## Fishtank Math

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

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### Overall Summary

###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations

### Focus & Coherence

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focusing on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for not assessing topics before the grade level in which the topic should be introduced.

##### Indicator {{'1a' | indicatorName}}
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. The materials do not assess topics before the grade level in which the topic should be introduced. Unit Assessments were examined for this indicator, and all materials are available digitally and downloadable PDFs.

Examples of assessment items aligned to grade-level standards include:

• Unit 1 Test, Question 7, “Which expressions are equivalent to $$3^{-8}$$ / $$3^{-4}$$? Select two correct answers. Answer choices: a. $$3^2$$, b. 1/$$3^2$$, c. 1/$$3^4$$, d. 1/$$3^12$$, e. $$3^{-2}$$" (8.EE.1)
• Unit 4 Test, Question 7,  “Which functions are not linear? Select three such functions. Answer choices: a. $$y=\frac {x}{5}$$, b. $$y=5-x^2$$, c. $$-3x +2y = 4$$, d. $$y = 3x^2+ 1$$, e. $$y = -5x - 2$$, f. $$y = x^3$$" (8.F.3)
• Unit 4 Test, Question 5, “Which set of ordered pairs represents a function?  Answer choices: a. {(2,7), (2,8), (3,8)} b. {(3,2), (3,3), (3,4)} c. {(4,1), (5,1), (4,4)} d. {(5,6), (8,6), (9,6)}” (8.F.1)
• Unit 5 Test, Question 3, “Line M passes through point A(1,7) and point B(-2,4). Determine if Line M also passes through point C(5,3). Use slope to justify your answer.” (8.F.4)
• Unit 7 Test, Question 3, “What is the value of the expression below?  8-3$$\sqrt16$$  Answer choices:  a. −40, b. −4, c. 2, d. 20”  (8.EE.2)

#### Criterion 1.2: Coherence

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for focus. The instructional materials meet expectations for not assessing topics before the grade level in which the topic should be introduced. The instructional materials devote at approximately 75% of instructional time to the major work of the grade.

##### Indicator {{'1b' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Match Fishtank Grade 8  meet expectations for spending a majority of instructional time on major work of the grade, using the materials as designed.

The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade:

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is seven out of eight units, which is approximately 88%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 99 out of 112, which is approximately 88%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 123 out of 143, which is approximately 86%.

A lesson level analysis is most representative of the instructional materials because the units contain major work, supporting work, and assessments. As a result, approximately 88% of the instructional materials focus on major work of the grade.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are also consistent with the progressions in the standards and foster coherence through connections at a single grade.

##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are connected to the major standards/clusters of the grade, for example:

• Unit 1, Exponents and Scientific Notation, Lesson 15, Anchor Problem 2, 8.NS supports 8.EE.1, 3, and 4 as students solve multi-step applications using scientific notation and properties of exponents. “This headline appeared in a newspaper. ‘Every day 7% of Americans eat at Giantburger Restaurants.’ Decide whether this headline is true using the following information: There are about $$8 \times 10^3$$ Giantburger restaurants in America. Each restaurant serves on average $$2.5 \times 10^3$$ people every day.  There are about $$3 \times 10^8$$ Americans. Explain your reasons and show clearly how you figured it out.”
• Unit 7, Pythagorean Theorem and Volume, Lesson 13, Anchor Problems 2 and 3 connect 8.NS.2 and 8.EE.2 as students define and evaluate cube roots. For example, Anchor Problem 2 is as follows: “Determine if there is a solution to each equation below.  If yes, then give the exact solution. If no, explain why there is no solution. a. $$x^3 = -27$$  b. $$x^2 = -9$$. Evaluate the square and cube roots below, if possible. If not possible, explain why not. a. $$-\sqrt64$$  b. $$\sqrt-64$$  c. $$-\sqrt[3]64$$  d.$$\sqrt[3]-64$$.”  Anchor Problem 3: “Compare each pair of values with <, >, or = . a. $$\sqrt200$$   $$\sqrt[3]200$$   b. $$\sqrt64$$     $$\sqrt[3]125$$    c. $$\sqrt16$$     $$\sqrt[3]64$$   d. $$\sqrt8$$     $$\sqrt[3]50$$”
• Unit 8, Bivariate Data, Lesson 3, Anchor Problem 1 connects 8.SP.1 and 8.F.3, 4, and 5 as students “identify and describe associations in scatter plots including linear/nonlinear associations, positive/negative associations, clusters, and outliers.” An example is as follows: “For the following five scatter plots, answer the following questions:  a. Does there appear to be a relationship between x and y?  b. If there is a relationship, does it appear to be linear?  c. If the relationship appears to be linear, is it a positive or negative linear relationship?  d. If applicable, circle the correct words in this sentence: There is a (positive/negative) association between x and y, because as x increases, then  y  tends to (increase/decrease).”
• Unit 8, Bivariate Data, Lesson 5, 8.SP.3 supports 8.F.4  as students “write equations to represent lines fit to data and make predictions based on the line. For example, Anchor Problem 2 states, “Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend’s house with a full battery. The pictures below show screenshots of the battery charge indicator after he plugs in the computer at 9:11a.m.” Questions: “1. The screenshots suggest an association between two variables.  What are the two variables in this situation? 2. Make a scatterplot of the data.  3. Draw a line that fits the data and find the equation of the line.  4. When can Jerry expect to have a fully charged battery?”
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

Instructional materials for Match Fishtank Grade 8 meet expectations that the amount of content designated for one grade-level is viable for one year.

The instructional materials can be completed in 143 days.  The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. Included in the 143 days are:

• 112 lesson days
• 23 review/flex days
• 8 assessment days

Each unit is comprised of 9 to 21 lessons that contain  a mixture of Anchor Problems, Problem Set Guidance, a Target Task, and a Mastery Response. These components align to the number of minutes needed to complete each part as provided in the Pacing Guide. Based on the Pacing Guide, the suggested lesson time frame is 60 minutes. The breakdown is as follows:

• 5 - 10 mins Warm up
• 25 - 30 mins Anchor Problems
• 15 - 20 mins Problem Set

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

The instructional materials for Match Fishtank Grade 8 meet expectations for the materials being consistent with the progressions in the standards. The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior or future grades is clearly identified and related to grade-level work. Prior grade knowledge is explicitly related to grade-level concepts. Each lesson provides the teacher with current standards and foundational standards which are addressed under the “Standards” tab. Through the Unit Overview, Tips for Teachers, and Unit Summary, teachers are provided explicit connections to prior and future knowledge for each standard.

The Unit Plan Summary section includes a list of foundational standards from earlier grades that are connected to the content standards addressed in that unit, as well as a list of future standards that relate. For example:

• Unit 1, Exponents and Scientific Notation, “In fourth and fifth grade, students learned the difference between multiplicative and additive comparisons and they interpreted multiplication as a way to scale. Students will access these prior concepts in this unit as they investigate patterns and structures in ratio tables and use multiplication to create equivalent ratios.”  Foundational Standards include: Numbers and Operations in Base Ten 5.NBT.1, 5.NBT.2, 4.NBT.1, Expressions and Equations 6.EE.1, 6.EE.2, 6.EE.2.c, The Number System 7.NS.2. Future Connections include: High School – Number and Quantity N.RN.1, N.RN.2, Seeing Structure in Expressions A.SSE.2, A.SSE.3.c, Arithmetic with Polynomials and Rational Expressions A.APR.6, A.APR.7. Students will use their knowledge from previous eighth-grade units, including work with single linear equations and functions from clusters 8.EE.B and 8.F.B.4. Students will continue their work with systems, working with linear, absolute value, quadratic, and exponential functions. They will also graph linear inequalities and consider what the solution of a system of linear inequalities looks like in the coordinate plane.”
• Unit 2, Solving One-Variable Equations reviews content from grades 6 and 7 in preparation for the remaining lessons in the unit. “In sixth grade, students developed the conceptual understanding of how the components of expressions and equations work. They learned how the distributive property can create equivalent forms of an expression and how combining like terms can turn an expression with three terms into an expression with one term. By the end of seventh grade, students fluently solved one- and two-step equations with rational numbers and used equations and inequalities to represent and solve word problems.” Additionally, the Unit Summary connects grade-level concepts to current and future standards. “Furthermore, these skills will be needed throughout high school as students are introduced to new types of equations involving radicals, exponents, multiple variables, and more.”
• Unit 4, Functions, “This unit introduces students to the concept of a function to describe a relationship. Though they have worked with functions prior to eighth grade with equations and proportional relationships, this is the first time they will formally define it. Through this unit and the next unit, students will explore functions in-depth; this lesson provides the basic definition of a function as a relationship of inputs and outputs where every input has exactly one output.”
• Unit 6, System of Equations Unit Summary, “Students will use their knowledge from previous eighth-grade units, including work with single linear equations and functions from clusters 8.EE.B and 8.F.B. They will also need to draw on concepts from sixth grade, where they understood solving an equation as a process of answering which values make an equation true.”
• Unit 7, Pythagorean Theorem and Volume, “Prior to this unit, students learned many skills and concepts that prepared them for this unit. Since elementary grades, students have been learning about and refining their understanding of area and volume. They have learned how to use composition and decomposition as tools to determine measurements, they have learned formulas and how to use them in problem-solving situations, and they have encountered various real-world situations. Standard 8.G.9 is a culminating standard in the Geometry progression in middle school, which will lay the foundation for much of the work they will do in high school geometry. In high school, students will more formally derive the distance formula and other principles, they will expand their work with right triangles to include trigonometric ratios, and they will solve more complex problems involving volume of cylinders, pyramids, cones, and spheres.”
• Unit 8, Bivariate Data Unit Summary, “Prior to eighth grade, students explored how and why data is collected—by thinking about statistical questions, samples, populations, and various ways to analyze data representations. Students worked with line plots, histograms, and box plots, and they considered what the shape, center, and spread of these data sets said about the data itself. In high school, students’ understanding of statistics is formalized. They analyze bivariate data using functions, design and carry out experiments, and make predictions about outcomes based on probabilities. Students use their knowledge of association between variables as a basis for correlation. They develop nonlinear models for data and formally analyze how closely the model fits the data. This unit addresses the content standards: 8.SP.1, 8.SP.2, 8.SP.3, and 8.SP.4 and identifies the foundational standards “Covered in previous units or grades that are important background for the unit”: 6.RP.3.c, 7.RP.3, 7.SP.1, 7.SP.2, 7.SP.5, 6.SP.2, and 6.SP.4 from previous grades, and 8.F.3, 8.F.4, and 8.F.5 from a previous unit.”

Lessons also include connections between grade-level work, standards from earlier grades, and future knowledge. For example:

• Unit 2, Solving One Variable Equations, Lesson 3, the Objective states, “Justify each step in solving a multi-step equation with variables on one side of the equation” (8.EE.7.a, 8.EE.7.b ). Tips for Teachers suggest this lesson may be extended over more than one day to ensure enough time for both analysis of work and procedural practice. Students will recall and apply the following Grade 7 standards that were listed on the lesson plan. (7.EE.1, 7.EE.4)
• Unit 4, Functions,  Lesson 1, the Objective states, “Define and identify functions.” (8.F.1). Tips for Teachers state "this lesson introduces students to the concept of a function to describe a relationship. Though they have worked with functions prior to eighth grade with equations and proportional relationships, this is the first time they will formally define it. Through this unit and the next unit, students will explore functions in-depth; this lesson provides the basic definition of a function as a relationship of inputs and outputs where every input has exactly one output."
• Unit 7, Pythagorean Theorem and Volume, Lesson 13 identifies Current Standards: 8.NS.2, the Number System and 8.EE.2, Expressions and Equations. Foundational Standards include: 7.NS.3, the Number System and 6.EE.5, Expressions and Equations. Tips for Teachers states, "This lesson is a parallel lesson to Lesson 1, where students investigated and learned about square roots. This lesson is placed at this point in the unit so it immediately precedes students' study of volume."

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Anchor Problems help students make sense of the mathematics of the lesson as outlined in the Criteria for Success and Objective by providing them multiple opportunities to engage in the grade-level content in meaningful ways. The Problem Set Guidance provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills. Target Tasks are aligned to the Objective and designed to cover key concepts and misconceptions students might have. Target Tasks can be used as an indicator of student understanding or mastery of the Objective. For example:

• Unit 3, Transformations and Angle Relationships, Lesson 5, in the Anchor Problem, students are given two figures shown in a coordinate plane. For example, the Anchor Problem reads, “Figure 1 is reflected over the y-axis to create Figure 2, as shown in the coordinate plane below. Describe what you notice about the coordinate points of a figure when it is reflected over the y-axis. What do you think happens to coordinate points of a figure when it is reflected over the x-axis?” (8.G.3)
• Unit 3, Transformations and Angle Relationships, Lesson 20, the Objective states, “Define and use the interior angle sum theorem for triangles 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.” Tips for Teachers has a reminder that students have experience working with triangles and angle measurements from Grade 7 when they investigated unique triangles (7.G.2) and that students may know that the angles in a triangle add up to 180°. In this lesson they have the chance to prove this fact using parallel line angle relationships using facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.5)
• Unit 7, Pythagorean Theorem and Volume, Lesson 2,  in Target Task Problem 1, students are given a choice of rational and irrational solutions and they must identify which are irrational.  “Which of the following are irrational numbers? Select all that apply. Answer choices: a. $$\sqrt200$$, b.  $$0.005\overline{7}$$, c. $$0.0057$$…, d. $$\frac{1}{191}$$, e. $$\frac{\sqrt121}{5}$$, f. $$\frac{121}{\sqrt5}$$” (8.NS.1)
##### Indicator {{'1f' | indicatorName}}
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials for Match Fishtank Grade 8 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings and problems and activities that connect two or more clusters in a domain or two or more domains, when these connections are natural and important.

The Units are divided into Lessons focused on domains. Grade 8 standards are clearly identified in the Pacing Guide, Standard Map Document and a CCSSM Lesson Map found in the Unit Summary of each Unit. Additionally, each lesson identifies the objectives that address specific clusters. Instructional materials shaped by cluster headings include the following examples:

• Unit 1, Exponents and Scientific Notation, Lesson 6, Objective, “Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.” (8.EE.A)
• Unit 3, Transformations and Angle Relationships, Lesson 6, Objective, “Describe and perform rotations between congruent figures” (8.G.A)
• Unit 3, Transformations and Angle Relationships, Lesson 9, Objective, “Describe multiple rigid transformations using coordinate points.” (8.G.A)
• Unit 5, Linear Relationships, Lesson 11, Objective, “Write linear equations using slope and a given point on the line.” (8.EE.B)
• Unit 6, Systems of Equations, Lesson 1, Objective, “Define a system of linear equations and its solution.” (8.EE.C)
• Unit 7, Pythagorean Theorem and Volume, Objective, “Find missing side lengths involving right triangles and apply to area and perimeter problems.” (8.G.B

Instructional materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important. For example:

• Unit 4, Functions, Lesson 6, 8.F.B and 8.F.A are connected when students use functions to model relationships between quantities and define, evaluate, and compare functions using multiple representations. Anchor Problem 2 reads, “In a laboratory, a scientist is tracking the temperature of a substance over time. Each hour, she takes the temperature and records it in the graph below.” Questions: a. “What is the rate of change of the substance’s temperature, in ºF per hour, between 12 PM and 3 PM?  b. What is the rate of change of the substance’s temperature in ºF per hour between 7pm and 9pm? c. What is the starting temperature of the substance? d. Does it appear that the temperature of the substance is a function of the time of day? Why or why not?”
• Unit 5, Linear Relationships, Lesson 7 connects 8.EE.B and 8.F.B as students determine slope from coordinate points. Target Task states, “Samantha found the slope of the line that passed through the points (2,6) and (-4,-8). Her work is shown below. $$\frac{8-6}{2-(-4)}= \frac{2}{2+4}= \frac{2}{6} = \frac{1}{3}$$. Samantha made an error in her work. Describe the error and then find the correct slope of the line through the two given points.”
• Unit 5, Linear Relationships, Lesson 7, connects 8.EE.6 and 8.F.4 through slope and constructing linear relationship. Anchor Problem 2 states, “Find the slope of the line in each group below.”
• Unit 6, Systems of Equations, Lesson 7, 8.F.B and 8.EE.C are connected as students use functions to model relationships between quantities and analyze and solve linear equations and pairs of simultaneous linear equations. Target Task states, “Maya buys greeting cards to give to her friends at school. She buys some greeting cards that cost $2.50 each and some greeting cards that cost$4 each. She buys 13 cards in all for a total of $40.50. How many greeting cards that cost$2.50 did Maya buy?”
• Unit 7, Pythagorean Theorem and Volume, Lesson 13, 8.G.3 supports 8.EE.2, as students use the formula for volume of cubes to solve equations in the form: “x^2= p and x^3= p”.  For example, Anchor Problem 1 states, “Two cubes are shown below with their volume in cubic units.” Questions: “ a.  What is the side length of each cube?  b. Describe the relationship between the side length of a cube and its volume.”

### Rigor & Mathematical Practices

The instructional materials for Match Fishtank Grade 8 meet the expectations for rigor and the Mathematical Practices. The materials meet the expectations for rigor that students develop and demonstrate conceptual understanding, procedural skill and fluency, and application. The materials meet the expectations for Mathematical Practices, and attend to the specialized language of mathematics.

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

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

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop and independently demonstrate conceptual understanding, procedural skill and fluency, and application with a balance in all three.

##### Indicator {{'2a' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Match Fishtank Grade 8 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. All units begin with a Unit Summary and indicate where conceptual understanding is emphasized, if appropriate. Lessons begin with Anchor Problem(s) that include Guiding Questions designed to help teachers build their students’ conceptual understanding. The instructional materials include problems and questions that develop conceptual understanding throughout the grade level, especially where called for in the standards (8.EE.B, 8.G.A, and 8.F.A). For example:

• Unit 1, Exponents and Scientific Notation, Lesson 10, Anchor Problem 1 reviews students’ understanding of large numbers and how they compare to one another: “There are about one million people living in Austin, Texas. There are twice as many people living in Houston, Texas. Phil says that means there are one billion people living in Houston. Explain why Phil is incorrect.”  (8.EE.3, 8.EE.4)
• Unit 1, Exponents and Scientific Notation, Lesson 1, Anchor Problem, Question 1, (from Robert Kaplinsky's: “How Did They Make Ms. Pac-Man”?) students are shown a video of Ms. Pac-Man under “The Situation” Then students discuss the following questions: “How can you describe Ms. Pac-Man’s movements? What do you think “translation” means? What do you think “reflection” means? How can we get more precise to describe how far she translates, in what direction she rotates,...?” (8.G.2)
• Unit 3, Transformations and Angle Relationships, Lesson 3, Anchor Problem 3, “Below are the coordinate points from an original figure and a translated figure.  A(1,2) → A′(−1,−1)   B(−1,4) → B′(−3,1)  C(5,4) → C’(3,1) Describe the translation that occurred. Guiding Question: How can you answer this question without using a coordinate plane?”  (8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.2, and 8.G.3)
• Unit 4, Functions, Lesson 2, Anchor Problem 2, students develop conceptual understanding of functions as they analyze two input/output tables and respond to the guiding questions, “Why is Table A not a function? How many different ways can you change Table A to make it a function? What needs to be true about Table B for it to not be a function?” (8.F.1)
• Unit 4, Functions, Lesson 5, Anchor Problem, Question 1, students are given four different graphs and answer: “Which one doesn’t belong? Why? What are some similarities that the graphs have?” (8.F.1)
• Unit 4, Functions, Lesson 8, Anchor Problem 2, “Determine which equations below represent linear functions. Be prepared to justify your reasoning.” Equation 1: y = x2 + 1; Equation 2: y = 2x + 1; Equation 3: y = x/2;  Equation 4: $$y = x^3$$. Guiding Questions state: “What general conclusions can you make about equations of linear functions? About nonlinear functions?” (8.F.1, 8.F.3)
• Unit 6, Systems of Linear Equations, Lesson 10, Anchor Problem, Question 2 states, “The sum of two numbers is 361, and the difference between the two numbers is 173.” Students write a system of equations, and use any method to solve it. (8.EE.8.b)

Grade 8 materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. For example:

• Unit 3, Transformations and Angle Relationships, Lesson 9, students "describe multiple rigid transformations using coordinate points." In the Target Task, students are given an image that has undergone two transformations, reflections across the x-axis and then translated 3 units left and 4 units up. “Explain how you can determine the coordinates for point E’ after the two transformations. Victoria determines that the new coordinates for point D after the two transformations will be (-5,5). She says that after the reflection, point D’ is located at (2-,1), and then the translation maps it to (-5,5). Is Victoria correct? Explain why or why not.” (8.G.1a, b, c and 8.G.3)
• Unit 4, Functions, Lesson 4 provides students the opportunity to independently demonstrate conceptual understanding of functions in the Problem Guidance Set, (EngageNY Mathematics Grade 8 Mathematics, Module 5, Topic A, Lesson 4, Problem Set) “You have just been served freshly made soup that is so hot that it cannot be eaten. You measure the temperature of the soup, and it is 210°F. Since 212°F is boiling, there is no way it can safely be eaten yet. One minute after receiving the soup, the temperature has dropped to 203°F. If you assume that the rate at which the soup cools is constant, write an equation that would describe the temperature of the soup over time.” (8.F.A)
• Unit 4, Functions, Lesson 8, students "determine if functions are linear or nonlinear when represented as table, graphs, and equations." In Target Task 2, students are given a table chart with some missing inputs and outputs, “Complete the table so it represents a linear function.” (8.F.1 and 8.F.3)
• Unit 4, Functions, Lesson 12, students "sketch graphs of functions given qualitative descriptions of the relationship." In the Target Task, “A child at a park sees a slide. She runs across the playground to the slide and slowly climbs up the stairs. At the top of the stairs, she pauses for a moment and then slides down to the bottom. Sketch two graphs for the situation: one that shows the child’s distance from the stairs of the slide as a function of time, and the other that shows the child’s speed as a function of time.” (8.F.5)
• Unit 5, Linear Relationships, Lesson 3, students "compare proportional relationships represented as graphs." In the Problem Set Guidance Activity, “Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $14 for every 400 envelops she finishes. Jason earns$9 for every 300 envelopes he finishes. Draw graphs and write equations that show the earnings, y as functions of the number of envelopes stuffed, n for Anna and Jason. Who makes more from stuffing the same number of envelopes? How can you tell this from the graph? Suppose Anna has savings of $100 at the beginning of the summer and she saves all her earnings from her job. Graph her savings as a function of the number of envelopes she stuffed. How does this graph compare to her previous earnings graph? What is the meaning of the slope in each case?” (8.EE.5) ##### Indicator {{'2b' | indicatorName}} Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. The instructional materials for Match Fishtank Grade 8 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The structure of the lessons includes several opportunities to develop these skills, for example: • Every Unit begins with a Unit Summary, where procedural skills for the content is addressed. • In each lesson, the Anchor problem provides students with a variety of problem types to practice procedural skills. • Problem Set Guidance provides students with a variety of resources or problem types to practice procedural skills. • There is a Guide to Procedural Skills and Fluency under Teacher Tools and Mathematics Guides. The instructional materials develop procedural skill and fluency throughout the grade level. The instructional materials provide opportunities for students to demonstrate procedural skill and fluency independently throughout the grade level, especially where called for by the standards (8.EE.7, 8.EE.8b). For example: • Unit 2, Solving One-Variable Equations, Lesson 1 develops procedural skills in solving linear equations. Anchor Problem 1, Number 2 states, “For each expression, write an equivalent simplified expression. Then verify that the expressions are equivalent by substituting a value in for x and solving: a. 2 + 3(x + 4); b. 2 + 3(x -4); c. 2 -3(x + 4); d. 2 -3(x-4).” (8.EE.7) • Unit 5, Linear Relationships, Lesson 6, students demonstrate procedural fluency when completing the Target Task to find slope. The Target Task states, “Find the slope of each graph below. Use a different pair of coordinate points in Graph B to show the slope of the line is the same through any two points on the line.” (8.EE.6) • Unit 6, Systems of Linear Equations, Lesson 5, students "solve systems of linear equations using substitution when one equation is already solved for a variable." In Anchor Problem 2, “Solve the system below using substitution. Write your final answer as a coordinate point.” 2xy=1 and y=14x+20 (8.EE.8.b) The instructional materials provide opportunities for students to independently demonstrate procedural skills (K-8) and fluencies (K-6). These can include problems from Open Up Resources Grade 6-8 Mathematics, Open Middle, Algebra by Example, and EngageNY, Great Minds. For example: • Unit 2, Solving One Variable Equations, Lesson 3, students solve multi-step equations using the distributive property. Anchor Problem 3 states, “Solve the equation 2(3m + 6) - 4(1 - 2m) = -20.” Target Task, Problem 1 states, “Solve the equation below. For each step, explain why each line of your work is equivalent to the one before it.” (8.EE.7) • Unit 2, Solving One Variable Equations, Lesson 5, Problem Set Guidance, provides students the opportunity to independently demonstrate procedural skills in simplifying expressions in problem 1 when students are asked to, “Simplify each expression: a. 5/3x - 4(x - 1/3) b. -1/2(-8x + 6x + 10) - 2x” (8.EE.7) • Unit 6, Systems of Linear Equations, Lesson 5 provides students the opportunity to independently demonstrate procedural skills while using substitution to solve linear equations. For example, the problem states, “Solve the system using substitution. Write your answer as a coordinate point. x+ 2y+ 4.” (8.EE.8.b) • Unit 6, Systems of Linear Equations, Lesson 8, students solve systems of equations using elimination. For example, Target Task Problem 2 states, “Solve the system. 9x + 2y = 9; 6x - 2y = -4.” (8.EE.8.b) • Unit 7, The Pythagorean Theorem and Volume , Lesson 14, students independently demonstrate procedural skill using formulas to find the volume of cones and cylinders. Target Task states, “Asher makes a cylinder with a radius of 3 inches and a height of 6 1/2 inches. How many cubic inches of clay did Asher use? Brandi makes a cone and uses approximately $$64in^3$$ of clay. The height of Brandi’s cone is 4 inches. What is the radius of the circular base of Brandi’s cone?” (8.G.9) ##### Indicator {{'2c' | indicatorName}} Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade The instructional materials for Match Fishtank Grade 8 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of mathematics. Engaging applications can be found in single and multi-step problems, as well as routine and non-routine problems. In the Problem Set Guidance and on the Target Task, students engage with problems that have real-world contexts and are presented opportunities for application, especially where called for by the standards (8.EE.8.c, 8.F.B). The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge. Students have opportunities to independently demonstrate the use of mathematics flexibly in a variety of contexts. These can include problems from Open Up Resources Grade 6-8 Mathematics, Open Middle, MARS Formative Assessment Lessons, Robert Kaplinsky, Yummy Math, EngageNY - Great Minds, and others. Examples of routine applications include but are not limited to: • Unit 2, Solving One-Variable Equations, Lesson 4, students "Write and solve multi-step equations to represent situations, with variables on one side of the equation." For example, Anchor Problem 3, “Todd and Jason are brothers. Todd says, “I am twice as old as Jason was two years ago.” The sum of the brother’s ages is 38. How old is each brother?” (8.EE.7b) • Unit 4, Functions, Lesson 9, Target Task, students compare properties of two functions where one is represented by an equation and the other by a graph: “Cora and Daniel are both saving money each month. The total amount in their savings accounts is a function of the number of months they have been saving. Who started with more money in their savings account? Who is saving at a faster rate? By how much? After 6 months, who will have more money in their savings account? ” (8.F.2) • Unit 6, Systems of Linear Equations, Lesson 4, students "Solve real-world and mathematical problems by graphing systems of linear equations." For example, Anchor Problem 2, “Genny babysits for two different families. One family pays her$6 each hour and a bonus of $20 at the end of the night. The other family pays her$3 every half hour and a bonus of $25 at the end of the night. Write a system of equations that represents this situation and then graph the system. At what number of hours do the two families pay the same for babysitting services from Genny?” (8.EE.8.c) • Unit 7, The Pythagorean Theorem and Volume, Lesson 11, students use the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. In Problem Set Guidance (Open Up Resources Grade 8 Unit 8 Practice Problems, Lesson 10, Problem 2) “At a restaurant, a trash can’s opening is rectangular and measures 7 inches by 9 inches. The restaurant serves food on trays that measure 12 inches by 16 inches. Jada says it is impossible for the tray to accidentally fall through the trash can opening because the shortest side of the tray is longer than either edge of the opening. Do you agree or disagree with Jada’s explanation? Explain your reasoning.” (8.G.7) Examples of non-routine application include, but are not limited to: • Unit 5, Linear Relationships, Lesson 12, Target Task, Problem 1 states, “Tickets to a concert are available for early access on a special website. The website charges a fixed fee for early access to the tickets, and the tickets to the concert all cost the same amount with no additional tax. A friend of yours purchases 4 tickets on the website for a total of$162. Another friend purchases 7 tickets on the website for $270. What function represents the total cost, y, for the purchase of x tickets on the website?” (8.EE.2.4, 8.F.2.4) • Unit 6, Systems of Linear Equations, Lesson 1, Anchor Problem states, “Ivan’s furnace has quit working during the coldest part of the year, and he is eager to get it fixed. He decides to call some mechanics and furnace specialists to see what it might cost him to have the furnace fixed. Since he is unsure of the parts he needs, he decides to compare the costs based only on service fees and labor costs. Shown below are the price estimates for labor that were given to him by three different companies. Each company has given the same time estimate for fixing the furnace. Company A charges$35 per hour to its customers. Company B charges a $20 service fee for coming out to the house and then$25 per hour for each additional hour. Company C charges a $45 service fee for coming out to the house and then$20 per hour for each additional hour. For which time intervals should Ivan choose Company A, Company B, or Company C? Support your decision with sound reasoning and representations. Consider including equations, tables, and graphs.” (8.EE.8.C)

The instructional materials in Grade 8 provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. For example:

• Unit 2, Solving One-Variable Equations, Lesson 7, students "Write and solve multi-step equations to represent situation, including variables on both sides of the equation." In the Target Task, “Melanie is looking for a summer job. After a few interviews, she ends up with two job offers. Blue Street Café pays $11.75 per hour plus$33 from tips each week. Fashion Icon Factory Store pays $14.50 per hour with no tips. If Melanie plans to work 10 hours per week, which job offer should she take to maximize her earnings? What if Melanie works 20 hours per week? How many hours would Melanie need to work in order for the pay at each job to be the same? Write and solve an equation.” (8.EE.7) • Unit 4, Functions, Lesson 12, students "Sketch graphs of functions given qualitative descriptions of the relationship." In Anchor Problem 2, “Two stories are shown below. For each one, draw a graph to represent the functional relationship between the two quantities. Story 1: Distance from home vs. Time. You leave home and walk to the corner store. At the store, you spend a few minutes shopping, but then realize that you forgot your wallet at home. You run home, find your wallet immediately, and then run back to the store where you pay for your items. You leave the store and slowly walk away in the opposite direction of your home, toward the basketball court. Once you get to the court, you look for your friend for a few minutes, but when you realize that he’s not there, you walk quickly back home. Story 2: Temperature vs. Time. At 8 AM on a summer day, the temperature in Hartford, Connecticut, was 60°F. By 10 AM, the temperature had risen 10°F, where it stayed until 12 PM. From noon to 3 PM, the temperature rose to 85°F, after which it dropped at a steady rate until it hit 65°F at 9 PM." (8.F.5) • Unit 5, Linear Relationships, Lesson 11, students "Write linear equations using slope and a given point on the line." In Anchor Problem 3, “A taxicab driver charges$2.40 per mile plus a one-time flat fee. A 3-mile ride costs you $10.30. a. Write a function to represent the cost of a taxicab ride, y, for x miles. b. How much will it cost you to travel 9 miles? (8.EE.2.6, 8.F.2.4) • Unit 6, Systems of Linear Equations, Lesson 10, students "Solve real-world and mathematical problems using systems and any method of solution." In Target Task, Problem 1, “Small boxes contain Blu-ray disks and large boxes contain one gaming machine. Three boxes of gaming machines and a box of Blu-rays weigh 48 pounds. Three boxes of gaming machines and five boxes of Blu-rays weigh 72 pounds. How much does each box weigh?” (8.EE.8.C) ##### Indicator {{'2d' | indicatorName}} Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. The instructional materials for Match Fishtank Grade 8 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the instructional materials. Many of the lessons incorporate two aspects of rigor with an emphasis on application. Student practice includes all three aspects of rigor, though there are fewer questions for conceptual understanding. There are instances where all three aspects of rigor are present independently throughout the instructional materials. For example: • Unit 8, Bivariate Data, Lesson 6, Target Task, students develop conceptual understanding while constructing scatter plots to interpret the relationship of the paired data. “According to the Bureau of Vital Statistics for the New York City Department of Health and Mental Hygiene, the life expectancy at birth (in years) for New York City babies is shown in the scatter plot below. An equation for a line fit to this data is represented by: y=338x - 597.4. Explain what the slope of this equation model means in terms of the context. Use the model to predict the life expectancy for a baby born in New York City in 2020.” (8.SP.3) • Unit 1, Exponents and Scientific Notation, Lesson 6, students, "Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions." In Anchor Problem 3, “Lucas thinks that since $$(ab)^2 =a^2b^2$$, then that must mean $$(a+b)^2 =a^2+b^2$$. Is Lucas’ reasoning correct? Explain or show why or why not.” (8.EE.1) • Unit 8, Bivariate Data, Lesson 8, students "Calculate relative frequencies in two-way tables to investigate associations in data." In the Target Task, “All the students at a middle school were asked to identify their favorite academic subject and whether they were in the 7th grade or 8th grade.” (A table is provided with the results.) “Is there an association between favorite academic subject and grade for students at the school? Support your answer by calculating appropriate relative frequencies using the given data.” (8.SP.4) Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example: • Unit 4, Lesson 12, Target Task, students develop their understanding of functions as they apply mathematics from verbal descriptions. “A child at a park sees a slide. She runs across the playground to the slide and slowly climbs up the stairs. At the top of the stairs, she pauses for a moment and then slides down to the bottom. Sketch two graphs for the situation: one that shows the child’s distance from the stairs of the slide as a function of time, and the other that shows the child’s speed as a function of time.” (8.F.1, 8.F.3, 8.F.5) • Unit 5, Linear Relationships, Lesson 2, Anchor Problem 2, students engage in application and conceptual understanding as they graph and interpret the following situation, “Nia and Trey both had a sore throat so their mom told them to gargle with warm salt water. Nia mixed 1 teaspoon salt with 3 cups water. Trey mixed 1/2 teaspoon salt with 1 1/2cups of water. Nia tasted Trey’s salt water. She said, 'I added more salt so I expected that mine would be more salty, but they taste the same.’ Explain why the salt water mixtures taste the same. Find an equation that relates s, the number of teaspoons of salt, with w, the number of cups of water, for both of these mixtures. Draw the graph of your equation from part (b). Your graph in part (c) should be a line. Interpret the slope as a unit rate.” (8.EE.5) • Unit 6, Systems of Linear Equations, Lesson 11, in Target Task, Problem 2, students engage in procedural skill and application. For example, Problem 2 states, “Kim has a small container and a large container as shown. It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container. What is the size of each of the two containers?” (8.EE.8.c) #### 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 Match Fishtank Grade 8 meet the expectations for practice-content connections. The materials identify, use the Mathematical Practices (MPs) to enrich grade-level content, provide students with opportunities to meet the full intent of the eight MPs, and attend to the specialized language of mathematics. ##### Indicator {{'2e' | indicatorName}} The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. The instructional materials reviewed for Match Fishtank Grade 8 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level. All Standards for Mathematical Practice are clearly identified throughout the materials in numerous places, including: • Each Unit Summary contains descriptions of how MPs are addressed and what mathematically proficient students should do. For Example, Unit 4: Functions, Unit Summary states, “As students progress through the unit, they analyze functions to better understand features such as rates of change, initial values, and intervals of increase or decrease, which in turn enables students to make comparisons across functions even when they are not represented in the same format. Students analyze real-world situations for rates of change and initial values and use these features to construct equations to model the function relationships (MP.4).” • Lessons usually include indications of Mathematical Practices within a lesson in one or more of the following sections: Criteria for Success, Tips for Teachers, or Anchor Problems Notes. For example, in Unit 2 Solving One Variable Equations, Lesson 5, Criteria For Success states, “Model a situation using an equation and make adjustments to the model as the situation changes (MP.4). De-contextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem (MP.2).” Lesson 8, Anchor Problem 2 states, “Students make use of structure to decide how to categorize each equation, looking for equations that have the same variable term on both sides of the equation and considering the values of any constants (MP.7). Lesson 9, Tips for Teachers states, “In this lesson, students use what they know about equations with no, infinite, or unique solutions to reason about solutions without having to completely solve the equation. For example, if they can simplify each side of an equation to one or two terms, they should be able to determine if a solution is possible and if so, if that solution is unique (MP.7).” • In some Problem Set Guidances, MPs are identified within the problem. For example, Unit 4 Functions, Lesson 11, MARS Formative Assessment Lesson for Grade 8 Interpreting Distance-Time Graphs states, “This lesson also relates to all the Standards for Mathematical Practice, with a particular emphasis on: 2. Reason abstractly and quantitatively, 7. Look for and make use of structure and 8. Look for and express regularity in repeated reasoning.” Evidence that the MPs are used to enrich (are connected to) the mathematical content: • MP7 enriches the mathematics in Unit 5, Lesson 6, as students analyze and find slope from a graph. Anchor Problem 2, Notes, states, “Before finding the slope, ask students to take a close look at the lines. Is the line rising to the left or right? Does the line appear steep or shallow? Using these observations of the lines, students can better their understanding of the numerical value of the slope as positive or negative, and the absolute value as greater than 1 or less than 1 (MP.7).” • MP2 enriches the mathematical content in Unit 2, Lesson 4, Criteria for Success, as students “decontextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in context of the problem”. Anchor Problem 3 states, “Todd and Jason are brothers. Todd says, 'I am twice as old as Jason was two years ago.' The sum of the brothers' ages is 38. How old is each brother?” • MP8 enriches the mathematical content in Unit 5, Lesson 6, Anchor Problem 3, Notes, states that when students use “understanding of similar triangles to reach the conclusion that the slope of a line is the same through any two points on the line”. “Using any two points on the line, you can create similar triangles, which will have side lengths in the same ratio. Since slope is the ratio of the vertical height of the triangle to the horizontal width, you can conclude that the slope through any two points will be the same.” Throughout Problem Set Guidance, students are provided opportunities to use two points on a line to find the slope. Target Task, Question 2 states, “Use a different pair of coordinate points in Graph B to show the slope of the line is the same through any two points on the line.” • MP4 enriches the mathematics in Unit 5, Linear Relationships, Lesson 4, Anchor Problem 1, Notes states, “Students can approach this problem in several ways using their understanding of proportional relationships (MP.4). For example, they may graph a line representing the new machine in the graph alongside the old machine. They may write an equation to represent each machine. They may determine the rate of change for each machine and use a proportion.” “At a factory, a machine fills jars with salsa. The manager of the factory is considering buying a new machine that will fill 78 jars of salsa every 3 minutes. To support his decision, he wants to compare the rate of the new machine to the rate of the old machine that is currently in the factory. The graph below shows the number of jars of salsa filled over time with the old machine.The manager is about to fill an order of 765 jars of salsa. How long would it take to fill this order on each machine? Should the manager consider replacing the old machine with the new one? Explain.” There is no evidence where MPs are addressed separately from the grade-level content. ##### Indicator {{'2f' | indicatorName}} Materials carefully attend to the full meaning of each practice standard The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for carefully attending to the full meaning of each practice standard. Materials attend to the full meaning of each of the 8 MPs. The MPs are discussed in both the unit and lesson summaries, as appropriate, when they relate to the overall work. They are also explained within specific Anchor Problems notes. Each practice is addressed multiple times throughout the year. Over the course of the year, students have ample opportunity to engage with the full meaning of every MP. Examples include: MP.1: Students make sense of problems and persevere in solving them. • Unit 6, Systems of Linear Equations, Lesson 10, Anchor Problem 3, students “make sense of how this information fits together, what unknowns they are looking to solve for, and how they can represent the relationships with equations that can be solved.” For example, Anchor Problem states, “A type of pasta is made of a blend of quinoa and corn. The pasta company is not disclosing the percentage of each ingredient in the blend, but we know that the quinoa in the blend contains 16.2% protein and the corn in the blend contains 3.5% protein. Overall, each 57-gram serving of pasta contains 4 grams of protein. How much quinoa and how much corn is in one 57-gram serving of the pasta?” • Unit 7, Pythagorean Theorem and Volume, Lesson 16, Anchor Problem 3 states, “Option #2 (Students choose or are assigned one of the five Anchor Problems to work on with a small group of peers. After collaboratively developing a strategy and preparing a solution, students should create a poster of their response.)” Shipping Rolled Oats: “Rolled oats (dry oatmeal) come in cylindrical containers with a diameter of 5 inches and a 9 1/2 height of inches. These containers are shipped to grocery stores in boxes. Each shipping box contains six rolled oats containers. The shipping company is trying to figure out the dimensions of the box for shipping the rolled oats containers that will use the least amount of cardboard. They are only considering boxes that are rectangular prisms so that they are easy to stack. a. What is the surface area of the box needed to ship these containers to the grocery store that uses the least amount of cardboard? b. What is the volume of this box?” In the Criteria for Success, students “Map out a solution pathway and use relevant formulas and math concepts to solve complex, real-world problems. (MP.1 and MP.4)” MP.2: Students reason abstractly and quantitatively. • Unit 2, Solving One Variable Equations, Lesson 4, students “decontextualize a situation to represent it algebraically, and re-contextualize to interpret the solution in the context of the problem.” For example, Anchor Problem 1 states, “The length of a rectangle is 3 cm less than twice the width of the rectangle. If the perimeter is 75 cm, what are the dimensions of the rectangle?” • Unit 8, Bivariate Data, Lesson 1, Anchor Problem 1, students “interpret ordered pairs (x,y) in scatter plots in context of the variables.” For example, students are shown a graph of weight and price for sugar and asked, “Each point on this graph represents a bag of sugar. Which point shows the heaviest bag? Which point shows the cheapest bag? Which points show bags with the same weight? Which points show bags with the same price? Which of F or C gives the best value for the money? How can you tell?” MP.4: Students model with mathematics. • Unit 4, Functions, Lesson 10, in Anchor Problem 1, students model a real-world context by comparing the properties of two functions represented in different ways. For example, “Sam wants to take his music player and his video game player on a car trip. An hour before they plan to leave, he realized that he forgot to charge the batteries last night. At that point, he plugged in both devices so they can charge as long as possible before they leave. Sam knows that his music player has 40% of its battery life left and that the battery charges by an additional 12 percentage points every 15 minutes. His video game player is new, so Sam doesn’t know how fast it is charging but he recorded the battery charge for the first 30 minutes after he plugged it in. If Sam’s family leaves as planned, what percent of the battery will be charged for each of the two devices when they leave? How much time would Sam need to charge the battery 100% on both devices? Students may choose to use any representation (equation, table, graph) for these functions in order to analyze and compare them.” • Unit 7, Pythagorean Theorem and Volume, Lesson 11, Anchor Problem 1 states, “Act 1: Watch the Taco Cart by Dan Meyer. What do you notice? What do you wonder? Who will reach the taco cart first? Make a guess. Act 2: Ask students what information they need to determine who will reach the taco cart first. Share the information below as it is requested. Note, the speeds refer to the speed of walking on the sand and the speed of walking on the concrete sidewalk. Act 3: Once students have reached their solutions, share the video answer.” Anchor Problem Notes state, “students model a real-world situation using the Pythagorean Theorem. They first make a guess and predict who will reach the taco cart first. Then, as new information is received, students determine how they will use that information to design and modify a model to accurately answer the question (MP.4).” • Unit 8, Bivariate Data, Lesson 5, Anchor Problem 2, students model and analyze data related to the relationship between time and percent battery charge. “Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend’s house with a full battery. The pictures below show screenshots of the battery charge indicator after he plugs in the computer at 9:11 A.M. The screenshots suggest an association between two variables. What are the two variables in this situation? Make a scatter plot of the data. Draw a line that fits the data and find the equation of the line. When can Jerry expect to have a fully charged battery?” Anchor Problem Notes state, “This problem engages students in MP.4, and asks students to analyze the relationship between time and percent battery charge. Information is given in an unconventional way and students must determine what the variables are, how to represent the relationship between then visually, and then what conclusions they can make.” MP.5: Students use appropriate tools strategically. • Unit 3, Transformations and Angle Relationships, Lesson 1, Anchor Problem 2 states, “For each pair of figures, decide whether these figures are the same size and same shape. Be prepared to justify your reasoning. You may use mathematical tools to make your decision.” Lessons in this unit ensure the full depth of MP5 by emphasizing student choice. • Unit 4, Functions, Lesson 8, Anchor Problem 2 states, “Determine which equations below represent linear functions. Be prepared to justify your reasoning; equation 1: $$y = x^2 +1$$, equation 2: y = 2x +1, equation 3: $$y = x^2$$, equation 4: $$y = x^2$$." “This should be an investigatory problem for students to explore using different strategies and tools.” MP.6: Students attend to precision. • Unit 1, Exponents and Scientific Notation, Lesson 2, Anchor Problem 3 states, “Students attend to precision as they use parentheses appropriately when substituting in negative values in order to convey multiplication and not subtraction. Evaluate the expression when x = 2 and y = -3; $$xy^2 + xy$$.” • Unit 3, Transformations and Angle Relationships, Lesson 7, Anchor Problem 1 states, “Figure 1 is shown in the coordinate plane below. Which figure(s) would Figure 1 map to if it were a. translated? b. reflected? c. rotated? The vertices are intentionally not named in this problem. Ensure students to use precision in their communication, adding labels or names as needed.” MP.7: Students look for and make use of structure. • Unit 2, Solving One Variable Equations, Lesson 8, Anchor Problem 2, students look for patterns and structures in one variable equations. For example, the Anchor Problem 2 states, “Sort the equations below into the three categories Guiding Questions: a. Ask yourself for each problem, is there a value that would make the equation true? If so, is there more than one value for ? b. At first look, how would you classify 3x = 2x? If you were to solve it, how would you go about it and what would the solution be? c. What other strategies can you use to categorize these equations?” • Unit 7, Pythagorean Theorem and Volume, Lesson 9, in Anchor Problem 2, students demonstrate an understanding of structure as they explain how to use the Pythagorean Theorem on triangles that are not right triangles. For example, students are told to “Find the area of the isosceles triangle below. Give your answer to the nearest tenth of a unit. This Anchor Problem highlights how knowing the Pythagorean Theorem can offer additional insight into other triangles and shapes by identifying the opportunity to create right triangles.” • Unit 7, Pythagorean Theorem and Volume, Lesson 16, Anchor Problem 2, students use their understanding of the overall structure of the formulas to solve for surface area of a cone and surface area of a sphere. For example, students are told"The diagram shows three glasses (not drawn to scale). The measurements are all in centimeters. The bowl of glass 1 is cylindrical. The inside is 5 cm and the inside height is 6 cm. The bowl of glass 2 is composed of a hemisphere attached to a cylinder. The inside diameter of both the hemisphere and the cylinder is 6 cm. The height of the cylinder is 3 cm. The bowl of glass 3 is an inverted cone. The inside diameter is 6 cm and the inside slant height is 6 cm. a. Find the vertical height of the bowl of glass 3. b. Calculate the volume of the bowl of each of these glasses. c. Glass 2 is filled with water and then half the water is poured out. Find the height of the water.” MP.8: Students look for and express regularity in repeated reasoning. • Unit 3, Transformations and Angle Relationships, Lesson 5, Anchor Problem 1, students explain patterns, discuss methods and solution strategies, and evaluate the result of a reflection over x and y axis. For example, the Anchor Problem 1 states, “Triangle LMN underwent a single transformation to become triangle PQR, shown below. a. What single transformation maps triangle LMN to triangle PQR ? Describe in detail. b. Name two things that are the same about both triangles. c. Name two things that are different about the triangles.” • Unit 7, Pythagorean Theorem and Volume, Lesson 4, in Anchor Problem 2, students “Follow the directions to approximate the location of 2/11 on the number lines below. a. On the topmost number line, label the tick marks. Next, find the first decimal place of 2/11 using long division and estimate where should be placed on the top number line. b. Label the tick marks of the second number line. Find the next decimal place of 2/11 by continuing the long division and estimate where should be placed on the second number line. Add arrows from the second to the third number line to zoom in on the location of 2/11. c. Repeat the earlier step for the remaining number lines. d) What do you think the decimal expansion of 2/11 is?” In this problem, students investigate the structure of the fraction 2/11, as it results in a repeated pattern in the decimal equivalent.” ##### Indicator {{'2g' | indicatorName}} Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by: ##### Indicator {{'2g.i' | indicatorName}} Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Student materials consistently prompt students to analyze the arguments of others. These can include problems from Open Up Resources Grade 6-8 Mathematics, Open Middle, MARS Formative Assessment Lessons, Robert Kaplinsky, Yummy Math, EngageNY - Great Minds, and others. For example: • Unit 2, Solving One Variable Equations, Lesson 3, Anchor Problem 2 states, “Two more students, Christian and Esther, are solving the same equation. They take a different approach to solving the equation, but they each make an error in the first two lines of their work, shown below. 15 - 3(x - 2) + 6x = 3(13). Explain the error that each student made.” • Unit 7, Pythagorean Theorem and Volume, Lesson 1, Target Task states, “The square below has an area of 20 square units. Taylor writes the equation $$s^2=20$$ to find the measure of the side length of the square. She reasons that the solution to the equation is $$\sqrt20$$ and concludes that the side length of the square is 10 units. Do you agree with Taylor? Explain why or why not. If you disagree, include the correct side length of the square.” • Unit 7, Pythagorean Theorem and Volume, Lesson 2, Problem Set Guidance, (EngageNY Mathematics, Grade 8 Mathematics, Module 7, Topic B, Lesson 11, Problem Set) Question 8 states, “Henri computed the first 100 decimal digits of the number 352/541 and got $$0.6506469500924214417744916820702402957486136783733826247689463955677079482439926062846580406654343807763401109057301294$$…. He saw no repeating pattern to the decimal and so concluded that the number is irrational. Do you agree with Henri’s conclusion? If not, what would you say to Henri?” • Unit 8, Bivariate Data, Lesson 6, Problem Set Guidance, (EngageNY Mathematics, Grade 8 Mathematics, Module 6, Topic C, Lesson 10), Problem Set, Problem 3 states, “Simple interest is money that is paid on a loan. Simple interest is calculated by taking the amount of the loan and multiplying it by the rate of interest per year and the number of years the loan is outstanding. For college, Jodie’s older brother has taken out a student loan for$4,500 at an annual interest rate of 5.6%, or 0.056. When he graduates in four years, he has to pay back the loan amount plus interest for four years. Jodie is curious as to how much her brother has to pay.  a. Jodie claims that her brother has to pay a total of $5,508. Do you agree? Explain. As an example, a$1,200 loan has an 8% annual interest rate. The simple interest for one year is $96 because (0.08)(1200) = 96. The interest for two years would be$192 because (2)(96) = 192.  b. Write an equation for the total cost to repay a loan of $???? if the rate of interest for a year is ???? (expressed as a decimal) for a time span of ???? years. c. If ???? and ???? are known, is the equation a linear equation? d. In the context of the problem, interpret the slope of the equation in words. e. In the context of the problem, interpret the ????-intercept of the equation in words. Does interpreting the intercept make sense? Explain.” Student materials consistently prompt students to construct viable arguments. For example: • Unit 1, Exponents and Scientific Notation, Lesson 8, Target Task states, “What errors were made in the examples below? Explain the mistake and then find an equivalent expression. $$x^3y^2/y^4x^2 = -1/y^6x^5$$” • Unit 4, Functions, Lesson 2, Target Task states, “A certain business keeps a database of information about its customers. Let C be the rule that assigns to each customer shown in the table his or her home phone number. Is C a function? Explain your reasoning. Let P be the rule that assigns to each phone number in the table above, the customer name associated with it. Is P a function? Explain your reasoning. Explain why a business would want to use a person's social security number as a way to identify a particular customer instead of their phone number.” • Unit 5, Linear Relationships, Lesson 4 states, “Water flows out of Pipe A at a constant rate. Pipe A can fill 3 buckets of the same size in 14 minutes. The graph below represents the rate at which Pipe B can fill the same-sized buckets. Write a linear equation that represents the number of buckets, y, that Pipe A can fill in x minutes. Which pipe fills buckets faster? Justify your answer.” • Unit 6, Systems of Linear Equations, Lesson 11, Problem Set Guidance MARS Summative Assessment Tasks for Middle School Chips and Candy states "4. Clancy has just$1. Does he have enough money to buy a bag of potato chips and a candy bar? Explain your answer by showing your calculation.”
• Unit 7,  Pythagorean Theorem and Volume, Lesson 4, Problem Set Guidance, (Open Up Resources, Grade 8 Unit 8 Practice Problems) Lesson 14, Question 1 states, “Andre and Jada are discussing how to write 17/20 as a decimal. Andre says he can use long division to divide 17 by 20 to get the decimal. Jada says she can write an equivalent fraction with a denominator of 100 by multiplying 5/5, then writing the number of hundredths as a decimal. Do both of these strategies work? Which strategy do you prefer? Explain your reasoning.”
• Unit 8, Bivariate Data, Lesson 3, Target Task Problem 1 states, “Which of the following scatter plots shows a negative linear relationship? Explain how you know.”
##### Indicator {{'2g.ii' | indicatorName}}
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for  Math FishTank Grade 8 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others through Guiding Questions and Teacher Notes. For example:

• Unit 1, Exponents and Scientific Notation, Lesson 4, Anchor Problem 2. Teachers are prompted to have students review incorrect statements. Guiding Questions are as follows: a. “What mistake was made in the first example?” b. “Before correcting the problem, what are other possible answers – right and wrong – that might represent the product? (For example, $$8^8$$, $$16^8$$, $$16^15$$, $$64^8$$, $$64^15$$ etc.)” c. “What strategy can you use to find the correct answer without evaluating the exponent? Can you use the same strategy for the second example? How convincing is your reasoning? How do you know your new answer is correct?”
• Unit 1, Exponents and Scientific Notation, Lesson 14, Guiding Questions are provided for teachers to support students in constructing viable arguments and analyzing the errors of others: a. “When multiplying with numbers in scientific notation, you are able to use the commutative property to multiply the two first factors together and then the two powers of 10. Why does this not work with addition?” b)\. “What is the place value of the “2” in 2.5×103?” c. “What is the place value of the “1” in $$1.3×10^4$$?” d.  “Can you add these two numbers together to get the digit ‘3’? Why or why not?” e. What do you notice about the powers of 10 in the two numbers? Why is this an important detail when adding numbers?”
• Unit 2,  Solving One Variable Equations, Lesson 8, Anchor Problem 2 states, “Sort the equations below into the three categories. Ask yourself for each problem, is there a value for x that would make the equation true? If so, is there more than one value for x? At first look, how would you classify 3x = 2x? If you were to solve it, how would you go about it and what would the solution be? What other strategies can you use to categorize these equations? Once students have sorted the equations into the three categories, have them defend their decisions by explaining the similarities between each equation within each category.”
• Unit 5, Linear Relationships, Lesson 6, Anchor Problem 1 states, “Three staircases are shown below. Which staircase is the steepest? Without doing any calculations, order the staircases from least steep to most steep. Slope is a measure of steepness. The greater the slope, the greater the steepness. Use the measurements provided in the diagram to justify the order of steepness you determined earlier.  Another staircase climbs 8 feet over a distance of 10 feet. Where does this staircase fall in the order of steepness?” Guiding Questions are as follows:  a. “How did you determine your order without doing any calculations?” b. “Discuss your order with a peer. Do you have the same order? How did you each determine your order? Will you change your order based on your conversation?” c. “What measurements are important to consider when finding slope? How do you use those measurements to determine slope?” d. “Explain how to find the steepness of any staircase that climbs a distance of y feet over a distance of x feet. How does this relate to the concept of slope? “Notes include the following: “Students will likely be able to determine the order of steepness intuitively by looking at the staircases. They are then challenged to find the numerical representation that supports their order. Some students may consider the area of the triangles formed by the staircase, or the fraction of width over height, or just consider the height in isolation; however, none of these measurements match the order of steepness A, C, B from least to greatest. Discuss the various strategies that come up in class and which seem valid and why”.
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations that materials use accurate mathematical terminology.

The Match Fishtank Grade 8 materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. The materials use precise and accurate terminology and definitions when describing mathematics and support students in using them.

Vocabulary is introduced at the Unit Level. It is reinforced through a Vocabulary Glossary and in the Criteria For Success. For example:

• A Vocabulary Glossary is provided in the Course Summary and lists all the vocabulary terms and examples. There is also a link to the vocabulary glossary on the Unit Overview page for teachers to access.
• Each Unit Overview also has a chart with an illustration that models for the teacher the key vocabulary used throughout the unit.
• Each Unit has a vocabulary list with the terms and notation that students learn or use in the unit. For example, in Unit 3, Transformations and Angle Relationships’ vocabulary includes the following words: translation, reflection, rotation, rigid transformation, dilation, congruent/congruence, scale factor, corresponding angles, alternate interior and exterior angles, vertical angles, and similar.
• Unit 4, Functions, Lesson 1, Criteria For Success states, “Define a function as a relationship between two sets in which every input has exactly one output.”

Anchor Problem Notes provide specific information about the use of vocabulary and math language (either informal or formal) in the lesson plan. For Example:

• Unit 3, Transformations and Angle Relationships, Lesson 4, Anchor Problem 1 states, “Use this problem to ensure students know a reflection is described by a line of reflection from which every point on the original image is the same distance as each corresponding point on the reflected image.”
• Unit 7, Pythagorean Theorem and Volume, Lesson 3, Anchor Problem 2 states, “When estimating the values, students must determine how precise they need to be in their estimates in order to find an appropriate location on the number line. For example, students may determine that $$\sqrt50+1$$ is between 8 and 9, but they must then determine if they should plot the point closer to the 8, closer to the 9, in the middle, etc.”
• Unit 8, Bivariate Data, Lesson 3, Anchor Problem 1. “In this Anchor Problem, students make the connection between positive linear associations and lines with positive slopes, and negative linear associations and lines with negative slopes. The language and vocabulary is scaffolded for students, as it is given to them in part (d). Throughout the rest of the lesson, listen for students using this language in other examples, and if need be, direct them back to this problem for reminders or guidance.”

The Match Fishtank Grade 8 materials support students at the lesson level by providing new vocabulary terms in bold print, and definitions are provided within the sentence where the term is found. Additionally, Anchor Problem Guiding Questions allow students to use new vocabulary in meaningful ways. For example:

• Unit 4, Functions, Lesson 7, Anchor Problem 1 states, “What do you think a linear function is? What does it look like?”
• Unit 5, Linear Relationships, Lesson 6, Anchor Problem 1 states, “What does slope mean? How do you measure it? These graphs do not include measurements like the staircases. How can you determine the measurements you need to find the slope?”
• Unit 7, Pythagorean Theorem and Volume, Lesson 5, Anchor Problem 1 states, “Recall the definition of a rational number. Why are all of these rational numbers?”

### Usability

##### Gateway 3
Partially 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 Match Fishtank Grade 8 meet expectations for use and design to facilitate student learning. Overall, the design of the materials balances problems and exercises, has an intentional sequence, expects a variety in what students produce, uses manipulatives as faithful representations of mathematical objects, and engage students thoughtfully with mathematics.

##### Indicator {{'3a' | indicatorName}}
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 for Match Fishtank Grade 8 meet the expectations that there is a clear distinction between problems and exercises in the materials.

There are eight units in each grade level. Each unit presents lessons in a consistent structure. During the Anchor Problems, which include guided instruction, step-by step procedures, and problem solving, students work on examples and problems to learn new concepts. The second half of each lesson uses a Problem Set, which contains a variety of exercises, allow students to independently master and demonstrate their understanding of the material. Each lesson concludes with a Target Task intended for formative assessment. For example,

• Unit 1, Exponents and Scientific Notation, Lesson 2, Anchor Problems, students   “Evaluate numerical and algebraic expressions with exponents using the order of operations.” through guided instruction. In the Problem Set Guidance, (EngageNY Mathematics Grade 6 Mathematics,Module 4, Topic B, Lesson 6, Problem Set), students are given additional problems for independent practice and mastery of this skill.  Exercise 2 asks students to analyze the expression $$4 + 9^2 \div 3 \times 2 - 2$$.  “What operation is evaluated first? What operations are evaluated next? What operations are always evaluated last? What is the final answer?”
• Unit 2, Solving One-Variable Equations, Lesson 4,Anchor Problems, students “Write and solve multi-step equations to represent situations, with variables on one side of the equation.” through guided instruction. In the Problem Set Guidance, (EngageNY Mathematics Grade 8 Mathematics, Module 4, Topic A,  Lesson 5, Examples, Exercises, and Problem Set), they are given additional problems allowing for independent practice and mastery. Example 1: “One angle is five degrees less than three times the degree measure of another angle. Together, the angles measures have a sum of 143°. What is the measure of each angle?”
• Unit 4, Functions, Lesson 4, Anchor Problems, students “Represent functions with equations” through guided instruction. In the Problem Set Guidance, (EngageNY Mathematics Grade 8 Mathematics, Module 5, Topic A, Lesson 4,  Problem Set), they are given additional problems allowing for independent practice and mastery. Example 3 asks students, “You have just been served freshly made soup that is so hot that it cannot be eaten. You measure the temperature of the soup, and it is 210°F. Since 212°F is boiling, there is no way it can safely be eaten yet. One minute after receiving the soup, the temperature has dropped to 203°F. If you assume that the rate at which the soup cools is constant, write an equation that would describe the temperature of the soup over time.”
• Unit 5, Linear Relationships, Lesson 3, Anchor Problems, students “Compare proportional relationships represented as graphs.” In the Problem Set Guidance,  (Open Up Resources, Grade 8 Unit 3 Practice Problems, Lesson 4, Problems 1 and 2), students are given additional problems for independent practice and mastery of this skill. Problem 1, “A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies. EZ Excavation gives its prices in a table. Happy Hauling Service gives its prices in a graph. [A picture of a line graph shows the cost of dirt] How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning. Calculate the rate of change for each relationship. What do they mean for each company? If the contractor has 40 cubic yards of dirt to haul and a budget of \$1000, which hauling company should she hire? Explain or show your reasoning.”
• Unit 8, Bivariate Data, Lesson 2, Anchor Problems, students “Create scatter plots for data sets and make observations about the data.” In the Problem Set Guidance, (Open Up Resources Grade 8 Unit 6 Practice Problems, Lesson 2), students are given additional problems for independent practice and mastery of this skill. Problem 1 asks students, “In hockey, a player gets credited with a “point” in their statistics when they get an assist or goal. The table shows the number of assists and number of points for 15 hockey players after a season. Make a scatter plot of this data. Make sure to scale and label the axes.”
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations that the design of assignments is intentional and not haphazard.

The lessons follow a logical, consistent format that intentionally sequences assignments, provides a natural progression, and leads to full understanding for students. For example:

• In the Anchor Problems, students are introduced to concepts and procedures through a problem-based situation. They are guided through the problem solving process via a series of Guiding Questions provided for teachers.
• In the Problem Set Guidance: This portion of instruction connects to the problem learned previously and is the substance of the lesson. It includes a list of suggested resources (including links to resources) or problem types for teachers to create a problem set aligned to the objective of the lesson. Teachers are encouraged to create a set of problems that best work for the needs of their students or for that particular lesson.
• Each lesson concludes with an independent Target Task designed to cover key concepts from the lesson and formatively assess student understanding and mastery.
##### Indicator {{'3c' | indicatorName}}
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials for Match Fishtank Grade 8 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example:

• Unit 2, Solving One-Variable Equations, Lesson 3. Students justify each step in solving a multi-step equation with variables on one side of the equation.
• Unit 4, Functions, Lesson 12: Students sketch graphs of functions given qualitative descriptions of the relationship.
• Unit 7, Pythagorean Theorem and Volume, Lesson 3: Students use number lines to compare values of irrational numbers.
• Unit 8, Bivariate Data, Lesson 4: Students use a best fit line to make predictions about the data.
##### Indicator {{'3d' | indicatorName}}
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The series includes a variety of suggestions for physical manipulatives, and links to physical, as virtual manipulatives, For example:

• Unit 3, Transformations and Angle Relationships, Lesson 1, Anchor Problem 2. Students use shapes to investigate congruent/non-congruent shapes.
• Unit 4, Functions, Lesson 1, Anchor Problem 1 uses survey questions and letter cards to introduce the “concept of a function by juxtaposing the clarity of a function next to the confusion of a non-function.”
• Unit 7, Pythagorean Theorem and Volume, Lesson 5, Problem Set Guidance: MARS Formative Assessment Lesson for Grade 8 Translating between Repeating Decimals and Fractions. This includes a card matching activity to build procedural fluency in converting between decimals and fractions.
##### Indicator {{'3e' | indicatorName}}
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials for Match Fishtank Grade 8 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

The entire digital series follows a consistent format, making it easy to follow. The page layouts in the Problem Set Guidance materials are user-friendly, and the pages are not overcrowded or hard to read. Because teachers pre-select material from the suggested sources, they are printed for the students, making it easier to navigate. Graphics promote understanding of the mathematics being learned. The digital format is easy to navigate and is engaging. There is ample space for students to write answers in the student pages and on the assessments.

#### 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 for Match Fishtank Grade 8 partially meet expectations that materials support teacher learning and understanding of the standards. The materials provide questions that support teachers to deliver quality instruction, and the teacher edition is easy to use, consistently organized, and annotated, and explains the role of grade-level mathematics of the overall mathematics curriculum. The instructional materials do not meet expectations in providing adult level explanations of the more advanced mathematical concepts so that teachers can improve their own knowledge of the subject.

##### Indicator {{'3f' | indicatorName}}
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials for Match Fishtank Grade 8 meet the expectations that materials provide teachers with quality questions for students.

In the materials, Facilitator Notes for each lesson includes questions that are included in Anchor Problem Notes for the teacher to guide students' mathematical development and to elicit students' understanding. The materials indicate that questions provided are intended to provoke thinking and provide facilitation through the mathematical practices as well as getting the students to think through their work. For example:

• Unit 3, Transformations and Angle Relationships, Lesson 3, Anchor Problem and Guiding Questions 3: “How can you answer this question without using a coordinate plane? What are the two pieces of information needed to describe a translation, and how can you see them in the coordinate points? What is the connection between the variables x and y and the movements horizontally and vertically?”
• Unit 4, Functions, Lesson 7, Anchor Problem and Guiding Questions 2: “What inputs does it make sense to use for this function? How many are appropriate to include in your table? Does the rate of change between any two points stay the same, or does it change?”
• Unit 5, Linear Relationships, Lesson 6, Anchor Problem 1 and Guiding Questions: “How did you determine your order without doing any calculations? Discuss your order with a peer. Do you have the same order? How did you each determine your order? Will you change your order based on your conversation? What measurements are important to consider when finding slope? How do you use those measurements to determine slope? Explain how to find the steepness of any staircase that climbs a distance of y feet over a distance of x feet. How does this relate to the concept of slope?”
• Unit 6, Systems of Linear Equations, Lesson 6, Anchor Problem 1 and Guiding Questions : “Do you have an equation that is already solved for either x or y? Why do you need an equation solved for either x or y? How can you rewrite one of the equations to be in this form? Is there more than one way to approach this problem? Which way is the easiest or most efficient?”
##### Indicator {{'3g' | indicatorName}}
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 Match Fishtank Grade 8 meet the expectations for containing a teacher 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 also include teacher guidance on the use of embedded technology to support and enhance student learning.

All lessons include a Tips for Teachers section.  This section provides teachers with resources and an overview of the lesson but provides little guidance on how to present the content. Due to the nature of the materials in a virtual format, there are no concrete student materials. For example:

• In Unit 4, Functions, Lesson 3, Tips for Teachers: “Lessons 3 and 4 focus on functions represented in tables, equations, and verbal descriptions. In Lesson 3, students analyze these representations to make sense of the relationships between the quantities (MP.2). They use their understanding of unit rate and constant of proportionality to determine the rate of change between quantities. They consider what a starting or initial value means in context of a situation, and how to determine these values from a table or equation.”

There is guidance for teachers in the forms of Guiding Questions and Notes for implementing Anchor Problems, Problem Set Guidance, and Target Tasks. Problem Set Guidance sections are optional problem sets with student facing materials. There is no student edition, so guidance for ancillary materials is not needed.

##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials for Match Fishtank Grade 8 do not meet the expectations that materials contain adult-level explanations so that teachers can improve their own knowledge.

There is an Intellectual Prep section which includes suggestions on how to prepare to teach the unit; however, these suggestions do not support teachers in understanding the advanced mathematical concepts.

• The teacher materials include links to teacher resources, but linked resources do not add to teacher understanding of the material.
• The materials list Anchor Problems and Target Tasks and provide answers and sample answers to problems and exercises presented to students; however, there are no adult-level explanations to build understanding of the mathematics in the tasks.
##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials for Match Fishtank Grade 8 meet expectations as they explain the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Each unit opens with a Unit Summary that includes a Lesson Map and a list of grade level standards addressed within the unit along with future connections.
• Each Lesson provides current standards addressed in the lesson.
• Each Lesson provides foundational standards which are standards that were covered in previous units or grades that are important background for the current lesson.
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials for Match Fishtank Grades 8 meet the expectations that materials cross-reference standards and provide a pacing guide.

The Course Summary includes a Pacing Guide. The Pacing Guide does not reference the standards covered but does provide an overview of the number of days expected per Unit. The standards are cross-referenced in multiple places including the Unit Summary at the beginning of each unit that shows the lesson map, vocabulary, standards, mathematical practices, and essential understandings for the Unit. The Lesson provides the objectives, standards, and criteria for success.

##### Indicator {{'3k' | indicatorName}}
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials for Match Fishtank Grades 8 do not contain strategies for informing parents or caregivers about the mathematics program or give suggestions for how they can help support student progress and achievement.

##### Indicator {{'3l' | indicatorName}}
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The instructional materials for Match Fishtank Grade 8 include explanations of the instructional approaches of the program. However, there is no identification of research-based strategies.

The Teacher Tools include several handouts that address the instructional approach of the program. For example, one handout included is “Components of a Math Lesson (Grades 6-12)”. In addition, there are handouts regarding several instructional strategies. For example,  “A Guide to Academic Discourse” and “A Guide to Supporting English Learners” are both provided.  The strategies are not identified as research-based.

#### 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 Match Fishtank Grade 8 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the CCSSM. The instructional materials provide strategies for gathering information about students’ prior knowledge and strategies for teachers to identify and address common student errors and misconceptions. The assessments do not clearly denote which standards are being emphasized.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials for Match Fishtank Grades 8 do not meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

There are no diagnostic, readiness assessments, or tasks to ascertain students' prior knowledge.

##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials for Match Fishtank Grade 8 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

The materials provided notes to provide teacher guidance for the Anchor Problems that addresses common misconceptions. For example:

• Unit 1, Exponents and Scientific Notation, Lesson 5, Anchor Problem 4 states,  “This Anchor Problem targets a common misconception that can happen when students over-apply a rule. They can become confused between when to add and when to multiply. Encourage students to explain the conceptual thinking behind the rule so that the concept stays connected to the procedure or rule.”
• Unit 8, Bivariate Data, Lesson 2 Tips for Teachers states, “A common misconception is to confuse causality with association. For example, students may misunderstand a relationship between two variables to imply that one variable causes another to change, when there is only evidence to show an association between the two variables. As students describe relationships between variables, ensure they use language to imply an association rather than a causal relationship (MP.6).”
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for Match Fishtank Grade 8 meet the expectations for the materials to provide opportunities for on-going review and practice, with feedback, for students in learning both concepts and skills.

Each lesson is designed with teacher-led Anchor Problems, Problem Set Guidance and Target Task. The lessons contain multiple opportunities for practice with an assortment of problems. The Anchor Problems provided the teacher with Guiding Questions and Notes in order to provide feedback for students’ learning. For example:

• Unit 5, Linear Relationships, Lesson 10, Anchor Problem 3, Notes, states,  “As students are playing, listen for how students are proving their matches and how other students express their agreement or disagreement. Ensure students are using appropriate vocabulary and language.”
• Unit 3, Transformations and Angle Relationships, Lesson 5, Anchor Problem 1. The Guiding Questions provided for teachers are designed to lead students to draw conclusions about what happens to the coordinate points of a figure as it is translated over the x- or y- axis. Notes: “Use this Anchor Problem to have students determine what impact reflections over axes have on coordinate points. One approach to using this Anchor Problem could be to have students work in small groups, each group with a different reflected image (like in the Anchor Problem above), and work together to answer the two questions. Then each group could share their findings with the class, observe patterns in the results from each group, and determine a general conclusion (MP.8).”
##### Indicator {{'3p' | indicatorName}}
Materials offer ongoing formative and summative assessments:
##### Indicator {{'3p.i' | indicatorName}}
Assessments clearly denote which standards are being emphasized.

The instructional materials for Match Fishtank Grade 8 meet the expectations for the assessments to clearly denote which standards are being emphasized.

Each unit provides an answer key for the Unit Assessment. The answer key provides each question number and the targeted standard. For example:

• Unit 6, Systems of Linear Equations, Assessment Item 11 correlates with 8.EE.8c.
• Unit 2, Solving One-Variable Equations, Assessment Item 4 correlates with 8.EE.7b.
##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials for Match Fishtank Grade 8 do not meet expectations for materials with assessments that include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each Unit provides a Unit Assessment answer key. The answer key provides the correct answer, limited scoring guidance, and no guidance for teachers to interpret student performance. For example:

• Unit 3, Transformations and Angle Relationships, Assessment question 12 states, in the “Correct Answer and Scoring Guidance”:
• Solution: “21 feet:
• 1 pt for accurate strategy or work shown,
• 1 pt for correct answer.”

There is no evidence of rubrics or guidance for teachers in terms of student performance and suggestions for follow-up.

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

The instructional materials for Match Fishtank Grade 8 do not provide any strategies or resources for students to monitor their own progress.

#### Criterion 3.4: Differentiation

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

The instructional materials for Match Fishtank Grade 8 do not meet expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations and include extension activities for advanced students, but do not present advanced students with opportunities for problem solving and investigation of mathematics at a deeper level. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

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

The instructional materials for Match Fishtank Grade 8 partially meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The Lesson Structure provides support for sequencing instruction. Each lesson includes a list of key skills and concepts that students should practice. The program overview states that the lesson core consists of Anchor Problems that lend better to whole group instruction, small group guided discovery, or both. The Guiding Questions can help scaffold and/or extend on each Anchor Problem but there is no instruction for teachers on how to do this or handle student misconceptions.

It is the teacher‘s discretion to decide how to use the suggestions in the Practice Set Guidance. There is little guidance for the teacher to determine what strategies or materials are provided for scaffolding instruction, how scaffolds are presented, if there is an appropriate mix of problems so all students can find an entry point, and how to identify any large-group misconceptions. The Teacher Tools include a webinar entitled, “ Leveraging Open Education Resources”, but there are no strategies for teachers who struggle to choose and implement the correct materials for each student.

Sequencing and scaffolding are built into each lesson so that teachers pose Anchor Problems with increasing complexity leading to a Target Task. However, if students need additional support, there is no guidance for teachers.

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

The instructional materials for Match Fishtank Grade 8 partially meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

The Tips for Teachers and Anchor Problem Notes include limited strategies to help teachers sequence or scaffold lessons. The notes are concise, such as, "ask students," “encourage students to look closely,” "remind students of a definition," or “point out to students.” For example:

• Unit 2, Solving One-variable Equations, Lesson 3, Anchor Problem 3 Notes read, “Encourage students to look closely at the structure of each equation to understand what is happening and how they may approach the problem efficiently.”
• Unit 4, Functions, Lesson 3, Anchor Problem 2, Notes read, “Ask students how they would determine the unit rate or cost per 1 pound of watermelon in part (a). Or if they were to graph the relationship in part (b), ask students what the graph would look like and where in the graph they would see the unit rate or constant of proportionality.”
##### 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 Match Fishtank, Grade 8 meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

Students engage in tasks throughout lessons in the Anchor Problems, Target Tasks, Problem Set Activities, the 3-Act Math Modeling, and the Mathematics Assessment Project activities all present multiple entry points for students. For example:

• Unit 1, Exponents and Scientific Notation, Lesson 4, Target Task states, “Jake believes that $$30^5/30^4 × 30 = 1$$. Do you agree with Jake? If yes, explain why he is correct. If not, then give the correct answer and an argument to convince Jake that your answer is correct.” This problem requires students to make their own assumptions and simplifications while providing students multiple entry points to begin solving.
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials for Match Fishtank Grade 8 partially meet expectations for suggesting options for support, accommodations, and modifications for English Language Learners and other special populations.

ELL have support to facilitate their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems). The ELL Design is highlighted in the Teaching Tools document, “A Guide to Supporting English Learners”, which includes strategies that are appropriate for all, but no other specific group of learners. There are no general statements about ELL students and other special populations within the units or lessons.

Specific strategies for support, accommodations, and/or modifications are mentioned in "A Guide to Supporting English Learner" that include sensory, graphic, and interactive scaffolding; oral language protocols which include many cooperative learning strategies, some of which mentioned in Teacher Notes; and using graphic organizers with focus on lighter or heavier scaffolding. For example, Oral Language Protocols provide structured routines to allow students to master opportunities and acquire academic language. Several structures are provided with an explanation on ways to incorporate them that include Turn and Talk, Simultaneous Round Table, Rally Coach, Talking Chips, Number Heads Together, and Take a Stand. Ways to adapt the lessons or suggestions to incorporate them are not included within lessons, units, or summaries.

There is no support for special populations.

##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials reviewed for Match Fishtank Grade 8 do not meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

There are limited notes/guidance in the instructional materials that provide strategies for advanced students.

##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for Match Fishtank Grade 8 meet the expectations that materials provide a balanced portrayal of various demographic and personal characteristics. For example:

• Different cultural names and situations are represented in the materials, ie., Lewis, Mari, Lucas, Juan, and Kristina.
• The materials avoid pronouns, referencing a role instead, ie., the manager, a taxicab driver, a scientist, the basketball team.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials for Match Fishtank Grades 8 provide limited opportunities for teachers to use a variety of grouping strategies.

"The Guide to Supporting English Learners" provides cooperative learning and grouping strategies which can be used with all students. However, there are very few strategies mentioned in the instructional materials.  There are no directions or examples provided for teachers to adapt the lessons or suggestions on when and how to incorporate them. For example:

• In Unit 4, Functions, Lesson 2 states, “This is a good opportunity for students to engage in conversation in small groups or pairs first, and then to bring those ideas to a larger whole class discussion. Use the Guiding Questions to guide the conversation. Ask students to rephrase in their own words what they hear their peers saying. Ask students if they agree with others’ ideas and why or why not.”
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials for Match Fishtank Grades 8 do not encourage teachers to draw upon home language and culture to facilitate learning.

Materials do not encourage teachers to draw upon home language and culture to facilitate learning although strategies are suggested in "The Guide to Supporting English Learners" found at the Teacher Tools link.

#### Criterion 3.5: Technology

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 Match Fishtank Grade 8 integrate technology in ways that engage students in the mathematics; are web-­based and compatible with multiple internet browsers; include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology; are intended to be easily customized for individual learners; and do not include technology that provides opportunities for teachers and/or students to collaborate with each other.

##### 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 Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

Digital materials reviewed for Math Fishtank Grade 8, are included as part of the core materials.  They are web-­based and compatible with multiple internet browsers, e.g., Internet Explorer, Firefox, Google Chrome, Safari, etc. In addition, materials are “platform neutral,” i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform. Materials allow for the use of tablets and mobile devices including iPads, laptops, Chromebooks, MacBooks, and other devices that connect to the internet with an applicable browser.

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

The materials reviewed for Math Fishtank Grade 8 do not  include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology.

##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials reviewed for Match Fishtank Grade 8 do not include opportunities for teachers to personalize learning, including the use of adaptive technologies.

The instructional materials reviewed for Match Fishtank Grade 8 are not customizable for individual learners or users. Suggestions and methods of customization are not provided.

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 Match Fishtank Grade 8 incorporate technology that provides opportunities for teachers and/or students to collaborate with each other.

Students and teachers have the opportunity to collaborate using the applets that are integrated into the lessons during activities.

##### 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 Match Fishtank Grade 8 integrate technology including interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the MPs.

Anchor Problems, Problem Set Guidance activities, and Target Tasks can be assigned to small groups or individuals. These activities consistently combine MPs and content.

Teachers and students have access to math tools and virtual manipulatives within a given activity or task, when appropriate. These links are designed using GeoGebra, Desmos, and other independent resources. For example:

• Unit 3, Transformations and Angle Relationships,  Lesson 2: Students have opportunities to use the GeoGebra applet to create translated figures in the coordinate plane.
• Unit 7, Pythagorean Theorem and Volume, Lesson 12: Students use a Desmos applet to find the distance between points in the coordinate plane using the Pythagorean Theorem.

## Report Overview

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

#### Math 3-5

The instructional materials reviewed for Match Fishtank Grades 3-5 meet the expectations for alignment. The assessments at all grade levels are focused on grade-level standards, the materials devote at least 65% of class time to major clusters of the grade, and all grades are coherent and consistent with the standards. Grades 3-5 meet expectations for Gateway 2, rigor and mathematical practices. The lessons include conceptual understanding, fluency and procedures, and application, and there is a balance of these aspects for rigor. The Standards for Mathematical Practice (MPs) are identified, used to enrich the learning, and meet the full intent of all eight MPs. Grades 3-5 partially meet the criteria for usability. The materials meet expectations for Use and Design to Facilitate Student Learning, and partially meet exceptions for Planning and Support for Teachers, Assessment, and Differentiation.

###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations

#### Math 6-8

The instructional materials reviewed for Match Fishtank Grades 6-8 meet the expectations for alignment. The assessments at all grade levels are focused on grade-level standards, the materials devote at least 65% of class time to major clusters of the grade, and all grades are coherent and consistent with the standards. Grades 6-8 meet expectations for Gateway 2, rigor and mathematical practices. The lessons include conceptual understanding, fluency and procedures, and application, and there is a balance of these aspects for rigor. The Standards for Mathematical Practice (MPs) are identified, used to enrich the learning, and meet the full intent of all eight MPs. Grades 6-8 partially meet the criteria for usability. The materials meet expectations for Use and Design to Facilitate Student Learning, and partially meet exceptions for Planning and Support for Teachers, Assessment, and Differentiation.

###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Partially Meets Expectations

## Report for {{ report.grade.shortname }}

### Overall Summary

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