## Alignment: Overall Summary

The instructional materials reviewed for Match Fishtank, Grade 3 meet expectations for alignment to the CCSSM. ​The instructional materials meet expectations for Gateway 1, focus and coherence, by assessing grade-level content, focusing on the major work of the grade, and being coherent and consistent with the Standards. The instructional materials meet expectations for Gateway 2, rigor and balance and practice-content connections, by reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations by giving appropriate attention to the three aspects of rigor. The materials meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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## Gateway 1:

### Focus & Coherence

0
7
12
14
14
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

## Gateway 2:

### Rigor & Mathematical Practices

0
10
16
18
18
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

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## Gateway 3:

### Usability

0
22
31
38
29
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

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Gateway One Details

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focus, the materials assess grade-level content, and spend approximately 77% of instructional time on the major work of the grade, and they also meet expectations for being coherent and consistent with the progressions of the standards.

### Criterion 1a

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

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for not assessing topics before the grade level in which the topic should be introduced.

### Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet the expectations for assessing grade-level content. The series is divided into units, and each unit contains a Unit Assessment available online to the teacher and can also be printed for students.

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

• Unit 1 Assessment, Question 3, Part A states, “Round to the nearest ten the number of people who went to the school play on each of the three days. Show or explain how you got your answers.” (3.NBT.1)
• Unit 1 Assessment, Question 5 states, “There are 545 magazines and 620 books in the library. How many more books than magazines are in the library?” (3.NBT.2)
• Unit 2 Assessment, Question 5 states, “Dinah is selling pieces of bubble gum to her friends. She buys six packs of gum. Each pack has 5 pieces of gum. She sells 3 pieces of gum each day. How many days does it take Dinah to sell all of her gum?” (3.OA.8)
• Unit 4 Assessment, Question 2 states, “A patio is in the shape of a rectangle with a width of 8 feet and a length of 9 feet. What is the area in square feet, of the patio?” (3.MD.7b)
• Unit 5 Assessment, Question 5 states, “Sonia wants to put a fence around her backyard. Her backyard is 5 meters long and 6 meters wide. What is the total length of fence, in meters, Sonia needs to place around the play area?” (3.MD.8)
• Unit 7 Assessment, Question 5 states, “Freda buys horse food in 20-kilogram bags. Her horse eats 8 bags of horse food per month. How much horse food does Freda’s horse eat in one month?” (3.MD.2)

### Criterion 1c - 1f

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

The instructional materials reviewed for Match Fishtank Grade 3 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

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

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 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:

• In Unit 1, Lessons 10, 13 and 14, students solve word problems (3.OA.8) involving addition and subtraction (3.NBT.2), using rounding (3.NBT.1) to assess the reasonableness of the solution. For example, Lesson 10, Anchor Tasks, Problem 2 states, “Luke and Josh collect baseball cards. Luke has 347 baseball cards. Luke has 34 fewer baseball cards than Josh. How many baseball cards does Josh have? Solve. Then assess the reasonableness of your answer.”
• In Unit 3, Lessons 17 and 18, students determine the unknown whole number in a multiplication or division equation relating three whole numbers (3.OA.4) and apply the properties of operations as strategies to multiply and divide (3.OA.5), as well as multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations (3.NBT.3). For example, Lesson 17, Anchor Tasks, Problem 1 states, “There are 6 tables in Mrs. Potter's classroom. There are 4 students sitting at each table. Each student has a dime to use as a place marker on a board game. a. What is the value of the dimes at each table? b. What is the value of the dimes in Mrs. Potter’s classroom?”
• In Unit 3, Lesson 28, Problem Set, students solve one- and two-step word problems (3.OA.8) using information presented in scaled picture and bar graphs (3.MD.3). Problem 3 states, “The bar graph shows the number of visitors to a carnival from Monday through Friday. a. There were 500 more visitors on Wednesday and Friday combined than on Tuesday. How many visitors were there on Friday? Add that bar to the bar graph. b. How many fewer visitors were there on the least busy day than on the busiest day? c. How many more visitors attended the carnival on Monday and Tuesday combined than on Thursday and Friday combined?”
• In Unit 6, Lessons 1-3, students understand a fraction $$\frac{1}{b}$$ as the quantity formed by one part when a whole is partitioned into b equal parts and understand a fraction $$\frac{a}{b}$$ as the quantity formed by a parts of size $$\frac{1}{b}$$ (3.NF.1), as they partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole (3.G.2). For example, Unit 6, Lesson 1, Target Task, Problem 1 states, “Build the shaded shape below with your pattern blocks. Then, name the fraction that each triangle represents.”
• In Unit 6, Lesson 27, students understand a fraction as a number on the number line (3.NF.2) to measure lengths of multiple objects with fractional units, then use this data to create line plots (3.MD.4). The Target Task states, “Heather is measuring the length of strips of paper to the nearest quarter inch. The lengths she has measured so far are in the table below. Measure the remaining paper strips and add their lengths to the table. Then use the data to draw a line plot below.”

### Indicator 1d

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

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet expectations that the amount of content designated for one grade-level is viable for one year. 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.

The Pacing Guide states, “We intentionally did not account for all 180 instructional days in order for teachers to fit in additional review or extension, teacher-created assessments, and school-based events.” As designed, the instructional materials can be completed in 145 instructional days (including lessons, flex days, and unit assessments).

• There are 126 content-focused lessons designed for 50-60 minutes. Each lesson incorporates: Anchor Tasks (25-30 minutes), Problem Set (15-20 minutes), and a Target Task (5-10 minutes).
• There are seven unit assessments, one day each.
• The pacing guide suggests 12 flex days be incorporated into the units throughout the year at the teacher’s discretion. It is recommended for units that include both major and supporting/additional work, that the flex days be spent on content that aligns with the major work of the grade.

### Indicator 1e

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

The instructional materials for Match Fishtank Mathematics Grade 3 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, relate grade-level concepts explicitly to prior knowledge from earlier grades, and use it to support the progressions of the grade-level standards, for example:

• The Unit 1 Summary states, “In the first module of Grade 3, students will build on their understanding of the structure of the place value system from Grade 2 (MP.7), start to use rounding as a way to estimate quantities (3.NBT.1), as well as develop fluency with the standard algorithm of addition and subtraction (3.NBT.2). Thus, Unit 1 starts off with reinforcing some of this place value understanding of thousands, hundreds, tens, and ones being made up of 10 of the unit to its right that students learned in Grade 2.”
• The Unit 1 Summary connects to future grade level content, “Thus, while the majority of the content learned in this unit comes from an additional cluster, they are deeply important skills necessary to fully master the major work of the grade with 3.OA.8, as well as a foundation for rounding and the standard algorithms used to any place value learned in Grade 4 (4.NBT.1-4) and depended on for many grade levels after that.”
• The Unit 6 Summary states, “In Unit 6, students extend and deepen Grade 1 work with understanding halves and fourths/quarters (1.G.3) as well as Grade 2 practice with equal shares of halves, thirds, and fourths (2.G.3) to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line. Throughout the module, students have multiple experiences working with the Grade 3 specified fractional units of halves, thirds, fourths, sixths, and eighths.”
• The Unit 6 Summary also connects to future grade level content, “This unit places a strong emphasis on developing conceptual understanding of fractions, using the number line to represent fractions and to aid in students' understanding of fractions as numbers. With this strong foundation, students will operate on fractions in Grades 4 and 5 (4.NF.3-4, 5.NF.1-7) and apply this understanding in a variety of contexts, such as proportional reasoning in middle school and interpreting functions in high school, among many others.”
• The CCSSM are listed for each unit at the very bottom of the main unit page. They categorize the list of standards by the content standards addressed in the grade level, foundational standards (standards from prior grades), future connections, and the MPs.

The instructional materials for Match Fishtank Mathematics Grade 3 attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All lessons within the units include an “Anchor Task,” where students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Problem sets provide students the opportunity to solve a variety of problems and integrate and extend concepts and skills. Each problem set is wrapped up with a “Discussion of Problem Set,” where students are provided an opportunity to synthesize and clarify their understanding of the day’s concepts. The lesson concludes with a “Target Task” for students to independently demonstrate their learning for the day. For example:

• Unit 1, Lesson 5, Target Task states, “Round each of the following numbers to the nearest hundred. Show or explain your thinking. a.  761_____ b.  135 _____ c. 84 _____” (3.NBT.1)
• Unit 2, Lesson 5, Anchor Task, Problem 1 states, “Presley has 10 markers. Her teacher gives her 2 boxes and asks her to put an equal number of markers in each box. Anthony has 10 markers. His teacher wants him to put 2 markers in each box until he is out of markers. a. Before you figure out what the students should do, write a multiplication sentence to correspond with each context above. b. Solve each problem for the missing factor.” (3.OA.3)
• Unit 3, Lesson 10, Problem Set, Problem 4 states, “Adriana wrote the expression shown below. $$(3 \times 1) + (3 \times 6)$$. Which of these shows another way to write Jody’s expression? a. $$3 \times 6$$   b. $$3 \times 7$$ c. $$6 \times 6$$ d. $$6 \times 7$$.” (3.OA.5)
• Unit 4, Lesson 6, Problem Set, Problem 4 states, “Mrs. Barnes draws a rectangular array. Mila skip-counts by fours and Jorge skip-counts by sixes to find the total number of square units in the array. When they give their answers, Mrs. Barnes says that they are both right. a. Use pictures, numbers, and words to explain how Mila and Jorge can both be right. b. How many square units might Mrs. Barnes’ array have had?” (3.MD.6, 3.MD.7a)
• Unit 5, Lesson 2, Anchor Task, Problem 1 states, “Use your ruler to find the perimeter, in inches, of the following shape.” (3.MD.8)
• Unit 6, Lesson 6, Discussion of Problem Set states, “Do you agree or disagree with the fraction in #2? What way was Marcos thinking about the model that resulted in the fraction $$\frac{17}{24}$$? Did students each eat $$\frac{10}{8}$$ or $$\frac{10}{16}$$ of a pan in #4? How do you know? What does $$\frac{10}{16}$$ represent? How many pizzas should Jeremy order in #6? How do you know? How can you tell just by looking at the numbers involved that it will be more than one pizza?” (3.NF.1)
• Unit 6, Lesson 1, Target Task, Problem 2 states, “Build the shaded shape below with your pattern blocks. Then, name the fraction that each triangle represents.” (3.G.2)
• Unit 7, Lesson 5, Discussion of Problem Set states, “How did you solve #1? Did you use the clock, draw a number line, or use some other strategy? Did you count forward or backward to solve #3? How did you decide which strategy to use? What made #6 and #8 slightly more difficult than the other problems? Did you solve them differently? How did we use counting as a strategy to problem solve today? How did you use hour benchmarks to problem solve today?” (3.MD.1)
• Homework is provided for each lesson to extend students’ engagement with the content.

The materials identify Foundational Standards related to the content of the grade level lesson. Guidance related to the lesson’s content is also provided for teachers. For example:

• In Unit 1, Lesson 4, the Foundational Standards include Number and Operations in Base Ten, 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:). The materials state, “3rd Grade Math- Unit 1: Place Value, Rounding, Addition and Subtraction. Students build on their understanding of the structure of the place value system, start to use rounding as a way to estimate quantities, and develop fluency with the standard algorithm of addition and subtraction. Students focus on the precision of their calculations, and use them to solve real-world problems.”
• In Unit 4, Lesson 4, the Foundational Standards include Measurement and Data, 2.MD.1. (Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.). The materials state, “3rd Grade Math - Unit 4: Area. Students develop an understanding of areas as how much two-dimensional space a figure takes up, and relate it to their work with multiplication from Units 2 and 3.”

### Indicator 1f

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

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

The materials include learning objectives that are visibly shaped by CCSSM cluster headings, for example:

• In Unit 2, Lesson 3, the lesson objective states, “Identify and create situations involving unknown group size and find group size in situations,” which is shaped by 3.OA.A, “Represent and solve problems involving multiplication and division.”
• In Unit 3, Lesson 19, the lesson objective states, “Solve two-step word problems involving all four operations and assess the reasonableness of solutions,” which is shaped by 3.OA.D, “Solve problems involving the four operations, and identify and explain patterns in arithmetic.”
• In Unit 3, Lesson 23, the lesson objective states, “Identify arithmetic patterns and explain them using properties of operations,” which is shaped by 3.OA.D, “Solve problems involving the four operations, and identify and explain patterns in arithmetic.”
• In Unit 4, Lesson 7, the lesson objective states, “Find the area of a rectangle through multiplication of the side lengths,” which is shaped by 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and addition.”
• In Unit 4, Lesson 11, the lesson objective states, “Recognize area as additive. Find areas of composite figures when not all dimensions are given,” which is shaped by 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and addition.”
• In Unit 5, Lesson 3, the lesson objective states, “Find perimeter of shapes with all side lengths labeled,” which is shaped by 3.MD.D, “Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.”
• In Unit 6, Lesson 3, the lesson objective states, “Partition a whole into equal parts, identifying and counting unit fractions using pictorial area models and tape diagrams, identifying the unit fraction numerically,” which is shaped by 3.NF.A, “Develop understanding of fractions as numbers.”

The materials include problems and activities that 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. For example:

• In Unit 2, Lesson 5 connects 3.OA.A to 3.OA.B when students relate multiplication and division and understand that division can represent situations of unknown group size or an unknown number of groups. For example, Unit 2, Lesson 5, Anchor Tasks, Problem 3 states, “Write a multiplication equation and a division equation to represent each of the following situations. a. Ross has 15 flowers that he wants to make into flower arrangements. Each flower arrangement will use 5 flowers. How many flower arrangements can he make? b. Heidi has 8 apps that she wants to place into rows of 4. How many apps will there be in each row?”
• In Unit 2, Lesson 10 connects 3.OA.A, 3.OA.B, and 3.OA.C by building fluency with multiplication and division facts using units of three. Students connect their conceptual understanding of multiplication and division to problems with an unknown value and demonstrate the commutative property. For example, Unit 2, Lesson 10, Problem Set, Problem 4 states, “a. Draw a model that shows 7 rows of 3. b. Write a multiplication sentence where the first factor represents the number of rows. ________ x ________ = ________.”
• In Unit 3, Lesson 1 connects 3.OA.B to 3.OA.D by having students study commutativity to find known facts of 6, 7, 8 and 9. Students also explore patterns on the multiplication chart to understand commutativity. For example, Unit 3, Lesson 1, Anchor Tasks, Problem 2 states, “Fill in the facts you know on the multiplication chart below. (A multiplication chart up to 10 is provided.)”

### Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The Match Fishtank Grade 3 instructional materials, when used as designed, spend approximately 77% of instructional time on the major work of the grade, or supporting work connected to major work of the grade.

### Indicator 1b

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

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet expectations for spending a majority of instructional time on major work of the grade.

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 5 out of 7, which is approximately 71%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 103 out of 133, which is approximately 77%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 117 out of 145, which is approximately 81%.

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 77% of the instructional materials focus on major work of the grade.

## Rigor & Mathematical Practices

#### Meets Expectations

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Gateway Two Details

The instructional materials for Match Fishtank Grade 3 meet the expectations for rigor and the Mathematical Practices. The materials meet the expectations for rigor, students develop and demonstrate conceptual understanding, procedural skill and fluency, and application. The materials meet the expectations for practice standards and attend to the specialized language of mathematics.

### Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
8/8
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Criterion Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 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 aspects of rigor.

### Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 3 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade-level, for example:

• In Unit 3, Lesson 17, students multiply a one-digit whole number by a multiple of ten (3.NBT.3) using base ten blocks, number lines, and properties of operations. For example, Anchor Tasks, Problem 3, Guiding Questions state, “How can you represent this problem with base ten blocks? How can you represent this problem on a number line?”
• In Unit 4, Lessons 2-4, students use square-inch and square-centimeter tiles to explore the concept of area (3.MD.5). For example, Lesson 2, Anchor Tasks, Problem 3, students make connections through the Guiding Questions, “Which square unit has greater area, a square centimeter or a square inch? How is that related to the amount of space taken up by each shape constructed from each of those units?”
• In Unit 6, Lesson 26, students measure lengths to the nearest quarter inch (3.MD.4) using square inch tiles and creating a ruler. For example, in Anchor Tasks, Problem 1, students make connections between concepts through the Guiding Questions, “How is a ruler similar to a number line? How is it different?”
• In Unit 7, Lesson 7, students use various objects (thumbtacks, dictionary, snap cubes, paper clips, etc.) to develop benchmarks for 1 kilogram and 1 gram (3.MD.2). For example, Anchor Tasks, Problem 3, Guiding Questions state, “About how many paperclips would it take to balance with a dictionary? How do you know?”

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade, for example:

• In Unit 2, Lesson 4, students identify, interpret, and create situations involving an unknown number of groups and find the number of groups in situations (3.OA.1,2). In Problem Set, Problem 5, students solve, “Leah’s favorite marbles come in bags of 10. If she wants to purchase 60 marbles, how many bags will she need to buy? a. Write a multiplication equation to represent the problem. b. Create a visual model of the marbles in the bags. c. How many bags of marbles are there?”
• In Unit 3, Lesson 5, students use arrays to explore the associative property (3.OA.5). In Anchor Tasks, Problem 3, students “a. Decompose the array into smaller arrays whose product you know from memory to be able to find the total product represented by the array. b. Find a second way to decompose the array.”
• In Unit 4, Lesson 2, students “find the area of a figure using square-inch and square-centimeter tiles, which can be used as concrete standard units” (3.MD.5). In Target Task, Problem 2, students, “Construct a rectangle whose area is 16 square inches. Then show your teacher.”
• In Unit 6, Lesson 1, students develop the concept of fractional parts (3.NF.1) by using pattern blocks to construct shapes (3.G.2) with fractional parts. In Anchor Task, Problem 3, students “Create pattern block shapes where one piece represents each of the following fractions. a. 1 half  b. 1 fourth c. 1 third d. 1 sixth.” Guiding questions state, “When I construct the whole, what do I need to make sure is true of each of my parts in order for them to represent 1 half, or 1 fourth or any other fraction? In order for each part to represent 1 half, how many equal parts must your whole be? What does that tell us about the number of pattern blocks we’ll need to construct a shape whose fractional unit is halves?”
• Unit 7, Lesson 3, students relate clocks to number lines (3.MD.1). In the Target Task, students “Plot points on the following number line that correspond with each time below. Label each point with its corresponding letter a - d. a. 5:45 p.m. b. (picture of a clock provided). c. 6:12 p.m. d. (picture of a clock provided).”

### Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 3 meet expectations for attending 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:

• In the Unit Summary, procedural skills for the unit are identified.
• Throughout the materials, Anchor Tasks provide students with a variety of problem types to practice procedural skills.
• Problem Sets provide 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 (3.OA.7 and 3.NBT.2). For example:

• In Unit 1, Lessons 8 and 9, students have multiple opportunities to develop fluency in adding two numbers (3.NBT.2) with multiple compositions within 100. Problem Set, Problem 1 states, “Solve. Show or explain your work.  a. $$46 + 5 =$$ _____ b. $$46 + 25 =$$ _____ c. $$46 + 125 =$$ _____   d. _____ $$= 59 + 30$$ e. $$509 + 83 =$$ _____   f. _____ $$= 597 + 30$$ g. $$29 + 63 =$$ _____   h. _____ $$= 345 + 294$$ i. $$480 + 476 =$$ _____.”
• In Unit 1, Lesson 11, students subtract two numbers with up to one decomposition within 1,000 (3.NBT.2). In Anchor Task, Problem 2, students, “Find the difference. Show or explain your work. a. $$82 - 56 =$$ _____   b. $$287 +$$ _____ $$= 308$$ c. _____ $$= 748 - 93$$.” Also, in Homework, Problem 1h, students independently solve, “$$803 + 542$$.”
• In Unit 1, Lesson 12, students subtract two numbers with up to one decomposition within 1,000 (3.NBT.2). In Target Task, Problem 1, students, “Solve. Show or explain your work. a. $$346 - 187 =$$ _____   b._____ $$= 1,000 - 592$$ c. $$239 = 305 -$$ _____.” Also, in Problem Set, Problem 1, students independently solve, “a. _____ $$= 340 - 60$$ b. $$340 - 260 =$$ _____     c. $$540 - 260 =$$ _____ d. $$513 -$$ ____ $$= 148$$ e. $$387 +$$ _____ $$= 641$$   f. $$934 - 488 =$$ _____ g. _____ $$= 700 - 52$$ h. $$700 - 452 =$$ _____  i. $$452 = 1,000 -$$ ____.”
• In Unit 2, Lessons 6, 8, and 10 address developing multiplication fluency (3.OA.7). Students multiply using arrays, skip counting, and independent practice. For example, in Lesson 10, Problem Set, Problem 3c, students “Solve. a. $$2 \times 3 =$$ ___   b. ___ $$= 3 \times 3$$ c. $$5 \times 3 =$$ ___ d. ___ $$= 10 \times 3$$”
• In Unit 2, Lesson 11, students develop fluency with multiplication and division facts using units of 4 (3.OA.7). In the Homework, Problem 9a, students independently solve the following equation, “$$8 \div 4 =$$ ___.”
• In Unit 2, Lesson 13, students determine the unknown whole number in a multiplication or division equation, including equations with a letter standing for the unknown quantity (3.OA.4,7,8). The Target Task, Problem Set and Homework sections provide students many opportunities to independently practice finding the unknown. For example, Target Task states, “1. $$z = 5 \times 9$$,  $$z=$$ ___,   2. $$20v = 5$$, $$v=$$ ___,   3. $$3 \times w = 24$$, $$w =$$___,   4. $$7=y \div 4$$, $$y=$$___.”
• In Unit 3, Lesson 6, students have multiple opportunities to skip-count to build fluency with multiplication facts using units of 6 (3.OA.7). Problem Set, Problem 1 states, “Skip-count by six to fill in the blanks. Match each number in the count-by with its multiplication fact. Then, use the multiplication expression to write the related division fact directly to the right.”
• In Unit 3, Lesson 17, students “multiply one-digit whole numbers by multiples of 10,” (3.NBT.3) as Guided Practice in the Anchor Tasks. Anchor task, Problem 1 states, “There are 6 tables in Mrs. Potter's classroom. There are 4 students sitting at each table. Each student has a dime to use as a place marker on a board game. a. What is the value of the dimes at each table? b. What is the value of the dimes in Mrs. Potter’s classroom?” In the Homework and Problem Set, students have numerous opportunities to independently practice multiplying by a multiple of 10. Homework, Problem 2e, “_____ $$= 60 \times 3$$.”

### Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

In Problem Sets and Target Tasks, students engage with real-world problems and have opportunities for application, especially where called for by the standards (3.OA.3 and 3.OA.8). 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. Examples of routine application include, but are not limited to:

• In Unit 1, Lesson 7, Target Task, students use place value understanding to round whole numbers to the nearest 10 or 100. For example, “Mrs. Needham knows there are 283 students in Grades 3, 4, and 5 at Match Community Day. She says that there are about 280 students. a. Did Mrs. Needham round to the nearest ten or hundred? b. Mrs. Needham rounded the number of Grade 3, 4, and 5 students to be able to set up seats in the gym for an assembly with those grades. Do you think Mrs. Needham made a good decision about how she rounded the number of students? Why or why not?” (3.NBT.1)
• In Unit 2, Lesson 9, students apply their understanding of multiplication to solve one-step word problems (3.OA.3). For example, Target Task, Problem 1 states, “Ms. McCarty has 8 stickers. She puts 2 stickers on each homework paper and has no more left. How many homework papers does she have?”
• In Unit 3, Lesson 3, students understand the role of parentheses and apply to solving problems (3.OA.5, 3.OA.8). For example, Target Task, Problem 2, students solve, “Marcos solves $$24 \div 6 + 2 =$$ ____. He says it equals 6. Iris says it equals 3. Show how the position of parentheses in the equation can make both answers true.”
• In Unit 5, Lesson 5, students solve word problems involving finding perimeter given the side lengths (3.MD.8). For example, Problem Set, Problem 7 states, “Kevin’s yard is a square. He wants to build a fence around it. Each side of the square is 12 feet long. His house is one side of the square, so he doesn’t need a fence on that side. Decide how many feet of fencing Kevin needs. Explain your thinking.”
• In Unit 6, Lesson 9, students identify a shaded fractional part in different ways, depending on the designation of the whole (3.NF.1). For example, Problem Set, Problem 5 states, “Mrs. Ingall has two apples. She cuts each one into 4 pieces. Mrs. Ingall thinks that one piece is $$\frac {1}{4}$$. Mr. Silver says one piece is $$\frac {1}{8}$$. What’s the reason for their disagreement?”
• In Unit 7, Lesson 6, students solve real world word problems involving all cases of elapsed time in minutes (3.MD.1). For example, Problem Set, Problem 4 states, “Tessa walks her dog for 47 minutes. Jeremiah walks his dog for 30 minutes. How many more minutes does Tessa walk her dog than Jeremiah?”
• In Unit 7, Lesson 12, students apply their understanding of volume in real world contexts (3.MD.2). For example, Target Task, Problem 2 states, “Elijah uses 275 mL of milk for a recipe. He has 367 mL of milk left. How much milk did Elijah have before using some for his recipe?”

Examples of non-routine application include, but are not limited to:

• In Unit 1, Lesson 14, students solve one- and two-step problems involving addition and subtraction, using rounding to assess the reasonableness of the solution. For example, Problem Set, Problem 6 states, “Third-grade students took a total of 1,000 pictures during the school year. Ted took 72 pictures. Mary took 48 pictures. Part A: What is the total number of pictures taken by the rest of the third-grade students during the school year? Part B: Ella took 8 more pictures than Ted took. How many more pictures did Ella take than Mary?” (3.OA.8).
• In Unit 3, Lesson 16, students solve one- and two-step word problems involving units up to 9 (3.OA.8). For example, Problem Set, Problem 7 states, “Solve. Show or explain your work. a. Roland ate three pancakes at IHOP. His sister Janice ate two more than that. The total price for the pancakes was $24. How much did each pancake cost? b. Janice’s dad decided to order 3 pancakes of his own and 2 glasses of juice. The bill, including the cost of Roland’s and Janice’s pancakes, now comes to$29. How much does each glass of juice cost?”
• In Unit 4, Lesson 8, students solve word problems involving area (3.MD.7b). For example, Problem Set, Problem 4 states, “A rectangular garden has a total area of 48 square meters. What are the possible length and width of the garden? Come up with two possibilities.”
• In Unit 5, Lesson 10, students solve a variety of word problems involving area and perimeter (3.MD.8). For example, Problem Set, Problem 5 states, “A path is built around a pool in the shape of a rectangle. The width of the pool is 7 yards. The area of the pool is 70 square yards. Find the length, in yards, of the pool. Find the perimeter, in yards, of the pool.”
• In Unit 6, Lesson 13, students place any fraction on a number line with endpoints greater than 0, (3.NF.2). For example, Problem Set, Problem 2 states, “A student was asked to place 6/2 on a number line from 2 to 6. Here is their work.” A picture of student work is shown, and the problem states, “Evaluate their work by thinking about: Is it correct? Why? If it is incorrect, what mistake did the student make?”

### Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 3 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 program materials.

Examples of Conceptual Understanding include:

• In Unit 2, Lesson 3, students “identify and create situations involving unknown group size and find group size in situations,” (3.OA.2). In Anchor Task, Problem 1 states, “Split 18 counters equally into two groups. a. How many counters do you have in each group? b. Write a multiplication equation to represent this situation.”
• In Unit 3, Lesson 1, students use arrays, number lines and tape diagrams to explore commutativity to find known facts of 6, 7, 8, and 9 (3.OA.5).  In Anchor Task, Problem 1 states, “Katia and Gerard are stocking shelves at the grocery store. Katia stocks 3 shelves with 6 boxes of cereal on each shelf. Gerard stocks 6 shelves with 3 boxes of cereal on each shelf. Katia says they put the same number of cereal boxes on each shelf. Gerard says they didn’t, since they stocked a different number of boxes of each of a different number of shelves. Who do you agree with, Katia or Gerard? Explain.” The Guiding Questions state, “Do you agree with Katia or Gerard? Why?  What could you have drawn to support your argument? Write an equation that represents your argument. Can you generalize this to more numbers? If you know the value of 8 fours, do you know the value of 4 eights? Why?” The Teacher’s Notes state, “Students will likely draw an array for this problem, since that is the representation encouraged by the problem context. But, they could also use a number line or tape diagram to support their answer.”
• In Unit 4, Lesson 9, students “compose and decompose rectangles, seeing and making use of the idea that the sum of the areas of the decomposed rectangles is equal to the area of the composed rectangle,” (3.MD.7c). In Anchor Task, Problem 1 states, “a. Cut out the large rectangle. Then cut it into two smaller rectangles along the darkened border. b. Find the area of each rectangle. c. Push the rectangles back together. Find the area of the new rectangle you made. What do you notice? What do you wonder?” Guiding Questions include but are not limited to, “What are the length and width of the combined rectangle? How are the areas of the separate rectangles related to the area of the combined rectangle?”
• In Unit 6, Lesson 3, students “partition a whole into equal parts, identifying and counting unit fractions using pictorial area models and tape diagrams, identifying the unit fraction numerically,” (3.G.2, 3.NF.1). In Anchor Task, Problem 2 states, “Make a model in which the shaded part represents the corresponding unit fraction. a. $$\frac {1}{3}$$ b. $$\frac {1}{2}$$ c. $$\frac {1}{6}$$” Students deepen their conceptual understanding with Guiding Questions, “How many pieces should we partition the whole into? How did you decide that based on the fraction? How many pieces should you shade? How did you decide that based on the fraction itself? Can we partition any of these shapes in different ways? Why is it possible to have equal parts of the same whole be different shapes? Can they be different sizes or just different shapes? Count each fractional unit for each model. (Count 1 third, 2 thirds, 3 thirds for Part (a) and similarly for Parts (b) and (c).)”

Examples of Procedural Skills and Fluency include:

• In Unit 1, Lesson 8, students “add two numbers with up to one composition within 1,000,” (3.NBT.2). Anchor Task, Problem 1 states, “Mr. Silver and Mrs. Ingall want to know the largest number they can represent with their base ten blocks. Mr. Silver has 4 tens, 2 hundreds, and 6 ones. Mrs. Ingall has 2 tens, 3 hundreds, and 8 ones. What’s the largest number they could represent with their base ten blocks? Show or explain how you know.”
• In Unit 2, Lesson 6, students “build fluency with multiplication facts using units of 2, 5, and 10,” (3.OA.7).  Anchor Task, Problem 2 states, “Solve. a. $$9 × 2 =$$ _____ b. _____ $$= 5 × 2$$ c. $$2 × 5 =$$ _____ d. _____ $$= 9 × 5$$ e. $$4 × 10 =$$ _____ f. _____ $$= 10 × 10$$.”
• In Unit 3, Lesson 12, students skip-count to build fluency with multiplication facts using units of 8 and 9 (3.OA.4,7). In Problem Set, Problem 3 states, “Skip count by nine to fill in the blanks. Match each number in the count-by with its multiplication fact. Then, use the multiplication expression to write the related division fact directly to the right.”

Examples of Application include:

• In Unit 1, Lesson 10, students “solve word problems involving addition, using rounding to assess the reasonableness of the solution,” (3.OA.8, 3.NBT.1,2). For example, the Target Task states, “Jesse practices the trumpet for a total of 165 minutes during the first week of school. He practices for 245 minutes during the second week. a. Estimate the total amount of time Jesse practices. b. How much time did Jesse actually spend practicing?”
• In Unit 2, Lesson 14, students “solve one-step word problems involving multiplication and division and write problem contexts to match expressions and equations” (3.OA.1-3). In Anchor Task, Problem 2 states, “Write a word problem that can be solved using the following expressions.  a.$$4 \times 6$$  b.$$15 \div 5$$”
• In Unit 3, Lesson 20, students “solve two-step word problems involving all four operations and assess the reasonableness of solutions,” (3.OA.8, 3.NBT.3). For example, Target Task states, “Solve. Explain why your answer is reasonable. There were 80 adults and 20 children at a school play. The school collected $8 for each adult’s ticket and$3 for each child’s ticket. The school donated $125 of the money from the tickets to a local theater program and used the remaining money to buy supplies for next year’s school play. How much money does the school have to buy supplies for next year’s play?” • In Unit 5, Lesson 7, students “solve more complex word problems involving perimeter, such as finding a missing side length given perimeter and other side lengths,” (3.MD.8). For example, Target Task, Problem 1 states, “Maya’s rectangular rug has a perimeter of 16 feet. The length of the rug is 5 feet. What is the width of the rug? a. 3 feet b. 9 feet c. 11 feet d. 13 feet” Examples of multiple aspects of rigor engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study include: • In Unit 3, Lesson 8, students use and apply the associative property to develop fluency with multiplication (3.OA.5,7,9). Problem Set, Problem 4 states, “What expression is another way to show $$7 \times 6$$? a. $$7 + (3 + 2)$$ b. $$7 \times (3 + 2)$$ c. $$7 + (3 \times 2)$$ d. $$7 \times (3 \times 2)$$.” • In Unit 7, Lesson 9, students apply their understanding of mass to real-world problems (3.MD.2). In Target Task, Problem 2 states, “Carla buys apples and peaches at the store. The mass of the apples is 724 grams. The mass of the peaches is 471 grams. How much greater is the mass, in grams, of the apples than the mass of the peaches?” ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 10/10 + - Criterion Rating Details The instructional materials reviewed for Match Fishtank Grade 3 meet the expectations for practice-content connections. The materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, provide students with opportunities to meet the full intent of the eight MPs, and attend to the specialized language of mathematics. ### Indicator 2e The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade-level. All Standards for Mathematical Practice are clearly identified throughout the materials in numerous places, that include but are not limited to: Unit Summaries, Criteria for Success, and Tips for Teachers. Examples include: • In Unit 3, the Unit Summary states, “students deepen their understanding of multiplication and division, including their properties. ‘Mathematically proficient students at the elementary grades use structures such as…the properties of operations…to solve problems’ (MP.7) (Standards for Mathematical Practice: Commentary and Elaborations for K–5, p. 9). Students use the properties of operations to convert computations to an easier problem (a Level 3 strategy), as well as construct and critique the reasoning of others regarding the properties of operations (MP.3). Lastly, students model with mathematics with these new operations, solving one- and two-step equations using them (MP.4).” • In Unit 2, Lesson 16, Criteria For Success states, “1. Make sense of a 3-Act Task and persevere in solving it (MP.1). 2. Solve two-step word problems involving addition, subtraction, multiplication, and division (MP.4). 3. Assess the reasonableness of a solution (MP.1).” • In Unit 6, Lesson 7, Tips for Teachers states, “Too often, when students are asked questions about what fraction is shaded, they are shown regions that are portioned into pieces of the same size and shape. The result is that students think that equal shares need to be the same shape, which is not the case. On the other hand, sometimes visuals do not show all of the partitions (Van de Walle, Teaching Student-Centered Mathematics, Grades 3–5, Vol. 2, p. 211). Thus, this lesson tries to address both of these potential misconceptions and deepen students’ conceptual understanding of fractions. Having students explain what it meant by ‘equal parts’ also provides opportunities for students to attend to precision. (MP.6).” Examples of the MPs being used to enrich the mathematical content include: • MP4 is connected to mathematical content in Unit 2, Lesson 9, Target Task, Problem 2, as students “solve one-step word problems involving multiplication or division with units of 2, 5, or 10, using a tape diagram to represent the problem if necessary (MP.4).” For example, “Jonathan is making lemonade for his lemonade stand. The recipe says you need 2 cups of sugar in each pitcher of lemonade. Jonathan wants to make 10 pitchers of lemonade. How many cups of sugar will he need?” • MP3, MP5, and MP6 are connected to the mathematical content in Unit 4, Lesson 2, Anchor Tasks, Problem 1, as students “Find the area of various figures by covering a space with concrete standard units without gaps or overlaps (MP.5, MP.6). Explain how two figures with the same number of square units but with different sized square units differ in size (MP.3).” For example, “Which of the following rectangles has the greatest area?” Show or explain your thinking.” Three different size rectangles are provided. Guiding Questions state, “Who decomposed and recomposed their rectangles to determine which one had the greatest area? Who tried to use some sort of area unit to find the area? What did you use for your area unit? I think Rectangle C has the greatest area because it is the longest. Do you agree or disagree? Why?” • MP1 and MP4 are connected to the mathematical content in Unit 7, Lesson 5, Anchor Tasks, Problem 2, as students “solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram, where the times cross the hour mark, including the following three cases: a. Where the end time is unknown. b. Where the start time is unknown. c. Where the duration is unknown (MP.1 and MP.4).” For example, “a. Ms. Banta leaves school at 4:52 p.m. She gets home at 5:13 p.m. How long was Ms. Banta’s commute home? b. Katherine wakes up from a nap at 2:26 p.m. Her watch tells her that she slept for 43 minutes. What time did Katherine fall asleep? c. Fernando leaves home at 7:48 a.m. It takes him 19 minutes to walk to school. What time will Fernando arrive at school?” ### Indicator 2f Materials carefully attend to the full meaning of each practice standard 2/2 + - Indicator Rating Details The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet expectations for carefully attending to the full meaning of each practice standard. The materials attend to the full meaning of each of the 8 Mathematical Practices (MPs). The MPs are discussed in both the Unit and Lesson Summaries as they relate to the overall content. The MPs are also explained, when applicable, within specific parts of each lesson, including but not limited to the Criteria for Success and Tips for Teachers. 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, but are not limited to: • MP1: In Unit 5, Lesson 8, Criteria for Success states, “Determine the dimensions of all possible rectangles with a given area (e.g., a 1-by-12 rectangle, 2-by-6 rectangle, and 3-by-4 rectangle all have an area of 12 square units) (MP.1).” For example, Anchor Task, Problem 1 states, “a. Create as many rectangles as you can with an area of 12 square units. b. Find the perimeter of each rectangle that you found. c. Record the information from Parts (a) and (b) in the table below. d. What do you notice about the rectangles you created? What do you wonder?” • MP2: In Unit 6, Lesson 3, Criteria For Success states, “Determine the unit fraction represented by an abstract description of a situation (MP.2).” For example, Problem Set, Problem 7 states, “A circle is divided into parts. Each part is 14 of the total area of the circle. Which sentence describes the circle? The circle has 1 small part and 3 large parts. The circle has 1 small part and 4 large parts. The circle has 4 parts that are each the same size. The circle has 5 parts that are each the same size.” • MP4: In Unit 3, Lesson 28, Criteria for Success states, “Solve one- and two-step word problems using information presented in scaled picture and bar graphs, including “how many more” and “how many less” problems (MP.4).” For example, Anchor Task, Problem 1 states, “The picture graph below shows how many trees of each kind were in the arboretum. a. How many more evergreen trees than maple trees are there? (Fir trees and spruce trees are evergreen trees. b. In total, there were 111 trees in the arboretum. All of the trees were either fir, spruce, maple or oak trees. How many oak trees are there in the arboretum? • MP5: In Unit 4, Lesson 1, Criteria for Success states, “Find the area of various figures by covering a space with concrete non-standard units without gaps or overlaps (MP.5, MP.6).” For Example, Anchor Task, Problem 2 states, “Area is the measure of how much flat space an object takes up. Compare the areas of the medium triangle and the parallelogram. Guiding Questions: Which shape has greater area? How do you know? What makes comparing the areas of the medium triangle and the parallelogram more difficult than comparing the area of the large triangle and the area of the square from Anchor Task #1?” • MP6: In Unit 6, Lesson 7, Tips for Teachers states, “Having students explain what it meant by ‘equal parts’ also provides opportunities for students to attend to precision (MP.6).” For example, Problem Set, Problem 3 states, “Draw a shape below such that the shaded part of it represents 3/8 of the whole shape. Try to make it as complex as possible. Then explain how you know that the shaded part represents 3/8 .” • MP7: In Unit 2, Lesson 2, Criteria For Success states, “Relate arrays to equal groups, relating rows to the number of groups and the number of objects in each row to the size of groups (MP.7).” For example, Anchor Task, Problem 2 states, “Can you rearrange the following groups so that they are in an array? Why or why not?” • MP8: In Unit 3, Lesson 2, Criteria for Success states, “Look for and express regularity and repeated reasoning when multiplying by 1 to generalize the pattern of multiplying any number by 1 results in a product that is just that number (i.e., $$1\times n=n$$) (MP.8).” For example, Anchor Task, Problem 1 states, “a. Rudy is waiting patiently for his new hen to lay some eggs. On Monday, he went to the henhouse to check their nests. He has 12 hens in the house, and each hen had laid 0 eggs. How many eggs did Rudy have in total?” b. On Tuesday when he went outside, he discovered that each of his 12 hens had laid 1 egg. How many eggs does he have now?” Guiding Questions include but are not limited to, “What if Rudy had 6 hens that each laid 1 egg? How many eggs would he have in total? Can you write an equation to represent this situation? What if Rudy had 20 hens that each laid 1 egg? How many eggs would he have in total? Can you write an equation to represent this situation?” ### Indicator 2g Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by: 0/0 ### Indicator 2g.i Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards. 2/2 + - Indicator Rating Details The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. The student materials consistently prompt students to construct viable arguments and analyze the arguments of others, for example: • In Unit 1, Lesson 7, Anchor Tasks, students “construct and critique reasoning for rounding two- and three-digit numbers to the nearest ten or hundred.” Problem 1 states, “A pair of pants cost$52. Mrs. Ingall says that the pants are about $50. Mr. Silver says they are about$100. Who is correct, Mr. Silver, Mrs. Ingall, both of them, or neither of them? Explain your answer.”
• In Unit 3, Lesson 1, Target Task, students “demonstrate and explain the commutativity of multiplication using models (MP.3).”  Problem 2 states, “Karen says, ‘If I know $$8 \times 3 = 24$$, then I know the answer to $$3 \times 8!$$’ Explain why this is true.”
• In Unit 4, Lesson 1, Anchor Task, students construct a viable argument to justify which shape takes up more space. Problem 1 states, “Does the large triangle or square take up more space? Justify your answer.”
• In Unit 5, Lesson 12, Anchor Task states, “Sort these shapes (cut out from Template: Polygons) into groups. You may sort them any way you want and into as many groups as you want.” Guiding Questions state, “What is true about all of these shapes?” and “Which shapes are quadrilaterals? For those shapes that are not quadrilaterals, are they still polygons? Why or why not?” Students “Classify polygons according to their attributes, like number of sides and angles, and justify this classification (MP.3).”
• In Unit 6, Lesson 21, Anchor Tasks, students compare fractions in order to choose which snack they would take a piece from, and then construct a viable argument to defend their choice. Problem 1 states, “Kiana bought two Fruit-by-the-Foot snacks to share with friends. She splits one of them into 3 equal-sized pieces and the other into 8 equal- sized pieces. If Kiana were sharing a piece of Fruit-by-the-Foot with you, which snack would you take a piece from, the 3-piece snack or the 8-piece snack? Explain why.”

### Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The teacher materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others through the Criteria for Success, Guiding Questions, and Tips for Teachers, for example:

• In Unit 1, Lesson 7, Tips for Teachers states, “This whole lesson provides an excellent opportunity for students to construct viable arguments and critique the reasoning of others regarding when to round and to what level of precision, based on the context of the problem (MP.3). ‘How close an estimate must be to the actual computation is a matter of context,’ and thus ‘the goal of computational estimation is to be able to flexibly and quickly produce an approximate result that will work for the situation and give a sense of reasonableness’ (Van de Walle, p. 195). Thus, these tasks offer an opportunity for a rich discussion where one’s decision about the degree of precision of an estimate should be supported by reasoning.”
• In Unit 3, Lesson 2, Criteria for Success states, “4. Explain why any number divided by 0 results in an impossible product by rewriting the division sentence as a multiplication one to see that no such value exists (e.g., $$6\div0 = a \rightarrow a\times0 = 6$$, and no such a exists since any number multiplied by 0 would have a product of 0) (MP.3).” In Anchor Tasks, Problem 3, Guiding Questions include, but are not limited to, “Imagine the equation $$9\div0 = e$$. What do you think the solution is? How can the relationship between multiplication and division help you to think about this problem? (Rewrite $$9\div0 = e$$ as $$e\times0=9$$, which will help students to see that no such number exists.)”
• In Unit 5, Lesson 9, Tips for Teachers states, “With strong and distinct concepts of both perimeter and area established, students can work on problems to differentiate their measures. For example, they can find and sketch rectangles with the same perimeter and different areas or with the same area and different perimeters and justify their claims” (MP.3).”
• In Unit 6, Lesson 2, Criteria for Success states, “5. Determine whether a model represents equal sharing/fractions and explain why or why not (MP.3).” In Anchor Task, Problem 3 states, “Noah believes the shape below represents 3 eighths. Explain why Noah is incorrect in his reasoning. Draw a correct model to represent 3 eighths. Explain why your model is correct.” Guiding Questions include, but are not limited to: “What must be true about the pieces in order for them to represent fractional parts of the whole? Is that true of Noah’s model? Let’s construct our own model to represent 3 eighths. How can we use our fraction strips from Anchor Task #2 to help us? How many equal pieces must our model have? How do you know? How many pieces are counted? How can we indicate the counted pieces in our model? Do our shaded pieces have to be right next to each other? Why or why not?”

### Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 3 meet expectations for explicitly attending to the specialized language of mathematics.

Examples of the materials providing explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols include:

• In Unit 1, Lesson 5, Tips for Teachers states, “You’ll want to avoid using terms like ‘round up’ and ‘round down’, since these terms can be confusing for students. ‘Rounding up’ a number results in a change in the value of the place to which you’re rounding, where ‘rounding down’ does not. Often students will change the value mistakenly as a result.”
• In Unit 2, Lesson 7, Tips for Teachers states, “Students need not use formal terms for the properties of operations, including the terms ‘commutative’ or commutative property.’ However, exposure to the term is helpful so that students can develop and use a common language and thus introduced in this lesson.”
• In Unit 3, Lesson 17, Tips for Teachers states, “Make sure to be precise in language use when discussing how basic multiplication facts are related to multiplication by multiples of ten (e.g., how $$2 \times 4$$ is related to $$2 \times 40$$). Avoid saying ‘add a zero,’ and instead discuss how the units shift. This serves two purposes: (1) it doesn’t conflate two operations, multiplication with addition, and (2) it is aligned to the work they’ll do in later grades of seeing how digits shift places when multiplying or dividing numbers by powers of ten, including decimals, where in fact ‘adding a zero’ after a decimal point won’t change its value.”
• In Unit 5, Lesson 11, Tips for Teachers states, “Students have learned much of the vocabulary used in today’s lesson in prior grade levels, but not all. New vocabulary includes parallel, right angle, parallelogram, and quadrilateral. The term quadrilateral in particular provides ‘the raw material for thinking about the relationships between classes. For example, students can form larger, superordinate, categories, such as the class of all shapes with four sides, or quadrilaterals, and recognize that it includes other categories, such as squares, rectangles, rhombuses, parallelograms, and trapezoids. They also recognize that there are quadrilaterals that are not in any of those subcategories’ (Geometry Progressions, p. 13).”
• In Unit 7, Lesson 7, Tips For Teachers states, “As noted in the Progressions, ‘the Standards do not differentiate between weight and mass. Technically, mass is the amount of matter in an object. Weight is the force exerted on the body by gravity. On the earth’s surface, the distinction is not important (on the moon, an object would have the same mass, would weigh less due to the lower gravity) (GM Progression, p. 2).’ Thus, the discussion is excluded from the lesson and the use of ‘mass’ and ‘weight’ interchangeably is avoided. But, it could be discussed if a student raises the issue.”

Examples of the materials using precise and accurate terminology and definitions when describing mathematics, and supporting students in using them, include:

• At the beginning of each unit, the Unit Prep provides vocabulary for the unit. As found in Unit 1, “Digit, estimate, interval, place, reasonable, value, etc.”
• In Unit 1, Lesson 3, Criteria for Success, students will, “Understand that a number line is a straight line with equally spaced intervals used to plot numbers.”
• In Unit 2, Lesson 1, Criteria for Success, students will, “Use the multiplication symbol to represent equal groups.”
• In Unit 5, Lesson 1, Criteria for Success, students will, “Understand perimeter to be the boundary of a shape.”
• In Unit 6, Lesson 1, Criteria for Success, students will, “Understand that a fraction is an equal share of a whole.”
• In Unit 7, Lesson 7, Anchor Task Problem 1, Guiding Question states, “The mass of an object is its heaviness. Which object has more mass, the thumbtack or the textbook? How do you know?”

## Usability

### Criterion 3a - 3e

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

The instructional materials reviewed for Match Fishtank Grade 3 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

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.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson.

There are seven instructional units in Grade 3. Lessons within the units include Anchor Tasks, Problem Sets, Homework, and Target Tasks. The Anchor Tasks serve either to connect prior learning or to engage students with a problem in which new math ideas are embedded. Students learn and practice new mathematics in the Anchor Tasks. For example:

• In Unit 6, Lesson 4, Anchor Task, Problem 2, students build and write non-unit fractions less than one whole (3.NF.1). The problem states, “Make a model in which the shaded part represents the corresponding unit fraction.” Students are given a circle to model, a rectangle to model, and a square to model.

In the Problem Set and Homework sections, students have opportunities to build on their understanding of each new concept. Each lesson ends with a Target Task which provides students the opportunity to apply what they have learned from the lesson, and can be used to formatively assess understanding of the content. For example:

• In Unit 2, Lesson 12, Problem Set, Problem 3, students solve one-step word problems involving multiplication and division using units of 3 and 4 (3.OA.1, 3.OA.2, 3.OA.3). The problem states, “Thirty third-graders go on a field trip. They are divided equally into 3 vans. How many students are in each van?”
• In Unit 4, Lesson 9, Homework, students compose and decompose rectangles, and learn that the sum of the areas of the decomposed rectangles is equal to the area of the composed rectangle (3.MD.7d). Problem 4 states, “Decompose the following area model into rectangles whose fact you can use to find the larger product.” Students are given a $$13 \times 7$$ rectangle on a grid to decompose.
• In Unit 5, Lesson 8, Target Task, students find rectangles with the same area and different perimeters (3.MD.8). The problem states, “Eddie wants to put a deck in his backyard. He has a few different options for sizes, one of which is shown below.” (A rectangle with the dimensions of 10 feet by 2 feet is shown.) a. What is the perimeter of Deck A above? b.  Deck B, another of Eddie’s options, has the same area as the one above by a different perimeter. Draw one possible shape for Deck B below. Explain how you found your answer.”

### Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for exercises within student assignments being intentionally sequenced.

Overall, Units, Lessons, Activities, and Target Tasks are intentionally sequenced, so students have the opportunity to develop understanding of the content. The structure of each lesson provides students the opportunity to activate prior knowledge. Anchor Tasks engage students in problems that are sequenced from the concrete to the abstract and increase in complexity. Each lesson closes with a Target Task which is typically two questions assessing the daily lesson objective. In the Problem Sets and Homework, students independently apply learning from the lesson.

### Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for having variety in what students are asked to produce.

The instructional materials prompt students to produce written answers and solutions in the Problem Sets, Homework, and Target Tasks. In the Anchor Tasks, whole group instruction provides students with the opportunity to produce oral arguments and explanations through discussion in whole group, small group, or partner settings. Written critiques of fictional students’ work are produced and include models, drawings, and calculations.

Students are prompted through the materials to use appropriate mathematical vocabulary in all their oral and written work. The materials introduce a variety of mathematical representations through sequenced lessons. Students choose which representation to use in later lessons. Examples include, but are not limited to:

• In Unit 1, Lesson 7, students construct and critique reasoning for rounding two- and three-digit numbers to the nearest ten or hundred (3.NBT.A.1). For example, Anchor Task, Problem 1 states, “A pair of pants cost $52. Mrs. Ingall says the pants are about$50. Mr. Silver says they are about \$100. Who is correct, Mr. Silver, Mr. Ingall, both of them, or neither of them? Explain your answer.”
• In Unit 3, Lesson 8, students use the associative property as a strategy to multiply by units of 6 (3.OA.5,7,9). For example, Problem Set, Problem 2 states, “Libby says the answer to the problem 5 x 2 x 3 = 25. Her work is shown. Step 1: $$5 \times 2 = 5 \times 2 = 10$$ Step 2: $$5 \times 3 = 15$$ Step 3: $$10 + 15 = 25$$ Which is true? A.  Libby’s answer is correct because $$10 + 15 = 25$$. B. Libby’s answer is correct because $$2 + 3 = 5$$ and $$5 \times 5 = 25$$. C. Libby’s answer is not correct because she multiplied $$5 \times 3$$ and $$5 \times 2$$. D. Libby’s answer is not correct because she should have multiplied $$10 \times 15$$.”
• In Unit 5, Lesson 8, students find rectangles with the same area and a different perimeter (3.MD.8). For example, Homework, Problem 7 states, “Imagine all of the rectangles you could build with an area of 25 square units. Which one do you think will have the least perimeter? Why?”

### Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 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 integrates hands-on activities that include the use of physical manipulatives.

Manipulatives and other mathematical representations are aligned to the standards, and the majority of manipulatives used are commonly available in classrooms. Lessons include paper templates of many manipulatives, and examples include, but are not limited to:

• In Unit 2, Lesson 3, counters are used to create equal groups when exploring the concept of multiplication.
• In Unit 4, Lesson 2, students use square tiles and centimeter cubes to understand the concept of area. Square centimeter grids and square inch grids cut into tiles are provided if tiles or cubes are not available.
• In Unit 6, Lesson 1, Anchor Task, Problem 1, students begin to investigate the concept of fractions using pattern blocks.

Manipulatives used in Grade 3 include, but are not limited to:

• Base ten blocks, number lines, place value charts, counters, tape diagrams, counters, grid paper, multiplication chart, square tiles, fraction strips, ruler, pattern blocks, analog scale, balance scale, beakers, containers of various capacities, digital scale, and snap cubes.
• Templates provided in place of three-dimensional manipulatives: tangrams, square inch grid, centimeter grid, and tetrominoes.

### Indicator 3e

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

The instructional materials for Match Fishtank Grade 3 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

• The digital lesson materials for teachers follow a consistent format for each lesson. The lessons include links to all teacher and student materials needed for each lesson. Notes for teachers are provided for most lessons to provide additional information or content support for the teacher to use when implementing the lesson. Unit overviews also follow a consistent format.
• Student digital materials follow a consistent format. Tasks within each lesson are numbered to match teacher materials. All print and visuals within the student pages are clear without any distracting visuals.
• Student problem pages include enough space for the student to respond and show their thinking.
• Graphics are clear and add to the instructional materials.

### Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
6/8
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Criterion Rating Details

The instructional materials for Match Fishtank Grade 3 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

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 meet the expectations for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Most math lessons contain Anchor Tasks Guiding Questions, Anchor Task Notes, and/or Discussions of Problem Sets. Examples include:

• The materials state, “Each Anchor Task is followed by a set of Guiding Questions. The Guiding Questions can serve different purposes, including: scaffolding the problem, extending engagement of students in the content of the problem, and extending the problem. Not all Anchor Tasks include Guiding Questions that address all three purposes, and not all Guiding Questions are meant to be asked to the whole class as there is discretion for the teacher to determine how, when, and which questions should be used with which students.” For example, Unit 3, Lesson 1, Anchor Task, Problem 1, “Do you agree with Katia or Gerard? Why? What could you have drawn to support your argument? Write an equation that represents your argument. Can you generalize this to more numbers? If you know the value of 8 fours, do you know the value of 4 eights? Why?”
• Anchor Task Notes are often included after the Guiding Questions. These Notes include problem-specific information that may be helpful in understanding or executing the problem.
• The Discussion of Problem Sets includes a list of “suggested questions for teachers to ask after students have worked on the Problem Set but before they attempt the Target Task. Similar to the Guiding Questions for Anchor Tasks, these questions can serve different purposes, including: connecting the content of the Problem Set to previous learnings (including major work and/or connections across clusters and domains, if applicable), more deeply engaging students in the content of the Problem Set, and extending on the Problem Set. Not all Discussions of Problem Sets include questions that cover all three purposes. Also, not all Discussion questions are meant to be asked to the whole class; rather, it should be at the discretion of the teacher to determine how, when, and which questions should be used with which students.” For example, Unit 3, Lesson 20 states, “In #1, how many more months will Lupe need to save so she has enough to buy the art supplies? How do you know? Explain the three unknowns you needed to find to solve #3. How did you solve #5? Which strategy did you use? Where did you draw your darts in the second part of #6? Is there more than one correct answer? How did you solve #7? Which strategy did you use? What made #8 challenging? What did you need to keep in mind in terms of finding the total number of rows on the airplane?”

### Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 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.

Tips for Teachers are present in most lessons, support teachers with resources, and include an overview of the lesson. The materials state, “Tips for Teachers serve to ensure teachers have the support and knowledge they need to successfully implement the content. This section includes helpful suggestions and notes to support understanding and implementation of the lesson.” Tips for Teachers includes, but is not limited to: guidance on pacing, connections to other lessons within the unit or in different units or grade-levels, prior skills or concepts students may need to access the lesson, standards for Mathematical Practice emphasized in the lesson, and potential misconceptions students may have with the content. For example:

• In Unit 2, Lesson 7, Tips for Teachers states, “Students need not use formal terms for the properties of operations, including the terms ‘commutative’ or ‘commutative property.’ However, exposure to the term is helpful so that students can develop and use a common language and thus is introduced in this lesson.”

In Unit 7, Lesson 5, Tips for Teachers states, “According to 3.MD.1, students are expected to ‘solve word problems involving addition and subtraction of time intervals in minutes.’ Bill McCallum notes on his blog, ‘Time intervals in minutes doesn’t have to mean “less than an hour.” For example, there’s no reason why Grade 3 students can’t say how many minutes it is from 3:30 to 5:00’ (Elapsed Time (3.MD.1 vs. 4.MD.2), Mathematical Musings). Thus, the Problem Set and Homework include problems where students will work with elapsed time that is still given in minutes, as the standard requires, but exceeds an hour.”

### Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
0/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 do not meet expectations for containing 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

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.
2/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 meets the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum. For example:

• Each grade opens with a Course Summary, that identifies the “key advancements from previous years.” For example, the Grade 3 Course Summary states, “Grade 3 focuses on four key advancements from previous years: (1) developing understanding of and fluency with multiplication and division within 100; (2) developing understanding of fractions, especially unit fractions; (3) developing understanding of rectangular arrays and of area; and (4) describing and analyzing two-dimensional shapes.” An explanation about how the units are sequenced is also provided.
• Each unit opens with a Unit Summary, which details the specific grade level content to be taught, as well as connections to previous and future grades.
• Each lesson provides current standards addressed in the lesson, as well as foundational standards taught in previous units or grades that are important background for the current lesson.

### Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 provide a list of lessons in the Teacher's Edition, cross-referencing the standards addressed, and a pacing guide.

There is a pacing guide for each grade, which details the amount of instructional days for lessons, unit assessments, and flex days. The pacing guide also includes the breakdown/lesson structure, along with a listing of the topic(s) of each unit. Additionally, each unit contains a specific number of lessons, a day for assessment, and a recommended number of flex days.

### Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 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

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

The instructional materials for Match Fishtank Grade 3 contain explanations of the program's instructional approaches and identification of research-based strategies in the “Our Approach” section.

From the materials, “The goal of our mathematics program is to provide our students with the skills and knowledge they will need to succeed in college and beyond. At Match, we seek to inspire our scholars to pursue advanced math courses, and we provide them with the foundations they will need to be successful in advanced math study. Our math curriculum is rooted in the following core beliefs about quality math instruction.” The materials state:

• Content Rich Tasks - “We believe that students learn best when asked to solve problems that spark their curiosity, require them to make novel connections between concepts, and may offer more than one avenue to the solution.”
• Practice and Feedback - “We believe that practice and feedback are essential to developing students’ conceptual understanding and fluency.”
• Productive Struggle - “We believe that students develop essential strategies for tackling complex problems, and build non-cognitive skills such as grit and resilience, through productive struggle.”
• Procedural Fluency and Conceptual Understanding - “We believe that knowing ‘how’ to solve a problem is not enough; students must also know ‘why’ mathematical procedures and concepts exist.”
• Communicating Mathematical Understanding - “We believe that the process of communicating their mathematical thinking helps students solidify their learning and helps teachers assess student understanding.”

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
6/10
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Criterion Rating Details

The instructional materials for Match Fishtank Grade 3 do not meet the expectations for providing strategies for gathering information about student’s prior knowledge, do not include aligned rubrics and scoring guidelines that provide sufficient guidance for teachers to interpret student performance and suggestions for follow-up, or provide strategies or resources for students to monitor their own progress. The materials partially meet the expectations for offering formative and summative assessments. The materials meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions, and provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grades 3 do not meet expectations for providing strategies for gathering information about student’s prior knowledge within and across grade levels.

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

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Examples include:

• In Unit 2, Lesson 1, Tips for Teachers states, “Students will learn to write factors in the conventional order, namely with the number of groups written as the first factor and the size of the groups as the second factor. But, since “some students bring th[e] interpretation of multiplication equations [where the meaning of the factors is switched] into the classroom, …it is useful to discuss the different interpretations and allow students to use whichever is used in their home” (OA Progression, p. 25), if it comes up. Thus, use the conventional way of writing factors when addressing the whole class, but allow individual students to write them in reverse order if they have experience doing so and they are able to explain the meaning of each factor. In Lesson 7, students will learn the commutative property, after which all students will be given much more free reign over the order in which they write their factors.”
• In Unit 5, Lesson 4, Tips for Teachers states, “‘Perimeter problems for rectangles and parallelograms often give only the lengths of two adjacent sides or only show numbers for these sides in a drawing of the shape. The common error is to add just these two numbers. Having students first label the lengths of the other two sides as a reminder is helpful,’ (MD Progression, p. 16).”

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

Each lesson is designed with teacher-led Anchor Tasks, Problem Sets, and Target Tasks. 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:

• In Unit 2, Lesson 4, Anchor Task, the Problem 2 Notes state, “You could introduce the use of skip-counting and/or repeated subtraction here to connect back to previous strategies used for multiplication. But since students are still either being given a model or asked to draw one for most problems, you can delay the discussion of those strategies.”
• In Unit 4, Lesson 5, Tips For Teachers states, “Today’s lesson is the first one where students will not be given concrete units in order to find the area of rectangles. Students may still want to draw individual units to find the area of rectangles, but hopefully most students are completing rows and columns instead. As the Progressions note, ‘less sophisticated activities of this sort were suggested for earlier grades so that Grade 3 students begin with some experience,’ so development towards this row and column understanding should be fairly straightforward (GM Progression, p. 17).”

### Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
2/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 meet the expectations for assessments clearly denoting which standards are being emphasized.

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

• In Unit 2, Multiplication and Division, Part 1, Assessment Item 2 correlates with 3.OA.1.
• In Unit 5, Shapes and Their Perimeter, Assessment Item 5 correlates with 3.MD.8.
• In Unit 7, Measurement, Assessment Item 7 correlates with 3.MD.2.

### Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 do not meet expectations for including 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 includes the correct answer, limited scoring guidance, and no guidance for teachers to interpret student performance. For example:

• In Unit 6, Multiplication and Division of Decimals, Unit Assessment, Item 1, “1 point for each part - no partial credit; a. 34.8 b. 7.78 c. 0.525 d. 2.7.”

There is no guidance for teachers to interpret student performance and suggestions for follow up.

### Indicator 3q

Materials encourage students to monitor their own progress.
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grades 3 do not provide any strategies or resources for students to monitor their own progress.

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
9/12
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Criterion Rating Details

The instructional materials for Match Fishtank Grade 3 do not meet expectations for supporting teachers in differentiating instruction for diverse learners. 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

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
1/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 partially meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. For example:

• At the beginning of each unit, the Unit Summary provides a look back at prior learning connected to the unit content, a detailed summary of the unit content with connections to the Math Practices, and ends with a forward look at where the content is going in future grades. Teachers can use this information to scaffold learning.
• The materials include a detailed pacing guide that outlines lessons and the recommended number of instructional days.
• Each lesson provides foundational standards that teachers may use to differentiate the lesson for struggling learners.
• Throughout the lessons, there are Notes, Tips for Teachers, and Guiding Discussion Questions.
• Prior to the Independent Practice problems and Homework, students practice new content in the Anchor Task guided by the teacher. However, there is no guidance for teachers on how to scaffold the instruction or address student misconceptions.
• Teachers use their discretion as to how to use the Practice Set problems. There is little to no guidance to determine what materials or strategies to use to scaffold instruction. No guidance is provided to determine how to present the Practice Problems for students to find an entry point or how to determine and address student misconceptions.
• Each lesson provides a Target Task as a diagnostic to assess the day’s learning. This assessment information can be used to scaffold upcoming lessons.

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
1/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 3 partially meet the expectations for providing teachers with strategies for meeting the needs of a range of learners. For example:

The units do not provide materials or a plan for differentiated instruction within teacher-guided, small-group options.

• The materials do provide some guidance on reteaching or modifying the lesson for struggling learners in Teacher Notes or Tips for Teachers. For example:
• In Unit 2, Lesson 6, Tips for Teachers provides guidance to reteach skip- counting by 2s, 5s, and 10s.
• In Unit 6, Lesson 26, students measure lengths to the nearest quarter inch. The Teacher Notes for Problem 3 suggest having “pre-created paper rulers on hand for those who physically or conceptually weren’t able to construct a precise ruler in Anchor Task #2.”
• The materials do not provide guidance or materials to extend learning for those students mastering lesson content.

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

Anchor Tasks, Problem Sets, Homework, and Target Tasks provide students opportunities to apply their learning from multiple entry points. Though the materials may present a concept using a specific strategy, most practice problems allow students to choose from a variety of strategies they have learned. For example:

• In Unit 2, Lesson 3, students learn about multiplication involving unknown group size and finding group size in situations. The Anchor Task presents the concept using arrays or equal groups. However, in the Problem Set, students are asked to, “Create a visual model of the stacks of paper.” Students may choose which visual model they use.
• In Unit 4, Lessons 1-8, students have experienced a variety of strategies to find area. In Lesson 8, students are allowed to choose the strategy that works best for them to solve area word problems.
• In Unit 6, Lesson 16, students use area models to find equivalent fractions. However, in the Problem Set, Problem 7, students are given the opportunity to draw any model to explain their answer.

### Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
1/2
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Indicator Rating Details

The instructional materials for Match Fishtank Grades 3 partially meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. In the Teacher Tools section, “A Guide to Supporting English Learners,” features the use of scaffolds, oral language protocols, and graphic organizers. However, there are no features on providing support or accommodations to English Language Learners and other special populations throughout the materials.

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

Specific strategies for support, accommodations, and/or modifications are mentioned in “A Guide to Supporting English Learner” that include sensory, graphic, and interactive scaffolding; oral language protocols which include many cooperative learning strategies, some of which mentioned in teacher notes; and using graphic organizers with empathize on lighter or heavier scaffolding. For example, Oral Language Protocols provide structured routines to allow students to master opportunities and acquire academic language. Several structures are provided with an explanation on ways to 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 provided for special populations.

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. For example:

• Unit 2, Lesson 16, Problem Set, Problem 7, “The cycle shop on Main Street sells bikes (two wheels) and trikes (three wheels). Yesterday, Sarah counted all of the cycles in the shop. There were seven bikes and four trikes in the shop. How many wheels were there on these eleven cycles?” “CHALLENGE: Today, Sarah counted all of the wheels of all the cycles in the shop. She counted that there were 30 wheels in all. There were the same number of bikes as there were trikes. How many bikes were there? How many trikes were there? Show how you figured it out.”

### Indicator 3w

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

The instructional materials reviewed for Match Fishtank Grade 3 meet expectations for providing a balanced portrayal of various demographic and personal characteristics. The lessons contain students that have a variety of demographic and personal characteristics that do not illustrate gender bias, lack of racial or ethnic diversity, or racial or naming stereotyping. For example:

• Different cultural names and situations are represented in the materials, for example: Spencer, Presley, Anthony, Karen, Heidi, Caesar, Lila, Mrs. Kozlow, and Marlene.
• In Unit 2, Lesson 1, Problem Set, Problem 4 states, “Caroline, Brian, and Marta share a box of chocolates. They each get the same amount. Circle the chocolates below to show 3 groups of 4. Then, write a repeated addition sentence and a multiplication sentence to represent the picture.” The problem does not have any student taking on a larger role than the other.

### Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grades 3 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, and there are no directions or examples for teachers to adapt the lessons or suggestions on when and how to incorporate then are not included in the teacher materials. For example:

• In Grade 3, Unit 3, Lesson 2, Discussion of the Problem Set states, "Discuss with a partner what patterns for multiplying and dividing by 0 and 1 helped you solve #1? #5?"
• In Grade 4, Unit 4, Lesson 9, Discussion of the Problem Set states, "Why is it important to be precise when drawing angles? Tell your partner how you can be precise when drawing angles."
• In Grade 5, Unit 5, Lesson 19, Discussion of Problem Set states, “Share your solution and compare your strategy for solving #3 with a partner.”

### Indicator 3y

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

The instructional materials for Match Fishtank Grades 3 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 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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Criterion Rating Details

The instructional materials for Match Fishtank Grade 3 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

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
0/0
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 are web-based and compatible with multiple internet browsers. Print resources may be downloaded from the website as teacher edition pages and PDF files for student resources.

The 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 compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, Safari, etc.).

The materials are compatible with various devices including iPads, Iaptops, Chromebooks, and other devices that connect to the internet with an applicable browser.

### Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grades 3 do not include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology.

### Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
0/0
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 do not include opportunities for teachers to personalize learning, including the use of adaptive technologies.

The instructional materials reviewed for Match Fishtank Grade 3 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.).
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grades 3 do not include or reference technology that provides opportunities for teachers and/or students to collaborate with each other in the form of websites, discussion groups, webinars, etc.

### Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 3 do not integrate technology that could include interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the MPs.

While there are a few game resources listed at the Public Schools of North Carolina, the links do not work. For example, Unit 1, Lesson 5, tips for teachers, “Before the Problem Set, you could have students play ‘Take Your Places’ from Building Conceptual Understanding and Fluency Through Games by the Public Schools of North Carolina.” Considering the usability of this technology resource, students do not have opportunities in the materials to engage in the content standards and MPs through technology.

abc123

Report Published Date: 2020/01/14

Report Edition: 2019

Fishtank Math instructional materials can be accessed at https://www.matchfishtank.org/.

This review was conducted May - December 2019 and reflects the materials available during review.

## Math K-8 Review Tool

The mathematics review criteria identifies the indicators for high-quality instructional materials. The review criteria supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our review criteria evaluates materials based on:

• Focus and Coherence

• Rigor and Mathematical Practices

• Instructional Supports and Usability

The K-8 Evidence Guides complements the review criteria by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

## Math K-8

K‑8 Evidence Guide K‑8 Review Criteria

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways.

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom.

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.