## Fishtank Math AGA

##### v1.5
###### Usability
Our Review Process

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## Report for High School

### Overall Summary

The materials reviewed for Fishtank Math AGA meet expectations for alignment to the CCSSM for high school. For focus and coherence, the series showed strengths in the following areas: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites, requiring students to engage in mathematics at a level of sophistication appropriate to high school, being mathematically coherent and making meaningful connections in a single course and throughout the series, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. In Gateway 2, for rigor, the series showed strengths in the following areas: supporting the intentional development of students' conceptual understanding, opportunities for students to develop procedural skills, working with applications, and displaying a balance among the three aspects of rigor. The materials intentionally develop all of the eight mathematical practices, but do not explicitly identify them in the context of individual lessons.

##### High School
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

### Focus & Coherence

The materials reviewed for Fishtank Math AGA meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites, requiring students to engage in mathematics at a level of sophistication appropriate to high school, being mathematically coherent and making meaningful connections in a single course and throughout the series, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. The materials partially meet expectations for attending to the full intent of the modeling process and letting students fully learn each non-plus standard.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus and Coherence

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”.

The materials reviewed for Fishtank Math AGA meet expectations for Focus and Coherence. The materials meet expectations for: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites, requiring students to engage in mathematics at a level of sophistication appropriate to high school, being mathematically coherent and making meaningful connections in a single course and throughout the series, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. The materials partially meet expectations for attending to the full intent of the modeling process and letting students fully learn each non-plus standard.

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Materials focus on the high school standards.

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Materials attend to the full intent of the mathematical content in the high school standards for all students.

The materials reviewed for Fishtank Math AGA meet expectations for attending to the full intent of the mathematical content contained in the high school standards for all students. Examples of standards addressed by the courses of the series include:

• N-Q.1: In Algebra 1, Unit 2, Lesson 15, Anchor Problem 1, students label axes with appropriate variables and units. Guiding Questions include, “How did you determine an appropriate scale?” In Algebra 2, Unit 1, Lesson 4, students use graphs to interpret units. Guiding Questions include, “How could George use the graph of f(g) to find the number of quarts that equals three-quarters of a gallon?” and “ Which function is more appropriate to use to find the number of quarts that equals a gallon?” In Geometry, Unit 6, Lesson 16, Anchor Problem 2, students use metric unit conversions to solve the problem.

• N-CN.2: In Algebra 2, Unit 2, Lesson 8, Anchor Problem 1, students add and subtract complex numbers, and to determine if properties of operations apply to the addition and subtraction of complex numbers. In Anchor Problem 2, students find the product of two complex numbers, and determine if properties of operations apply to the multiplication of complex numbers.

• A-REI.2: In Algebra 2, Unit 4, Lesson 14, Anchor Problem 3, students compare two radical equations graphically to see that there are no solutions, although it may appear there are solutions if students attempt to solve them algebraically. In Lesson 15, Anchor Problem 1, students generate two solutions, but when they test their solutions, they discover one does not work in the original equation.

• F-IF.7c: In Algebra 2, Unit 3, Lesson 3, Anchor Problem 1, students are given sketches of two different functions and the factored form of one of them. Using Guiding Questions (“What is similar about the graphs?, What is different?,” and “How do these differences help you determine which graph matches the equation?”), students can match the factored form to the correct graph. Other Guiding Questions lead students to determine the end behaviors of the graphs. Within the same lesson, Anchor Problem 2 has students use the roots of a cubic function to sketch the function.

• G-C.5: In Geometry, Unit 7, Lesson 11, Anchor Problem 2, students use Guiding Questions to develop a conceptual understanding of the proportional relationship between the radius of a circle and the length of an arc. Guiding Questions include, "What would be the ‘arc length’ if you were to measure the entire outside of the circle?” and “What portion of the entire circumference are you measuring (for a 30-degree angle)?” In Lesson 12, Anchor Problem 2, students use Guiding Questions and a diagram of concentric circles to develop a conceptual understanding of the proportional relationship between the radius and arc lengths. Finally, in Lesson 13, Anchor Problem 1, students find the area of a sector using its proportional relationship with the whole circle. With the use of Guiding Questions, students write a general formula to determine the sector area of a circle with respect to its central angle measure and radius length.

• G-GPE.6: In Geometry, Unit 5, Lesson 2, Anchor Problem 1, students identify locations that would partition a piece of wood into a 3:5 ratio. Students use a number line to justify their answers. In Anchor Problem 2, students use a number line to partition a line segment into a 3:4 ratio. In Anchor Problem 3, students use coordinates on a plane, and partition the vertical line segment into a 1:2 ratio. In Lesson 3, Anchor Problem 1, students find the midpoint of a directed line segment on a coordinate plane. In Anchor Problem 2, students partition a directed line segment into a 1:3 ratio.

• S-ID.4: In Algebra 1, Unit 2, Lesson 8, students annotate a standard deviation on a curve with correct values.Through calculations, they locate two points between which 68% of the contextual data falls and then calculate a percent of the data falling between two specified points. In Algebra 2, Unit 8, Lesson 8, Anchor Problem 2, students revisit and build a deeper understanding of normal distributions with the use of a contextual problem involving heights of 8 year old boys. Students use the information given in the problem and a graph of the normal distribution to calculate percentages related to the data. In Lesson 9 of the same unit, Anchor Problem 1, students revisit the problem involving the normal distribution of heights of 8 year old boys to calculate z-scores (number of standard deviations that a score is away from the mean).

• S-IC.5: Algebra 2, Unit 8, Lesson 13, Anchor Problem 1, students use a dotplot of the difference of means to compare plant growth in standard and nutrient-treated soils. The Guiding Questions include, "What would the distribution of data look like for you to confidently conclude that there is not enough evidence to say the nutrient-treated soil contributed to growth?" TheTarget Task has a histogram that represents another problem involving the difference of means in relation to plant growth in different soils. Students consider whether the difference of the means is due to the way the sample was taken or whether the treatment had an effect.

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Materials attend to the full intent of the modeling process when applied to the modeling standards.

The materials reviewed for Fishtank Math AGA partially meet expectations for attending to the full intent of the modeling process when applied to the modeling standards. In this series, various aspects of the modeling process are present in isolation or combinations, yet opportunities for the complete modeling process are absent for the modeling standards throughout the materials.

Examples of problems that allow students to engage in some aspects of the modeling process include, but are not limited to:

• Algebra 1, Unit 2, Lesson 21: An Anchor Problem contains data involving percent pass-completion rates for top paid NFL quarterbacks and their salaries. Students organize the data, represent it visually, and calculate bivariate statistical measures. Students can use Guiding Questions to help them formulate a problem related to the data. Examples of Guiding Questions include: “How did you organize this data set when the values of the salaries are so high?,” “Why did you decide to use the graph you did?,” and “What formulas will you use to either find the measures you need to make the graph or calculate center and spread?” Students make decisions about how to organize and represent the data graphically and ways to use the data. How the data is used will determine what statistical measures they need to calculate. Students can analyze and interpret the data to solve a problem, but there are no explicit instructions for how they should report their findings (N-Q.1, S-ID.6, S-ID.7, S-ID.8, S-ID.9).

• Algebra 1, Unit 8, Lesson 12, EngageNY Mathematics, Algebra 1, Module 4, Topic B, Lesson 16: “The Exploratory Challenge,” provides a scenario where a fence is being constructed. Students are given the variables to use when writing an expression; thus, not allowing students to formulate their own. Students find the maximum area and determine if their answer is surprising. This allows for students to interpret and validate their response; however, there is no clear way that students should report their answer. (A-CED.2, F-IF.8a).

• Algebra 2, Unit 2, Lesson 9: Students focus on quadratic functions in context. The Target Task has two people throw a baseball in the air. One ball is modeled by a function, the other by a graph. One person says his ball goes higher and the students must decide if he is correct, determine how long each ball was in the air, and construct a graph of the function given to back up claims from the first two parts. Students do not have opportunities to formulate the mathematical model, but do have opportunities to validate and interpret their responses in relation to the problem. However, there is no directed way for students to communicate and/or report their findings to others (A-CED.1, A-CED.2, F-IF.6, F-BF.1).

• Algebra 2, Unit 6, Lesson 14, Problem Set, EngageNY Mathematics, Algebra II, Module 2, Topic B, Lesson 13: “Tides, Sound Waves, and Stock Markets,” students write a sinusoidal function to fit a set of data. Students manipulate their function as the data will not lie exactly on the graph of the function. Students then analyze their model to predict a later time and height. Reflection questions prompt students to consider variance during different times of the year. There are other, similar modeling questions in the links to afford students opportunities to improve their ability to fit and analyze sinusoidal curves. However, there is no requirement for students to write a report and communicate their findings (F-TF.5).

• Geometry, Unit 6, Lesson 15, Anchor Problem 2: Students are given an image of four packages that all contain the same amount of candy, and then asked to rank the packages based on the least amount of packaging used to the most. The Guiding Questions give students a series of questions to consider, then asks them to determine a different configuration that would have a better packaging choice than one of the four presented. Students do not use the Guiding Questions to represent this problem mathematically. Guiding Questions assist students with rationalizing their responses, and developing their thinking on how to know if their answers are reasonable. With the use of the Guiding Questions, students can manipulate the model and validate and interpret their responses in relation to the problem, but there are no explicit instructions for how they should report their findings (G-MG.1).

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Materials provide students with opportunities to work with all high school standards and do not distract students with prerequisite or additional topics.

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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 materials reviewed for Fishtank Math AGA, when used as designed, meet expectations for allowing students to spend the majority of their time on the CCSSM widely applicable as prerequisites (WAPs) for a range of college majors, postsecondary programs and careers.

Examples of standards addressed by the series that have students engaging in the WAPs include:

• N-Q: In Algebra 1, Unit 1, Lesson 1, students model contextual linear data graphically, using appropriate scales and key graph features (N-Q.1). In Geometry, Unit 6, Lesson 2, students calculate and justify composite area and circumference of circles by defining appropriate units and levels of precision of measurement (N-Q.2 and N-Q.3). In Algebra 2, Unit 1, Lesson 4, Anchor Problem 1, students consider appropriate scaling for graphs with respect to units and use graphs to define appropriate quantities related to a problem context (N-Q.1 and N-Q.2). In Algebra 2, Unit 4, Lesson 17, students analyze unit relationships found in context data and associate units with variables to write expressions that model the data (N-Q.1).

• A-CED: In Algebra 1, Unit 3, Lesson 6, Anchor Problem, students are given the formula that describes a quantity related to getting to a destination via walking and riding a bus. The Guiding Questions ask how they would solve for one of the variables to determine the meaning of a specific variable (A-CED.4). In addition, they find the units associated with the variable, attending to N-Q.1. Lastly, students determine the domain restrictions that would be placed on different variables in the context of the problem (F-IF.5). In Geometry, Unit 5, Lesson 14, students write a system of inequalities to represent the polygon in a coordinate plane (A-CED.3). In Algebra 2, Unit 1, Lesson 6, Anchor Problem 2, students write and solve a one-variable equation in context (A-CED.1), then use that solution to write a system of equations in two variables and answer questions in context (A-CED.2 and A-CED.3).

• F-IF: In Algebra 1, Unit 1, Lesson 1, students calculate the average time per mile for various commutes (F-IF.6). In Algebra 1, Unit 4, Lesson 3, Anchor Problem 1, students calculate the slope of a function using a table of values (F-IF.6), and in Anchor Problem 2, compare properties of two functions represented algebraically and numerically in a table (F-IF.9). In Algebra 1, Unit 4, Lesson 4, Anchor Problems 1 and 2, students associate the domain with inputs as they explore contextual restrictions (F-IF.1), and evaluate functions for inputs and interpret function notation in context (F-IF.2). In Algebra 1, Unit 6, Lessons 11-15, and Algebra 2, Unit 5, Lesson 1, students define and write explicit and recursive formulas for arithmetic and geometric sequences (F-IF3). In Algebra 2, Unit 3, Lessons 1 and 3, students begin graphing polynomials using tables. Students are given a sketch of two different graphs and the factored form of one of the graphs. Students need to match the correct graph to the factored form of the function. Additionally, they identify the end behavior of the function (F-IF.7c,9).

• G-CO: In Geometry, Unit 1, Lessons 1-5, students define and construct geometric figures using a straightedge and a compass, including: angles and angle bisectors, an equilateral triangle inscribed in a circle, perpendicular bisectors and altitudes of triangles (G-CO.1, G-CO.12 and G-CO.13). In Geometry, Unit 4, Lesson 1 and Unit 6, Lessons 4 and 5, students define parts of the right triangle, describe the terms “point, line, and plane,” define polyhedrons (prisms and pyramids), and define cylinders and cones (G-CO.1). Throughout Geometry Units 1,4 and 6, G-CO.1 is addressed and applied with other WAPs standards (G-SRT.4-8) to develop and use working definitions for angle, circle, perpendicular line, parallel lines, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

• S-IC.1: In Algebra 1, Unit 2, Lesson 1, students explore graphs to discuss how randomness and statistics are used to make decisions. In Algebra 2, Unit 8, Lesson 7, students use sample results from several trials to make predictions about the shape of a population.

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Materials when used as designed allow students to fully learn each standard.

The materials reviewed for Fishtank Math AGA, when used as designed, partially meet expectations for allowing students to fully learn each standard. Examples of the non-plus standards that would not be fully learned by students include:

• N-RN.3: In Algebra 1, Unit 6, Lesson 9, students have opportunities to find products of rational numbers, irrational numbers, and a rational number and an irrational number. Guiding Questions found in Anchor Problems 1-3 of this lesson lead students to writing explanations and/or general rules for determining whether products will be rational or irrational. However, in Algebra 1, Unit 6, Lesson 10, students have opportunities to find sums of rational numbers, irrational numbers, and a rational number and an irrational number, but limited opportunities are provided for students to generalize a rule for whether the sums will be rational or irrational.

• A-SSE.3b: In Algebra 1, Unit 8, Lessons 2, 3, and 4 and Algebra 2, Unit 2, Lesson 6, students have opportunities to complete the square to write a quadratic function in vertex form, and students have opportunities to associate minimum and maximum function values with the vertex of a graph. Students have opportunities to identify the vertex of a graph using the vertex form of the function. However, opportunities are not provided for students to complete the square with the explicit intent of revealing the minimum or maximum value of the function.

• A-APR.6: In Algebra 2, Unit 4, Lesson 6, and Lessons 8-12, students have multiple opportunities to rewrite and simplify rational expression in different forms. However, there are limited opportunities for students to use long division to find quotients that have remainders which can be written in the form q+r(x)/b(x).

• A-REI.7: In Algebra 1, Unit 8, Lessons 14 and 15, and Algebra 2, Unit 2, Lesson 11, teachers are advised to create their own problem sets for students. Although a list of types of problems to be included in the problem sets is provided, there are limited resources from which to create the problem sets.

• F-BF.1b: In Algebra 1, Unit 3, Lesson 6, Target Task, students write the area of two triangles in a trapezoid and are instructed to write a formula for the area of the trapezoid using the area of the two triangles. In Algebra 2, Unit 3, Lesson 6, students are given practice with adding and subtracting polynomial functions. No opportunities were found for students to combine functions using multiplication and division.

• S-ID.6a: In Algebra 1, Unit 2, Lessons 15-19, students have multiple opportunities to fit linear models to data represented by scatter plots. Students do not have sufficient practice with fitting non-linear (quadratic and/or exponential) function models to data. In Algebra 1, Unit 2, Lesson 15, the Problem Set contains one link (EngageNY Mathematics: Algebra 1, Module 2, Topic D, Lesson 13), that contains a discussion about quadratic and exponential function models, but not in the context of a data set. In Algebra 1, Unit 6, Lesson 18, there is an EngageNY Mathematics link (Algebra 1, Module 3, Topic B, Lesson 14, Example 3) that contains an opportunity for students to model data with an exponential function, but this lesson is not tagged with the standard.

Throughout the materials, there are some standards for which Guiding Questions and/or problems from the resources listed under Problem Set must be incorporated for the students to fully learn the standard. Examples include, but are not limited to:

• N-CN.7: In Algebra 2, Unit 2, Lesson 7, students do not solve quadratic equations with real coefficients that have complex solutions, rather, they only identify such equations. In order for students to fully learn the standard, the EngageNY lesson linked in the Problem Set is needed. In addition, the Kuta free worksheets allow unlimited practice of solving quadratic equations with complex solutions.

• F-IF.7a: In Algebra 1, Unit 7, Lesson 2, this standard is clearly addressed in the Criteria for Success, but students are not explicitly required to “show” the intercepts. The only situations where students are required to “show intercepts, maxima, and minima” are within the Problem Set Links.

• S-ID.7: In Algebra 1, Unit 2, Lessons 17 and 19-22, students have limited opportunities to interpret slopes (rates of change) and the intercepts (constant terms) of linear models in data contexts. In order for students to have sufficient opportunities, the Guiding Questions and the problems from the extra resources are needed. For example, Lesson 17, the EngageNY lesson linked in the Problem Set is needed to interpret slope and y-intercept in context and is needed for students to fully learn the standard.

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Materials require students to engage in mathematics at a level of sophistication appropriate to high school.

The materials reviewed for Fishtank Math AGA meet expectations for engaging students in mathematics at a level of sophistication appropriate to high school. The materials regularly use age appropriate contexts, use various types of real numbers, and provide opportunities for students to apply key takeaways from Grades 6-8.

Examples of problems that allow students to engage in age appropriate contexts include:

• Algebra 1, Unit 4, Lesson 4, Anchor Problem 1: Students analyze two graphs involving lemonade sales to determine which graph makes the most sense for predicting the number of sales needed to reach a fundraiser goal. Students interchange the independent and dependent variables to decide which graph is most sensible to use.

• Algebra 2, Unit 6, Lesson 2, Anchor Problem 2: Students view a video referencing the Dan Meyer’s Ferris Wheel task. Students use graphs of trigonometric functions and their critical thinking skills to determine problem solutions.

• Geometry, Unit 4, Lesson 19, Target Task: Students find the total length of a triathlon given that the race begins with a swim along the shore followed by a bike ride of specific length. After the bike ride, racers turn a specific degree and run a given distance back to the starting point.

• Geometry, Unit 8, Lesson 4, Anchor Problem 1: Students utilize a Venn diagram to display the coffee preferences of diner customers and calculate probabilities related to the preferences.  Students also determine characteristics of the events by answering a series of questions related to the probabilities (Which two events are complements of each other ?...etc.).

Examples of problems that allow students to engage in the use of various types of real numbers include:

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This is not an assessed indicator in Mathematics.

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This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Fishtank Math AGA do not meet expectations for Assessment. The materials partially include assessment information that indicate which standards and practices are assessed and partially provide assessments that include opportunities for students to demonstrate the full intent of course-level standards.The materials do not provide multiple opportunities throughout the courses to determine students’ learning or sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

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Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Fishtank Math AGA partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. The materials identify the standards and practices assessed for some of the formal assessments.

There is a Post-Unit Assessment for each unit in a course. Assessment item types include short-answer, multiple choice, and constructed response. For the Algebra 1 and Geometry courses, there are Post-Unit Assessment Answer Keys for each unit. The Algebra 1 and Geometry Post-Unit Assessment Answer Keys for each unit contains the following: question numbers, aligned standards, item types, point values, correct answers and scoring guides, and aligned aspects of rigor for each question. However, neither the Post-Unit Assessment or the Post-Unit Answer Keys identify the mathematical practice. Examples of Algebra 1 and Geometry Post-Unit Assessment questions and aligned standards include:

• Algebra 1, Unit 3: For Post-Unit Assessment question 4, students solve a multi-step inequality.The answer key shows the aligned standard as A-REI.3. This is a short-answer question with a point value of 2, and the rubric explains how the two points are determined based on the detailed accuracy of the student’s answer.The aspect of rigor for this question is referenced as P/F (procedural fluency).

• Algebra 1, Unit 5: For Post-Unit Assessment question 3, students are given a system of equations and the graph of both functions (One is a linear function and the other is an absolute value function). For part 3a, students need to identify the solution(s) for the system of equations; then for part 3b, they need to algebraically show that the point(s) are solution(s) to the system. Each part of this question aligns with standard A-REI.11 and each part has a point value of 2. Part 3a item type is considered as short-answer and part 3b’s item type is identified as constructed response. Aspects of rigor for this question are referenced as C P/F (conceptual understanding/ procedural fluency).

• Geometry, Unit 5: For Post-Unit Assessment question 3, students are given a constructed response task consisting of the graph of a triangle (CAB) and 3 related questions; students need to calculate \frac{2}{3} of the distance between points C and A (part a), and points C and B (part b). Students label these new coordinate points D and E respectively, found by completing these calculations. Students then calculate the perimeter of triangle CDE in radical form (part c). The aligned standard for the first two parts of this question is G-GPE.6 and the aligned standard for the third part is G-GPE.7. A point value of 1 is assigned to each of the first two parts of the question and a point value of 2 is assigned to the third part of the question.

For the Algebra 2 Course, Post-Unit Assessments have no answer keys and there is no alignment of questions to the standards. Examples of Algebra 2 Post-Unit Assessments that have no answer keys or standards referenced include, but are not limited to: Algebra 2, Units 1, 2, 5, and 9. The following Algebra 2 Post-Unit Assessments have some solutions and standards referenced in links to original sources:

• Algebra 2, Unit 3, only have references for questions 8, 9, and 13

• Algebra 2, Unit 4, only have references for questions 2, 4, 5, and 14

• Algebra 2, Unit 7, only have references for questions 1, 2, 4, 6, and bonus question

Many of these reference links do not work, such as for Regents Exams in units 4 and 7 and in “Algebra II Paper-based Practice Test from Mathematics Practice Tests,” from unit 3.

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Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Fishtank Math AGA do not meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. The Assessment system does not provide multiple opportunities to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up with students.

The assessments for the materials include a post assessment after every unit and Target Task(s) at the end of each lesson. These provide little guidance to teachers for interpreting student performance or suggestions for follow-up. In Algebra 1 and Geometry, there is an Answer Key for each Post-Unit Assessment with point values assigned for each question. However, there are no rubrics or other explanations as to how many points different kinds of responses are worth. An example of this includes, but is not limited to:

• Algebra 1, Unit 8: For Post-Unit Assessment question 6, students are given the following question: “Jervell makes the correct claim that the function below does not cross the x-axis. Describe how Jervell could know this and show that his claim is true.” The answer key states the following: “The discriminant of the quadratic formula tells how many real roots a quadratic function has (or how many times a parabola intersects with the x-axis). Since the discriminant of this function is − 32, there are no real roots to this function. (Equivalent answers acceptable)” This is worth 3 points, but there is no guidance for and no sample responses for which 0 points, 1 point or 2 points might be assigned.

In the Target Tasks, there are no answer keys, scoring criteria, guidance to teachers for interpreting student performance, or suggestions for follow-up.

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Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Fishtank Math AGA partially meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices across the series.

The Assessments section found under Math Teacher Tools contains the following statement: “Pre-unit and mid-unit assessments as well as lesson-level Target Tasks offer opportunities for teachers to gather information about what students know and don’t know while they are still engaged in the content of the unit. Post-unit assessments offer insights into content that students may need to revisit throughout the rest of the year to ensure continued work towards mastery. Student self-assessments provide space for students to reflect on their learning and monitor their own progress.” The materials reviewed do not contain Pre-Unit, mid-unit, or student self-assessments, the system of assessments included is twofold: Target Tasks and Post-Unit Assessments. All of the Post-Unit Assessments have to be printed and administered in person. For the Algebra 1 and Geometry unit assessments, answer keys are provided, however no answer keys are provided for the Algebra 2 unit assessments.The unit assessment item types include multiple choice, short answer, and constructed response. However, the assessment system leaves standards unassessed.

Examples of how standards are not assessed or only partially assessed in Post-Unit Assessments include, but are not limited to:

• In Algebra 1, Unit 3, students solve equations and inequalities. However, students are not prompted to explain each step. ( A-REI.1)

• In Algebra 1, Unit 8, students identify the vertex, minimum or maximum, axis of symmetry, and y-intercept, but they do not indicate where the function is increasing or decreasing or whether the function is positive or negative (F-IF.4).

• In Algebra 2, Unit 8, there are several questions that involve random sampling, but students do not explain how randomization relates to the context.

• In Geometry, Unit 1, students construct an equilateral triangle by copying a segment (G-CO.12). G-CO.13 is identified as being addressed in the same unit, but it is not assessed in the Post-Unit assessment.

In Post-Unit Assessment Keys for Algebra 1 and Geometry, Common Core Standards are identified for each assessment item, but mathematical practices are not identified for any of the assessment items. Examples of Post-Unit Assessment multiple choice items include:

• Algebra 2, Unit 2, question 2 asks, “Which equation has non-real solutions? a. 2x^2+4x-12=0  b. 2x^2+3x=4x+12 c. 2x^2+4x+12=0  d. 2x^2+4x=0

• Geometry, Unit 7, question 1 states, “A designer needs to create perfectly circular necklaces. The necklaces each need to have a radius of 10 cm. What is the largest number of necklaces that can be made from 1000 cm of wire? A. 16, B. 15, C. 31  D. 32.”

Examples of Post-Unit Assessment short answer items include:

• Algebra 1, Unit 6, question 5 states, “Multiply and simplify as much as possible: \sqrt{8x^3 \cdot \sqrt{50x}}

• Algebra 2, Unit 1, question 1 states, “Let the function f  be defined as f(x)=2x+3a  where a is a constant. a. If f(-5)= -4  , what is the value of the y-intercept? b. The point (5,k) lies of the line of the function f . What is the value of k?”

Examples of Post-Unit Assessment constructed response items include:

• Algebra 1, Unit 5, question 6 states, “A new small company wants to order business cards with its logo and information to help spread the word of their business. One website offers different rates depending on how many cards are ordered. If you order 100 or fewer cards, the rate is $0.40 per card. If you order over 100 and up to and including 200 cards, the rate is$0.36 per card. If you order over 200 and up to and including 500 cards, the rate is $0.32 per card. Finally, if you order over 500 cards, the rate is$0.29 per card.

• Part A: Write a piecewise function, p(x), to model the pricing policy of the website.

• Part B: Calculate p(250-p(200), and interpret its meaning in context of the situation.

• Part C: The manager of the company decides to order 500 business cards, but the marketing director says they can order more cards for less money. Is the marketing director’s claim true? Explain and justify your response using calculations from the piecewise function.”

• Algebra 2, Unit 8, question 9 states, “A brown paper bag has five cubes, 2 red and 3 yellow. A cube is chosen from the bag and put on the table, and then another cube is taken from the bag.

• Part A: What is the probability of two red cubes being chosen in a row?

• Part B: Is the event of choosing a red cube the first time you pick and choosing a red cube the second time you pick from the bag independent events? Why or why not?”

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Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Fishtank Math AGA do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

According to Math Teacher Tools, Assessment Resource Collection, “ The post-unit assessment is designed to assess students’ full range of understanding of content covered throughout the whole unit...It is recommended that teachers administer the post-unit assessment soon, if not immediately, after completion of the unit. The assessment is likely to take a full class period.” While all students take the post-unit assessment, there are no accommodations offered that ensure all students can access the assessment.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Fishtank Math AGA do not meet expectations for Student Supports. The materials provide: extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity and provide manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials partially provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning course-level mathematics. The materials do not provide strategies and supports for students in special populations to support their regular and active participation in learning course-level mathematics.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for Fishtank Math AGA do not meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning series mathematics. There are no strategies, supports, or resources for students in special populations to support their regular and active participation in grade-level mathematics.

The materials have Special Populations under the Math Teacher Tools link. Within Special Populations, there is a link to Areas of Cognitive Functioning. Eight areas of cognitive functioning: Conceptual Processing, Visual Spatial Processing, Language, Executive Functioning, Memory, Attention and/or Hyperactivity, Social and/or Emotional Learning and Fine Motor Skills, are discussed in this section. While these areas of cognitive functioning are discussed in relation to mathematics learning, there are no specific suggestions and/or strategies for how teachers can assist students with their learning, if presented with these behaviors. Found in the Overview for the section on Areas of Cognitive Functioning, there is a statement that says: “To learn more about how teachers can effectively incorporate strategies to support students in special populations in their planning, see our Teacher Tools, Protocols for Planning for Special Populations and Strategies for Supporting Special Populations.” However, the protocols and strategies teacher tools  are not available in Fishtank Math AGA.

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for Fishtank Math AGA meet expectations for providing extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity.

Opportunities for students to investigate course-level mathematics at a higher level of complexity are found with the lesson Anchor Problems. Each lesson contains Anchor Problems that are accompanied by Guiding Questions. The Guiding Questions assists students with critically engaging in the math content of the problem. Also, Guiding Questions prompt students to engage in purposeful investigations and extensions related to the problem. Examples of lessons that include the use of Guiding Questions for prompting students to engage in lesson content at higher levels of complexity include:

• Algebra 1, Unit 2, Lesson 19: In Anchor Problem 1, students use screenshots of a battery charge indicator to determine when a laptop will be fully charged. Students need to represent the data in a scatter plot, determine the correlation coefficient for this data to determine the strength of the association, assign a line of best fit either through least squares regression or estimation, and determine if a linear function is the best model for this data through plotting the residuals. Guiding Questions that accompany this problem include:

• How do the correlation coefficient and the residual plot help you to assess the validity of the answer to the question?

• Why is it useful to have a line of best fit for this problem? How does this allow you to make a prediction?

• How can you communicate your confidence in your answer to the question using correlation and the residual plot?

• Algebra 1, Unit 5, Lesson 16: For Anchor Tasks Problem 2, students use the Desmos activity, Transformations Practice, and are tasked to write an equation that represents the blue graph for each transformation. At the end of the activity, there are two challenge transformations for students to complete. Guiding Questions for this problem include:

• How can you tell if a reflection is involved?

• How can you tell if a dilation or scaling of the graph is involved?

• How can you tell if a translation of the graph is involved?

• How are these moves represented in the equation?

• Algebra 2, Unit 4, Lesson 18: Anchor Problem 1 involves two participants in a 5-kilometer race. The participants’ distances are modeled by the following equations: a(t)=\frac{t}{4} and b(t)=\sqrt{2t-1} where t represents time in minutes. Students need to determine who gets to the finish line first? Guiding Questions for this problem include:

• What is the time for each person when the total distance run is 5 kilometers?

• How can you use this information to determine who wins the race?

• If the participants have a constant speed, how many different times would you expect they would be side by side?

• How would you determine at what time(s) the participants are side by side?

Sometimes teachers are directed to create problem sets for students that engage students in mathematics at higher levels of complexity.  Examples include:

• Geometry, Unit 7, Lesson 2: The lesson objective is: Given a circle with a center translated from the origin, write the equation of the circle and describe its features. For the Problem Set, teachers are to create the problems for students. Teacher directives for creating the problems include three bullet points labeled EXTENSION. These bullet points read as follows:

• Include problems such as “What features are the same/different between the two circles given by the equations: x^2+y^2=16 and 2x^2+2y^2=16? Show your reasoning algebraically.”

• Include problems with systems of equations between two circles, which is discussed in Algebra 2.

• Include problems such as “What are the x-intercepts of the circle?”

• Algebra 2, Unit 1, Lesson 12: The objective for this lesson is: Write and evaluate piecewise functions from graphs. Graph piecewise functions from algebraic representations. For the Problem Set, one of the directives to teachers states include problems: “where based on a description of number of pieces, continuous or discontinuous, students create a piecewise function graphically and algebraically (This is an extension, and we’ll come back to this at the end of the unit.)”

• Algebra 2, Unit 2, Lesson 2: The lesson objective is: Identify the y-intercept and vertex of a quadratic function written in standard form through inspection and finding the axis of symmetry. Graph quadratic equations on the graphing calculator. For the Problem Set, teachers create the problems and one of the directives to teachers is: “Include problems where students are challenged to write multiple quadratic equations given the constraint of vertex AND y-intercept in standard form. Ask students to explain what they have discovered about the possible values.”

Additionally, there are no instances of advanced students doing more assignments than their classmates.

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for Fishtank Math AGA partially provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials provide a variety of approaches for students to learn the content over time. Each lesson has Anchor Problems/Tasks to guide students with a series of questions for students to ponder and discuss, and the Problem Set, gives students the option to select problems and activities to create their own problem set. The Tips for Teachers, when included in the lesson, guides teachers to additional resources that the students can use to deepen their understanding of the lesson. However, while students are often asked to explain their reasoning, there are no paths or prompts provided for students to monitor their learning or self-reflect.

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Fishtank Math AGA partially provide opportunities for teachers to use a variety of grouping strategies.

Some general guidance regarding grouping strategies is found within the Math Teacher Tools, Academic Discourse section, however there is limited guidance on how to group students throughout the Fishtank Math AGA materials. Grouping strategies are suggested within lessons, however these suggestions are not consistently present or specific to the needs of particular students. Occasionally, there will be some guidance in the Tips for Teachers on how to facilitate a lesson, but this is limited and inconsistent. Examples include:

• In Algebra 1, Unit 8, Lesson 13: In the Tips for Teachers, there is a bullet point that states, “There is only one Anchor Problem for this lesson, as there is a lot to dig into with this one problem. Students can also spend an extended amount of time on independent, pair, or small-group practice working through applications from Lessons 11–13.” While grouping students is suggested, no guidance is given to teachers on how to group students based on their needs.

• In Geometry, Unit 6, Lesson 6: Problem 3 Notes state: “Students should spend time discussing and defending their estimates before being given the dimensions of the glasses. Students should first identify information that is necessary to determine a solution and ask the teacher for this information, which can be given through the image “The Dimensions of the Glasses.” However, no particular grouping arrangement is mentioned.

##### Indicator {{'3q' | indicatorName}}

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for Fishtank Math AGA partially meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to meet or exceed grade-level standards through active participation in grade-level mathematics, but not consistently.

While there are resources within Math Teacher Tools, Supporting English Learners, that provide teachers with strategies and supports to help English Learners meet grade-level mathematics, these strategies and supports are not consistently embedded within lessons. The materials state, “Our core content provides a solid foundation for prompting English language development, but English learners need additional scaffolds and supports in order to develop English proficiency as they build their content knowledge. In this resource we have outlined the process our teachers use to internalize units and lessons to support the needs of English learners, as well as three major strategies that can help support English learners in all classrooms (scaffolds, oral language protocols, and graphic organizers). We have also included suggestions for how to use these strategies to provide both light and heavy support to English learners. We believe the decision of which supports are needed is best made by teachers, who know their students English proficiency levels best. Since each state uses different scales of measurement to determine students’ level of language proficiency, teachers should refer to these scales to determine if a student needs light or heavy support. For example, at Match we use the WIDA ELD levels; students who are levels 3-6 most often benefit from light support, while students who are levels 1-3 benefit from heavy support.”Regular and active participation of students who read, write, and/or speak in a language other than English is not consistently supported because specific recommendations are not connected to daily learning objectives, standards, and/or tasks within grade-level lessons.

Within Supporting English Learners there are four sections, however only one section, Planning for English Learners, is available in Fishtank Math AGA. Planning for English Learners is divided into two sections, Intellectually Preparing a Unit and Intellectually Preparing a Lesson.

• The “Intellectually Preparing a Unit” section states, “Teachers need a deep understanding of the language and content demands and goals of a unit in order to create a strategic plan for how to support students, especially English learners, over the course of the unit. We encourage all teachers working with English learners to use the following process to prepare to teach each unit.” The process is divided into four steps where teachers are prompted to ask themselves a series of questions such as: “What makes the task linguistically complex?”, “What are the overall language goals for the unit?”, and “What might be new or unfamiliar to students about this particular mathematical context?”

• The “Intellectually Preparing a Lesson” section states, “We believe that teacher intellectual preparation, specifically internalizing daily lesson plans, is a key component of student learning and growth. Teachers need to deeply know the content and create a plan for how to support students, especially English learners, to ensure mastery. Teachers know the needs of the students in their classroom better than anyone else, therefore, they should also make decisions about where to scaffold or include additional supports for English learners. We encourage all teachers working with English learners to use the following process to prepare to teach a lesson.” The process is divided into two steps where teachers are prompted to do certain objectives such as , “Unpack the Objective, Target Task, and Criteria for Success” or “Internalize the Mastery Response to the Target Task” or to ask themselves a series of questions such as: “What does a mastery answer look like?”, “What are the language demands of the particular task?” , and “If students don't understand something, is there a strategy or way you can show them how to break it down?”

Regular and active participation of students who read, write, and/or speak in a language other than English is not consistently supported because specific recommendations are not connected to daily learning objectives, standards, and/or tasks within grade-level lessons.

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Fishtank Math AGA do not provide a balance of images or information about people, representing various demographic and physical characteristics. No images are used in these materials. However lessons do include a variety of problem contexts that could interest students of various demographic populations. Examples include:

• Algebra 1, Unit 1, Lesson 4: Any student could relate to Anchor Problem 1: “You are selling cookies for a fundraiser. You have a total of 25 boxes to sell, and you make a profit of \$2 on each box.” In Lesson 5, Anchor Problem 3: “You leave from your house at 12:00 p.m. and arrive to your grandmother’s house at 2:30 p.m. Your grandmother lives 100 miles away from your house. What was your average speed over the entire trip from your house to your grandmother’s house?”

• Algebra 1, Unit 7, Lesson 13: There is a link in the Problem Set to Engage NY Mathematics: Algebra 1,Module 4,Topic A,Lesson 9, Exercise 3, Example 3: “A science class designed a ball launcher and tested it by shooting a tennis ball straight up from the top of a 15-story building. They determined that the motion of the ball could be described by the function: h(t)= -16t2^+144t+160 where 𝑡 represents the time the ball is in the air in seconds and h(t)represents the height, in feet, of the ball above the ground at time 𝑡. What is the maximum height of the ball? At what time will the ball hit the ground?” Students graph the function and use the graph to determine problem solutions.

Names used in problem contexts are not representative of various demographic and physical characteristics. The names used can typically be associated with one population and therefore lack representation of various demographics. Examples include, but are not limited to:

• Algebra 1, Unit 3, Lesson 7: Anchor Problem 1 begins with: “Joshua works for the post office and drives a mail truck.”

• Algebra 2, Unit 1, Lesson 1: Anchor Problem 3 begins with: “Allison states that the slope of the following equation is 3.” In Lesson 3: Anchor Problem 2 begins with: “Alex is working on a budget after getting a new job.”

• Geometry, Unit 8, Lesson 2: Anchor Problem 2 begins with: “Dan has shuffled a deck of cards.”

Other names found in the materials that are not representative of all populations include: Mary, Beverly, Andrea, Lisa, Greg, and Jessie.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Fishtank Math AGA do not provide guidance to encourage teachers to draw upon student home language to facilitate learning. There is no evidence of promoting home language knowledge as an asset to engage students in the content material or purposefully utilizing student home language in context with the materials.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Fishtank Math AGA do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. Within the About Us, Approach, Culturally Relevant, the materials state, “We are committed to developing curriculum that resonates with a diversity of students’ lived experiences. Our curriculum is reflective of diverse cultures, races and ethnicities and is designed to spark students’ interest and stimulate deep thinking. We are thoughtful and deliberate in selecting high-quality texts and materials that reflect the diversity of our country.” Although this provides a general overview of the cultural relevance within program components, materials do not embed guidance for teachers to amplify students’ cultural and/or social backgrounds to facilitate learning.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Fishtank Math AGA do not provide supports for different reading levels to ensure accessibility for students. There are no supports to accommodate different reading levels to ensure accessibility for students. The Guiding Questions, found within the lessons, offer some opportunities to identify entrance points for students. However, these questions provide teacher guidance that may or may not support struggling readers to access and engage in course-level mathematics.

##### Indicator {{'3v' | indicatorName}}

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

The materials reviewed for Fishtank Math AGA meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

While there are missed opportunities to use manipulatives, there is strong usage of virtual manipulatives such as Desmos and Geogebra throughout the materials to help students develop a concept or explain their thinking.They are used to develop conceptual understanding and connect concrete representations to a written method. Examples of the usage of virtual manipulatives include:

• Algebra 1, Unit 1, Lesson 10, Anchor Problem 2, in the notes Teachers are instructed to show students a video of three people eating popcorn at different rates. The notes states that, “This video is essential to show students so they can graph this scenario accurately. You will likely need to show it several times.”

• Algebra 2, Unit 9, Lesson 1: The Problem Set contains a link to the Desmos activity, “Domain and Range Introduction.”

• In Geometry, Unit 3, Lesson 10, Anchor Problem 2, animation in Geogebra is used for students to describe the transformation(s) that map one figure onto the other figure.

Opportunities for students to use manipulatives are sometimes missed as the materials provide pictures but do not prescribe manipulatives. An example of this includes, but is not limited to:

• In Algebra 2, Unit 8, Lesson 1, Anchor Problem 2, a picture of a spinner is shown, no physical or virtual spinner is provided. Cubes are mentioned in Anchor Problem 3, but there are no suggestions as to how to make simple cubes. In the Target Task, Game Tools listed include a spinner and a card bag, but there are no suggestions to teachers to provide these manipulatives.

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Fishtank Math AGA integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in series standards. The materials do not include or reference digital technology that provides opportunities for collaboration among teachers and/or students. The materials have a visual design that supports students in engaging thoughtfully with the subject, and the materials do not provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Fishtank Math AGA integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the series standards, when applicable.

DESMOS is used throughout the materials and it is customizable as teachers can copy and change activities or completely design their own. Examples include:

• Algebra 1, Unit 2, Lesson 17: Tips for Teachers encourages teachers to use Desmos to help students understand Regressions.

• Algebra 1, Unit 5, Lesson 12: Tips for Teachers explains: “Desmos activities are featured in these lessons in order to capture the movements inherent in these transformations”.

• Algebra 2, Unit 1, Lesson 12: The Problem Set contains a link to a DESMOS activity where students explore Domain and Range of different functions.

Examples of other technology tools include:

• Algebra 1, Unit 2, Lesson 6: Contains a link in the Problem Set to an applet with which students can explore Standard Deviation.

• Algebra 2, Unit 8, Lesson 11: Contains a link in the Teacher Tips to a “Sample Size Calculator” that can be used to determine the sample size needed to reflect a particular population with the intended precision.

• Geometry, Unit 1, Lesson 2: Tips for Teachers contains links to Math Open Reference “Constructions”, and an online game called “Euclid: The Game” designed with Geogebra that assists students in understanding geometric constructions.

• Geometry, Unit 6, Lesson 10: In Tips for Teachers the following suggestion is made: ”The following GeoGebra applet may be helpful to demonstrate Cavalieri’s principle, which can be done after Anchor Problem #1: GeoGebra, “Cavalieri’s Principle,” by Anthony C.M OR.”

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Fishtank Math AGA do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

While there are opportunities within activities in this series for students to collaborate with each other, the materials do not specifically include or reference student-to-student or student-to-teacher collaboration with digital technology.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Fishtank Math AGA have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within the units and lessons that supports learning on the digital platform. Each lesson contains the following components: Lesson Objective, Common Core Standards, Foundational Standards, Criteria for Success, Anchor Problems, and Target Tasks. In addition to these components, most lessons contain Tips for Teachers and Problem Set links.

While there is a consistent design within the units and lessons that supports learning on the digital platform, this design mainly supports teachers by giving guidance for lesson presentations and providing links to learning resources. There are no separate materials for students. Student versions of the materials have to be created by teachers.  While the visual layout is appealing, there are various errors within the materials. Examples include, but are not limited to:

• Algebra 1, Unit 1, Lesson 8, Anchor Problem 1 has a link to a video of a ball rolling down a ramp so that students can sketch a graph of the distance the ball travels over time; however, the YouTube video says it is unavailable and is a private video. Also, in Anchor Problem 2, the fourth bullet under Guiding Questions is incomplete: “The equation that represents a quadratic function is. How can you verify the points you created on the graph using this equation?”

• Algebra 1, Unit 5, Lesson 13, Anchor Problem 2, the first and second questions under Guiding Questions have an equation and then the word “{{ h}}ave” following it. The brackets should not be in either question.

• Algebra 2, Unit 7, Lesson 13, Problems Set, two of the three links do not work. The first one gives an “Error 404 - Not Found” when clicked and the third link says “Classzone has been retired.”

• Geometry, Unit 5, Lesson 8, Anchor Problem 3, under Notes, there is a link to NCTM’s Illuminations. However, when clicked, a “Members-Only Access” page appears.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Fishtank Math AGA do not provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable. While teacher implementation guidance is included for Anchor Problems/Tasks, Notes, Problem Set, and Target Task, there is no embedded technology within the materials.

## Report Overview

### Summary of Alignment & Usability for Fishtank Math AGA | Math

#### Math High School

The materials reviewed for Fishtank Math AGA meet expectations for alignment to the CCSSM for high school. For focus and coherence, the series showed strengths in the following areas: attending to the full intent of the mathematical content contained in the standards, spending the majority of time on the content from CCSSM widely applicable as prerequisites, requiring students to engage in mathematics at a level of sophistication appropriate to high school, being mathematically coherent and making meaningful connections in a single course and throughout the series, and explicitly identifying and building on knowledge from Grades 6-8 to the high school standards. In Gateway 2, for rigor, the series showed strengths in the following areas: supporting the intentional development of students' conceptual understanding, opportunities for students to develop procedural skills, working with applications, and displaying a balance among the three aspects of rigor. The materials intentionally develop all of the eight mathematical practices, but do not explicitly identify them in the context of individual lessons. In Gateway 3, the materials do not meet expectations for Usability as they partially meet expectations for Teacher Supports (Criterion 1), do not meet expectations for Assessment (Criterion 2), and do not meet expectations for Student Supports (Criterion 3).

##### High School
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

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### Overall Summary

###### Alignment
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###### Usability
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