions so students can model all solutions with a quadratic expression.
• In Mathematics I, Topic 13, Student Activity Sheet 1, students find the next three terms of a given sequence and explain their method. Students then determine whether the sequence is arithmetic or geometric. Students must persevere when the pattern is not obvious or their method for determining the type of sequence needs refinement.
• In Mathematics II, Topic 6, Exploring, students use a graph and table of revenues for two different smartphone manufacturers to consider “if these trends continue, how will the revenue of the two manufacturers compare in future years? Explain how you know.” Although students are provided with the data, they make sense of the problem by predicting future revenues and justifying that prediction. They persevere in solving the problem by exploring beyond just the given data.

Examples where students attend to precision include:

• In Mathematics II, Topic 2, MARS Task: Graphs, students comparing linear and quadratic functions. Students determine points of intersection by examining two graphs and then verify the coordinates algebraically. Students generate another graph and use algebra to determine its intersection point(s) with the original graphs. Students must identify precise coordinates, accurately set up equations, and maintain exact values while solving to test whether the two methods produce equivalent points of intersection.
• In Mathematics III, Topic 15, Student Activity Sheet 3, students solve the equation 2+3ln(x)=4-2ln(x) algebraically and verify the solution using a table and graph. Students compare an exact solution from algebra with an approximate solution from the graph. They grapple with precision in determining how different solutions can be numerically different while still being considered equivalent.
• In Mathematics II, Topic 13, Exploring, students draw a scalene triangle and dilate it by a factor of 3 around a given point. Students measure corresponding angles and sides of their triangles using rulers and protractors. Students must be precise in their transformation and measurements to verify that angle measures are preserved and lengths are three times longer.
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The materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Agile Mind Integrated series meet expectations that the materials support the intentional development of reasoning and explaining (MPs 2 and 3), in connection to the high school content standards.

Examples where students reason abstractly and quantitatively include:

• In Mathematics II, Topic 21, Overview, students are given a real-world problem of determining the maximum height for a truck to travel through a tunnel. Students are shown how a coordinate grid can be used to determine the maximum height of a vehicle. This scenario provides students an opportunity to reason abstractly as they use both the coordinate grid and the Pythagorean Theorem to solve the problem. In addition, students use the given information about the radius of the tunnel and the width of the truck to quantitatively determine the maximum height of a vehicle that can pass through the tunnel.
• In Mathematics I, Topic 10, Student Activity Sheet 1, students are provided constraints on Desmond’s mowing operations. Students must reason abstractly about the information provided to create a system of linear equations. Students must also reason abstractly and quantitatively about their solutions to determine which option Desmond should choose based on the amount of time left in the mowing season.
• In Mathematics III, Topic 3, Student Activity Sheet 2, students are asked, “In a random survey of 100 adults, 50% responded ‘yes’ to the question ‘Should parents monitor teens’ cell phone usage?’” Then students are asked, “Describe a simulation to develop a margin of error for this study.” and “Execute the simulation. What is the margin of error? What is the interval in which we can be confident our true population value lies?” Students make sense of the data they collected and represent the data symbolically. Students are also expected to determine the confidence interval and provide justification.

Examples where students construct viable arguments and critique the reasoning of others include:

• In Mathematics III, Topic 3, Overview, students are presented with a report stating that “Most Americans think there is intelligent life on other planets” and provides students with additional data from the report. Students are then asked if the conclusion drawn in the article is justified. This provides students with an opportunity to share and justify their own reasoning/argument and to support their reasoning based on the information given in the report. As students share their own justification, they are also provided with the opportunity to critique the reasoning of others.
• In Mathematics I, Topic 14, Student Activity Sheet 1, students are given a picture of the golden rectangle with the Fibonacci spiral in the center as well as the Sierpinski's triangle. Students are asked, “Take a few minutes to explore these two patterns. Then, in your own words, explain how each pattern is generated.” Students interpret the images, describe the patterns, justify their conclusions, analyze the problem using definitions, and establish results in constructing their arguments.
• In Mathematics III, Topic 18, Student Activity Sheet 4, students are given information from two fictitious students, Albert and Sonya: “An isosceles triangle has an area of 4 square feet. The base is twice as long as each of the two legs. Find the three side lengths of the triangle.” They are then asked to “Explain what Sonya means by this” concerning a comment that there is “no such triangle.” Students examine Sonya’s comments and decide if they agree or disagree and then explain why or why not.
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The materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Agile Mind Integrated series meet expectations that the materials support the intentional development of modeling and using tools (MPs 4 and 5), in connection to the high school content standards.

The materials fully develop MPs 4 and 5 as students build upon prior knowledge to solve problems, create and use models within many lessons, and choose and use appropriate tools strategically across the courses. The materials pose problems connected to previous concepts and a variety of real-world contexts. Students are provided meaningful real-world problems in which to model with mathematics and use tools.

Examples where students model with mathematics include:

• In Mathematics I, Topic 6, Exploring, students examine a graph of shoe size versus height of a person. Students create a function to model the information provided in the graph. Students are able to use previous knowledge to show a correlation between each of the figures and thus draw a trend line. The students formulate the problem (with some help from the book), then are asked to compute the trend line that would correlate that data and lastly students check their work and report out. This process is present for multiple scenarios within the Guided Practice and More Practice sections.
• In Mathematics III, Topic 16, Student Activity Sheet 4, students are given data representing the number of hours of daylight in Tallahassee, Florida for the year 1998. Students are asked to “Make a scatterplot of these data using your graphing calculator. What type of function do you think would model these data? Do you think these data are periodic?” Later, students are asked: “What trigonometric function would you use to model the data? What is the period of the graph? What is the amplitude of the sinusoidal graph? Is the graph shifted horizontally and/or vertically from the parent function $$y = sin x$$? If so, by how much is it shifted? Transform the parent function, $$y = sin x$$, to fit the data.” Finally, students are asked to “Use your model to find the days when Tallahassee had more than 12 hours of daylight.” Through this set of problems, students apply prior knowledge to new problems; identify important relationships; map relationships with tables, diagrams, graphs, and rules; draw conclusions as they pertain to a situation; and create and use models.
• In Mathematics II, Topic 2, MARS Task: Functions, students “model each of two subsets of a set of points on a scatterplot. Students must go beyond simple visual inspection of a graph to sort the set into two subsets and justify their sorting by applying their knowledge of fundamental characteristics of different function families.” In this activity, students must write a linear function to represent the scatterplot and determine a non-linear model for the rest of the points in the scatterplot. Students must verify their solutions with their partner and report their findings.

Examples where students choose and use appropriate tools strategically include:

• In Mathematics I, Topic 18, Block 1, Advice for Instruction, students follow a paper-and-pencil activity with a construction activity in which they are to “use tools of their choice.” Later in the same block, in Technology tip, pages 6-7, Exploring “Congruent segment and angle bisector constructions,” students choose between compass and straightedge or an online construction tool.
• In Mathematics II, Topic 11, Block 4, Advice for Instruction states, “Encourage students to use tools to help them make sense of the problem of dividing a triangle into sixths. Make Patty Paper, rulers, protractors, dynamic geometry software (optional) and scissors available to students. Give students enough time to really try to answer this question.”
• In Mathematics III, Topic 3, Student Activity Sheet 2, Question 10, students design and carry out a simulation. They choose from a variety of tools to carry out the simulation, including a coin, a random number table, a random number generator, or a statistical software package.
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The materials support the intentional development of seeing structure and generalizing (MPs 7 and 8), in connection to the high school content standards, as required by the mathematical practice standards.

The instructional materials reviewed for Agile Mind Integrated series meet expectations that the materials support the intentional development of seeing structure and generalizing (MP7 and MP8), in connection to the high school content standards. The majority of the time MP7 and MP8 are used to enrich the mathematical content. Across the series, there is intentional development of MP7 and MP8 that reaches the full intent of the math practices.

Examples where students look for and make use of structure include:

• In Mathematics III, Topic 7, Exploring- Comparing Direct and Inverse Variation and Exploring- Investigating Inverse Variation, students explore and compare the differences of direct and inverse variation using real-world examples such and the speed of a train, the time is takes to reach its destination, and the cost of tickets to Math Land based on how many students attend. Students explore and construct equations using tables and graphs of direct and inverse variation. Students have the opportunity to look for and make use of structure as they reason about the differences and similarities between the two equations, graphs, and scenarios and the different ways these situations can be expressed algebraically.
• In Mathematics III, Topic 14, Exploring- The Basics of Logarithms, students explore a population of fire ants doubling over time by modeling the number of fire ants as a function of the number of weeks that have passed. Students explore the structure of this function by creating a graph and writing a logarithmic function rule that models number of weeks as a function of the number of fire ants.
• In Mathematics II, Topic 15, Student Activity Sheet 2, students are given a set of three problems that have been worked out. Students are asked to “Identify the mistake in each solution, and then solve correctly, showing your work.” In this process, students must look for, develop, and generalize relationships and patterns. Students must apply their knowledge of patterns and properties to this new situation. Students also must not only know the rules of exponents, but be able to apply them and combine them into complex problems.

Examples where students look for and express regularity in repeated reasoning include:

• In Mathematics I, Topic 8, Exploring- Solving Linear Equations, students use equations to model the rental of a dune buggy and solve the equation if the rental fee is \$75. Students solve linear equations and systems of linear equations algebraically using a balance model and identify the algebraic property for each step in the process. Students view an animation of a balance scale and use algebra tiles to model the steps in solving an equation or systems of equations. These experiences provide students with an understanding of repeated reasoning used when solving equations and systems of equations.
• In Mathematics I, Topic 3, Student Activity Sheet, students are given a scenario about the online retailers “We-stock-it.com” and “Discountstore.com” and the costs for shipping and handling. Each question asks the student to take a step in working with the function. One question asks students “If you made a graph of each retailers’ shipping and handling costs, which variable would you graph along the x-axis? Which variable would you graph along the y-axis? Why?” Another question asks students to graph the data. Students look for shortcuts using patterns and repeated calculations. Students think about what the data means, how to use it, what they notice, what is happening in this situation, and what would happen if they switched the values on the x-axis and y-axis.
• In Mathematics III, Topic 12, Student Activity Sheet 4, students are given a picture of a set of six exponential functions. Students are asked “What do you notice about these graphs? Show that $$y=\frac{1}{2}^x$$ is the same as $$y=2^{-x}$$.” Students look at general methods and shortcuts in the function graphs (the applications of transformation rules) and attend to the details of the calculations and movements. Students must consider the reasonableness of their results.

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials reviewed for Agile Mind Integrated series 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.

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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.

The instructional materials reviewed for Agile Mind Integrated series 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. In these explorations, 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, providing 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. 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 include MARS Tasks where students apply concepts they have learned within the topic and connect concepts from other topics.

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Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Agile Mind Integrated series 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. For example in Mathematics I, Topic 3,  Functions, the Exploring section consists of Function Notation, Modeling with Functions and Graphs.

Within the explorations for each topic, problems progress from simpler to more complex, incorporating knowledge from prior problems or topics. This progression helps students to make connections among mathematical concepts.  For example, in Mathematics I, Topic 5, Moving Beyond Slope Intercept, students create linear models for data that incorporates and builds on content from Topic 4, Rate of Change.

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.

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There is variety in how students are asked to present the mathematics. For example, students are asked to produce answers and solutions, but also, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials reviewed for Agile Mind Integrated series meet the expectations 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. The Student Activity Sheets provide opportunities for students to explain their thinking and show their own approach to solving a problem.

The types of responses required vary in intentional ways. For example, concrete models or visual representations are expected when a concept is introduced.  As students progress in their knowledge, they transition to more efficient solution strategies and representations.

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Manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Agile Mind Integrated series 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 hands-on activities that allow the use of physical manipulatives as well as a variety of virtual manipulatives.

Most of the physical manipulatives used in Agile Mind Integrated are commonly available: ruler, patty paper, graph paper, algebra tiles, and graphing calculators. Due to the digital format of the materials, students use virtual manipulatives to develop a conceptual understanding of the mathematics in that topic. Each topic has a Prepare Instruction section that lists the materials needed for the topic. Manipulatives accurately represent the related mathematics. For example, in Mathematics II, Topic 3, Operations on Polynomials, Exploring, Multiplying Polynomials, students use virtual algebra tiles to multiply binomials.  This relates back to the area model used in multiplying multi-digit numbers.

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The visual design (whether in print or digital) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials reviewed for Agile Mind Integrated series 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 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials reviewed for Agile Mind Integrated series 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. Different sets of interactive, print, and video essays provide teachers with adult-level explanations or examples of advanced mathematics concepts to help them 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.

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

The instructional materials reviewed for Agile Mind Integrated series 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 Mathematics I, Topic 7, Descriptive Statistics, Block 6, students “think about the different measures of center and spread they have learned about in this topic.”  Students consider “When is it more appropriate to report the mean? Median? When is it more appropriate to report the standard deviation? Interquartile range?”
• In Mathematics I, Topic 7, the students consider, “In which ways can you compare two different data sets? How do you know which statistic to use when comparing data?”
• In Mathematics II, Topic 1, Absolute Value and Other Piecewise Functions, Block 2, students access their prior knowledge such as,  “In the functions you have previously studied, how did you represent a vertical translation of the function? How did you represent a horizontal translation? A vertical stretch or compression?”

At the end of each lesson, Deliver Instruction included Further Questions that support a deeper exploration of the mathematics content.  For example:

• In Mathematics II, Topic 1, Absolute Value and Other Piecewise Functions, after students have explored the concept using an interactive app, they consider “How will changing the value of a to 3 affect the graph? How will changing the value of h to 2 affect the graph?”
• In Mathematics II, Topic 8, Rational Expressions and Functions, students consider “Do all rational functions have vertical asymptotes? If no, give an example of one that doesn't. Can the graph of a function ever cross a horizontal asymptote? Explain.”
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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.

The instructional materials reviewed for Agile Mind Integrated series meet the expectation for containing 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, 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 when each part of the materials should be used. The Classroom Strategies include questions to ask, connections to mathematical practices, and 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, the following exchange occurs in the Deliver Instruction section of Mathematics II, Topic 2, Introduction to Quadratic Functions, Block 1:

• The teacher “play[s] the animation on page 1 to demonstrate the tiling project, pausing after a 2' × 2' area is laid with the tiles (4 total tiles).”
• Students “follow along by coloring in appropriate areas on their own square grids and fill in the data values in their tables for the first two edge lengths, and then to complete their diagrams and tables for edge lengths of 3, 4, and 5.”
• The Teacher “play[s] the animation on page 2 to highlight the patterns in the data.”
• Students “develop a rule to generalize the pattern in the data.”
• Students “use their graphing calculators to make a scatterplot of the data from the table and then to graph the function rule over the scatterplot.”
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition that contains full, adult--level explanations and examples of the more advanced mathematics concepts and the mathematical practices so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials reviewed for Agile Mind Integrated series 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 is a group of four interactive essays in each course entitled “Developing Concepts Across Grades,” and the topics for these four essays are Functions, Volume, Rate, and Proportionality. Each essay examines the progression of the concept from Grades 6-8 through Mathematics I, Mathematics II, Mathematics III, and beyond. These interactive essays give teachers the opportunity to not only make connections between the courses they are teaching and previous courses, but they also give teachers the opportunity to improve their own knowledge in regards to connections that will be made between the courses they are teaching and future courses.

In addition to “Developing Concepts Across Grades,” each course also contains a section of interactive essays entitled “Going Beyond This Course.” In Mathematics I, there are three essays in this section: "Average and Instantaneous Rates of Change," "The Slope of a Curve," and "The Relationship Between Exponential and Logarithmic Functions." In Mathematics II, there are two essays in this section: "Trigonometric Functions" and "Radians." In Mathematics III, there are three essays in this section: "Linearizing Data Using Logarithms," "From Rates of Change to Derivatives," and "Understanding Area of Irregular Shapes using Calculus." 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.

In Professional Learning, there are also sets of Video or Print Essays. The Print Essays are divided as either Research to Practice or Content to Pedagogy, which, in Mathematics III, includes a series of three essays titled “Rational Functions and Crossing Asymptotes” that addresses mathematical concepts that extend beyond Mathematics III. The Video Essays are: "Teaching with Agile Mind," "More Teaching with Agile Mind," and "Dimensions of Mathematics Instruction."

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Materials contain a teacher's edition that explains the role of the specific mathematics standards in the context of the overall series.

The instructional materials reviewed for Agile Mind Integrated series partially meet the expectation for explaining the role of the specific grade-level mathematics in the context of the overall mathematics curriculum. In the course materials for Mathematics I, Mathematics II, and Mathematics III, the specific reference to the Standards is the following statement in the Plan the Course materials: “Alignment to standards. To support the use of our Integrated Mathematics III course, you will find correlations from Agile Mind topics to your state learning standards. These alignments can be found in Course Materials.” There are no specific references within the online lesson materials as to the standards that are being taught for the courses. A Scope and Sequence is provided where the standards for each lesson are listed for each Topic.

Within Professional Support, Practice Standards Connections is provided. Also, the materials include a table for each Standard for Mathematical Practice that lists examples of where the MPs are used within the course. “The citations below are examples from the Integrated Mathematics III program that show how the materials provide students with ongoing opportunities to develop and demonstrate proficiency with the Standards for Mathematical Practice.” Teachers are able to make connections between the standards being taught and the activities and instruction for the lesson.

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Materials provide a list of lessons in the teacher's edition, cross-- referencing the standards addressed and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials reviewed for Agile Mind Integrated provide a list of lessons in the teacher's Advice for Instruction and the Scope and Sequence document, cross­‐referencing the standards addressed and providing an estimated instructional time for each topic and block. The Plan the Course section provides the following advice: “Agile Mind materials, Opening the lesson, Framing questions, Lesson activities, Further questions, and Suggested assignment. This section is divided into blocks, each one focused on related key ideas within a topic. Each block provides advice on lesson activities to support a 45-minute period of instruction.”

For each course, the materials provide a Scope and Sequence document which includes the number of blocks of instruction, 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 the materials do not align blocks to specific content standards. The materials provide an 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.

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Materials contain strategies for informing students, parents, or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials reviewed for Agile Mind Integrated series 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.

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Materials contain explanations of the instructional approaches of the program and identification of the research--based strategies.

The instructional materials reviewed for Agile Mind Integrated series 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 and clips of teachers using Agile Mind in Mathematics I, Mathematics II, and Mathematics III. There are also Print Essays where there are articles or essays that speak to instructional practices for specific mathematics content or research behind instructional practices.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials for Agile Mind Integrated series 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 opportunities for students to monitor their own progress, and there are assessments that explicitly identify prior knowledge within and across grade levels. The materials include opportunities to identify common misconceptions, and strategies to address common errors and misconceptions are found in Deliver Instruction topics.

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Materials provide strategies for gathering information about students' prior knowledge within and across grade levels/ courses.

The instructional materials reviewed for Agile Mind Integrated series meet the expectations for providing strategies for gathering information about students' prior knowledge within and across grade levels. The materials provide assessments that are specifically designed for the purpose of gathering information about students’ prior knowledge, and the materials also include indirect ways for teachers to gather information about students’ prior knowledge if teachers decide to use them that way.

Each course includes additional Topics intended to assess students’ prior knowledge. Mathematics I includes computations with rational numbers and foundations of solving equations. Mathematics II includes computations with rational numbers and foundations of functions and linear equations. Mathematics III includes computations with rational and irrational numbers, operations with exponents, and foundations of linear and quadratic functions and equations.

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 Mathematics I, Topic 1: Constructing Graphs, Advice for Instruction, the prerequisite skills are “Plotting points and labeling axes, Identifying independent and dependent variables, Reading data from a table or from a graph.”
• Int Mathematics II, Topic 1: Absolute value and other piecewise functions, the heading “About This Topic” has several references to framing students’ thinking, “This topic, Absolute value and other piecewise functions, builds on students' prior work with absolute value functions in earlier courses and deepens their knowledge of this function type while also introducing students to other piecewise functions.”
• In the Deliver Instruction section for Mathematics III, Topic 1: Arithmetic and geometric sequences and series, guides the teacher, “Classroom strategy, The material on these two pages are designed to activate students' prior learning from previous courses, but keep it in the context of setting the stage for new learning in this course. Do not succumb to the temptation of re-teaching everything students should have learned in prior courses. Instead, use the material on these pages to actively engage students in recall of prior work, facilitating students' conversations to resurface what they have learned previously about these key function families. This will set students up for success not only for this topic but also for work in future topics with new function families.”
##### Indicator {{'3n' | indicatorName}}
Materials provide support for teachers to identify and address common student errors and misconceptions.

The instructional materials reviewed for Agile Mind Integrated series meet the expectation for providing strategies for teachers to identify and address common student errors and misconceptions. Across the series, common student errors and misconceptions are identified and addressed in Deliver Instruction as parts of Classroom Strategy, but Classroom Strategy is not solely used for identifying and addressing common student errors and misconceptions. Examples of supports from the materials include:

• In the Deliver Instruction section for Mathematics I, Topic 9: Absolute Value Functions and Equations, guidance for absolute values is given: “Classroom strategy. Some students may incorrectly think that absolute value means to take the opposite of any number; others may think that the solutions to an absolute value equation are always a number and its opposite. Encourage students to use the values in the table they built as they think through the statements in the puzzle. Students often think that a variable with no sign or a plus sign is positive, and one with a minus sign is negative. You can address this misunderstanding by relating the numbers in the table to the variable in the puzzle. Explain that the variable can stand in for a positive or a negative number, even though the sign is not written.”
• In the Deliver Instruction section for Mathematics II, Topic 4: Solving Quadratic Equations, guidance for similar graphs is given: “Classroom strategy. When modeling motion data with quadratic functions (as in the case of the balloon launcher) students will often confuse the actual path (which is height versus horizontal distance) with the graph of height versus time. Both are parabolic, so spend some time relating the two. It may be helpful to spend some time looking at the path of the balloon in the Overview with the associated table of distances and times and relating the times to the graph of the path through the common distances.”
• In the Deliver Instruction section for Mathematics III, Topic 1: Arithmetic and geometric sequences and series, guidance for connecting numeric and geometric ideas is given: “Classroom strategy. Give students equilateral triangle pattern blocks to help them make sense of the problem. This will support their understanding of how the perimeter grows and help them discern the pattern and underlying structure in the problem, connecting the numerical representation of the perimeter to the geometry of the figures. This strategy is particularly important for some students with learning differences to help them move from concrete to abstract representations.”
##### Indicator {{'3o' | indicatorName}}
Materials provide support for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials reviewed for Agile Mind Integrated series 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, and 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.

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Materials offer ongoing assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials reviewed for Agile Mind Integrated series partially meet the expectation for assessments clearly denoting which standards are being emphasized.

The pre-made assessments 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 CCSSM are being emphasized.

Agile Assessment is an optional resource that can be licensed along with the Agile Mind Integrated Math series, and Agile Assessment allows educators to create their own assessments by selecting from a repository of items aligned to standards and level of difficulty. Reports from assessments created with Agile Assessment denote which standard is being assessed.

##### Indicator {{'3p.ii' | indicatorName}}
Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials reviewed for Agile Mind Integrated series 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 and selected Constructed Response items in Mathematics II are accompanied by rubrics aligned to the task or item 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 remainder of the Constructed Response items in Mathematics III, along with all of the Constructed Response items in Mathematics I and Mathematics II, are accompanied by complete solutions, but rubrics aligned to these 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 most of the MARS Tasks or the Constructed Response items. In Mathematics I, there are four Constructed Response items that are accompanied by a professional essay titled “Learning from Student Work," and Mathematics I and Mathematics II each include a MARS Task that is accompanied by a professional essay that provides guidance to teachers for interpreting student performance and suggestions for follow-up.

##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials reviewed for Agile Mind Integrated series offer 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.

Students can also monitor their progress on assignments and quizzes assigned by their teacher from the Agile Mind Integrated courses. There is a set of reports for students that appear on their dashboard about active assignments and quizzes from that day,  there is another set of reports in the student’s Report area from which students can view data on all the assignments they have completed throughout the year. These reports allow students to monitor their progress and learning related to the topics in the course.

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials for Agile Mind Integrated series partially 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 also provide strategies for ELL and other special populations, but they do not provide strategies for advanced students to deepen their understanding of the mathematics. Grouping strategies are designed to ensure roles for each group member.

##### Indicator {{'3r' | indicatorName}}
Materials provide teachers with strategies to help sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials reviewed for Agile Mind Integrated series 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, materials for Practice, Assessment, and Activity Sheets, along with a MARS Tasks if applicable for the topic. In each topic, the Overview introduces the mathematics concept with a real-world example. The Deliver Instruction provides guiding questions that asks students questions about the real-world scenario. The scaffolding within the Overview and Exploring provide a pace that allows students to focus on a particular idea or concept in small pieces. In the Advice for Instruction for each topic, Deliver Instruction for each block contains instructional notes and classroom strategies that provide teachers with key mathematics concepts to develop, sample questions to ask, ways in which to share student answers, and other similar instructional supports.

##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials reviewed for Agile Mind Integrated series partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners. Overall, the instructional materials embed multiple visual representations of mathematical concepts where appropriate, include audio recordings in many explorations, and give students opportunities to engage physically with the mathematical concepts.

However, the instructional notes provided to teachers do not consistently highlight 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 the Deliver Instruction for Mathematics II, Topic 6: Modeling Quadratic Relationships, Block 4, as students are exploring a graph and table of cell phone revenues, the instructional notes provide questions to ask the students and a task for the students to do. There is a lack of strategies to support a range of learners other than, “Give students a few minutes to analyze the data and graph. Push students to go beyond the shape of the graph and discuss the patterns in the data that indicate a quadratic model might be appropriate” and, “Give students time, working in pairs, to build the models and respond to the questions about the models related to the smartphone case scenario presented on page 10.”

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. 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. For struggling students, teachers are occasionally provided with strategies or questions they can use to help move a student’s learning forward. For example, in Mathematics II, Topic 27: Spheres, Block 1, Advice for Instruction states, “To differentiate instruction, you can give constraints to the spheres that students create. For example, you can limit the side lengths to whole numbers. Students may have individual modifications that allow them to use a calculator."

##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials reviewed for Agile Mind Integrated series 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 of the topics have multiple entry-points and can be solved using a variety of solution strategies or representations. For example, in Mathematics II, Topic 10: Lines, Transversals, and Triangles, Exploring, A Triangle or Not?, pages 2-6, students can explore the difference of rigidity between a triangle and a square in various ways, including using straws and string or an online interactive app.

##### Indicator {{'3u' | indicatorName}}
Materials provide 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).

The instructional materials reviewed for Agile Mind Integrated series 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 throughout each course in the series. In Prepare Instruction for Topic 1 of each course, Teaching Special Populations of Students refers teachers to the Print Essay entitled “Teaching English Language Learners” in Professional Support, and that essay 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, and these strategies include 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, and strategies specific to other special populations can also be found in Classroom strategy or Language strategy. Examples include:

• The Deliver Instruction for Mathematics III, Topic 8: Rational Expressions and Equations, Block 1 provided the guidance, “Support for ELL/other special populations. Provide the sentence stem ‘A rational function is _______. An example of a rational function is _______.’ Consider creating a concept map to help students. Make sure the concept map of rational function includes a definition, examples and non-examples. Sentence stems like this one help students with some learning differences focus their thinking.”
• In Mathematics I, Topic 4: Rate of Change, Block 4, Language Strategy, teachers are directed “Have students practice using the language of direct variation as it applies to the blue jeans situation. For example, asking students to restate the statement ‘y is proportional to x’ in terms of the blue jeans context will help the terms make more sense to them. Choral responses like these help students with some learning differences, such as auditory processing disorders, appropriately use and internalize the meaning of academic language.”
• In Mathematics II, Topic 4: Solving Quadratic Equations, Block 1 provides a strategy to support ELLs/other special populations with graphs of piecewise functions, “Ask students to sketch 2-3 other graphs that they think represent piecewise defined functions. After students have sketched their graphs, have them turn to a partner and explain why they think their examples represent piecewise defined functions. A sentence frame such as ‘This function is a piecewise function because one piece can be modeled with the function _______ and another piece can be modeled with the function _______.’ may help students understand that piecewise defined functions are composed of two or more different functions. Be on the lookout for students who create piecewise functions that are composed of three or more linear functions or that use non-linear functions. Monitor the conversations as students are talking and choose some students to share their graphs and explanations with the whole class.”
##### Indicator {{'3v' | indicatorName}}
Materials provide support for advanced students to investigate mathematics content at greater depth.

The instructional materials reviewed for Agile Mind Integrated series partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth. The problems provided in the materials are on course level, and the materials are designed to assign most of the problems to all students. However, there are a few problems that are on course level and not assigned to all students, and these problems could be used for advanced students to investigate mathematics content at greater depth. Examples include:

• In Mathematics I, Topic 4: Rate of Change, the MARS Task: Differences could be assigned only to advanced students.
• In Mathematics II, Topic 21: Algebraic representations of circles, optional Block 5, students investigate another curve of constant width as they study Reuleaux triangles.
• In Mathematics III, Topic 19: Relating 2-D and 3-D objects, optional Block 5, students investigate orthographic and isometric drawings.
##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials reviewed for Agile Mind Integrated series provide 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' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials reviewed for Agile Mind Integrated series provide opportunities for teachers to use a variety of grouping strategies. The Deliver Instruction, Lesson Activities include suggestions for when students could work individually, in pairs, or in small groups. When small groups are advised, there are no specific roles suggested for group members.  Teachers are given suggestions to ensure the involvement of each group member. For example:

• In Deliver Instruction for Mathematics I, Topic 3: Functions, Block 1, teachers are told to “have students work in small groups to list at least 3 examples of dependent relationships such as those shown on this page,” and “after a few minutes, ask each group to share 3 of their function statements and record them on a class chart.”
• In Deliver Instruction for Mathematics III, Topic 10: Square Root and Cube Root Functions and Equations, Block 1, the students do a pendulum activity.  The materials suggest students answer questions in pairs or groups.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials reviewed for Agile Mind Integrated series 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 3.5: Technology Use

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

The instructional materials for Agile Mind Integrated series are web-based and platform neutral but do not include the ability to view the teacher and student editions in their entirety 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, except for Agile Assessment, 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' | indicatorName}}
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 Mac and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials reviewed for Agile Mind Integrated series 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, and students can complete assignments on smartphones.

However, the navigation between the online student and teacher materials and resources are cumbersome and time consuming. The online interface makes it difficult to compare the student and teacher materials since they cannot be seen in their entirety simultaneously. Teachers can review the printed, spiral-bound teacher materials while viewing the online curriculum projected in class (and what the student also sees when they log into the system).

##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials reviewed for Agile Mind Integrated series include opportunities to assess students’ 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' | indicatorName}}
Materials can be easily customized for individual learners.
##### Indicator {{'3ac.i' | indicatorName}}
Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.

The instructional materials reviewed for Agile Mind Integrated series 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.

##### Indicator {{'3ac.ii' | indicatorName}}
Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials reviewed for Agile Mind Integrated series cannot be easily customized for local use. Within My Courses, there are no options for modifying the sequence or structure of the Topics or any of the sections within the Topics.

Agile Assessment is an optional resource that can be licensed along with the Agile Mind Integrated Math series, and Agile Assessment allows educators to create their own assessments by selecting from a repository of items aligned to standards and level of difficulty.

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.).

The instructional materials reviewed for Agile Mind Integrated series 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. My Agile Mind does not allow teachers to collaborate with other teachers or students to virtually collaborate with other students.

##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The instructional materials reviewed for Agile Mind Integrated series 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 for some examples as to how the interactive tools and virtual manipulatives can be used.

## Report Overview

### Summary of Alignment & Usability for Agile Mind Integrated Mathematics | Math

#### Product Notes

Upon completing the review of the High School Integrated series from Agile Mind, EdReports.org determined that revisions and enhancements made within the Integrated series had also been made to the materials for the Traditional series and Grades 6-8 from Agile Mind. As a result, EdReports.org revised the reports for the Traditional series and Grades 6-8 to reflect the revisions and enhancements that have been made to the materials.

#### Math High School

The instructional materials reviewed for the Agile Mind Integrated series meet expectations for alignment to the CCSSM for high school, Gateways 1 and 2, and they meet the expectations for instructional supports and usability indicators, Gateway 3. In Gateway 1, the instructional materials attend to the full intent of the non-plus standards, allow students to fully learn each non-plus standard, and foster coherence through meaningful connections in a single course and throughout the series. In Gateway 2, the instructional materials meet the expectation that materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials reviewed meet the expectations for making sense of problems and persevering in solving them as well as attending to precision; reasoning and explaining; and seeing structure and generalizing and partially meet the expectations for modeling and using tools. In Gateway 3, the materials meet the expectations for having use and design to facilitate student learning and teacher planning and learning for success with CCSS.

##### High School
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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###### Usability
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