Alignment: Overall Summary

The instructional materials reviewed for Match Fishtank, Grade 5 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

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Match Fishtank Grade 5 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 78% of instructional time on the major work of the grade, and they also meet expectations for being coherent and consistent with the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 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.
2/2
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Indicator Rating Details

​The instructional materials reviewed for Match Fishtank Mathematics Grade 5 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 10 states, “Which is greater, 0.13 or 0.031? Explain. Which is greater, 0.203 or 0.21? Explain.” (5.NBT.3b)
• Unit 2 Assessment, Question 2 states, “A construction team uses 184 sheets of plywood for each house it builds.  The team will build 12 houses this year. What is the total number of sheets of plywood the team will use to build all 12 houses?” (5.NBT.5)
• Unit 3 Assessment, Question 5 states, “A cereal box has a height of 32 centimeters. It has a base with an area of 160 square centimeters. What is the volume, in cubic centimeters, of the cereal box?” (5.MD.5b)
• Unit 4 Assessment, Question 7 states, “Solve. 14.4 - 5.63.” (5.NBT.7)
• Unit 5 Assessment, Question 5 states, “Jim uses ribbon to make bookmarks. Jim has 9 feet of ribbon. He uses $$\frac{1}{3}$$ foot of ribbon to make each bookmark. What is the total number of bookmarks Jim makes with all 9 feet of ribbon?” (5.NF.7)
• Unit 6 Assessment, Question 6 states, “Tom has a water tank that holds 5 gallons of water. Tom uses water from a full tank to fill 6 bottles that each hold 16 ounces and a pitcher that holds $$\frac{1}{2}$$ gallon. How many ounces of water are left in the water tank?” (5.MD.1)
• Unit 7 Assessment, Question 3 states, “Dante and Helen each created a number pattern that started with the number 0. Dante used the rule “Add 3”. Helen used the rule “Add 6”. a. Complete the following table with both Dante’s and Helen’s pattern (table provided). b. Describe any patterns you see in the corresponding terms in Dante’s pattern and Helen’s pattern. Why do you think that pattern exists?” (5.OA.3)

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 5 instructional materials, when used as designed, spend approximately 78% 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 5 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 6 out of 7, which is approximately 86%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 100 out of 128, which is approximately 78%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 119 out of 140, which is approximately 85%.

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 78% of the instructional materials focus on major work of the grade.

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 5 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 5 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 2, Lesson 20, Anchor Tasks, students write and interpret numerical expressions (5.OA.A) to solve word problems involving multi-digit multiplication and division (5.NBT.5,6). Problem 4 states, “On Saturday, the owner of a department store gave away a 15 gift card to every 25th customer. A total of 8,879 customers came to the store on Saturday. What is the total value of the gift cards the owner gave away? How many additional customers would need to have come in for another gift card to be given away?” • In Unit 5, Lesson 24, Problem Set, students use equivalent fractions as a strategy to add and subtract fractions (5.NF.A) to solve problems involving information presented in a line plot (5.MD.2). Problem 3 states, “The line plot below shows the lengths of all the pieces of string Emma used for an art project. She cut all these pieces from one original piece of string. Emma had 1 foot of string left over. How long, in feet, was the original piece of string?” • In Unit 6, Lesson 24, Target Task, students add and subtract decimals (5.NBT.7) to solve real-world problems involving measurement conversions (5.MD.1). Problem 1 states, “Solve. Show or explain your work. Owen lives 1.2 kilometers from school. Lucia lives 0.86 kilometers from school. Ignacio lives 90 meters from school. If Ben, Alice, and Walter all walk to and from school, how far, in kilometers, did they all walk in total?” Indicator 1d The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. 2/2 + - Indicator Rating Details The instructional materials reviewed for Match Fishtank Mathematics Grade 5 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 140 instructional days (including lessons, flex days, and unit assessments). • There are 121 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. 2/2 + - Indicator Rating Details The instructional materials for Match Fishtank Mathematics Grade 5 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, “Unit 1 starts off with reinforcing some of this place-value understanding of multi-digit whole numbers to 1 million, building up to that number by multiplying 10 by itself repeatedly. After this repeated multiplication, students are introduced to exponents to denote powers of 10. Then, students review the relationship in a whole number between a place value and the place to its left (4.NBT.1) and learn about the reciprocal relationship of a place value and the place to its right (5.NBT.1). Students also extend their work from Grade 4 on multiplying whole numbers by 10 to multiplying and dividing them by powers of 10 (5.NBT.2). After extensive practice with whole numbers, students then divide by 10 repeatedly to extend their place-value system in the other direction, to decimals. They then apply these rules and perform these operations with powers of 10 to decimal numbers. Lastly, after deepening their understanding of the base-ten structure of our place-value system, students read, write, compare, and round numbers in various forms (5.NBT.3-4).” • The Unit 1 Summary also connects future grade level content: “This content represents the culmination of many years’ worth of work to deeply understand the structure of our place-value system, starting all the way back in Kindergarten with the understanding of teen numbers as ‘10 ones and some ones’ (K.NBT.1). Moving forward, students will rely on this knowledge later in the Grade 5 year to multiply and divide whole numbers (5.NBT.5—6) and perform all four operations with decimals (5.NBT.7). Students will also use their introduction to exponents to evaluate more complex expressions involving them (6.EE.1). Perhaps the most obvious future grade-level connection exists in Grade 8, when students will represent very large and very small numbers using scientific notation and perform operations on numbers written in scientific notation (8.EE.3-4).” • The Unit 7 Summary states, “Students have coordinated numbers and distance before, namely with number lines. Students were introduced to number lines with whole-number intervals in Grade 2 and used them to solve addition and subtraction problems, helping to make the connection between quantity and distance (2.MD.5-6). Then in Grade 3, students made number lines with fractional intervals, using them to understand the idea of equivalence and comparison of fractions, again connecting this to the idea of distance (3.NF.2). For example, two fractions that were at the same point on a number line were equivalent, while a fraction that was further from 0 than another was greater. Then, in Grade 4, students learned to add, subtract, and multiply fractions in simple cases using the number line as a representation, and they extended it to all cases, including in simple cases involving fraction division, throughout Grade 5 (5.NF.1-7). Students’ preparation for this unit is also connected to their extensive pattern work, beginning in Kindergarten with patterns in counting sequences (K.CC.4.c) and extending through Grade 4 work with generating and analyzing a number or shape pattern given its rule (4.OA.3).“ • The Unit 7 Summary also connects future grade level content: “This work lays an important foundation for content that students will study deeply throughout middle school—proportional relationships and functions (6 - 7.RP, 6 - 8.EE, 8.F). This then deeply informs students’ work in all high school courses.” • 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 5 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. Examples include: • Unit 1, Lesson 8, Anchor Task, Problem 1 states, “1. Solve. a. $$0.05\times10=$$ ______, b. $$0.106\times10=$$ ______, c. $$34.8\times10=$$ ______ ; 2. What do you notice about #1? What do you wonder?” (5.NBT.1,2) • Unit 2, Lesson 4, Problem Set, Problem 5 states, “For which of the following expressions would 200,000 be a reasonable estimate? Explain how you know. $$2,146\times12$$ $$21,467\times121$$ $$2,146\times121$$ $$21,477\times1,217$$.” (5.NBT.2,5) • Unit 3, Lesson 3, Target Task, Problem 1 states, “Use the figure to the right to answer the following questions. a. How many layers are in the figure to the right? b. How many cubes are in each layer? c. What is the volume of the figure? d. Explain how you could find the volume of the figure using a different number of layers.” (5.MD.5) • Unit 4, Lesson 10, Anchor Task, Problem 2 states, “Joe is baking cookies. He needs a total of 2 cups of sugar for the recipe. Joe bought a $$4\frac{1}{2}$$ cup bag of sugar and has used $$2\frac{3}{4}$$ cups already. Without solving the problem, does Joe have enough sugar? Explain your thinking.” (5.NF.2) • Unit 5, Lesson 2, Target Task, Problem 1 states, “Gordon has paper strips that are all equal in length. He lines them up end to end. When the line of paper strips is 3 feet long, Gordon says there are 12 paper strips. What is the length, in feet, of one paper strip if Gordon is correct?” (5.NF.3) • Unit 6, Lesson 23, Problem Set, Problem 2 states, “Lincoln had 2 books in his backpack. One book has a mass of 3 pounds 7 ounces, and the other book has a mass of 2 pounds 10 ounces. What was the total mass, in ounces, of the books? a. 60 b. 77 c. 80 d. 97.” (5.MD.1) • Unit 7, Lesson 1, Anchor Task, Problem 1 states, “Mr. Ingall, Mrs. Ingall’s husband, spotted a fly on the wall in their house. He wanted to catch it and let it free outside, but he hates bugs. How should he describe to Mrs. Ingall where the fly is on the wall so that she can catch it?” (5.G.1) • Unit 7, Lesson 10, Discussion of Problem Set states, “What method would you choose in #1(d)? Can he expect to always get those results? What other things might affect the growth of the tomatoes? When did Howard likely get paid in #2(d)? Why do you think that? When did Howard likely buy a television? How do you know? How did you find the answer for #3(c)? Did you use subtraction or just look for the steepest line? How did you set up your work when solving for #3(e)? Would the graph of a different rainy day have the same shape as the graph in #3? How might it be the same? Different?” (5.G.2) • 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 10, the Foundational Standards include Number and Operations in Base Ten, 4.NBT.2 (Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons). The materials state, “5th Grade Math - Unit 1: Place Value with Decimals. Students build upon their understanding of the place-value system by extending its patterns to decimals, and continue to read, write, compare and round numbers, including decimals, in various forms.” • In Unit 5, Lesson 4, the Foundational Standards include Numbers and Operations- Fractions, 4.NF.4 (Apply and extend previous understandings of multiplication to multiply a fraction by a whole number). The materials state, “5th Grade Math - Unit 5: Multiplication and Division of Fractions. Students deepen their understanding of fraction multiplication and begin to explore to fraction division (and fractions as division), as well as apply this new understanding to the context of line plots.” 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. 2/2 + - Indicator Rating Details The instructional materials reviewed for Match Fishtank Grade 5 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 1, Lesson 12, the lesson objective states, “Use place value understanding to round decimals to the nearest whole,” which is shaped by 5.NBT.A, “Understand the place value system.” • In Unit 2, Lesson 2, the lesson objective states, “Write expressions that record calculations with numbers, and interpret expressions without evaluating them,” which is shaped by 5.OA.A, “Write and interpret numerical expressions.” • In Unit 3, Lesson 1, the lesson objective states, “Understand volume as an attribute of solid figures that is measured in cubic units. Find the volume of concrete three-dimensional figures,” which is shaped by 5.MD.C, “Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.” • In Unit 4, Lesson 11, the lesson objective states, “Add and subtract more than two fractions,” which is shaped by 5.NF.A, “Use equivalent fractions as a strategy to add and subtract fractions.” • In Unit 5, Lesson 1, the lesson objective states, “Use area models to model fractions as division and solve word problems involving division of whole numbers with answers in the form of fractions or mixed numbers,” which is shaped by 5.NF.B, “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.” • In Unit 6, Lesson 6, the lesson objective states, “Multiply a decimal to tenths by a decimal to hundredths,” which is shaped by 5.NBT.B, “Perform operations with multi-digit whole number and with decimals to hundredths.” • In Unit 7, Lesson 10, the lesson objective states, “Solve real-world problems by graphing information represented in a table in the coordinate plane and interpret coordinate values of points in the context of the situation,” which is shaped by 5.G.A, “Graph points on the coordinate plane to solve real-world and mathematical problems.” 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 3, Lessons 3 - 8, students connect 5.MD.C and 5.NBT.B by exploring volume of three dimensional shapes and connecting it to the operation of multiplication. For example, Unit 3, Lesson 3, Anchor Tasks, Problem 2 states, “Build a 2cm x 3cm x 4cm rectangular prism with your centimeter cubes. a. How many layers are there in the following figure? How many cubes are in each layer? What is the volume of the figure? b. Find another way to think of the layers in the figure.” • In Unit 5, Lessons 3 and 4, students connect their understanding of the operation of multiplication (5.NBT.B) to their work multiplying fractions (5.NF.B). Students use previous multiplication models (set models, area models and tape diagrams) to model multiplying a fraction times a whole number. For example, Unit 5, Lesson 3, Target Task, Problem 2 states, “Out of 18 cookies, 23 are chocolate chip. How many of the cookies are chocolate chip?” • In Unit 6, Lessons 1-16, students connect their procedural knowledge of multiplication and division with whole numbers (5.NBT.B) and their understanding of multiplication and division with fractions (5.NF.B) to multiply and divide with decimals (5.NBT.B) and reason about the placement of the decimal point (5.NBT.A). For example, Unit 6, Lesson 1, Anchor Tasks, Problem 1 states, “Solve. Show or explain your work. a. $$3\times2$$ tenths = _________ b. $$3\times3$$ tenths = _________ c. $$4\times3$$ tenths = _________.” Gateway Two Rigor & Mathematical Practices Meets Expectations + - Gateway Two Details The instructional materials for Match Fishtank Grade 5 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 + - Criterion Rating Details The instructional materials reviewed for Match Fishtank Grade 5 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. 2/2 + - Indicator Rating Details The instructional materials for Match Fishtank Mathematics Grade 5 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 2, Lesson 13, Anchor Tasks, students find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division (5.NBT.6). In Anchor Tasks, Problem 1 states, “Find the missing side length of each of the rectangles below. Then find their combined length.” Guiding Questions state, “How can you find the missing side length of each rectangle? How can you find the combined side length? How can you represent the side length of the combined rectangles with an expression? What is another way to write an equivalent expression? (Write $$(60\div3)+(9\div3)=69\div3$$.) The quotients of $$60\div3$$ and $$9\div3$$ are called the partial quotients. What did you do with the partial quotients in order to find the total quotient? How can we record what we did to compute $$69\div3$$ vertically? Recording our product vertically using the partial quotients algorithm, how are our area model and our partial quotients similar? How are they different? Recording our quotient vertically using the standard algorithm, how are the area model and the standard algorithm similar? How are they different?” • In Unit 4, Lesson 4, students add and subtract fractions with unlike denominators (5.NF.1). Anchor Tasks, Problem 3, students “Solve. Show your work with an area model and a number line. $$\frac{1}{3}+\frac{1}{2}$$ .” Guiding Questions state, “Can we add 1 third plus 1 half? What model can we draw to represent each fraction? How can we make like units in our model? What fractional unit have we made for each whole? How many shaded units are in $$\frac{1}{3}$$? How many shaded units are in $$\frac{1}{2}$$? What is our addition sentence now? What is our sum? Can it be simplified?” • In Unit 6, Lesson 1, students add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (5.NBT.7). In Anchor Tasks, Problem 2 state, “Solve. Show or explain your work. a. $$2\times0.04=$$ ______ b. $$3\times0.32=$$ ______ c. $$4\times0.67=$$ ______.” The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade, for example: • In Unit 1, Lesson 7, students build numbers to thousandths by dividing by 10 repeatedly (5.NBT.3). In Target Task, Problem 2, students solve, “Jossie drew a picture to represent 0.024: (visual model provided). She said, ‘The little squares represent tenths and the rectangles represent hundredths, which makes sense because ten little squares make one rectangle, and ten times ten is one hundred.’ a. Explain what is wrong with Jossie's reasoning. b. Name two numbers that Jossie's picture could represent. In each case, what does a little square represent? What does a rectangle represent?” • In Unit 3, Lesson 1, students “understand volume as an attribute of solid figures that is measured in cubic units. They find the volume of concrete three-dimensional figures” (5.MD.3). In Problem Set, Problem 2, students “Build 2 different structures with the following volumes using your unit cubes. Then, show your classmate or teacher the figures. a. 4 cubic units b. 7 cubic units c. 8 cubic units.” • In Unit 3, Lesson 2, students “find the volume of pictorial three-dimensional figures,” (5.MD.4). Centimeter cubes are recommended for students to use if they need more concrete experiences with finding volumes of three-dimensional figures. In Problem Set, Problem 3 states, “Find the total volume of each figure below and explain how you found it. Be sure to include units.” Six pictorial representations are provided. Students fill in a table for the calculated volume and an explanation. • In Unit 5, Lesson 1, students “model fractions as division using area models and solve word problems involving division of whole numbers with answers in the form of fractions or mixed numbers,” (5.NF.3). In Problem Set, Problem 3, students solve, “Six people are sharing four sandwiches. a. Draw a picture to show how they could equally share the sandwiches. How much of a sandwich does each person get? b. Write an equation using division to show the fraction of a sandwich each person gets. Explain how the equation you wrote represents this situation. c. Write an equation involving multiplication to show how all the parts make up the four sandwiches. Explain how the equation you wrote represents the situation. d. Write an equation involving addition to show how together all the parts make up the four sandwiches. Explain how the equation you wrote represents the situation.” • In Unit 5, Lesson 18, students solve real world problems involving division of unit fractions by whole numbers using tape diagrams and number lines (5.NF.7a). In Anchor Tasks, Problem 1, students solve, “Nolan gives some Fruit-by-the-Foot to his 3 friends to share equally. a. If he has 3 feet of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive? b. If he has 1 foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive? c. If he has $$\frac{1}{2}$$ foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive? d. If he has $$\frac{1}{3}$$ foot of Fruit-by-the-Foot, how many feet of Fruit-by-the-Foot will each friend receive?” 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. 2/2 + - Indicator Rating Details The instructional materials for Match Fishtank Mathematics Grade 5 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 (5.NBT.5). For example: • In Unit 2, Lesson 4, students “Multiply multiples of powers of ten. Estimate multi-digit products by rounding numbers to their largest place value,” (5.NBT.5). In Anchor Tasks, Problem 2 states, “Solve. $$1. 60\times5=$$ ____ 2. $$60\times50=$$ ____ 3. $$60\times500=$$ ____ 4. $$60\times5,000=$$ ____.” • In Unit 2, Lesson 5, students “multiply two-digit, three-digit, and four-digit numbers by one-digit numbers,” (5.NBT.5). Students are provided with multiple opportunities to practice multiplication using the standard algorithm in the Problem Set, Homework, and Target Tasks. In Problem Set, Problem 1 states, “Solve. Then assess the reasonableness of your answer. a. $$45\times6=$$ b. $$32\times5=$$ c. $$67\times3=$$ d. $$324\times2=$$ e. $$106\times4=$$ f. $$624\times8=$$ g. $$9,856\times3=$$ h. $$4,352\times2=$$ i. $$2,781\times7=$$ .” • In Unit 2, Lesson 8, students “multiply four-digit numbers by two-digit numbers,” (5.NBT.5). Students are provided with multiple opportunities to practice multiplication using the standard algorithm in the Problem Set, Homework, and Target Tasks. In Anchor Tasks, Problem 1 states, “Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer. a. $$1,634\times74$$ b. $$5,803\times46$$ c. $$65\times2,116$$.” • In Unit 3, Lesson 4, students solve more complex problems involving volume by applying the formula V = b x h (5.MD.5). Students are provided with multiple opportunities to practice multiplication by finding volume in the Problem Set, Homework, and Target Tasks. In the Homework, Problem 2 states, “A rectangular present has a base area of 40 square inches. What is the volume of the box if it is 6 inches tall?” 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 2/2 + - Indicator Rating Details The instructional materials for Match Fishtank Mathematics Grade 5 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 (5.NF.6, 5.NF.7c). 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 3, Lesson 6, students “solve more complex problems involving volume by applying the formula V = l x w x h,” (5.MD.5). For example, Problem Set, Problem 2 states, “Geoffrey builds rectangular planters. Geoffrey’s first planter is 8 feet long and 2 feet wide. The container is filled with soil to a height of 3 feet in the planter. What is the volume of soil in the planter?” • In Unit 4, Lesson 12, students solve two- and multi-step word problems involving addition and subtraction of fractions (5.NF.2). For example, the Target Task states, “Each student in a class plays one of three sports: soccer, volleyball, or basketball. $$\frac{3}{5}$$ of the number of students play soccer. $$\frac{1}{4}$$ of the number of students play volleyball. What fraction of the number of students play basketball?” • In Unit 5, Lesson 6, students solve real-world problems involving multiplication of fractions and whole numbers and create real-world contexts for expressions involving multiplication of fractions and whole numbers (5.OA.2, 5.NF.4,6). For example, Problem Set, Problem 1 states, “The table shows the number of computers donated to a school by each of 4 companies. All the donated computers were shared equally by 5 classrooms. Which expression represents the number of companies each classroom received? a. $$120\times\frac{5}{4}$$ b. $$120\times\frac{1}{4}$$ c. $$120\times\frac{4}{5}$$ d. $$120\times\frac{1}{5}$$” • In Unit 5, Lesson 7, students “multiply a fraction by a fraction without subdivisions using tape diagrams and number lines” (5.NF.6). For example, Target Task, Problem 2 states, “A newspaper’s cover page is $$\frac{5}{6}$$ text, and photographs fill the rest. If $$\frac{2}{5}$$ of the text is an article about endangered species, what fraction of the cover page is the article about endangered species?” • In Unit 5, Lesson 19, students divide a whole number by a unit fraction (5.NF.7b, 5.NF.7c). For example, Problem Set, Problem 5 states, “Avery and Megan are cutting paper to make origami stars. They need $$\frac{1}{5}$$ of a sheet of paper in order to make each star. If they have 6 sheets of paper, how many stars can they make? Explain your work and draw a picture to support your reasoning.” • In Unit 5, Lesson 20, students solve real-world problems involving division with fractions and create real-world contexts for expressions involving division with fractions (5.NF.7c). For example, Target Task, Problem 2 states, “There are 7 math folders on a classroom shelf. This is $$\frac{1}{3}$$ of the total number of math folders in the classroom. What is the total number of math folders in the classroom?” • In Unit 7, Lesson 11, students “solve real-world problems by graphing information given as a description of a situation in the coordinate plane and interpret coordinate values of points in the context of the situation,” (5.OA.3, 5.G.2). For example, Target Task states, “Jordan has10 in the bank. Jordan earns $5 each week for doing chores, and he puts the money in the bank. After a certain number of weeks of doing chores, Jordan has$35. A graph is set up so that Jordan can record the total amount of money in the bank each week after putting in $5.” Students are given an incomplete coordinate grid (of quadrant 1) and asked, “Part A: Which ordered pair represents the amount of money Jordan has in the bank before doing any chores? Part B: Which ordered pair represents the amount of money Jordan has after 4 weeks of doing chores? Part C: After how many weeks does Jordan have$35? Show or explain your work.”

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

• In Unit 2, Lesson 3, students write expressions that represent real-world situations and evaluate them (5.OA.1,2). For example, the Target Task states, “Part A: A jar with 64 fluid ounces of water is used to fill cups. The jar is used to fill 3 cups each with 8 fluid ounces of water and 2 cups each with 9 fluid ounces of water. Write an expression that represents the number of fluid ounces left in the jar after filling all of the cups.Then solve your expression. Part B: A different jar has 42 fluid ounces of water. All of the water in the jar is used to fill cups. Write an expression to show how many cups can be filled if each cup is filled with 7 fluid ounces of water. Use p as the unknown number of cups in your question. Do not solve the equation.”
• In Unit 3, Lesson 8, students “Understand that volume is additive. Find the volume of composite solid figures when not all dimensions are given and/or they must be decomposed. (5.MD.5c). For example, Problem Set, Problem 3 states, “A rectangular tank with a base area of 24 cm square is filled with water and oil to a depth of 9 cm. The oil and water separate into two layers when the oil rises to the top. If the thickness of the oil layer is 4 cm, what is the volume of the water?”
• In Unit 4, Lesson 12, students apply their understanding of adding and subtracting fractions to solve two- and multi-step, real world, word problems (5.NF.2). For example, Problem Set, Problem 5 states, “The table below shows part of the operating budget of a small dairy farm for last year. The only expense not listed in the table is maintenance.” A table of “Last Year’s Operating Budget” is provided. The problem further states, “This year, the managers of the farm will change the fraction of the budget for housing to 18 but will leave the fraction of the budget for food and medical care the same. Again, the remaining portion of the budget will be for maintenance expenses. What is the difference between the fraction of the budget for maintenance this year and last year?”
• In Unit 5, Lesson 18, students divide unit fractions by whole numbers, (5.NF.7c). For example, Target Task, Problem 2 states, “Larry spends half of his workday teaching piano lessons. If he sees 6 students, each for the same amount of time, what fraction of his workday is spent with each student?”
• In Unit 6, Lesson 17, students solve real-world problems involving multiplication and division of decimals (5.NBT.7). For example, Problem Set, Problem 6 states, “Katie went to a craft store to purchase the supplies she needs to make two types of jewelry. This table shows the cost of the supplies Katie needs. (A table with the cost of beads and charms is provided). This table shows the supplies needed to make each piece of jewelry. (A table with the type of jewelry, with how many beads and charms each piece requires is provided.) Katie purchased the exact amount of supplies to make 1 bracelet and 2 necklaces. Write an expression to determine the cost of supplies to make 1 bracelet. Write an expression to determine the cost of supplies to make 2 necklaces. Katie started with $40. How much did she have left after purchasing the supplies?” • In Unit 6, Lesson 23, students solve real-world problems involving measurement conversions (5.MD.1). For example, Problem Set, Problem 5 states, “Regina buys 24 inches of trim for a craft project. a. What fraction of a yard does Regina buy? b. If a whole yard of trim costs$6, how much did Regina pay?”

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 5 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 1, Lesson 12, students “Use place value understanding to round decimals to the nearest whole.” (5.NBT.4). For example, Lesson 12, Anchor Task, Problem 1 states, “Is 7.6 closer to 7 or closer to 8? Plot 7 and 8 on the two outermost spots on the number line below. Then plot 0.6 to prove your answer.”
• In Unit 2, Lesson 6, students “multiply two-digit numbers by two-digit numbers,” (5.NBT.5).  In Anchor Task, Problem 1 states, “Here are two ways to find the area of a rectangle that is 23 units by 31 units. a. What do the area models have in common? How are they alike? b. How are they different? c. If you were to find the area of a rectangle that is 37 units by 49 units, which of the three ways of decomposing the rectangle would you use? Why?”
• In Unit 4, Lesson 14, students “subtract decimals,” (5.NBT.7). In Anchor Task, Problem 2 states, “Solve. Show your work with an area model. a 0.8 – 0.2 b. 0.94 – 0.6 c.0.7 – 0.13.”
• In Unit 5, Lesson 3, students multiply a fraction by a whole number (5.NF.4a,6) using set models. For example, Anchor Task, Problem 1 states, “a. Kyle has 6 Skittles. $$\frac{1}{3}$$ of them are red. How many of Kyle’s Skittles are red?  B. Samantha has 6 Reese’s Pieces. $$\frac{2}{3}$$ of them are yellow. How many of Samantha’s Reese’s Pieces are yellow?”

Examples of Procedural Skills and Fluency include:

• In Unit 2, Lesson 9, students multiply three- and four-digit numbers by three-digit numbers using the standard algorithm, (5.NBT.5). For example, Problem Set, Problem 5 states, “Solve. Show or explain your work. a. $$8,401\times305$$  b. $$7,481\times350$$ c. $$1,346\times297$$ d. $$1,346\times207$$.”
• In Unit 6, Lesson 6, students multiply a decimal to tenths by a decimal to hundredths (5.NBT.7). For example, Target Task, students are given the following equations to solve independently, “1. $$0.35\times0.4$$   2. $$2.02\times4.2$$ 3. $$2.2\times0.42$$.”

Application:

• In Unit 2, Lesson 20, students apply multi-digit multiplication and division when solving word problems (5.OA.1,2, 5.NBT.5,6). For example, the Target Task states, “Sixteen students in a drama club want to attend a play. The ticket price is $35 for each student, and the transportation and meals for everyone will cost$960. To pay for the trip, the students design sweatshirts to sell for a profit of $18 per sweatshirt. If each student sells the same number of sweatshirts, how many sweatshirts must each student sell so that there will be enough money to pay for the entire cost of the trip?” • In Unit 5, Lesson 6, students “Solve real-world problems involving multiplication of fractions and whole numbers and create real-world contexts for expressions involving multiplication of fractions and whole numbers” (5.OA.2, 5.NF.4,6). For example, the Target Task states, “In a classroom, $$\frac{1}{4}$$ of the students are wearing blue shirts and 23are wearing white shirts. There are $$\frac{3}{6}$$ students in the class. How many students are wearing a shirt other than a blue or white?” • In Unit 5, Lesson 20, students “solve real-world problems involving division with fractions and create real-world contexts for expressions involving division with fractions,” (5.NF.7c). In Anchor Task, Problem 1 states, “Jenny buys 2 feet of string. If this is one-third the amount she needs to make a bracelet, how many feet will she need? Draw a diagram to represent the problem. Write an expression to represent the problem. Find how many feet of string Jenny needs.” • In Unit 6, Lesson 17, students apply the procedure of multiplying and dividing with decimals to solving real-world problems (5.NBT.7). For example, Problem Set, Problem 4 states, “Mr. Hower can buy a computer with a down payment of$510 and 8 monthly payments of $35.75. If he pays cash for the computer, the cost is$699.99. How much money will he save if he pays cash for the computer instead of paying for it in monthly payments?”

Examples of multiple aspects of rigor engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study include:

• In Unit 1, Lesson 4, students, “Explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10” (5.NBT.2). For example, the Target Task, Problem 1 states, “Solve. a. $$450\times1,000=$$ ___ b. $$67 \times 10^4=$$ ____.”  Problem 2 states “Explain the pattern in the number of places the digits shift in each of the products above and relate it to the numbers on the left side of the equations.”
• In Unit 6, Lesson 10, students apply the concept of estimation to the procedure of dividing a decimal by a two-digit multiple of ten (5.NBT.1,2,6,7). For example, Anchor Task, Problem 3 states, students are directed to, “Estimate the following quotients. 1. $$39.1\div17$$   2. $$3.91\div17$$.”
• In Unit 7, Lesson 11, students “Solve real-world problems by graphing information given as a description of a situation in the coordinate plane and interpret coordinate values of points in the context of the situation,” (5.G.2, 5.OA.3).  For example, Problem Set, Problem 3 states, “Three chocolate chip cookies cost $4 at the grocery store. a. Create a table and a graph for how much 3, 6, 9, and 12 cookies cost. b. What does the coordinate (9, 12) represent in the context of this problem? c. How many cookies can you buy with$24? Show or explain your work. d. How much would 15 cookies cost? Show or explain your work.”

Criterion 2e - 2g.iii

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

The instructional materials reviewed for Match Fishtank Grade 5 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.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 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 2, Lesson 11, Tips for Teachers states, “Throughout Lessons 11-19, students see and make use of structure (MP.7) and attend to precision (MP.6) as they decompose numbers into sums of multiples of base-ten units to multiply or divide them.”
• In Unit 4, Lesson 5, Criteria For Success, students “Solve one-step word problems involving the subtraction of two fractions with unlike denominators whose sum is less than 1 (MP4).”
• In Unit 6, the Unit Summary states, “Reasoning about the placement of the decimal point affords students many opportunities to engage in mathematical practice, such as constructing viable arguments and critiquing the reasoning of others (MP.3) and looking for and expressing regularity in repeated reasoning (MP.8). For example, “students can summarize the results of their reasoning as specific numerical patterns and then as one general overall pattern such as ‘the number of decimal places in the product is the sum of the number of decimal places in each factor’” (NBT Progression, p. 20). “

Examples of the MPs being used to enrich the mathematical content include:

• MP8 is connected to the mathematical content in Unit 1, Lesson 4, Criteria for Success, Anchor Task, Problem 1, as students “Generalize the pattern that multiplying a number by a power of 10 results in the digits in the number shifting one place to the left for each power of 10 (MP.8).” For example, “1. Solve. a. $$4\times10=$$ ____  b. $$4\times100=$$ ____ c. $$4\times1,000=$$ ____ . 2. What do you notice about #1? What do you wonder? 3. Use your conclusions form #2 to solve the following equations. a. $$6\times100,000=$$ ____ b. $$78\times1,000,000=$$ ____ c. $$530\times10,000=$$ ____.”
• MP7 is connected to the mathematical content in Unit 3, Lesson 9, Anchor Task, Problem 2, as students “classify polygons into a hierarchy based on properties (MP.7).” For example, “Sort the polygons from Anchor Task #1 (provided on Template: Polygons) however you’d like. You can create as many groups as you’d like.”
• MP6 is connected to the mathematical content in Unit 6, Lesson 3, Criteria for Success as students use “estimation when the product is difficult to estimate, such as computing $$8\times0.09$$ (MP.6).” For example, Target Task, Problem 1 states, “Use reasoning to choose the correct value for each expression. a. $$0.51\times2$$  (choices include: 0.102, 1.02, 10.2, 102) b. $$4\times8.93$$ (choices include: 3.572, 35.72, 357.2, 3572.)

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 5 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 11, Criteria for Success states, “1. Understand when a problem calls for the use of multiplication and when other operations are called for in a problem involving two fractions (MP.1, MP.4).” For example, Anchor Task, Problem 1 states, “Some of the problems below can be solved by multiplying, while others need a different operation. Select the ones that can be solved by multiplying these two numbers. For the remaining, tell what operation is appropriate. In all cases, solve the problem (if possible) and include appropriate units in the answer. a. Two-fifths of the students in Anya’s fifth-grade class are girls. One-eighth of the girls wear glasses. What fraction of Anya’s class consists of girls who wear glasses? b. A farm is in the shape of a rectangle $$\frac{1}{8}$$ of a mile long and $$\frac{2}{5}$$ of a mile wide. What is the area of the farm? c. There is $$\frac{2}{5}$$ of a pizza left. If Jamie eats another $$\frac{1}{8}$$ of the original whole pizza, what fraction of the original pizza is left over? d. In Sam’s fifth-grade class, $$\frac{1}{8}$$ of the students are boys. Of those boys, $$\frac{2}{5}$$ have red hair. What fraction of the class is red-haired boys? e. Only $$\frac{1}{20}$$ of the guests at the party wore both red and green. If $$\frac{1}{8}$$ of the guests wore red, what fraction of the guests who wore red also wore green? f. Alex was planting a garden. He planted $$\frac{2}{5}$$ of the garden with potatoes and $$\frac{1}{8}$$ of the garden with lettuce. What fraction of the garden is planted with potatoes or lettuce? g. At the start of the trip, the gas tank on the car was $$\frac{2}{5}$$ full. If the trip used $$\frac{1}{8}$$ of the remaining gas, what fraction of a tank of gas is left at the end of the trip? h. On Monday, $$\frac{1}{8}$$ of the students in Mr. Brown’s class were absent from school. The nurse told Mr. Brown that $$\frac{2}{5}$$ of those students who were absent had the flu. What fraction of the absent students had the flu? i. Of the children at Molly’s daycare, $$\frac{1}{8}$$ are boys and $$\frac{2}{5}$$ of the boys are under 1 year old. How many boys at the daycare are under 1 year old? j. The track at school is $$\frac{2}{5}$$ of a mile long. If Jason has run $$\frac{1}{8}$$ of the way around the track, what fraction of a mile has he run?”
• MP2: In Unit 3, Lesson 5, Criteria for Success states, “Reason abstractly and quantitatively to see that the dimensions can be multiplied together in any order and the volume will remain the same (MP.2).” For example, Anchor Task, Problem 3 states, “Akiko and Philip are finding the volume of the following rectangular prism. Philip says that you have to multiply length by width by height, so you have to multiply $$10\times14\times2$$. Akiko says the computation will be easier if you multiply $$10\times2\times14$$. Is Philip correct? Must the dimensions be multiplied in that order? Show or explain your thinking. Why do you think Akiko thinks that multiplying $$10\times2\times14$$ will be an easier computation? Is it possible to multiply the dimensions in that order? Show or explain your thinking. Use what you’ve concluded from Parts (a) and (b) to explain how you would calculate the volume of a rectangular prism whose length is 4 feet, width is 7 feet, and height is 15 feet.”
• MP4: In Unit 5, Unit Summary states, “Students also solve myriad word problems, seeing the strategies they used to solve word problems with whole numbers still apply but that special attention should be paid to the whole being discussed (5.NF.6, MP.4).”  In Lesson 18, Criteria for Success states, “2. Solve partitive division word problems that involve the division of a unit fraction by a whole number (MP.4).” For example, Anchor Task, Problem 2 states, “Alexis has a lot of studying to do over the holiday break. She wants to complete 14of her homework equally over 2 days. What fraction of her homework will she do on each day?”
• MP5: In Unit 5, Lesson 15, Criteria for Success states, “Decide which generalized method for computing products of mixed numbers will be most efficient for a particular problem and use it to compute the product (MP.5).” For example, Anchor Task, Problem 1 states, “Sophia and Zack are multiplying $$2\frac{2}{3}$$ and $$3\frac{1}{4}$$. Sophia decides to multiply using partial products, like we did in yesterday’s lesson. Zack decides to convert the mixed numbers to fractions and multiply. Will their strategies result in the same product? Why or why not?”
• MP6: In Unit 5, Lesson 22, Criteria for Success states, “Evaluate expressions with and without grouping symbols that include fractions using the order of operations (MP.6).” For example, Anchor Task, Problem 2 states, “Write numerical expressions that records the following calculations. Then evaluate them. a. Twice the sum of 35 and $$1\frac{1}{2}$$ b. Half the sum of $$\frac{3}{5}$$ and $$1\frac{1}{2}$$. c. $$\frac{1}{2}$$ subtracted from $$\frac{3}{4}$$ and then divided by 3.”
• MP7: In Unit 3, Lesson 3, Criteria for Success states, “Look for and make use of structure to understand that rectangular prisms can be decomposed into layers in different ways (MP.7).” For example, Target Task, Problem 1 states, “Use the figure to the right to answer the following questions. a. How many layers are in the figure to the right? b. How many cubes are in each layer? c. What is the volume of the figure? d. Explain how you could find the volume of the figure using a different number of layers.”
• MP8: In Unit 6, Unit Summary states, “Reasoning about the placement of the decimal point affords students many opportunities to engage in mathematical practice, such as constructing viable arguments and critiquing the reasoning of others (MP.3) and looking for and expressing regularity in repeated reasoning (MP.8).” For example, Lesson 13, Anchor Task, Problem 3 states, “Solve. Show or explain your work. a. $$8\div0.01$$ b. $$8.3\div0.01$$ c. $$8.37\div0.01$$” Guiding Questions: “How many hundredths are in 8? How is Part (b) similar to Part (a)? How is it different? How is Part (c) similar to Part (b)? How is it different?Do you notice a pattern when you divide a number by one hundredth?”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

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.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 5 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 1, Problem Set, Problem 4 states, “Jose thinks that $$10\times10\times10$$ is 100 because there are two instances of multiplication, and if you shift the place values over two places, you get 100. Do you agree or disagree? Explain.” Students analyze the argument of others (MP.3).
• In Unit 2, Lesson 10, Target Task, Problem 2 states, “a. Use estimation to explain why Elmer’s answer is not reasonable. b. What error do you think Elmer made? Why do you think he made that error? c. Find the correct product of $$179\times64$$.” Students analyze the argument of others (MP.3).
• In Unit 3, Lesson 9, Problem Set, Problem 7 states, “Edwin says that a polygon is always a pentagon and his sister says that he has it backwards. Instead, a pentagon is always a polygon. With whom do you agree? Why?” Students analyze the argument of others (MP.3).
• In Unit 4, Lesson 1, students “Determine whether two fractions are equivalent using an area model, a number line, or multiplication/division (MP.3).” In the Anchor Task, Problem 1 states, “Ms. Kosowsky makes brownies in two pans of the same size. She cuts the pans in the following ways.” Students are shown two rectangles. One is divided in half, and the other is divided into eighths. They are then given the following prompt, “Ms. Kosowsky gives one brownie from Pan A to Ms. Kohler and keeps four brownies from Pan B for herself. Ms. Kohler thinks it isn’t fair since she go one brownie and Ms. Kosowsky got four. Ms. Kosowsky thinks it’s fair. Who do you agree with, Ms. Kosowsky or Ms. Kohler? Why?” Students critique the reasoning of others (MP.3).
• In Unit 5, Lesson 9, Anchor Task, Problem 2b states, “Presley and Julia are cutting ft. square poster board to make a sign for the new park. Presley cut her poster so that the length of the top and bottom are $$\frac{1}{2}$$ ft. and the length of the sides are $$\frac{3}{4}$$ ft. Julia cut her poster so that the lengths of the top and bottom are 34 ft. and the length of the sides are $$\frac{1}{2}$$ ft. Draw a diagram of each poster board. Label the values on the diagram. How are their poster boards similar and different? Justify your reasoning.” Students construct a viable argument in order to justify their reasoning of how the poster boards are similar and different.
• In Unit 6, Lesson 1, Problem Set, Problem 3 states, “Miles incorrectly gave the product of $$7\times2.6$$ as 14.42. What is Miles’ mistake? Find the correct value of $$7\times2.6$$. Show your work or explain your answer.” Students analyze the reasoning of others (MP.3).

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 5 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 4, Lesson 1, Criteria for Success, “3. Determine whether two fractions are equivalent using an area model, a number line, or multiplication/division (MP.3).” In Anchor Task, Problem 1, students analyze the arguments of others, “Ms. Kosowsky makes brownies in two pans of the same size. She cuts the pans in the following way: (Pan A and Pan B displayed) Ms. Kosowsky gives one brownie from Pan A to Ms. Kohler and keeps four brownies from Pan B for herself. Ms. Kohler thinks this isn’t fair since she got one brownie and Ms. Kosowsky got four. Ms. Kosowsky thinks it’s fair. Who do you agree with, Ms. Kosowsky or Ms. Kohler? Why?” Guiding Questions include, but are not limited to, “ How much of each brownie pan did each teacher get? Do you agree with Ms. Kosowsky or Ms. Kohler? Equivalent fractions are fractions that represent the same portion of the whole and the wholes are equal-sized. Are these two fractions equivalent? How can we represent that with an equation? What do you notice about the numerators and denominators of the equivalent fractions? How can you use the area models to explain why this happens? How can you represent this using multiplication or division?”
• In Unit 5, Lesson 17, Criteria for Success states, “2. Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number, recognizing multiplication by whole numbers greater than 1 as a familiar case (MP.3).” In Anchor Task, Problem 3 states, “Cai, Mark, and Jen were raising money for a school trip. Cai collected $$2\frac{1}{2}$$ times as much as Mark. Mark collected $$\frac{2}{3}$$ as much as Jen. Who collected the most? Who collected the least? Explain.” Guiding Questions include but are not limited to, “What can you draw to represent the relationship between how much money Cai raised and how much money Mark raised? Why is it possible to represent this relationship with a model even though we don’t know the exact quantities? What can you add to your model to represent the relationship between how much money Mark raised and how much money Jen raised? Did Cai or Mark raise more money? How do you know? Did Mark or Jen collect more money? How do you know? Did Cai or Jen raise more money? How do you know? Who raised the most money? Who raised the least? What is the relationship between how much money Cai raised and how much money Jen raised? In other words, how many times more money did Cai raise than Jen?”
• In Unit 7, Lesson 8, Criteria for Success states, “1. Given a set of points, plot them in the coordinate grid and identify and explain what shape they form when connected (MP.3).” In Anchor Task, Problem 2 states, “Alonso wants to create a triangle on the coordinate grid below. Two of the vertices are located at point F (2, 3) and point G (7, 3). a. If Alonso wants to make a right triangle, what could be the ordered pair of the third vertex? b. Alonso decides to use his original two points to form a square instead. Where should he place the other two points, and why?” Guiding Questions include, but are not limited to, “What attributes does a right triangle have? How can you be sure that the shape you construct has these attributes? Is there more than one correct right triangle you could create? Can you create a right triangle where is the longest side? Where would the right angle be? How can you be sure it is a right angle? What attributes does a square have? How can you be sure that the shape you construct has those attributes? Where can you plot the other vertices? Is there more than one correct square you could create?”

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 5 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:

• At the beginning of each unit, the Unit Prep lists the Vocabulary for the unit. For example, in Unit 2, some of the key vocabulary is, “Equation, expression, grouping symbols (parentheses, brackets, braces), etc.”
• In Unit 3, Lesson 6, Tips for Teachers states, “Lesson 6’s 3-Act task addresses the idea of ‘filling’ volume. As the Geometric Measurement Progression states, ‘solid units are ‘packed,’ such as cubes in a three-dimensional array, whereas liquid ‘fills’ three-dimensional space, taking the shape of the container… The unit structure for liquid measurement may be psychologically one-dimensional for some students’ (GM Progression, p. 26).”
• In Unit 4, Lesson 2, Tips for Teachers states, “‘The term ‘improper’ can be a source of confusion because it implies that this representation is not acceptable, which is false. Instead it is often the preferred representation in algebra. Avoid using this term and instead use ‘fraction’ or ‘fraction greater than one’ (Van de Walle, Teaching Student-Centered Mathematics, 3-5, Vol. 2, p. 217). Further, fractions do not always need to be converted from ‘improper’ fractions to mixed numbers, since the need to do so often depends on the context (e.g., in the case of fractional coefficients in algebra, they are often written as fractions greater than one, which are generally easier to manipulate).”

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

• In Unit 1, Lesson 8, Criteria for Success, students will, “Understand that a digit in one place (including decimal places) represents ten times what it represents in the place to its right, 100 times what it represents two places to its right, etc.”
• In Unit 3, Lesson 1,Criteria for Success, students will, “Define volume as the measurement of how much space an object takes up.”
• In Unit 5, Lesson 18, Tips for Teachers states, “There are two interpretations for division, (a) partitive division, also called equal group with group size unknown division, and (b) measurement division, also called equal group with number of groups unknown.”
• In Unit 6, Lesson 19, Criteria for Success, students will, “Understand the meaning of different prefixes for metric units and how they relate to the base unit (e.g., kilo- means 1,000, so a kilogram is 1,000 times as large as a gram).”

Usability

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 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.
2/2
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson.

There are seven instructional units in Grade 5. 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 5, Lesson 4, Anchor Task, students multiply a fraction by a whole number using tape diagrams and number lines (5.NF.4a,6). Problem 2 states, “Aurelia buys 3 dozen roses. Of these roses,  are red. How many red roses are there?”

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 in which students have the opportunity to apply what they have learned from the activities in the lesson, and can be used to formatively assess understanding of the lesson content. For example:

• In Unit 2, Lesson 20, Problem Set, students solve word problems involving multi-digit multiplication and division (5.OA.1,2, 5.NBT.5,6). Problem 2 states, “An employee at a home improvement store is putting boxes of nails on shelves. There are 137 boxes of large nails. Each box of large nails contains 125 nails. There are 284 boxes of small nails. Each box of small nails contains 275 nails. Part A: What is the total number of nails in all the boxes of large nails? Part B: What is the total number of nails in all the boxes of small nails?”
• In Unit 4, Lesson 12, Homework, students solve two- and multi-step word problems involving addition and subtraction of fractions (5.NF.2). Problem 4 states, “Matt went running on four days. The table shows the distance he ran on each day (table provided). On which two days did Matt run an estimated total distance that was closest to 3 miles? A. Sunday and Tuesday B. Monday and Tuesday C. Monday and Wednesday D. Sunday and Wednesday.”
• In Unit 5, Lesson 6, Target Task, students solve real-world problems involving multiplication of fractions and whole numbers, and create real-world contexts for expressions involving multiplication of fractions and whole numbers (5.OA.2, 5.NF.4,6). The materials state, “In a classroom, $$\frac{1}{4}$$ of the students are wearing blue shirts and $$\frac{2}{3}$$ are wearing white shirts. There are 36 students in the class. How many students are wearing a shirt other than blue or white?”

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 5 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 5 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 4, students explain patterns in the number of zeros of the product when multiplying a whole number by powers of 10 (5.NBT.2). For example, Anchor Task, Problem 1 states, “1.  Solve. a. $$4\times10=$$___ b. $$4\times100=$$ ___ c. $$4\times1,000=$$ ___ 2. What do you notice about #1? What do you wonder? 3. Use your conclusions from #2 to solve the following equations.a. $$6\times100,000=$$ ___ b. $$78\times1,000,000=$$ ___ c. $$530\times10,000=$$ ___.”
• In Unit 3, Lesson 9, students classify shapes as polygons versus non-polygons and classify polygons according to their number of sides (5.G.3,4). For example, Problem Set, Problem 7 states, “Edwin says that a polygon is always a pentagon and his sister says that he has it backwards. Instead, a pentagon is always a polygon. With whom do you agree? Why?”
• In Unit 5, Lesson 7, students multiply a fraction by a fraction without subdivisions using tape diagrams and number lines (5.NF.4,5,6). In the Target Task, Problem 1 states, students must explain their thinking to the following problem, “$$\frac{1}{3}$$ of $$\frac{3}{8}$$.”

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 5 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 3, Lesson 2, centimeter cubes are used to explore volume.
• In Unit 4, Lesson 4, square-sized paper is used to generate equivalent fractions.
• In Unit 5, Lesson 3, Anchor Task, Problem 1, students use a two-sided counters to make set models to represent fractions.

Manipulatives used in Grade 5 include but are not limited to:

• Base ten blocks, number lines, place value charts, place value disks, tape diagrams, centimeter cubes, rulers, tape diagrams, and two-sided counters.
• Templates provided in place of three-dimensional manipulatives: paper hundreds flat, nets for three-dimensional models, square-sized paper, and inch grid paper.

Indicator 3e

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

The instructional materials for Match Fishtank Grade 5 are not distracting or chaotic and support students in engaging thoughtfully with the subject. For example:

• 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 5 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 5 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 6, Lesson 6, Anchor Task, Problem 1 states, “How can you connect what you know about multiplication with whole numbers to multiplication with fractions? What is the whole that is being referred to in the problem? Why does looking for key words in a problem not always work as a strategy? (You could use Part (e) as an example here - “of” does not imply that these quantities should be multiplied together.)”
• 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.

Discussion of Problem Sets include 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 2, Lesson 5 states, “Look at #4. Can the expression $$8\times(3,000+600+5)$$ be used to find the value of $$3,605\times8$$? Why or why not? What other expressions can be used to solve $$3,605\times8$$? How do you know? Look at #5. What is an example of when Nina’s claim is true? What is an example of when Nina’s claim is not true? What was the value of the question mark in #6? How did you figure that out? Look at #7. What is a possible number that Casey multiplies 178 by? Is there more than one right answer?”

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 5 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, “Throughout the remainder of the unit, the focus will be on the standard algorithm instead of the partial products algorithm or the area model. However, you may decide to include those models in your discussions, depending on student need.”
• In Unit 5, Lesson 6, Tips for Teachers states, “This lesson connects the work of solving real-world problems involving multiplication of fractions and mixed numbers (5.NF.6) with writing and interpreting numerical expressions (5.OA.A), connecting content across domains.”

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 5 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 5 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 5 Course Summary states, “Grade 5 focuses on three key advancements from previous years: (1) developing fluency with addition and subtraction of fractions, and developing understanding of multiplication and division of fractions in certain cases; (2) integrating decimal fractions into the place value system and developing fluency with operations with whole numbers and decimals to hundredths; and (3) developing understanding of volume.” 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).
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 5 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.
Narrative Evidence Only
+
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 5 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.
Narrative Evidence Only
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 5 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 5 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 5 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 5 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Examples include:

• In Unit 2, Lesson 13, Anchor Task, the Problem 3 Notes state, "If students struggle to see why the process for checking the quotient involves both multiplication and addition, relate it to the area model. This will help students see that multiplying the length (quotient) and the width (divisor) to get the area (partial dividend), then adding the area that wasn’t able to be partitioned (the remainder) results in the total dividend.”
• In Unit 6, Lesson 22, Anchor Task, the Problem 1 Notes state, “Students may initially suggest dividing by the whole-number conversion factor that they’ve used in the past few lessons, which certainly works. However, this will force students into computations they are not yet able to compute (e.g., $$6,700 \div 1,000,000$$ in Part (e) or, more complicatedly, $$7\frac{1}{2}\div16$$ in Lesson 23 Anchor Task #2). Thus, you should encourage students to multiply by the decimal conversion factors in cases with metric measurement and the fraction conversion factors in cases with customary measurement, since this strategy will work for any and all cases of unit conversion they will see in Grade 5."

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 5 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 Tasks provided the teacher with guiding questions and notes in order to provide feedback for students’ learning. For example:

• In Unit 1, Lesson 4, Problem 1, Guiding Questions state, “How can you use a place value chart to solve #1? How is $$4\times10$$ related to $$4\times100$$? How can you use $$4\times10$$ to solve $$4\times100$$? (It may help to write this as “$$4\times100=4\times(10\times10)=(4\times10)\times10=40\times10=400$$, using parentheses to facilitate the use of the associative property.) What do you notice about your products? What do you wonder? How can you use those patterns to solve #3? ​”
• In Unit 6, Lesson 2, Problem 2, Procedure states, “Ask, ‘How can we use what we learned in Anchor Task #1 to solve $$5.1\times6$$?’ Then discuss solving $$51\times6$$ using the standard algorithm. If students would like to use an area model or the partial products algorithm, though, they may.”

Indicator 3p

Materials offer ongoing formative and summative assessments:

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 5 meet 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 1, Place Value with Decimals, Assessment Item 6 correlates with 5.NBT.2.
• In Unit 4, Addition and Subtraction of Fractions and Decimals, Assessment Item 8 correlates with 5.NF.2.
• In Unit 7, Patterns and the Coordinate Plane, Assessment Item 5a correlates with 5.G.1.

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 5 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:

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Match Fishtank Grades 5 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Match Fishtank Grades 5 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 5 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grades 5 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 do not include opportunities for teachers to personalize learning, including the use of adaptive technologies.

The instructional materials reviewed for Match Fishtank Grade 5 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.).
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials for Match Fishtank Grades 5 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.
Narrative Evidence Only
+
-
Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 5 typically do not integrate technology that could include interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the MPs. Two technology resources were found in fourth grade: Illuminations Equal Fractions Applet and DESMOS Blue Point Rule.

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.

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.