 ## 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 7 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 7 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 7 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 PDF documents.

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

• Unit 1 Test, Question 6, “In the morning, a farm worker packed 3 pints of strawberries every 4 minutes. In the afternoon, she packed 2 pints of strawberries every 3 minutes. What was the difference between her morning and afternoon packing rates, in pints per hour? Show your work clearly.” (7.RP.1)
• Unit 2 Test, Question 3, “Which expression is equivalent to 4 - (-7)? Answer choices: a. 7 + 4, b. 4 - 7, c. -7 - 4, d. - 4 + 7.” (7.NS.1.c)
• Unit 3 Test, Question 7, “Find the value of the algebraic expression when $$a=-1$$ and $$b=2$$.”  (7.NS.3)
• Unit 5 Test, Question 5, “A museum opened at 8:00am. In the first hour, 350 people purchased admission tickets. In the second hour, 20% more people purchased admission tickets than in the first hour. Each admission ticket cost 17.50. What is the total amount of money paid for all the tickets purchased in the first two hours?” (7.EE.3). • Unit 8 Test, Question 10, “Dana has 8 baseball cards, 10 football cards, 4 hockey cards, and 14 basketball cards. All the cards are the same size and shape. Dana will select one card at random. What is the probability that the card selected will be a hockey card? Show all of your work.” (7.SP.1) #### 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 7 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 7 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 chapters (units, modules, topics, etc) devoted to major work of the grade (including assessments and supporting work connected to the major work) is six out of eight units, which is approximately 75%. • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 104 out of 117, which is approximately 89%. • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 115 out of 143, which is approximately 80%. 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 89% 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 7 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 7 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 6, Geometry, Lesson 4, 7.G.5 supports 7.RP.2 as students connect finding the unknown angle measurement using proportional relationships. Anchor Problem 2 is as follows: “Two lines meet at a point that is also the endpoint of two rays. Questions: 1. Describe the angle relationships you see in the diagram. 2. Set up and solve an equation to find the value of x. 3. Find the measurements of ∠BAC and BAH.” • Unit 7, Statistics, Lesson 4, Target Task, supporting standards 7.SP.B connect to major cluster standards 7.NS.A to meet the lesson objective: analyze data sets using measures of center and interquartile range. The Target Task is as follows: “While waiting for their bus to arrive after school one day, 10 students wondered how many baskets from the free-throw line they could each make in 5 minutes. Each student took his or her turn. The results are: 14, 8, 12, 6, 20, 26, 9, 6, 11, 12. Questions: a. Find the mean and median number of baskets made by the students. b. Which measure of center better represents the typical number of baskets made? c. Ten players on the co-ed basketball team determined the number of baskets he or she could make from the free-throw line in 5 minutes. The interquartile range of their data set was 3. Which data set has the greater variability?” • Unit 7, Statistics, Lesson 7 connects 7.SP.A and 7.RP.A when representing sample spaces for compound events connects to analyzing proportional events in real-world problems. Anchor Problem 1: “Akilah is running for seventh grade class president. There are 100 students in the seventh grade at her school. To better understand her chances of winning, Akilah asks a random sample of 20 seventh graders if they plan to vote for her. In her sample, 12 of the 20 students said they planned to vote for her. Akilah asks several friends to also ask a random sample of 20 students. Together, they combine their results to get a better understanding of her chances of winning. After winning the election, Akilah finds out that 55 out of the 100 seventh graders at her school voted for her. Using the situation above, define and describe the following terms: sample, population, sample population, population proportion, sample distribution.” • Unit 8, Probability, Lesson 2 connects 7.SP.C and 7.RP.A as students define probability and sample space, and estimate probabilities from experimental data. Anchor Problem 2 is as follows: “A spinner with different colors on it was spun 20 times. The data recording the color of each spin is shown below. Questions: “a. What is the sample space of the spinner? b. Does it seem that each color is equally likely? Explain your reasoning. c. Estimate the probability of spinning each color on the spinner.” ##### 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 7 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: • 117 lesson days • 18 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 • 5 - 10 minutes Target Task ##### 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 7 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, Proportional Relationships, the Unit Plan Summary is as follows: “In sixth grade, students were introduced to the concept of ratios and rates. They learned several strategies to represent ratios and to solve problems, including using concrete drawings, double number lines, tables, tape diagrams, and graphs. They defined and found unit rates and applied this to measurement conversion problems. Seventh grade students will draw on these conceptual understandings to fully understand proportional relationships. In seventh grade, all of these skills and concepts come together as students now operate with all rational numbers, including negative numbers. By the time students enter eighth grade, students should have a strong grasp on operating with rational numbers, which will be an underlying skill in many algebraic concepts. In eighth grade, students are introduced to irrational numbers, rounding out their understanding of the real number system before learning about complex numbers in high school.” Foundational Standards identified: 6.RP.1-3, 6.NS.1, 6.EE.7 & 9, and 5.NF.6; while Future Standards listed are 8.EE.5 & 6, and 8.F.1-5. • Unit 2, Operations With Rational Numbers, the Unit Plan Summary states the following: “Starting in first grade, students learn about the commutative and associative properties of addition, and the relationship between addition and subtraction. In third grade, students extend their understanding of the properties of operations to include multiplication and the distributive property.” Additionally, the Unit Summary connects grade-level concepts to current and future standards. An example is located in Unit 2, Lesson 16, the lesson objective is: compare and order rational numbers, and write and interpret inequalities to describe the order of rational numbers. (7.NS.1 and foundational standard 6.NS.7) In Unit 3: Numerical and Algebraic Expressions identifies Foundational Standards from: Expressions and Equations 6.EE.2, 6.EE.2.c, 6.EE.3, 6.EE.4, The Number System, 7.NS.1, 7.NS.2 Future Connections identified include: Geometry 7.G.4, 7.G.5, 7.G.6, Expressions and Equations 8.EE.7, 8.EE.8, 7.EE.4. • Unit 5, Percents and Scaling, the Unit Plan Summary states the following: “These standards are foundational to this seventh-grade unit, and the first four lessons in this unit incorporate these concepts and skills. In eighth grade, students will refine their understanding of scale and scale drawings when they study dilations in their transformations unit. They will define similar figures and use dilations and other transformations to prove that two images are similar or scale drawings of one another.” • Unit 5, Percents and Scaling, the Unit Plan Summary states the following: “In sixth grade, students learned several strategies to solve ratio and rate problems, including tables, tape diagrams, double number lines, and equations. They also defined percent as a rate per 100 and solved percent problems to find the whole, part, or percent.” The lessons also include connections between grade-level work, standards from earlier grades, and future knowledge. For example: • Unit 1, Proportional Relationships, Lesson 1, “This lesson approaches standards 7.RP.1 and 7.RP.2 by reviewing concepts and skills from 6th grade standards in the Ratios and Proportions domain. These standards are foundational to this 7th grade unit, and will support students in later lessons.” • Unit 6, Geometry, Lesson 1, “Students studied angles in fourth grade, where they recognized angles as shapes formed when two rays share a common endpoint. They understood that angle measures are additive, and they solved addition and subtraction problems to find missing angles. In this lesson, students formally define complementary and supplementary angles, and they start to develop their understanding of angle relationships and how they can represent these relationships using equations.” • For each unit in Grade 7, the Unit Summary connects the current grade-level skills to prior and future grade-level standards. The Unit 3 Numerical and Algebraic Expressions Unit Summary states that, “In sixth grade, students learned how the same rules that govern arithmetic also apply to algebraic expressions. They learned to expand and factor expressions using the distributive property, and they combined terms where variables are the same. With new knowledge of the number system, students go from working with expressions like 5(6x+3y) in sixth grade to those with rational numbers such as -(a+b) - 3/2(a - b) in the seventh grade.The next seventh-grade unit, Unit 4, Equations and Inequalities, will continue to engage students in working with expressions with rational numbers. In eighth grade, students will work with expressions and equations in one variable and two variables, solving single linear equations and systems of linear equations. Throughout all of their future work with expressions, students’ ability to look for and make use of the structure in expressions will be as important as their ability to work with them procedurally.” 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. Target Tasks can be used as an indicator of student understanding or mastery of the Objective. For example: • Unit 1, Proportional Relationships, Lesson 7, Anchor Problem 1 states, “In a video game, for every 3 coins you collect, you earn 4 points. a. Create a table of values to represent the relationship, b. Graph the relationship c. Determine the equation that represents the relationship.” (7.RP.2) • Unit 5, Percent and Scaling, Lesson 3, the Target Task states, “At the Blackman High school, 86 seniors submitted college applications for early decision. This represented approximately 34% of the senior class. The Truman High School, across town from the Blackman High School, has 266 seniors. Which high school has the larger senior class?” (7.RP.3) • Unit 3: Numerical and Algebraic Expressions, Lesson 6, the Target Task states, “Two expressions are given below. Expression A: 5q - r Expression B: -2q + 3r - 4, a. Write a simplified expression that represents A + B. b. Write a simplified expression that represents A - B.” (7.EE.1) • Unit 5, Percent and Scaling, Lesson 10, Anchor Problem 3 states, “Tyler bought two tickets to a basketball game on the website Game Finder. Each ticket cost65, and the website charged a convenience fee that was a small percent of the ticket cost. If Tyler’s total bill came to $132.60, what percent was the convenience fee?” (7.RP.3) ##### 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 7 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 7 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, Proportional Relationships, Lesson 4, the Objective states, “Write equations for proportional relationships presented in tables” connects with the major cluster of analyze proportional relationships and use them to solve real-world and mathematical problems (7.RP.A) • Unit 2, Operations with Rational Numbers, Lesson 3, the Objective states, “Describe situations in which opposite quantities combine to make zero.” (7.NS.A) • Unit 3, Numerical and Algebraic Expressions, Lesson 10, the Objective states, “Solve multi-step, real-world problems with rational numbers.” (7.EE.B) • Unit 4, Equations and Inequalities, Lesson 7, the Objective states, “Model with equations in the form px+q=r and p(x+q)=r” connects with the major cluster solve real-life and mathematical problems using numerical and algebraic expressions and equations.” (7.EE.B) • Unit 8, Probability, Lesson 4, the Objective states, “Use probability to predict long-run frequencies.” (7.SP.C) 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 1, Proportional Relationships, Lesson 11, Anchor Problem 1, 7.RP.1 connects with 7.NS.3 as students solve real-world problems involving the four operations with rational numbers. The Anchor Problem states, “A proportional relationship is shown in the graph. a. Describe a situation that could be represented by this graph. b. Write an equation for the relationship. Explain what each part of the equation represents.” • Unit 1, Proportional Relationships, Lesson 16, 7.RP.A and 7.EE.A are connected as students use their understanding of proportional relationships and equations in ratio and rate problems by setting up a proportion, including part-part-whole problems. For example, the Target Task states, “The table below shows the combination of dry prepackaged mix and water to make concrete. The mix says for every 1 gallon of water, stir 60 pounds of dry mix. We know that 1 gallon of water is equal to 8 pounds of water. Using the information in the table, complete the remaining parts.” • Unit 3, Numerical and Algebraic Expressions, Lesson 7 connects 7.NS.A and 7.EE.A when students simplify algebraic expressions that include rational numbers. Anchor Problem 2 states, “Which expressions below are equivalent to 4 - 3(6x - 3)? Select all that apply.” Answer choices “ a. ( 4 - 18) x + 9 b. (4 + 9) - 18x c. 4 - (18x - 9) d. 4 - 18x - 3 e. 4 - 18x + 9 f. 6x - 3.” • Unit 3, Numerical and Algebraic Expressions, Lesson 2, connects 7.NS.3 and 7.EE.1 as students apply properties of operations while solving real world problems with rational numbers. Anchor Problem 2 states, “Write an expression for each sequence of operations. 1: Add 3 to x, subtract the result from 1, then double what you have. Expression 2: Add 3 to x, double what you have, then subtract 1 from the result.” • Unit 3, Numerical and Algebraic Expressions, Lesson 10 connects 7.NS.C and 7.EE.C when students solve real world problems using positive and negative rational numbers. Anchor Problem 1 states, “Below is a table showing the number of hits and the number of times at bat for two Major League Baseball players during two different seasons. A player’s batting average is the fraction of times at bat when the player gets a hit. Who has the better batting average? Justify your answer.” • Unit 5, Percent and Scaling, Lesson 3 connects 7.RP.A and 7.NS.A as students find the whole given a part and percent. Anchor Problem 1 states, “At the Kennedy Middle School, 280 students attended the end-of-year carnival, representing 80% of the students in the school. a. Draw a visual representation of the problem. For example, you could draw a tape diagram or a double number line. b. Determine how many students are at the Kennedy Middle School. Choose any strategy. c. Find a peer who used a different strategy to solve than you did. Compare and discuss your strategies and solution.” • Unit 5, Percent and Scaling, Lesson 5, Anchor Problem 2 connects 7.EE.2 and 7.RP.3 as students use proportional relationships to solve percentage problems and rewrite the expression in different forms. Anchor Problem 2 states, “On Sunday, 1,460 customers shopped at Pine Village Bookstore. On Monday, there were 60% fewer customers at the bookstore. Draw a diagram and use it to solve. Explain your reasoning.” • Unit 6, Geometry, Lesson 12 connects 7.G.A and 7.G.B as students draw geometric shapes based on angles. Anchor Problem 4 states, “A triangle has an angle measure of 50º. The two side lengths that form this triangle are 3 inches and 4 1\2inches long. Draw the triangle described above. Then determine the measure of the third side and the other two angles.” ###### Overview of Gateway 2 ### Rigor & Mathematical Practices The instructional materials for Match Fishtank Grade 7 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 7 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 7 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 (7.NS.A, and 7.EE). For example: • Unit 2, Operations with Rational Numbers, Lesson 1, in Anchor Problem 3 , students develop conceptual understanding of rational numbers by representing integers on a number line with arrows and use the length of the arrows to understand absolute value. The number line is used to model addition and subtraction with integers to help develop the concept visually: “Jessica says she’s thinking of two numbers. They are 24 units apart on the number line, and they are opposites. What are the two numbers?” (7.NS.1) • Unit 2, Operations with Rational Numbers, Lesson 5, the Anchor problems continue to guide students to understanding the addition of rational numbers by modeling traveling along a number line. Given several contextual problems, students are asked to model situations and them to explain what happens. One problems states, “Joshua travels 5 miles west and then 2 miles west, represented by the equation: -5 + (-2) = -7. a) Model this situation on the number line using arrows and explain what each term in the equation represents in the context. b) Explain, using the context of the situation, why adding two negative integers will always give you a smaller negative integer.” (7.NS.1.b and 7.NS.1.d) • Unit 3, Numerical and Algebraic Expressions, Lesson 2, Anchor Problem 1 presents the expressions “$$a^2-b$$ and (2ab).” Students determine “Is the expression greater when a = -1 and b = 1 or when a = 1 and b = -1?(7.NS.3 and 7.EE.1) • Unit 3, Numerical and Algebraic Expressions, Lesson 2, Anchor Problem 2 states, “Write an expression for each sequence of operations: Expression 1: Add 3 to x, subtract the result from 1, then double what you have. Expression 2: Add 3 to x, double what you have, then subtract 1 from the result.” “Evaluate each expression for x = 2” develops conceptual understanding through the Guiding Questions: “What part of both expressions will be the same? What part of each expression will be different? What role do parentheses play in these expressions? Are the two expressions equivalent? How do you know?” (7.NS.3 and 7.EE.A) • Unit 3, Numerical and Algebraic Expressions, Lesson 6, Anchor Problem 2 states, “Subtract: (3x + 5y − 4) − (4x + 11).” The Guiding Question helps develop conceptual understanding. Guiding Question states: “How can you rewrite the problem without parentheses?” (7.EE.1) • Unit 3, Numerical and Algebraic Expressions, Lesson 9, Anchor Problem 2, students develop conceptual understanding by using area models to learn how to write expressions: “A square fountain area with side length feet is bordered by a single row of square tiles as shown. What are three different ways to represent the number of tiles needed for the border? Show each representation using the diagram.” (7.EE.2) • Unit 5, Percent and Scaling, Lesson 2, Anchor Problem 2 states the following: “According to the U.S. Environmental Protection Agency, in 2013, people in the United States produced about 254 million tons of trash. Approximately 34.3% of this trash was recycled or composted. About how many million tons of trash were recycled or composted in 2013?” Conceptual understanding of the relationship between percent, part and whole is developed through the Guiding Questions: “Make an estimate of the amount of trash that was recycled or composted. What is the part, percent, and whole in the situation? What would a visual representation of this situation look like? What strategy will you use to solve this problem? Compare your solution to your estimate. Does it seem reasonable?” (7.RP.3 and 7.NS.3) • Unit 6, Geometry, Lesson 10, Anchor Problem 1, students develop conceptual understanding as they use the formula for the area of the circle: "The circumference of a circle is 24π cm. What is the exact area of the circle? Draw a diagram to assist you in solving the problem." (7.G.4) Grade 7 materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. These can include problems from Open Up Resources Grade 6-8 Mathematics, Open Middle, Illustrative Mathematics, EngageNY, Great Minds, and others. For example: • Unit 1, Proportional Relationships, Lesson 5, Problem Set Guidance: (Open Up Resources Grade 7 Unit 2 Practice Problems, Lesson 5, Problem 2): Students independently develop conceptual understanding of equivalent ratios: “In one version of a trail mix, there are 3 cups of peanuts mixed with 2 cups of raisins. In another version of trail mix, there are 4.5 cups of peanuts mixed with 3 cups of raisins. Are the ratios equivalent for the two mixes? Explain your reasoning.” (7.RP.2) • Unit 2, Operations with Rational Numbers, Lesson 3, Target Task, students are shown how positive and negative numbers relate to zero on a number line by combining opposite quantities. An example is as follows: “Rami leaves his house to drive to school. After driving west for 8 3/4 miles, he realizes that he forgot his backpack at home. How far and in what direction does Rami have to travel to get back to his house? Represent the situation on a number line, including labels for Rami’s house and school, and arrows to show his trips.” (7.NS.1) • Unit 2, Operations with Rational Numbers, Lesson 4, Target Task, students use number lines to build their understanding by finding the solution and graphing it on a number line: “Represent each addition problem on a number line and find each sum. Then choose one problem and write a real-world situation that could be modeled by the problem." (7.NS.1.b and 7.NS.1.d) • Unit 3, Numerical and Algebraic Expressions, Lesson 4, Target Task, students simplify expressions by combining like terms with both integer and rational coefficients, as well as with two variables. An example is as follows: “The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use a diagram if needed.” (7.EE.1) • Unit 8, Probability, Lesson 2, Target Task, students are asked to independently demonstrate conceptual understanding of experimental vs theoretical probability in the following scenario. “Each of the 20 students in Mr. Anderson’s class flipped a coin ten times and recorded how many times it came out heads. a. How many heads do you think you will see out of ten tosses? b. Would it surprise you to see 4 heads out of ten tosses? Explain why or why not. c. Here are the results for the twenty students in Mr. Anderson’s class. Use this data to estimate the probability of observing 4, 5, or 6 heads in ten tosses of the coin. (It might help to organize the data in a table or in a dot plot first.”) (7.SP.6) ##### 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 7 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 teachers 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 (7.NS.A, 7.EE.1, 7.EE.4a). For example: • Unit 2, Operations With Rational Numbers, Lesson 16, Anchor Problem 2, students convert rational numbers to decimals using long division, “Write each decimal as a fraction.” Answer choices: a. 0.35; b. 1.64; c. 2.09; d. -3.125. (7.NS.2.d) • Unit 3, Numerical and Algebraic Expressions, Lesson 6, Anchor Problem 2, students apply properties of operations as strategies to add, subtract, and expand linear expressions with rational coefficients, “Subtract: (3x + 5y − 4) − (4x + 11).” (7.EE.1) • Unit 4, Equations and Inequalities, Lesson 4, Anchor Problem 3, students solve equations in the forms px + q = r and p(x + q) = r algebraically, “Solve the equations. Answer choices: a. 12(x - 2) = 72 b. -1/3(x) + 4 = -2 c. 5.6 - 2p = 13.” Guiding questions are as follows: “What operation will you undo in each equation first? How do you know that you are maintaining balance in each step you take? How can you check your answer at the end to make sure it is a solution?” (7.EE.4.a). • Unit 4, Equations and Inequalities, Lesson 5 includes a MARS Formative Assessment Lessons for Grade 7 Solving Linear Equations. An example is as follows: “The numbers 5, 6 and 7 are an example of consecutive numbers, as one number comes after another. Another three consecutive numbers are added together so that the first number, plus two times the second number, plus three times the third number gives the total. Which of these expressions could represent the total? Check all that apply. Answer choices: Total = x + 2x + 3x; Total = x + 2x + 2 + 3x + 6; Total = x + 2(x +1) + 3 (x + 2); Total = x + (2x + 1) + (3x + 2). Explain your answer.” (7.EE.3 and 7.EE.4.a) 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, and EngageNY, Great Minds. For example: • Unit 2, Operations with Rational Numbers, Lesson 6, in Target Task, Problem 2, students have the opportunity to independently demonstrate procedural skills in addition of rational numbers . They are asked to, “Find the sums. a. -3 + (-2 1/4); b. 5.7 + (-12.2); c. -9 + 3 2/5 ; d. -10/3 + 18; e. -2 + 3 + (-1) + 5.” (7.NS.1.d) • Unit 2, Operations With Rational Numbers, Lesson 9, students use the same procedure for adding and subtracting signed rational numbers as they do when adding and subtracting integers. For example, Anchor Problem 2 states, “Find each sum or difference.” Answer choices: a. - 40 2/3 - 8 1/2; b. -9.08 + 16.52 ; c. 52 + (-15) (7.NS.1.b and 7.NS.1.c) • Unit 4, Equations and Inequalities, Lesson 7, students use the distributive property to organize information in word problems in order to write and solve equations. For example, Target Task states, “A batch of 8 cookie ice cream sandwiches weighs 1,092 grams. On average, each cookie weighs 12 grams, and the same amount of ice cream is used for each sandwich. A pint of ice cream has approximately 450–460 grams of ice cream. How many pints of ice cream would you need to make another batch of 8 cookie ice cream sandwiches?” (7.EE.3 and 7.EE.4a) • Unit 4, Equations and Inequalities, Lesson 10, in the Target Task, students are given the opportunity to independently demonstrate procedural skills in solving inequalities: “Match each inequality to one of the solutions. Justify that your solution is correctly matched to your inequality. Inequalities: -10 - 6x > 26; -10 + 6x > 46. Solutions: x > -6; x > 6; x < -6; x < 6” (7.EE.4.b) • Unit 8, Probability, Lesson 1, students use probability to describe impossible, unlikely, equally likely or unlikely, likely, or certain. Problem Set Guidance suggests the following: “Decide where each event would be located on the scale above. Place the letter for each event in the appropriate place on the probability scale. Answer choices, a. You will see a live dinosaur on the way home from school today. b. A solid rock dropped in the water will sink. c. A round disk with one side red and the other side yellow will land yellow side up when flipped. d. A spinner with four equal parts numbered 1–4 will land on the 4 on the next spin. e. Your full name will be drawn when a full name is selected randomly from a bag containing the full names of all of the students in your class. f. A red cube will be drawn when a cube is selected from a bag that has five blue cubes and five red cubes. g. Tomorrow the temperature outside will be −250 degrees.” (7.SP.7.a) ##### 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 7 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 (7.RP.A, 7.NS.3, 7.EE.3). 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, Illustrative Mathematics, EngageNY, Great Minds, and others. Examples of routine application include, but are not limited to: • Unit 1, Proportional Relationships, Lesson 18, in Problem Set Guidance (Illustrative Mathematics, Cider Versus Juice - Variation 2), students apply knowledge of solving multi-step problems with rational numbers to solving problems with ratios, rates, and unit rates. Students are given a picture of a gallon size juice and a box of juice with prices, “Assuming you like juice and cider equally, which product is the better deal? Suppose the juice boxes go on sale for$1.79 for the eight 4.23-ounce juice boxes, and the cider goes on sale for $6.50 per gallon. Does this change your decision?” (7.RP.1 and 7.RP.3) • Unit 3, Numerical and Algebraic Expressions, Lesson 2, Anchor Problem 3, students write and evaluate expressions for mathematical and contextual situations. For example, “Three friends went to the movies. Each purchased a medium-sized popcorn for p dollars and a small soft drink for d dollars. The friends paid together with two twenty-dollar bills. a) Write an expression to represent the amount of money the friends get back in change after paying for their snacks. b) How much change will the friends get back if the concession stand charges$6.50 for a medium-sized popcorn and $4.00 for a small soft drink? (7.NS.3, 7.EE.1) • Unit 4, Equations and Inequalities, Lesson 5, in the Target Task, students apply knowledge of solving equations using a real-world context: “Mrs. Canale’s class is selling frozen pizzas to earn money for a field trip. For every pizza sold, the class makes$5.35. They have already earned $182.90, but they need$750. How many more pizzas must they sell to earn $750?” (7.EE.3 and 7.EE.4) • Unit 5, Percent and Scaling, Lesson 10, Anchor Problem 3, students solve percent applications involving simple interest, commissions, and other fees. For example, “Tyler bought two tickets to a basketball game on the website Game Finder. Each ticket cost$65, and the website charged a convenience fee that was a small percent of the ticket cost. If Tyler’s total bill came to $132.60, what percent was the convenience fee?” (7.RP.3) Examples of non-routine application include, but are not limited to: • Unit 1, Proportional Relationships, Lesson 12, Target Task, students use different strategies to represent and recognize proportional relationships. For example, “Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If k represents the number of kilometers and m represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why. a) Oscar wrote the equation k = 1.6m, and he said that the unit rate 1.6/1 represents kilometers per mile. b) Maria wrote the equation k = 0.625m, and she said that the unit rate 0.625 represents kilometers per mile. ‘Sketch a graph that represents the correct proportional relationship between kilometers and miles.” (7.RP.1.2.A, 7.RP.1.2.B, 7.RP.1.2.C, 7.RP.1.2.D) • Unit 4, Equations and Inequalities, Lesson 5, students solve word problems using equations in the form px + q = r and P (x + q) = r,. Each of the Anchor Problems is presented in a real-world or mathematical context. Anchor Problem 1 states, “At the candy store, M&Ms and Skittles are sold for$0.50 per ounce. Kevita puts some M&Ms in a bag and then added 8 ounces of Skittles. The total cost for her bag of candy is $6.50. Kevita and Mary write the equation 0.5(x + 8) = 6.50 to represent the situation, where x represents the number of ounces of M&Ms. Kevita says that to solve this equation, you first distribute the 0.5 through the parentheses to get 0.5x + 4 = 6.50. Mary says that to solve this equation, you first divide by 0.5 on both sides to get x + 8 = 13. .Do you agree with either Kevita or Mary? Why? Finish solving the problem to find out how many ounces of M&Ms Kevita put in her bag of candy.” (7.EE.3 and 7.EE.4.A) The instructional materials for Grade 7 provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. For example: • Unit 1, Proportional Relationships, Lesson 5, Anchor Problem 1, students write equations for proportional relationships from word problems. For example, “A repair technician replaces cracked screens on phones. He can replace 5 screens in 3 hours. a) Write an equation you can use to determine how long it takes to replace any number of screens. b) Write an equation you can use to determine how many screens can be replaced in a certain number of hours. c ) Use one of your equations to determine how long it would take to replace 30 screens. d) Use one of your equations to determine how many screens could be replaced in 12 hours.” (7.RP.1.2, 7.RP.1.2.C) • Unit 2, Operations with Rational Numbers, Lesson 18, Anchor Problem 2 gives students the opportunity to use mathematics in carpentry. Anchor Problem 2 states, “Michael’s father bought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal lengths for his shelves. a)The saw blade that Michael will use to cut the board will change the length of the board by -0.125 inches for each cut. How will this affect the total length of the board? b) After making his cuts, what will the exact length, in inches, of each shelf be?” (7.NS.3) • Unit 4, Equations and Inequalities, Lesson 12, Anchor Problem 1, gives students the opportunity to use mathematics with food. 3-Act Math Task Sweet Snacks. “Show Act 1 video. Ask, ‘What do you notice? What do you wonder?’ Show Act 2 video. Ask, ‘What new information do you have? What different combinations of Teddy Grahams and Circus Animals can he buy with$20? How many combinations can you find?’  Show Act 3 - the solution. Ask, ‘how many of the combinations shown did you find? Which combinations did you find that are not shown in the solution video? Are there other combinations that work?” (7.EE.3 and 7.EE.4.A)
• Unit 5, Percent and Scaling, Lesson 5, Anchor Problem 2 gives students the opportunity to use mathematics in a restaurant. Anchor Problem 2 states,  “A restaurant raises its prices by 10% to account for rising prices of supplies and ingredients. The restaurant’s signature pasta dish costs $14 before the price increase. What is the new price of the pasta dish?” a. Solve this problem using any strategy. b. Mariam solves this problem by finding 110% of$14. Explain why Mariam’s strategy is correct. How does this strategy compare to yours?” (7.RP.1.3, 7.EE.1.2)
##### 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 7 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 4, Equations and Inequalities, Lesson 3, Anchor Problem 1, students develop conceptual understanding as they work in groups to solve equations and inequalities. Anchor Problem 1 states, “Divide students into five to seven groups, and give each group the introduction and one of the scenarios below. In each group, students should: a) Represent the scenario with a tape diagram and equation. b) Collaborate on a sequence of operations to find the solution.” Problem Introduction, “The Sanchez family just got back from a family vacation. Jon and Ava are summarizing some of the expenses from their family vacation for themselves and their three children, Louie, Missy, and Bonnie.” A chart with the costs of various items is included chart. “Students are given various scenarios. “Scenario 1: During one rainy day on the vacation, the entire family decided to go watch a matinee movie in the morning and a drive-in movie in the evening. The price for a matinee movie in the morning is different than the cost of a drive-in movie in the evening. The tickets for the matinee movie cost $6 each. How much did each person spend that day on movie tickets if the ticket cost for each family member was the same? What was the cost for a ticket for the drive-in movie in the evening? Scenario 2: For dinner one night, the family went to the local pizza parlor. The cost of a soda was$3. If each member of the family had a soda and one slice of pizza, how much did one slice of pizza cost? They summarize the information in a chart and are asked the following questions: “ 1. Determine the cost of 1 airplane ticket, 2 nights at the motel, and 1 evening movie.  2. Determine the cost of 1 t-shirt, 1 ticket to a baseball game, and 2 days of the rental car.” (7.EE.3 & 7.EE.4.a)
• Unit 2, Operations with Rational Numbers, Lesson 9, Anchor Problem 2, students use procedural skills and fluency to “Find each sum or difference. Rewrite subtraction problems into addition problems or use a number line as needed. a. 18 1/5 − (−5),  b.  −40 2/3 − 8 1/2,  c. −9.08+16.52,  d.  −6−(−12),  e. −11 1/6−(−3), f. 52+(−15),  g. -36.125 + (-14.6)” (7.NS.1.c & 7.NS.1.d)
• Unit 5, Percent and Scaling, Lesson 2, Anchor Problem 1, students apply their knowledge of mathematics to solve: “In a school election, 60 students voted for the next student body president. Aliyah won 45% of the votes. a. Draw a visual representation of the problem. For example, you could draw a tape diagram or a double number line.   b. Determine how many votes Aliyah won. Choose one of the following strategies: table, percent equation, proportion.” (7.RP.3, 7.NS.3)

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 2, Operations with Rational Numbers, students build conceptual understanding of adding integers and apply in real-world problems.  Students analyze a number line and are prompted to use a number line in the exercises. For example, Lesson 6, Anchor Problem 3 states,  “The temperature of water in a lake at 9:00 a.m. is -2.6˚C. By noon, the temperature of the water rises by 5.1˚C. By 9:00 p.m., the temperature of the water falls by 12.8˚C from what it had been at noon. Write an addition problem to represent the changing temperature of the water, and find the temperature of the water at 9:00 p.m.” (7.NS.1.b & 7.NS.1.d)
• Unit 2, Operations with Rational Numbers, Lesson 18, students build conceptual understanding of fraction computations and apply them in real-world problems. For example, Anchor Problem 2 states, “Michael’s father bought him a 16-foot board to cut into shelves for his bedroom. Michael plans to cut the board into 11 equal lengths for his shelves.  a. The saw blade that Michael will use to cut the board will change the length of the board by -0.125 inches for each cut. How will this affect the total length of the board?  b. After making his cuts, what will the exact length, in inches, of each shelf be?” (7.NS.3)
• Unit 4, Equations and Inequalities, Lesson 11, students build conceptual understanding of inequalities and apply to real-world problems. For example, Target Task states, “The members of a singing group agree to buy at least 250 tickets for an outside concert. The group buys 20 fewer lawn tickets than balcony tickets. What is the least number of balcony tickets bought? Write and solve an inequality. Explain your answer in the context of the situation.” (7.EE.4.b)
• Unit 6, Geometry, Lesson 6, Target Task, students build conceptual understanding and demonstrate procedural skill as they solve, “Describe the relationship between the circumference of a circle and its diameter. The top of a can of tuna is in the shape of a circle. If the distance around the top is approximately 251.2 mm, what is the diameter of the top of the can of tuna? What is the radius of the top of the can of tuna?” (7.G.4)

#### 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 7 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.

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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 7 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 the Standards for Mathematical Practices are addressed and what mathematically proficient students should do. For example, Unit 8, Probability, “Students encounter and use a variety of tools including spinners, dice, cards, coins, etc., and organizational tools such as organized lists, tables, and tree diagrams when they study compound probability (MP.5).”
• Lessons usually include indications of Math 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 1,  Proportional Relationships, Lesson 7, Tips for Teachers, “Students reason abstractly as they represent proportional situations using tables and graphs, and interpret the information to identify the constant of proportionality and write an equation. Given a graph of a proportional relationship, students re-contextualize information represented in coordinate points to explain what (0,0) and (0,r) mean in context of the problem (MP.2).” Lesson 11, Anchor Problem 2, “In solving part (c), students may use their graph to estimate a time, however, they will realize that the graph alone cannot provide an exact answer. Students may use proportional reasoning to determine the exact rate at which the brothers are running or to write an equation to represent the distance each brother travels over time (MP.4).” Lesson 14, Criteria For Success, “Organize information and map out a solution process for a multi-step problem (MP.1).”

In some Problem Set Guidance sections, MPs are identified within the problem. For example, Unit 5, Percent and Scaling, Lesson 2, MARS Formative Assessment Lesson, Ice Cream, “This lesson also relates to all the Standards for Mathematical Practice, with a particular emphasis on: 2. Reason abstractly and quantitatively, 4. Model with mathematics  and 7. Look for and make use of structure.”

Evidence that the MPs are used to enrich (are connected to) the mathematical content:

• MP.1 enriches the mathematical content in Unit 5, Lesson 8, Tips for Teachers,  when “Students make sense of the quantities in each problem, how they are related, what they mean in context, etc., and then determine what strategy or approach they will use to solve (MP.1).” Anchor Problem 1 states, “Sarita is collecting signatures to put a question on her town’s voting ballot.  a. So far, she has collected 432 signatures. This is 36% of the number of signatures she needs. How many signatures does Sarita need to collect?  b. After a week, Sarita now has 582 signatures. By what percent did the number of Sarita’s signatures increase over the week?  c. A friend of Sarita’s says he will help her collect signatures by collecting 12% of the number of signatures she needs. How many signatures will the friend collect?”
• MP2 enriches the mathematical content in Unit 1, Lesson 7, Tips for Teachers, as “Students reason abstractly as they represent proportional situations using tables and graphs, and interpret the information to identify the constant of proportionality and write an equation.” Students are “given a graph of a proportional relationship, students re-contextualize information represented in coordinate points to explain what (0,0) and (0,r) mean in context of the problem (MP.2).” Anchor Problem 2 states, “Three toy cars race down a straight path. The distance each car traveled in meters, over time measured in seconds, is shown in the graph below. At what speed is each car traveling? Where can you see each speed in the graph? Explain the significance of the coordinate point (1,r). What do you think the “r” represents?”
• MP4 enriches the mathematical content in Unit 3, Lesson 9, when students use expressions to model the number of tiles needed for the border of a fountain. Anchor Problem 2 states, “A square fountain area with side length feet is bordered by a single row of square tiles as shown. Each different expression represents the border in a different way, yet all expressions are equivalent as a total number of tiles.  What are three different ways to represent the number of tiles needed for the border? Show each representation using the diagram.”

There is no evidence where MPs are addressed separately from the grade-level content.

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Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Fish MatchTank Grade 7 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 Problem 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 to a solution.

• Unit 2, Operations with Rational Numbers, Lesson 6, Target Task 1, students use number lines to represent subtraction of two integers to explore the idea that subtraction of a number is the same as adding its opposite. “Students can make sense of this abstract problem by substituting in specific values for p and q.” “Point A is located at -4.5, and point B is 3.25 units from point A. Write two addition equations that could be used to determine the location of point B. Model this on the number line below.”
• Unit 5, Percent and Scaling, Lesson 7, Anchor Problem 2 states, “There were 24 boys and 20 girls in a chess club last year. This year the number of boys increased by 25%, but the number of girls decreased by 10%. Was there an increase or decrease in overall membership? Find the overall percent change in membership of the club.” Notes: “Students need to map out a solution pathway. In order to find the percent change, students will first need to find the new number of boys and girls in the club this year using strategies from Lesson 5. Students may do this efficiently by finding 125% of 24 boys and 90% of 20 girls. Highlight and showcase examples of students using this efficient approach.”

MP.2: Students reason abstractly and quantitatively.

• Unit 1, Proportional Relationships, Lesson 11, Anchor Problem 1, “A proportional relationship is shown in the graph below. a) Describe a situation that could be represented with this graph. b) Write an equation for the relationship. Explain what each part of the equation represents.” In this problem, “Students “take an abstract graph and apply a context to it that makes sense with the values given. Students ensure the contexts chosen represent true proportional relationships that could be represented with an equation in the form y=kx.”
• Unit 3, Numerical and Algebraic Expressions, Lesson 3, Anchor Problem 2 states, “What could be the missing dimensions of the rectangular array? Which set of dimensions uses the greatest common factor of the two terms? Factor the expression below by using a rectangular array. Use the greatest common factor as the representation of the width. 24d - 8e + 6” Students “reason quantitatively in this problem considering the expressions as a whole and also the individual relationship between q and r and the rest of the parts of the expression.”

MP.4: Students model with mathematics.

• Unit 3, Numerical and Algebraic Expressions, Lesson 9, Anchor Problem 2, students write and interpret expressions by demonstration three different ways using tiles. “A square fountain area with side length s feet is bordered by a single row of square tiles as shown. What are three different ways to represent the number of tiles needed for the border? Show each representation using the diagram. Anchor Problem Notes state, “Students use expressions to model the number of tiles needed for the border. Each different expression represents the border in a different way, yet all expressions are equivalent as a total number of tiles (MP.4).”
• Unit 5, Percent and Scaling, Lesson 14, Anchor Problem 1, students apply the mathematics they know and proportional reasoning to model and determine actual measurements by using a scale. “Vincent proposes an idea to the student government at his school to install a basketball hoop along with a court, as shown in the diagram below. The school administration tells Vincent that his plan will be approved if it fits on the empty lot, which measures 25 feet by 75 feet, on the school property. Will the lot be big enough for the court Vincent planned? Justify your answer.”

MP5: Students use tools strategically.

• Unit 3, Numerical and Algebraic Expressions, Lesson 11, Anchor Problem 1 states, “Central High School won the league softball championship game last weekend. The team would like to make a display stand for the trophy. The stand will be a rectangular prism. The players plan to paint the stand white so they can each paint a handprint on the stand in different colors. The players want to fit each of their handprints on the stand without overlapping with any other handprints. There are 24 players on the team. Design a display stand that meets the requirements above. What are its dimensions? Show or explain how you found the dimensions using words, pictures, and/or numbers.” Students work in groups to solve a real-world problem. Teachers are instructed to, “allow students to request any tools they may find valuable to solve their problems.”
• Unit 5, Percent and Scaling, Lesson 15, Anchor Problem 2 states, “The map below shows Boston Common and Boston Public Garden. Perla walked around the outside perimeter of the Common and the Public Garden. About how far did she walk?”  Students use appropriate tools strategically as they determine the measurement. “Some students may also ask to use string or some other flexible measuring tool (such as Wikki Stix) because of the curved lengths around the Boston Common.”

MP6: Students attend to precision

• Unit 3, Numerical and Algebraic Expressions, Lesson 2, Anchor Problem 1 states, “Given the expression: $$(a^2-b)-(2ab)$$.  Is the expression greater when a = -1, b = 1 or when a = 1 and b = -1?  Students must use precision when representing (-1) and substitute it into the expression to ensure it represents multiplication and not subtraction.”
• Unit 5, Percent and Scaling, Lesson 12, Anchor Problem 2 states, “Five figures are shown below. a) Which figures are scale images of Figure 1? Explain your reasoning why. b) Which figures are not scale images of Figure 1? Explain your reasoning why.” In the Anchor Problem Notes state, “Students can use the grid to find the measurements of the side lengths to support their reasoning with precision. For example, the dimensions in Figure 3 are half the dimensions of Figure 1, which means they are proportional, but in Figure 5, only the width was doubled and the length stayed the same, which means they are not proportional.”

MP.7: Students look for and make use of structure.

• Unit 2, Operations with Rational Numbers, Lesson 16, Anchor Problem, Students look for structure in the denominator written in powers of 10. “Malia found a "short cut" to find the decimal representation of the fraction 117/250. Rather than use long division, she noticed that because 250 × 4 =1000. This Anchor Problem encourages students to be thoughtful and efficient in their work. By understanding the structure of the denominator written as a power of 10, students can find an alternative approach to long division in converting a fraction to a decimal; students should develop an awareness that using the general approach of long division is not always the best approach and that thinking critically about the fraction at hand may open up easier approaches.”
• Unit 6, Geometry, Lesson 2, Anchor Problem 2, students use structure when identifying which terms in an algebraic expression are like terms using vertical angles. For example, “In the diagram below, line CD intersects line AB through point E , Ray EF extends from point E. Callie says that angle CEB is vertical to angle AEF. Explain why her reasoning is incorrect and name the angle that is vertical to angle CEB. A common misconception with vertical angles is to choose angles that appear to be vertical but are not created by two intersecting lines. Have students trace over the lines that intersect to support their understanding of the structure of the diagram, and the significance of the intersecting lines in creating the vertical angles.”

MP.8: Students look for and express regularity in repeated reasoning.

• Unit 4, Equations and Inequalities, Lesson 10, Anchor Problem 1 states, “Students who need support with inequality  −3x < 12,  will make a chart of values substituting x values into other inequalities so students can see the repeated results as that make an inequality true.”  For example, “In the chart below, one equation and three inequalities are shown. For each one, write the solution and use the space in the last row to check your solution.”
• Unit 6, Geometry, Lesson 6, Anchor Problem 1 states, “Using the circles handout, measure the circumference and diameter of each circle and record your results in the table below. Create a graph to show the relationship between circumference and diameter. Place the values for diameter along the x-axis and the values for circumference along the y-axis. What is the constant of proportionality? Write an equation to relate the circumference and diameter of any circle. This Anchor Problem engages students in the discovery of $$C=\pi d$$ by measuring the circumference and diameter of several circles and, through repeated reasoning, finding the proportional relationship between the two quantities.”
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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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 7 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, Operations With Rational  Expressions, Lesson 8, Target Task states, “Two seventh-grade students, Monique and Matt, both solved the following math problem. The temperature drops from 7 °F to -17 °F. By how much did the temperature decrease?  The two students came up with different answers. Monique said the answer is 24 °F, and Matt said the answer is 10 °F. Who is correct? Explain, and support your written response using a number sentence and a vertical line diagram.”
• Unit 3, Numerical and Algebraic Expressions, Lesson 5, Target Task states, “Students in Mr. Jackson’s class are simplifying an expression written on the board: −12p − 5n + 8n + 20. Amal simplified the expression to be 8p + 3n, and Andre simplified the expression to be −32p − 13n. Mr. Jackson saw a few different answers around the classroom, so he gave the students a hint on the board, writing: −12p−5n+8n+20p, −12p+20p−5n+8n; (−12+20)p+(−5+8)n. a. What did Mr. Jackson do in each step he wrote on the board? B. Is either Amal or Andre correct? Explain why.”
• Unit 4, Equations and Inequalities, Lesson 5, Problem Set Guidance, (Illustrative Mathematics Guess My Number), states, “Laila tells Julius to pick a number between one and ten. “Add three to your number and multiply the sum by five,” she tells him. Next she says, “Now take that number and subtract seven from it and tell me the new number.” “Twenty-three,” Julius exclaims. Write an expression that records the operations that Julius used. What was Julius’ original number? In the next round Leila is supposed to pick a number between 1 and 10 and follow the same instructions. She gives her final result as 108. Julius immediately replies: “Hey, you cheated!” What might he mean?”
• Unit 5, Percent and Scaling, Lesson 12 , Target Task states, “Li drew two images of the letter T in a grid, as shown below. Li says the larger T is a scaled image of the smaller T because the larger T is twice the height of the smaller T. Do you agree with Li? Explain why or why not.”
• Unit 7, Statistics, Lesson 6, Problem Set Guidance, (Open Up Resources Grade 7 Unit 8 Practice Problems, Lesson 15), states, “Clare estimates the students at her school spend an average of 1.2 hours each night doing homework. Priya estimates the students at her school spend an average of 2 hours each night watching TV. Which of these two estimates is likely to be closer to the actual mean value for all the students at their school? Explain your reasoning.”
• Unit 8, Probability, Lesson 6, Target Task states, “Aimee has two sisters in her family. She thinks the probability of a family having three children who are all girls is 1/4 because there can be 0 girls, 1 girl, 2 girls, or 3 girls. Aimee designs a simulation to test her prediction. She flips a coin three times in a row and records the results. She uses heads to represent a girl and tails to represent a boy. After 10 trials of this simulation, Aimee gets the following results.  [a table of the results are given from ten trials] Does 1/4 seem like a reasonable probability of having 3 girls? Explain your reasoning. Estimate the probability of having 3 girls using the results from Aimee’s simulation.”

Student materials consistently prompt students to construct viable arguments. For example:

• Unit 1, Proportional Relationships, Lesson 9, Target Task states, “Is the perimeter of an equilateral triangle proportional to the side length of the triangle? For any regular polygon, is the perimeter of the polygon proportional to the side length of the polygon? Explain your reasoning.”
• Unit 4, Equations and Inequalities, Lesson  9, Problem Set Guidance, (Open Up Resources Grade 7 Unit 6 Practice Problems, Lesson 13, Problem 2) “How are the solutions to the inequality -3x ≥ 18 different from the solutions to -3x > 18? Explain your reasoning.”
• Unit 6, Geometry, Lesson 3, Problem Set Guidance, (Open Up Resources Grade 7 Unit 7 Practice Problems), Lesson 5, Problem 3: “If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.”
• Unit 8, Probability, Lesson 1, Problem Set Guidance, (Open Up Resources Grade 7 Unit 8 Practice Problems), Lesson 2, Problem 1, “The likelihood that Han makes a free throw in basketball is 60%. The likelihood that he makes a 3-point shot is 0.345. Which event is more likely, Han making a free throw or making a 3-point shot? Explain your reasoning.”
• Unit 8, Probability, Lesson 5, Problem Set Guidance, (EngageNY Mathematics, Grade 7, Mathematics, Module 5, Topic B, Lesson 10), Problem Set, Question 1c: “How do the simulated probabilities in part (b) compare to the theoretical probabilities of part (a)?”
##### 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 7 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, Proportional Relationships, Lesson 3, Anchor Problem 2, teachers are prompted to encourage students to construct viable arguments when determining if a proportional relationship exists between two objects. Guiding Questions: a. “Why might one of these hoses not have a proportional relationship between time and the amount of water?” b. “If a relationship is not proportional, can you determine other missing values in the relationship?” c. “Why or why not?” Notes: “This is a good opportunity for students to construct arguments and to hear and critique the arguments of others.”
• Unit 2, Operations with Rational Numbers, Lesson 8, Anchor Problem 3 states, “Darnell thinks that –4 is less than –6 because 4 is smaller than 6, and –4 is closer to 0 than –6 is. Draw a number line to show the numbers 0, –4, and –6. Then explain why Darnell is incorrect.” The following Guiding Questions are provided to assist teachers in analyzing the reasoning of Darnell, “What happens to the size of numbers when you move to the right on a number line? To the left? What integer is directly to the right of 0? Directly to the left? Are –4 and –6 to the right or left of 0 on the number line? Which number, –4 or –6, is farther to the left of 0? What is an example of a number that is less than –6? Greater than –4?”
• Unit 3, Numerical and Algebraic Expressions, Lesson 7, Anchor Problem 1, Guiding Questions are provided to support students in constructing a viable argument and analyzing the arguments of others. Example is as follows:  “What action did each student (Len, Monty, Nailany) take in their first step to simplify the expression? For the students who made a misstep, how would you explain it to them? How might Oscar’s rewritten expression help Len understand what to do? What is the expression written in simplified form?”
• Unit 6, Geometry, Lesson 5, Anchor Problem 3 states, “Hilary is ordering a large circular pizza from her local pizza shop. She asks about the size of the pizza and is given 3 different values: 14 inches, 44 inches, and 7 inches. Hilary knows three measurements that are used to describe circles: radius, diameter, and circumference. Which value best matches each measurement? Explain your reasoning.” Teachers are given the following Guiding Questions to engage students in constructing a viable argument:  a. “Circumference is similar to perimeter of polygons in that it is the distance around a circle. What part of the pizza best relates to the circumference?”  b. “Is the radius smaller or greater than the diameter?”  c. “Do you think the circumference is smaller or greater than the diameter? Why?” In the Notes, teachers are given suggestions to engage student in analyzing the reasoning of others: “This is a good opportunity to pair up students who arrive at different answers. Each student can defend his or her matches and try to convince their peers of their answer. “
• Unit 6, Geometry, Lesson 15, Anchor Problem 1 states, “This is a good opportunity for students to construct arguments to defend their determinations, and to proactively seek any counterexamples that may be used to show more than one triangle can be created.”
• Unit 8, Probability, Lesson 4, Anchor Problem 3 states, “A six-sided number cube includes the numbers 1, 3, 5, and 7, as shown below (1 and 5 appear twice). Han predicts that out of 150 rolls of the number cube, the number 1 will appear exactly 50 times. Do you agree with Han? Explain your reasoning.” Guiding Questions are provided for teachers to engage students in critiquing the arguments of others: a. “Is this a fair number cube?” b. “What is a reasonable low number of times for the number 1 to appear over 150 rolls?” c. “What is a reasonable high number of times for the number 1 to appear over 150 rolls?” d. “How can you adjust Han’s claim to make it more reasonable?” e. “What other predictions can you make about the number cube being rolled?”
##### Indicator {{'2g.iii' | indicatorName}}
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Match Fishtank Grade 7 meet the expectations that materials use accurate mathematical terminology.

The Match Fishtank Grade 7 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 4, Equations and Inequalities' vocabulary includes the following words: equation, solution, inequality, substitution, and tape diagram.
• Unit 2, Operations with Rational Numbers, Lesson 16, Criteria For Success, “Define terminating decimals as numbers with a finite number of digits after the decimal point, and define repeating decimals as numbers with an infinite number of digits after the decimal point in which a digit or group of digits repeats indefinitely.”

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 2, Operations with Rational Numbers,  Lesson 5, Anchor Problem 3 states, “Listen for precise use of language in students’ responses to the first problem. For example, saying the sum in part (a) is positive because ‘4 is the bigger number and 4 is positive’ is not accurate because the same reasoning does not hold true for part (c) where 7 is the bigger number but the sum is not positive. Listen for students describing the absolute value of numbers in their consideration of the signs of the sums.”
• Unit 7, Statistics, Lesson 2, Anchor Problem 2 states, “Use this Anchor Problem to introduce the concept of random sampling, in which every person in the population has an equal chance of being chosen for a sample. In discussing these methods, students should construct arguments as to why method E is the only one that would not be biased or unrepresentative.”

The Match Fishtank Grade 7 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, Equations and Inequalities, Lesson 1, the term “solution” is in bold print, and the definition is provided within the sentence: “Define and understand a solution to an equation as a number for a variable that makes the equation a true statement when substituted in.”
• Unit 5, Percent and Scaling, Lesson 10, Anchor Problem 1, “What is interest? Explain in your own words. If you were to graph the relationship between time and interest, what shape would the graph be?”
• Unit 6, Geometry, Lesson 5, Anchor Problem 1 states, “Draw a circle in two ways. Based on your drawings, how would you define a circle? Define a circle as a closed shape defined by the set of all points that are the same distance from the center point of the circle.”

### 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 7 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 7 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 allows students to independently master and demonstrate their understanding of the material. 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. Each lesson concludes with a Target Task intended for formative assessment. For example:

• Unit 2, Operations with Rational Numbers, Lesson 2. In Anchor Problem 1, students compare and order rational numbers. In the Problem Set Guidance,  students can play an Integer War card game using a deck of cards allowing for independent practice and mastery.
• Unit 6, Geometry, Lesson 3, Anchor Problems, students “Use equations to solve for unknown angles” through guided instruction. In the Problem Set Guidance, (Open Up Resources Grade 7 Unit 7 Practice Problems, Lesson 5), additional problems allow for independent practice and mastery. For example, Problem 5 states, “Segments AB, DC, and EC intersect at point C. Angle DCE measures 148 degrees. Find the value of x.”
• Unit 8, Probability, Lesson 4, Anchor Problems, students, “Use probability to predict long-run frequencies.”  In the Problem Set Guidance, (Open Up Resources Grade 7 Unit 8 Practice Problems, Lesson 4), additional problems allow for independent practice and mastery.  Problem 1 states, “A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there’s a red mark on the bottom of the duck, the person wins a small prize. If there’s a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.”
• Unit 2, Operations with Rational Numbers, Lesson 2, Anchor Problem 1, students compare and order rational numbers. In the Problem Set Guidance, students can play an Integer War card game using a deck of cards allowing for independent practice and mastery.
• Unit 6, Geometry, Lesson 3. In the Anchor Problems, students “Use equations to solve for unknown angles” through guided instruction. In the Problem Set Guidance, (Open Up Resources Grade 7 Unit 7 Practice Problems, Lesson 5), they are given additional problems allowing for independent practice and mastery. For example, Problem 5 states, “Segments AB, DC, and EC intersect at point C. Angle DCE measures148 degrees. Find the value of x.”
• Unit 8, Probability, Lesson 4. In the Anchor Problems, students “Use probability to predict long-run frequencies.”  In the Problem Set Guidance, (Open Up Resources Grade 7 Unit 8 Practice Problems, Lesson 4), additional problems allow for independent practice and mastery. For example, Problem 1 states, “A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there’s a red mark on the bottom of the duck, the person wins a small prize. If there’s a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.”
##### Indicator {{'3b' | indicatorName}}
Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials reviewed for Match Fishtank Grade 7 meet the expectations that the design of assignments is intentional and not haphazard.

The lessons follow a logical, consistent format that intentionally sequence assignments, providing for a natural progression, leading 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 7 meet the expectations that the instructional materials prompt students to show their mathematical thinking in a variety of ways. For example:

• Unit 2, Operations with Rational Numbers, Lesson 2: Students write inequalities to compare rational numbers, and use number lines to justify their answers.
• Unit 3, Numerical and Algebraic Expressions, Lesson 11: Students analyze and critique the work of their peers as they model real-world problems involving rational numbers using reasoned estimates.
• Unit 4, Equations and Inequalities, Lesson 2: Students use tape diagrams to represent equations.
• Unit 7, Statistics, Lesson 7: Students use proportional reasoning to estimate population quantities based on population proportions.
• Unit 8, Probability, Lesson 7: Students list the sample space for compound events using organized lists, tables, or tree diagrams.
##### 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 7 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 1, Proportional Relationships, Lesson 18, Problem Set Guidance: Desmos Tile Pile. Students work with this virtual manipulative to reinforce proportional reasoning in solving problems.
• Unit 5, Percent and Scaling, Lesson 4, Problem Set Guidance: Andrew Stadel's 3-Act Math Tasks iPad Usage.  This virtual manipulative is used to reinforce finding percents given a part and the whole.
• Unit 6, Geometry, Lesson 6, Anchor Problem 1. Students use a virtual manipulative, GeoGebra, “Circumference of a Circle” (Drag the center dot to “unroll” the circle, and drag the blue dot to change the diameter.), to explore the relationship between the diameter and circumference of a circle.
##### 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 7 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 7 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 7 meet the expectations that materials provide teachers with quality questions for students.

In the materials, facilitator notes for each lesson include 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 2, Operations with Rational Numbers, Lesson 4, Anchor Problem and Guiding Questions 3: “Where on the number line should you start in each problem? For part (a), how long will each arrow be to represent each addend? For part (a), which direction will each arrow go? For part (b), how long is each arrow and in what direction? For part (b), what does “5” represent? Why is “5” not an addend in the addition problem?”
• Unit 4, Equations and Inequalities, Lesson 8, Anchor Problem and Guiding Questions 2: “How do you read the inequalities in the problem? What are some values that make each inequality true? What are some values that make each inequality not true? What is the difference between ≤ and <? How does that appear on the number line? Why is a ray used to represent the solutions to an inequality? How many points are on a ray?”
• Unit 6, Geometry, Lesson 20, Anchor Problem 1 and Guiding Questions: “Describe the shape of Owen’s birdhouse in your own words. What do the prism and the pyramid have in common? Why is this a volume problem? What numerical expression represents the volume of the birdhouse?”
• Unit 8, Probability, Lesson 6, Anchor Problem and Guiding Questions 2: “Do you think each horse has an equally likely chance of winning? Why or why not? What do you notice about how each horse moves as you progress through the game? Do some horses move faster or slower than others? Do the finishing positions of the horses look similar or different from the two games you play? Looking at finishing positions for your whole class, is there much variation? If you were to play again, which horse would you choose? Why?”
##### 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 7 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 which provides teachers with resources and an overview of the lesson but provide 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 2, Operations with Rational Numbers, Lesson 8, Tips of Teachers: “This may be a good lesson to do the How Much to 0? mental math activity, described in the 7th Grade Math Fluency Building Exercises included in this unit's materials.”

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 7 do not meet the expectations that materials contain adult-level explanations so that teachers can improve their own knowledge.

There is an Intellectual Prep 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 7 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 7 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, 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 7 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 7 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: “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”. 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 7 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 7 do not meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

There are no diagnostic or readiness assessments, or tasks to ascertain student 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 7 meet the expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

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

• Unit 6, Geometry, Lesson 16, Anchor Problem 1 states, “Prior to this Anchor Problem, it may be valuable to discuss the word “slice” with students, as there may be various understandings or interpretations of the word. In the context of this lesson, a slice refers to a single straight cut through a three-dimensional figure, similar to how you slice a loaf of bread or slice off a piece of a cheese.”
• Unit 2, Operations with Rational Numbers, Lesson 4, Anchor Problem 3 states, “A common misconception when writing an equation for a number line diagram is to use the values on the number line where the arrows end, rather than using the length of the arrows. For example, an incorrect answer may be −1+5+(−3). Have students look at how they modeled part (a), and reinforce the concept that the length of the arrow represents the magnitude of the change.”
##### 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 7 meet the expectations for the materials to provide opportunities for ongoing 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 1, Proportional Relationships, Lesson 2, Anchor Problem 1: Students are presented with a table showing weight v. cost of frozen yogurt. The Guiding Questions provided for teachers lead students to conceptual understanding of a proportional relationship, and ask them to apply the ratio to new amounts. Notes: “Use this Anchor Problem to introduce the concept of a proportional relationship. In the table, students should identify the relationship between weight and cost that is repeatedly shown for each dish in the table (MP.8). Start with the idea of equivalent ratios, a concept that students are familiar with, and extend that idea to define a proportional relationship as a collection of equivalent ratios.”
• Unit 5, Percent and Scaling, Lesson 4, Anchor Problem 2, Notes: “This Anchor Problem has students compare two different quantities as percentages of each other, going beyond saying “Jamie raised more than Cole” and determining that Jamie raised 120% of what Cole raised.”
##### 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 7 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 item number and the target standard. For example:

• Unit 4, Equations and Inequalities, Assessment Item 3 correlates with 7.EE.4a.
• Unit 8, Probability, Assessment Item 1 correlates with 7.SP.5.
##### 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 7 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 2, Operations with Rational Numbers Assessment question 6a states, in the “Correct Answer and Scoring Guidance”:
• Solution “4:
• 2 pts full credit for correct answers,
• 1 pt partial credit for 1 error.”

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 7 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 7 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 7 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 7 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, Operations with Rational Numbers, Lesson 4, Anchor Problem 2, Notes: “Ask students for predictions first, and ask them what a parallel problem with positive numbers might look like. Test out several more examples for students to see the repeated conclusion that addition of integers is commutative.”
• Unit 7, Statistics, Lesson 8, Anchor Problem 1,:Notes: “Ensure students provide adequate explanation that addresses both populations, not just details about one.”
##### 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 7 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 2, Operations with Rational Numbers, Lesson 4, Target Task states the following: “Two seventh-grade students, Monique and Matt, both solved the following math problem. The temperature drops from 7 °F to -17 °F. By how much did the temperature decrease? The two students came up with different answers. Monique said the answer is 24 °F, and Matt said the answer is 10 °F. Who is correct? Explain, and support your written response using a number sentence and a vertical line diagram.” 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 7 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 Learners" 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 empathize on lighter or heavier scaffolding. An example is as follows: 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 incorporation 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 7 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 7 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., Jonathan, Terrance, Brianna, Isabelle, and Felix.
• The materials avoid pronouns, referencing a role instead, ie., a motorcycle dealer, a repair technician, a scientist, a vet.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials for Match Fishtank Grades 7 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 for teachers to adapt the lessons or suggestions on when and how to incorporate them are not included in the teacher materials. For example:

• In Unit 1, Proportional Relationships, Lesson 3: “This is a good opportunity for students to construct arguments and to hear and critique the arguments of others as they discuss the guiding questions that are listed for the teacher. Students can work in pairs or small groups to share and discuss their answers to part (b).”
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials for Match Fishtank Grades 7 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 7 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 7, are included as part of the core materials and 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 7 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 7 do not include opportunities for teachers to personalize learning, including the use of adaptive technologies.

The instructional materials reviewed for Match Fishtank Grade 7 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 7 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 7 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 1, Proportional Relationships, Lesson 11: Students use a Desmos applet to use proportional reasoning to make predictions.
• Unit 4,  Equations and Inequalities, Lesson 4: Students have opportunities to use the SolveMe Mobiles applet to create and solve equations.

## 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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