Alignment: Overall Summary

The instructional materials reviewed for Match Fishtank, Grade 4 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).

See Rating Scale Understanding Gateways

Alignment

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Meets Expectations

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

Usability

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Partially Meets Expectations

Not Rated

Gateway 3:

Usability

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

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Match Fishtank Grade 4 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 86% 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 4 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 4 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 2 states, “The value of the digit 8 in the number 85,673 is ten times the value of the digit 8 in what number? A. 38,625 B. 286,379 C. 852,345 D. 516,800.” (4.NBT.1)
  • Unit 2 Assessment, Question 5 states, “Which of these numbers are prime numbers? Select the three numbers that are prime. A. 15 B. 19 C. 27 D. 37 E. 43 F. 51.” (4.OA.4)
  • Unit 3 Assessment, Question 6 states, “A truck delivers 9 cases of canned corn. Each case holds 36 cans of corn. When the cases are unpacked, 15 of the cans are missing. The store manager places 7 cans of corn on each shelf. What is the fewest number of shelves the manager will need for all of the cans of corn delivered by the truck.” (4.OA.3)
  • Unit 4 Assessment, Question 3 states, “Draw an obtuse angle.” (4.G.1)
  • Unit 5 Assessment, Question 2 states, “Fill in the blanks below with <, >, or = to make true number sentences. a. $$\frac{5}{12}$$__$$\frac{6}{10}$$  b. $$\frac{8}{6}$$__$$\frac{8}{7}$$.” (4.NF.2)
  • Unit 5 Assessment, Question 4 states, “Of the students in one school, $$\frac{1}{12}$$ play soccer, $$\frac{3}{8}$$ play basketball, $$\frac{2}{5}$$ take music lessons, and $$\frac{2}{6}$$ take dance lessons. Which list orders the fractions from least to greatest? A. $$\frac{1}{12}$$,  $$\frac{2}{5}$$,  $$\frac{2}{6}$$,  $$\frac{3}{8}$$   B. $$\frac{2}{5}$$,  $$\frac{3}{8}$$,  $$\frac{2}{6}$$,  $$\frac{1}{12}$$   C. $$\frac{2}{5}$$,  $$\frac{3}{8}$$,  $$\frac{2}{6}$$,  $$\frac{1}{12}$$   D. $$\frac{1}{12}$$,  $$\frac{2}{6}$$,  $$\frac{3}{8}$$,  $$\frac{2}{5}$$.” (4.NF.2) 
  • Unit 6 Assessment, Question 5 states, “Explain how to find $$2\times\frac{5}{12}$$ using the number line. Find the product.” Students are provided with a number line from 0 to 1 marked off in sixths. (4.NF.4b)
  • Unit 7 Assessment, Question 7 states, “Plot the following points on the number line below: 7.11, 7.06, 7.6, 7.90, and 7.75. The first one has been done for you.” A number line is provided with 7.11 marked. (4.NF.7)
  • Unit 8 Assessment, Question 6 states, “Ms. Ravelo bought a gallon of paint to paint her living room. She only used half of it. How much paint does she have left in cups? Show or explain your work.” (4.MD.2)

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 4 instructional materials, when used as designed, spend approximately 86% 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 4 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 7 out of 8, which is approximately 88%.
  • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 125 out of 145, which is approximately 86%.
  • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 144 out of 158, which is approximately 91%. 

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 86% 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 4 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 4 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 3, Lesson 11, Anchor Tasks, students apply the formulas for area and perimeter (4.MD.3) in real-world and mathematical problems involving all four operations (4.OA.3). Problem 1 states, “Edris wants to build a garden in his backyard to grow vegetables. He buys 60 yards of fencing to put around the garden to keep animals out. He wants the garden to be 12 feet long. What should the length of his garden be so that he uses all of the fencing he bought?”
  • In Unit 3, Lesson 16, Problem Set, students explore number and shape patterns (4.OA.5) using the four operations to draw conclusions about them (4.NBT.B). Problem 1 states, “Here is part of a repeating pattern. a. Draw the next 4 shapes in this pattern. b. What will be the 75th shape in the pattern? Explain how you know.”
  • In Unit 6, Lessons 22, Anchor Tasks, students extend their understanding of fraction equivalence and ordering (4.NF.A) to solve problems using information presented in line plots (4.MD.4). Problem 2 states, “Fourth-grade students interested in seeing how heights of students change for kids around their age measured the heights of a sample of eight-year-olds and a sample of ten-year-olds. Their data are plotted below. Describe the key differences between the heights of these two age groups.”
  • In Unit 8, Lessons 1, Anchor Tasks, students use their understanding of place value (4.NBT.1) to express metric length measurements in terms of a smaller unit (4.MD.1). Problem 2 states, “Fill in the following conversion tables” and Guiding Questions include, “How many times larger is a kilometer than a meter? How many meters are equal to 1 kilometer? 2 kilometers? How did you convert from kilometers to meters in the last case? Write an equation to represent the computation. (Write ‘6 x (1 km) = 6 x (1,000 m) = 6,000 m.’)”

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
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 4 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 158 instructional days (including lessons, flex days, and unit assessments). 

  • There are 137 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 eight unit assessments, one day each. 
  • The pacing guide suggests 13 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
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 4 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, “Because students did not focus heavily on place value in Grade 3, Unit 1 begins with where things left off in Grade 2 of understanding numbers within 1,000. Students get a sense of the magnitude of each place value by visually representing the place values they are already familiar with and building from there. Once students have a visual and conceptual sense of the “ten times greater” property, they are able to articulate why a digit in any place represents 10 times as much as it represents in the place to its right (4.NBT.1).” There are more examples that follow to illustrate the relation to grade-level concepts. 
  • The Unit 1 Summary also connects future grade level content, for example, “In subsequent grade levels, students generalize their base ten understanding to decimals. While students do some work with tenths and hundredths later on in Grade 4 (4.NF.5-7), students in Grade 5 are able to extend the decimal system to many more place values, seeing that a digit represents 110 of what it represents in the place to its left (5.NBT.1-3). Students subsequently round, compare, and operate on decimals as they did with numbers greater than one in Grade 4. Thus, this unit sets a precedent for a deep understanding of the number system that supports much of their mathematical knowledge later this year and in years to come.”
  • The Unit 8 Summary includes states, “In previous grades, students have worked with many of the metric and customary units (2.MD.1-6, 3.MD.1-2). They’ve noticed the relationship between some units to help them understand various measurement benchmarks but have not yet done any unit conversions. Not only does this unit build on measurement work from previous grades, but it also relies on myriad skills and understanding developed throughout Grade 4.” 
  • The Unit 8 Summary also connects future grade level content, “The unit not only looks back on the year in review, it also prepares students for work in future grades, including the very direct link to converting from smaller units to larger ones in Grade 5 (5.MD.1) and also to ratios and proportions in the middle grades (6.RP.1) as well as many other areas to come.”
  • 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 4 attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All lessons within the units include an “Anchor Task,” where students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Problem sets provide students the opportunity to solve a variety of problems, and integrate and extend concepts and skills. Each problem set is wrapped up with a “Discussion of Problem Set,” where students are provided an opportunity to synthesize and clarify their understanding of the day’s concepts. The lesson concludes with a “Target Task” for students to independently demonstrate their learning for the day. For example:

  • Unit 1, Lesson 4, Anchor Task, Problem 1 states, “Look at your paper base ten blocks. The ones piece is the smallest square. Then tens piece is a $$10\times1$$ strip. The hundreds piece is the larger $$10\times10$$ square. a. Use the paper base ten blocks to construct 1,000. Use tape as needed. b. Use the paper base ten blocks to construct 10,000. Use tape as needed. c. What comes next? What shape will it be?” (4.NBT.1)
  • Unit 2, Lesson 12, Problem Set, Problem 2 states, “Estimate. Then solve. Show or explain your work. a. $$5\times17$$ b. $$94\times2$$ c. $$9\times22$$ d. $$91\times7$$.” (4.NBT.5)
  • Unit 3, Lesson 10, Target Task, Problem 1 states, “Solve. Show or explain your work. Then check your work. a. $$92\div 3$$  b. $$7,040\div 4$$.” (4.NBT.6)
  • Unit 5, Lesson 4, Problem Set, Problem 5 states, “Explain how you know $$\frac{5}{8}$$ is equal to $$\frac{5\times6}{8\times6}$$. Use a model to explain your thinking.” (4.NF.1)
  • Unit 6, Lesson 6, Anchor Task, Problem 1 states, “1. Estimate the following sums. a. $$\frac{3}{4}+\frac{2}{4}$$   b. $$\frac{5}{6}+\frac{3}{6}$$ Solve for the actual sums in #1 above.” (4.NF.3a)
  • Unit 8, Lesson 3, Target Task, Problem 2 states, “________________ mL is equal to 342 L 645 mL.” (4.MD.1)
  • Unit 8, Lesson 12, Problem Set, Problem 1 states, “A short string is 1.8 meters. It is 70 centimeters shorter than a longer string. How many centimeters long is the longer string?” The Discussion of Problem Set states, “How did you interpret the remainder in #2? In #7(a), how many different ways were 7 halves represented? (30 min 7, as $$\frac{7}{2}$$ and as $$\frac{6}{2}+\frac{1}{2}$$) What advantage is there to knowing all of these representations when it comes to solving a problem like this one? What shortcuts or efficiencies did you use today when solving your problems? How do you decide whether to start by converting to a smaller unit or to work with the mixed number or decimal measurements?” (4.MD.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 2, Lesson 6, the Foundational Standards include Operations and Algebraic Thinking, 3.OA.7 (Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that $$8\times5=40$$, one knows $$40\div5=8$$) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers). The materials states, “4th Grade Math - Unit 2: Multi-Digit Multiplication. Students deepen their understanding of multiplication by exploring factors and multiples, multiplicative comparison, as well as multi-digit multiplication.” 
  • In Unit 7, Lesson 9, the Foundational Standards include Numbers and Operations- Fractions, 3.NF.2 (Understand a fraction as a number on the number line; represent fractions on a number line diagram). The materials state, “4th Grade Math - Unit 7: Decimal Fractions. Students expand their conception of what a ‘number’ is as they are introduced to an entirely new category of number, decimals, which they learn to convert, compare, and add in simple cases.” 

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
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Grade 4 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards. 

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

  • In Unit 2, Lesson 6, the lesson objective states, “Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors,” which is shaped by 4.OA.B, “Gain familiarity with factors and multiples.”
  • In Unit 4, Lesson 1, the lesson objective states, “Identify and draw points, lines, line segments, rays and angles,” which is shaped by 4.G.A, “Draw and identify angles, and classify shapes by properties of their lines and angles.”
  • In Unit 4, Lesson 10, the lesson objective states, “Identify and measure angles as turns and recognize them in various contexts,” which is shaped by 4.MD.C, “Geometric Measurement: understand concepts of angle and measure angles.”
  • In Unit 5, Lesson 4, the lesson objective states, “Recognize and generate equivalent fractions with smaller units using multiplication,” which is shaped by 4.NF.A, “Extend understanding of fraction equivalence and ordering.”
  • In Unit 6, Lesson 8, the lesson objective states, “Decompose and compose non-unit fractions greater than two as a sum of unit fractions and as a whole number times a unit fraction,” which is shaped by 4.NF.B, “Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.”
  • In Unit 7, Lesson 10, the lesson objective states, “Compare two or more decimals written in various forms,” which is shaped by 4.NF.C, “Understand decimal notation for fractions, and compare decimal fractions.”
  • In Unit 8, Lesson 8, the lesson objective states, “Express time measurements in terms of a smaller unit, recording measurement equivalents in a two-column table. Solve one-step word problems that require time unit conversion,” which is shaped by 4.MD.A, “Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.”

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 1, Lesson 15 connects 4.OA.A with 4.NBT.A,B as students solve multi-step word problems involving addition, and assess the reasonableness of answers using rounding. For example, Unit 1, Lesson 15, Target Task states, “In January, Scott earned $8,999. In February, he earned $2,387 more than in January. In March, Scott earned the same amount as in February. 1. Choose a place value to round to, then use those rounded values to estimate the amount Scott earned altogether during those three months. 2. Exactly how much did Scott earn in those three months? 3. Assess the reasonableness of your answer in (b). Use your estimate from (a) to explain.”
  • In Unit 3, Lesson 12, students connect 4.OA.A to 4.NBT.B by solving two-step word problems, including those involving interpreting the remainder. For example, Unit 3, Lesson 12, Problem Set, Problem 2 states, “The first grade went on a field trip to the museum. There are 26 students in each class and four classes in total. Each van can hold 7 students. How many vans were needed to get all the students to the museum?”
  • In Unit 5, Lesson 3 connects 4.NF.A to 4.OA.A as students generate equivalent fractions with smaller units using the area model. For example, Unit 5, Lesson 3, Anchor Tasks, Problem 1 states, “a. A garden is divided into rows of various vegetables. Three out of four rows are tomatoes. Partition and shade the square below to show how much of the garden is tomatoes. b. The garden is going to be shared with family and friends so that each person’s share of the harvest is three-fourths tomatoes. How would you partition the garden if it’s shared by two people? Show on the model above. c. What fraction of the newly divided garden is corn when it is shared by two people? Write an equation to show this relationship. d. Go through the same process for the garden but now splitting it evenly for three and five people on the models below.”

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials for Match Fishtank Grade 4 meet the expectations for rigor and the Mathematical Practices. The materials meet the expectations for rigor, students develop and demonstrate conceptual understanding, procedural skill and fluency, and application. The materials meet the expectations for practice standards and attend to the specialized language of mathematics.

Criterion 2a - 2d

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

The instructional materials reviewed for Match Fishtank Grade 4 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
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 4 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 4, Lesson 5, students create a wedge from folding a paper circle, then measure angles (4.MD.5) in wedges. In the Anchor Tasks, Problem 3, Guiding Questions state, “How can we use our wedge to measure the angles in Anchor Task 1? Why is it important to make sure there are no gaps or overlaps when we mark and move forward our wedges? How is this similar to other units of measurement like square units for area or length units for length?” 
  • In Unit 5, Lesson 3, students draw area models to recognize and generate equivalent fractions (4.NF.1). In the Anchor Tasks, Problem 2 states, “Find two fractions that are equivalent to each of the following: a. $$\frac{1}{8}$$  b. $$\frac{5}{12}$$  c. $$\frac{4}{3}$$.” Guiding Questions state, “What can we draw to represent 1/8? How can we use that picture to find another equivalent fraction?”
  • In Unit 8, Lesson 1, students explore the relationships between millimeters, centimeters, and meters on a meter stick (4.MD.1). In the Anchor Tasks, Problem 1 states, “Find the millimeter, centimeter, and meter measurement on the meter stick. a. What do you notice about the relationship between the length of a millimeter and the length of a centimeter? b. What do you notice about the relationship between the length of a centimeter and the length of a meter? c. What do you notice about the relationship between the length of a millimeter and the length of a meter?” Guiding Questions state, “How many times as large as a millimeter is a centimeter? How do you know? (Ask similar questions that correspond to parts (b) and (c).) We can’t use the meter stick to see the relationship between a meter and a kilometer. But, the prefix ‘kilo-’ means ‘thousand.’ Based on the meaning of the prefix, what do you think is the relationship between a kilometer and a meter? What are some things that are approximately a millimeter long? A centimeter? A meter? A kilometer? What is the length of your desk in millimeters? In centimeters? In meters? What do you notice about those values?”

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

  • In Unit 1, Lesson 10, students use a number line to understand the concept of rounding (4.NBT.3). In Anchor Task, Problem 1, students are given a blank number line and solve, “Is 4,125 closer to 4,000 or 5,000? Plot 4,000 and 5,000 on the two outermost spots on the number line below. Then plot 4,125 to prove your answer.” 
  • In Unit 5, Lesson 2, students use number lines to generate equivalent fractions (4.NF.1). The Target Task states, “The fraction $$\frac{1}{4}$$ is represented on the number line below. Use the number line to find two more equivalent fractions.”
  • In Unit 5, Lesson 8, students compare fractions with different denominators by using visual models to represent both fractions (4.NF.2). In the Anchor Tasks, Problem 1, students decide, “Would you rather have the leftover brownies in Scenario A or Scenario B? The pans in which the brownies were cooked are the same size.” Guiding Questions include but are not limited to, “What fraction of each brownie pan is left in Scenario A and Scenario B? How could we represent the common numerator or common denominator in each area model? Why does it matter that the brownie pans were the same size? How might your answer change if they weren’t the same size?”
  • In Unit 6, Lesson 5, students “decompose non-unit fractions less than or equal to 2 as a sum of unit fractions and as a whole number times a unit fraction” (4.NF.3b,4a) through tape diagrams, number lines and various picture models in the Problem Set. In the Anchor Tasks, Problem 2, students “a. Represent the following fractions as a sum of unit fractions, a sum of non-unit fractions, and a multiple of a unit fraction. Write your answer as an equation and justify your equation with a tape diagram or number line. $$\frac{5}{3}$$  b. Use your work in part (a) to show why $$\frac{5}{3}=1\frac{2}{3}$$.”

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
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 4 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 (4.NBT.4). For example:

  • In Unit 1, Lesson 13, students “fluently add multi-digit whole numbers using the standard algorithm (4.NBT.4) involving up to two compositions. Solve one-step word problems involving addition.’ In Anchor Tasks, Problem 2, students “Estimate. Then solve. a. $$40,762 + 30,473 =$$___  b. ___ $$= 258,209 + 48,906$$.”
  • In Unit 1, Lesson 14, students fluently add multi-digit whole numbers using the standard algorithm (4.NBT.4). Students have opportunities to practice in the Problem Set, Homework, and Target Task. For example, Problem Set, Problem 1 states, “Solve. a. $$6,314 + 2,493$$   b. $$8,314 + 2,493$$ c. ____$$= 12,378 + 5,463$$ d. $$52,098 + 6,048 $$ e.____ $$- 34,698 = 71,840$$ f. $$544,811 + 356,445$$ g. $$527 + 275 + 752 = g$$ h. $$478,295 + 353,067$$ i.____ $$= 38,193 + 6,376 + 241,457$$.”
  • In Unit 1, Lesson 16, students “fluently subtract multi-digit whole numbers using the standard algorithm involving two decompositions” (4.NBT.4). In the Target Task, students “Solve, Show or explain your work. a. $$8,512 - 2,501$$  b. $$18,042 - 4,122$$ c. $$19,850 - 15, 761$$.”
  • In Unit 1, Lesson 19, students solve multi-step word problems involving addition and subtraction,” (4.OA.3, 4.NBT.4). In the Homework, Problem 3 states, “There were 22,869 children, 49,563 men, and 2,872 more women than men at the fair. How many people were at the fair?”
  • In Unit 2, Lesson 23, students “solve multi-step word problems involving multiplication, addition, and subtraction,” (4.OA.3, 4.NBT.4). The Target Task states, “Solve. Show or explain your work. Michael earns $9 per hour. He works 28 hours each week. David earns $8 per hour. He works 40 hours each week. After 6 weeks, who earns more money? How much more money?”
  • In Unit 3, Lesson 3, students “divide multiples of 10, 100, and 1,000 by one-digit numbers,” (4.NBT.6). Anchor Tasks, Problem 1 states, “1. Solve. a. $$9\div3$$   b. $$90\div3$$  c. $$900\div3$$   d. $$9,000\div3$$.  2. What do you notice about #1? What do you wonder?”

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
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Indicator Rating Details

The instructional materials for Match Fishtank Mathematics Grade 4 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 (4.OA.3, 4.NF.3d, 4.NF.4c). 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 2, Lesson 23, students solve multi-step, real-world problems involving multiplication, addition and subtraction (4.OA.3). For example, Problem Set, Problem 4 states, “There will be 45 adults going to a museum. There will be twice as many students as adults. Adult tickets cost $25 each. Students tickets cost $12 each. What is the total cost for the students and adults?” 
  • In Unit 3, Lesson 11, students apply the formulas for area and perimeter in real-world and mathematical problems involving all four operations (4.OA.3, 4.MD.3). For example, Problem Set, Problem 3 states, “Mr. Felton will use exactly 42 feet of fencing to surround a garden that is in the shape of a rectangle. His garden has a length of 12 feet. The equation below represents the perimeter of Mr. Felton’s garden. $$w + w + 12 + 12 = 42$$ What is the width, in feet, of Mr. Felton’s garden?”
  • In Unit 3, Lesson 13, students solve multi-step word problems involving the four operations (4.OA.3). For example, Problem Set, Problem 2 states, “Your class is collecting bottled water for a service project. The goal is to collect 400 bottles of water. Sarah wheels in 6 packs, each containing 6 bottles of water. Sarah brought in twice as many packs as Max. After counting Sarah and Max’s bottles, how many packs of water still need to be collected?” 
  • In Unit 6, Lesson 17, students solve word problems involving addition and subtraction of fractions (4.NF.3d). For example, Target Task, Problem 1 states, “Mrs. Cashmore bought a large melon. She cut a piece that weighed $$1\frac{1}{8}$$ pounds and gave it to her neighbor. The remaining piece of melon weighed $$2\frac{5}{8}$$ pounds. How much did the whole melon weigh?” 
  • In Unit 6, Lesson 20, students solve word problems involving multiplication of fractions (4.NF.4c). For example, Target Task, Problem 2 states, “If a bucket holds $$2\frac{1}{2}$$ gallons and 43 buckets fill a tank, how much does the tank hold?”

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

  • In Unit 2, Lesson 23, students solve multi-step word problems involving multiplication, addition, and subtraction (4.OA.3). For example, Problem Set, Problem 8 states, “The table below shows the number of tickets sold at a movie theatre on Friday. (table provided) The number of each type of ticket sold on Saturday is described below. Adult tickets - 2 times as many as the number of adult tickets sold on Friday. Children’s tickets - 3 times as many as the number of children’s tickets sold on Friday. Complete the table above to show the numbers of tickets sold on Saturday. What is the total number of tickets sold over these two days?”
  • In Unit 6, Lesson 21, students solve word problems involving addition, subtraction, and multiplication of fractions (4.NF.3d and 4.NF.4c). For example, Target Task states, “The table below shows the sizes and weights of containers of potato salad sold at a store. Kim purchased 6 small containers of potato salad and Seth purchased 2 extra-large containers of potato salad. What is the difference in the weights, in pounds, of Kim's and Seth's purchases?”
  • In Unit 7, Lesson 12, students solve word problems involving the addition of decimals and decimal fractions (4.NF.5). For example, in Problem Set, Problem 6 states, “A team of three ran a relay race. The final runner’s time was the fastest, measuring 29.2 seconds. The middle runner’s time was 1.89 seconds slower than the final runner’s. The starting runner’s time was 0.9 seconds slower than the middle runner’s. What was the team’s total time for the race?”
  • In Unit 8, Lesson 4, students solve multi-step, real-world problems that require metric unit conversions of length, mass, and capacity (4.MD.2). For example, in Problem Set, Problem 4 states, “Enya walked 2km 309m from school to the store. Then, she walked twice that amount from the store back home. How far, in meters, did she walk in total?”
  • In Unit 8, Lesson 12, students solve word problems involving converting fractional and decimal measurements to a smaller unit. (4.MD.2). For example, in Problem Set, Problem 2 states, “Five ounces of pretzels are put into each bag. How many bags can be made from 22 3/4 pounds of pretzels?”

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 4 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 9, students use number lines to locate multi-digit numbers and explain their placement (4.NBT.2). For example, Anchor Task, Problem 1 states, “Based on where 0 and 100 are, what number do you think the question mark is on? Explain your choice.” 
  • In Unit 5, Lesson 2, students “recognize and generate equivalent fractions with smaller units using number lines (4.NF.1).” Anchor Task, Problem 1 states, “a. What fraction represents the point shown on the number line below? B. What fraction represents the point shown on the number line below? C. Use the pictures to explain why the two fractions represented above are equivalent.”
  • In Unit 6, Lesson 5, students “decompose non-unit fractions less than or equal to 2 as a sum of unit fractions and as a whole number times a unit fraction (4.NF.3,4).” Anchor Task, Problem 1 states, “During Lesson 1, Francisco and Harry were playing with their fraction strips. Part A: They filled the outline as follows: What fraction of the original outline is each piece? Part B: Then Francisco and Harry build another shape, as shown below: What fraction of the original outline is this new shape? Explain your answer.”

Examples of Procedural Skills and Fluency include:

  • In Unit 1, Lesson 13, students “Fluently add multi-digit whole numbers using the standard algorithm involving up to two compositions. Solve one-step word problems involving addition,” (4.NBT.4). In Problem Set, Problem 3 states, “Elizabeth solved the problem $$70,912 + 24,628$$ using the standard algorithm, as shown below. a. Identify the mistake in Elizabeth’s work. b. Show or explain how Elizabeth can correct her mistake.”
  • In Unit 1, Lesson 17, students “Fluently subtract multi-digit whole numbers using the standard algorithm involving multiple decompositions. Solve one-step word problems involving subtraction,” (4.NBT.4). In Anchor Task, Problem 1 states, “Place any digit, 1 through 9, in the boxes below to create the smallest possible difference. Each digit can only be used once.”
  • In Unit 2, Lesson 6, students find factor pairs for numbers to 100 (4.OA.3,4). For example, Problem Set, Problem 2 states, “Find all factors for the following numbers.” Students complete tables of the factor pairs for 25, 28, and 29. 

Examples of Application include:

  • In Unit 2, Lesson 22, students “solve two-step word problems involving multiplication, addition, and subtraction and assess the reasonableness of answers,” (4.OA.2,3). For example, the Target Task states, “Solve. Show or explain your work. Jennifer has 256 beads. Stella has 3 times as many beads as Jennifer. Tiah has 104 more beads than Stella. How many beads does Tiah have?”
  • In Unit 6, Lesson 20, students “solve word problems involving multiplication of fractions,” (4.NF.4c). In Anchor Task, Act 2 states, “Share the following information with students:  One can of soda has $$\frac{4}{15}$$ cup of sugar in it. There are 12 cans in the whole pack. Have students work on the task to determine how much sugar is in the whole pack.”
  • In Unit 8, Lesson 4, students “solve multi-step word problems that requires metric unit conversions of length, mass, and capacity,” (4.MD.2). For example, Problem Set, Problem 2 states, “Kiera likes to mix apple juice with cranberry juice in her glass. She has 1 L of juice in all. She puts three times as much apple juice as cranberry juice in her glass. How many mL of apple juice did she put in her glass?”

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 16, students, “Fluently subtract multi-digit whole numbers using the standard algorithm involving up to two decompositions. (4.NBT.4) Students also, “solve one-step word problems involving subtraction.” For example, Problem Set, Problem 2 states, “Chuck’s mom spent $19,155 on a new car. She had $30,067 in her bank account. How much money does Chuck’s mom have after buying the car? Show or explain your work.” 
  • In Unit 2, Lesson 10, students use their conceptual understanding of rounding to estimate multi-digit products when multiplying multiples of 10, 100, and 1,000 by one-digit numbers (4.NBT.5). For example, Problem Set, Problem 4 states, “Estimate the following products.” In Problem 4k, students solve the following problem, “$$3\times9,268$$.”
  • In Unit 6, Lesson 17, students use their conceptual understanding of addition and subtraction to “solve word problems involving addition and subtraction of fractions,” (4.NF.3d). For example, the Target Task states, “Mrs. Cashmore bought a large melon. She cut a piece that weighed $$1\frac{1}{8}$$ pounds and gave it to her neighbor. The remaining piece of melon weighed $$2\frac{5}{8}$$ pounds. How much did the whole melon weigh?”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
10/10
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Criterion Rating Details

The instructional materials reviewed for Match Fishtank Grade 4 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 4 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade-level.

All Standards for Mathematical Practice are clearly identified throughout the materials in numerous places, that include but are not limited to: Unit Summaries, Criteria for Success, and Tips for Teachers. Examples include:

  • In Unit 3, Unit Summary, “Throughout the unit, students are engaging with the mathematical practices in various ways. For example, students are seeing and making use of structure (MP.7) as they ‘decompos[e] the dividend into like base-ten units and find the quotient unit by unit”’(NBT Progressions, p. 16). Further, "by reasoning repeatedly (MP.8) about the connection between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities” (NBT Progression, p. 14). Lastly, as students solve multi-step word problems involving addition, subtraction, and multiplication, they are modeling with mathematics (MP.4).”
  • In Unit 5, Lesson 4, Criteria for Success states, “2. Understand how the numbers and sizes of parts differ even though the two fractions are the same size, and connect this idea to the general method of using multiplication to find an equivalent fraction (MP.7). 4. Determine whether two fractions are equivalent using multiplication, and support that work with a visual model (MP.3, MP.5).”
  • In Unit 8, Lesson 5, Tips for Teachers, “As mentioned in the Progressions, “relating units within the traditional system provides an opportunity to engage in mathematical practices, especially ‘look for and make use of structure’ (MP.7) and ‘look for and express regularity in repeated reasoning’ (MP.8).”

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

  • MP7 is connected to the mathematical content in Unit 2, Lesson 5, Target Task, Problem 1, as students “make use of structure (MP.7) by using the divisibility rules stated above to determine whether a number larger than 100 is a multiple of 2, 3, 5, 6, 9, or 10.” For example, “What do all multiples of 9 have in common?”
  • MP4 is connected to the mathematical content in Unit 3, Lesson 8, Problem Set, Problem 4, as students “Solve one-step division word problems, including those that require the interpretations of the remainder.” For example, “Zach filled 581 one-liter bottles with apple cider. He distributed the bottles to 4 stores. Each store received the same number of bottles. Zach kept the leftover bottles to be distributed the next day. How many bottles did Zach keep?”
  • MP6 is connected to the mathematical content in Unit 4, Lesson 2, Anchor Task, Problem 3, as students “Draw right, obtuse, and acute angles.” For example, “Draw an example of a right angle, an acute angle, an obtuse angle, and a straight angle.”
  • MP4 is connected to the mathematical content in Unit 8, Lesson 8, Target Task, Problem 2, as students “solve one-step word problems that require time unit conversions, including problems that involve elapsed time (MP.4)” For example, “Jacob needs to do his chores. It takes Jacob an hour and 45 minutes to mow the lawn and 20 minutes to clean his room. If he starts his chores at 2:00 PM, what time will he finish?”

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 4 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 nit 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 3, Lesson 2, Criteria for Success states, “Interpret the remainder in the context of the word problem, including: c. Having the remainder be the answer to the problem (such as when wanting to know how much Halloween candy the teacher gets to keep after distributing some to students) (MP.1).” For example, Anchor Task, Problem 1 states, “Solve the following problems. Think about the main differences between each one. a. A teacher has 21 batteries. Each calculator uses 4 batteries. How many calculators can the teacher fill with batteries? b. Four children can ride in a car. How many cars are needed to take 21 children to the museum? c. Ms. Cole wants to share 21 pieces of candy with 4 students. If Ms. Cole gets to eat the pieces of candy that can’t be split evenly, how many pieces of candy will Ms. Cole get?” 
  • MP2: In Unit 2, Lesson 21, Tips for Teachers states, “When engaging in the mathematical practice of reasoning abstractly and quantitatively (MP.2) in work with area and perimeter, students think of the situation and perhaps make a drawing. Then they recreate the ‘formula’ with specific numbers and one unknown number as a situation equation for this particular numerical equation. (GM Progression, p. 22)” For example, Problem Set, Problem 4 states, “The rectangular projection screen in the school auditorium is 5 times as long as 5 times as wide as the rectangular screen in the library. The screen in the library is 9 feet long and 12 feet wide. What is the perimeter of the screen in the auditorium?”
  • MP4: In Unit 8, Lesson 1, Criteria for Success states, “Solve one-step word problems that require metric length unit conversions (MP.4).”  For example, Anchor Task, Problem 3 states, “Mr. Duffy wants to buy a new pair of skis. Skis are sold based on their length in centimeters. If Mr. Duffy wants to buy a pair of skis that are his exact height, and he is 1 meter 83 centimeters tall, what length skis should Mr. Duffy buy? How can we determine what length skis Mr. Duffy should buy? Write an equation to represent the computation. (Write “1 m 83 cm = 1 x (1 m) + 83 x (1 cm) = 1 x (100 cm) + 83 x (1 cm) = 100 cm + 83 cm = 183 cm.”) How many centimeters is 5 m 4 cm? How many millimeters is 3 m 75 mm? How many centimeters is 20 km 45 m?”
  • MP5: In Unit 4, Lesson 14, Criteria for Success states, “1. Classify triangles according to their side length, and understand each type as equilateral (has all three sides of equal length), isosceles (has two sides of equal length), and scalene (has no sides of equal length) (MP.2, MP.5). 2. Classify triangles according to their angle measure and understand each type as acute (has all three angles that are acute), right (has a right angle), and obtuse (has an obtuse angle) (MP.2, MP.5).” For example, in Problem Set, Problem 1a, students are prompted to choose their own tool to determine right triangles, “Which of these polygons are right triangles. Choose a measuring tool to help you determine this.”
  • MP6: In Unit 1, Lesson 11, Criteria for Success states, “Understand the advantages and disadvantages of rounding a value to various place values, including the precision of rounding a number to a smaller place value (MP.6) and ease of working/operating when rounding a number to a larger place value.” In the Target Task, Problem 2 states, “There are 16,850 Star coffee shops around the world. Round the number of shops to the nearest thousand and ten thousand. Which answer is more precise? Explain your thinking using pictures, numbers or words.”
  • MP7: In Unit 3, Lesson 3, Tips for Teachers states, “Throughout Lesson 3-10, students are seeing and making use of structure (MP.7) as they ‘decompose the dividend into like base-ten units and find the quotient unit by unit’ (Progressions for the Common Core State Standards in Mathematics, Number and Operations in Base Ten, K-5, p. 16). (4.NBT.6)” For example, Problem Set, Problem 4 states, “What is the missing number in the equation below? $$5,600\div8=?$$ a. 7 b. 70 c. 700 d. 7,000”
  • MP8: In Unit 3, Lesson 3, Criteria for Success states, “Identify patterns in division of multiples of 10, 100, and 1,000 by single digits (MP.8).” For example, Anchor Task, Problem 2, students solve, “a. $$32\div4$$ b. $$320\div4$$ c. $$3200\div4$$.” Students then answer, “What do you notice about #1? What do you wonder?” 

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for Match Fishtank Mathematics Grade 4 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 3, Lesson 4, Problem Set, Problem 2 states, “Jillian says, I know that 20 times 7 is 140 and if I take away 2 sevens that leaves 126. So $$126\div7 = 18$$. a. Is Jillian’s calculation correct? Explain. b. Draw a picture showing Jillian’s reasoning. c. Use Jillian’s method to find $$222\div6$$.” Students “Understand and explain why various simplifying strategies work (MP.3),” when dividing two-, three-, and four-digit numbers by one-digit numbers. 
  • In Unit 4, Lesson 4, Problem Set, Problem 3 states, “Ms. Glynn said that the line segments that make up the E are parallel. Is she correct? Why or why not?” Students construct a viable argument in order to respond to the word problem (MP.3).
  • In Unit 5, Lesson 4, Target Task, Problem 1 states, “Determine if the following fractions $$\frac{5}{3}=\frac{15}{9}$$ are equivalent. Then explain how you know.” Students construct an argument by determining if the given fractions are equivalent, then justify their conclusions (MP.3). 
  • In Unit 6, Lesson 10, Problem Set, Problem 5 states, “Simone changed the mixed number 4 1/3 to a fraction. First, Simone change the whole number 4 to the fraction 4/3. Then she added the two fractions together. Her work is shown. $$4\frac{1}{3}=4+\frac{1}{3}=\frac{4}{3}+\frac{1}{3}=\frac{5}{3}$$  Explain the error in Simone’s reasoning. Find the correct equivalent fraction. Describe another method you can use to change the mixed number $$4\frac{1}{3}$$ to a fraction.” Students analyze the reasoning of others (MP.3). 
  • In Unit 7, Lesson 7, Anchor Task, Problem 2 states, “Fill in the blank with <, =, or > to complete the equation. Justify your comparison.  0.8 and 0.3, 0.01 and 0.11, 0.2 and 0.20, 0.6 and 0.41, 0.07 and 0.70, 0.57 and 0.75.” Students justify their reasoning of comparisons of decimal equations (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 4 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 2, Lesson 11, Criteria for Success states, “2. Understand and explain why various simplifying strategies work (MP.3).” In Problem Set, Problem 2 states, “Connor solves $$8\times16$$. He says, ‘I can find the product if I multiply $$8\times15$$ and then add 8.’ Select the statement that best explains if Connor’s strategy is correct. a. Connor is correct, because he can change the 16 to use an easier number to multiply by, like 15. b. Connor is incorrect, because $$8\times16$$ is the same as 4 groups of 8, but 4 groups of 8. c. Connor is correct, because $$8\times16$$ is the same as 15 groups of 8, plus 1 group of 8. d. Connor is incorrect, because he should add 16 instead of 8.” The Discussion of the Problem Set provides teachers with the following questions to support students constructing viable arguments: “What was the best option for #2? Were there other options that were decent options but not the best option? How did you decide which was the better option of the two?”
  • In Unit 3, Lesson 10, Criteria for Success states, “3. Critique the reasoning of others regarding any of the above cases (MP.3).” Anchor Task, Problem 1, Guiding Questions include, but are not limited to, “How do you know that Geraldo’s answer is wrong? What was the error that Geraldo made? What is the correct answer? How did you solve? Is our answer reasonable? How can we check our work?”
  • In Unit 5, Lesson 8, Criteria for Success states, “1. Compare two fractions where both fractions need to be replaced with an equivalent one to be able to compare common units (denominators) or common number of units (numerator) (MP.3).” In Anchor Task, Problem 1 states, “Would you rather have the leftover brownies in Scenario A or Scenario B? The pans in which the brownies were cooked are the same size.” Guiding Questions include, but are not limited to, “Why does it matter that the brownie pans were the same size? How might your answer change if they weren’t the same size?”
  • In Unit 6, Lesson 13, Tips for Teachers states, “Throughout Lessons 13–17, “calculations with mixed numbers provide opportunities for students to compare approaches and justify steps in their computations (MP.3)” (NF Progression, p. 12).”
  • In Unit 7, Lesson 6, Anchor Task, Problem 1 notes, “This task provides an opportunity to construct viable arguments and critique the reasoning of others (MP.3).”  Guiding Questions include, but are not limited to, “What place value unit does a one-dollar bill represent? A dime? A penny? What would 4 one-dollar bills and 1 dime be in pennies? How can we express that value using place value units? What about 42 dimes? If you wanted to represent 42 dimes using the largest possible monetary units, how could we do that? What about 413 pennies?”

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 4 meet expectations for explicitly attending to the specialized language of mathematics.

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

  • In Unit 1, Lesson 7, Tips for Teachers states, “Remember from Lesson 4 that when saying or writing a number in word form, the word ‘and’ implies a decimal point and therefore should not be used when naming whole numbers. For example, 217,350 is read ‘two hundred seventeen thousand three hundred fifty,’ not ‘two hundred and seventeen thousand three hundred and fifty.’ Even though students have not yet seen decimals, it is important to read numbers correctly before they do.”
  • In Unit 2, Lesson 5, Tips For Teachers states, “Note that the lesson, including the objective, does not contain the language of ‘divisible’ or ‘divisibility.’ This is because it is not language called for in the standards. You may decide to use it, though.”
  • In Unit 3, Lesson 5, Tips for Teachers states, “‘Language plays an enormous role in thinking conceptually about the standard division algorithm. More adults are accustomed to the ‘goes into’ language that is hard to let go. For the problem $$583\div4$$, here is some suggested language, ‘I want to share 5 hundreds, 8 tens, and 3 ones among these 4 sets. There are enough hundreds for each set to get 1 hundred. That leaves 1 hundred that I can’t share. I’ll trade the remaining hundred for 10 tens. That gives me a total of 18 tens. I can give each set 4 tens and have 2 tens left over. Two tens are not enough to go around the 4 sets. I can trade 2 tens for 20 ones and put those with the 3 ones I already had. That makes a total of 23 ones. I can give 5 ones to each of the four sets. That leaves me with 3 ones as a remainder. In all, I gave each group 1 hundred, 4 tens, and 5 ones, with 3 ones left over.’ *Van de Walle, Teaching Student-Centered Mathematics, Grades 3-5, Vol. 2, p. 191).”
  • In Unit 7, Lesson 2, Tips for Teachers states, “When saying a number in word form, make sure to only use the word ‘and’ in place of the decimal place and nowhere else. For example, 7.5 is read ‘seven and five tenths.’”
  • In Unit 7, Lesson 1, Tips For Teachers states, “While mathematicians and scientists often read 0.5 aloud as ‘zero point five’ or ‘point five,’ refrain from using this language until you are sure students have a strong sense of place value with decimals (NF Progression, p. 15).”

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

  • At the beginning of each unit, the Unit Prep provides Vocabulary for the unit. As found in Unit 1, vocabulary includes, but is not limited to, “Ten thousands, millions, hundred millions, hundred thousands, ten millions, variable, etc.”
  • In Unit 2, Lesson 7, Criteria for Success, students will, “Understand that a prime number is a whole number that has exactly two factors, 1 and itself.”
  • In Unit 3, Lesson 1, Criteria for Success, students will, “Understand that a remainder is the number left over when one number is divided by another.”
  • In Unit 4, lesson 3, Criteria for Success, students will, “Understand that perpendicular line segments are line segments that intersect to form right angles.”
  • In Unit 4, Lesson 16, Tips For Teachers, “The term ‘trapezoid’ is sometimes defined in two different ways: a quadrilateral with exactly one pair of parallel sides, or quadrilateral with at least one pair of parallel sides. In our curriculum, we choose to use the inclusive definition; a trapezoid as a quadrilateral with at least one pair of parallel sides.” 
  • In Unit 5, Lesson 1, Criteria for Success, students will, “Understand that equivalent fractions are fractions that refer to the same whole and are the same size.”

Gateway Three

Usability

Partially Meets Expectations

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 4 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 4 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson.

There are eight instructional units in Grade 4. 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 2, Lesson 3, Anchor Task, Problem 1, students solve multiplicative comparison problems with an unknown multiplier and interpret a multiplication equation as a comparison (4.OA.1,2).  The problem states, “Mrs. Ingall wants to place students’ pencil boxes on her bookshelf for the start of the school year. We know her bookshelf is 24 inches long. Each pencil box is 2 inches wide. a.How many pencil boxes can she line up along the bookshelf? b.How can you use your answer from Part (a) to determine how many times as long the bookshelf is than the pencil box?”

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 4, Lesson 8, Problem Set, students measure angles that are greater than 180 (4.MD.5,6). Problem 2 states, “Maria says that this angle measures 153. Is she correct or incorrect? Why?” Students are given an angle to measure.
  • In Unit 7, Lesson 12, Homework, students solve word problems involving the addition of decimals and decimal fractions (4.NF.5). Problem 2 states, “The snowfall in Year 1 was 2.03 meters. The snowfall in Year 2 was 1.6 meters. How many total meters of snow fell in Years 1 and 2?”
  • In Unit 7, Lesson 5, Target Task, students express customary length measurements in terms of a smaller unit, and record measurement equivalents in a two-column table (4.MD.1). In Problem 2, students “Answer ‘true’ or ‘false’ for the following statements. If the statement is false, change the right side of the comparison to make it true. a.12 yards < 40 feet ______ b.  7 feet 1 inch > 70 inches ______ .”

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 4 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 4 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 9, students locate multi-digit numbers on a number line and explain their placement (4.NBT.2,3). For example, in Anchor Task, Problem 1, Part 1, a number line from 0 to 100 with a question mark about two-thirds of the way between the two marks is provided. The problem states, “Look at the line below. Based on where 0 and 100 are, what number do you think the question mark is on? Explain your choice.”
  • In Unit 3, Lesson 6, students solve two-digit dividend division problems with a remainder in the tens and/or ones place with smaller divisors and quotients (4.NBT.6). For example, Problem Set states, “Cayman says that $$59\div4$$ is 10 with a remainder of 19. He reasons this is correct because $$(4\times10)+19=59$$. What mistake has Cayman made? Explain how he can correct his work.”
  • In Unit 5, Lesson 6, students recognize and generate equivalent fractions with larger units using division (4.NBT.1). For example, Target Task, Problem 2 states, “Explain how you know  is equivalent to. Use a model to support your reasoning.”

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 4 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

 The series integrates hands-on activities that include the use of physical manipulatives.

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

  • In Unit 2, Lesson 6, square tiles are used to find all factors of a number. 
  • In Unit 4, Lesson 15, Anchor Task, Problem 2, students use a protractor to draw an obtuse isosceles triangle.
  • In Unit 5, Lesson 1, tape diagrams are used to generate equivalent fractions.

 Manipulatives used in Grade 4 include but are not limited to: 

  • Base ten blocks, tape diagrams, number lines, grid paper, dice, square tiles, counters, pattern blocks, protractors, rulers, hundreds chart, millions place value chart, fraction strips, metric and customary weights, volume containers, meter stick, and yard stick.
  • Templates provided in place of three-dimensional manipulatives: paper hundreds flat and square-sized 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.
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 4 are not distracting or chaotic and support students in engaging thoughtfully with the subject.

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

Criterion 3f - 3l

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

The instructional materials for Match Fishtank Grade 4 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 4 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 2, Lesson 1, Anchor Task, Problem 1 states, “How can the length of The Twits help us to figure out the length of the bookshelf? How many copies of The Twits can fit on the bookshelf? We can express this relationship by saying the bookshelf is 6 times as long as the book. How can we represent this relationship with a tape diagram? With an equation?”
  • Anchor Task Notes are often included after the Guiding Questions. These Notes include problem-specific information that may be helpful in understanding or executing the problem.
  • The Discussion of Problem Sets includes a list of “suggested questions for teachers to ask after students have worked on the Problem Set but before they attempt the Target Task. Similar to the Guiding Questions for Anchor Tasks, these questions can serve different purposes, including: connecting the content of the Problem Set to previous learnings (including major work and/or connections across clusters and domains, if applicable), more deeply engaging students in the content of the Problem Set, and extending on the Problem Set. Not all Discussions of Problem Sets include questions that cover all three purposes. Also, not all Discussion questions are meant to be asked to the whole class; rather, it should be at the discretion of the teacher to determine how, when, and which questions should be used with which students.” For example, Unit 7, Lesson 8 states, “Look at #1f. 1.9 has 2 digits and 1.21 has three digits, and yet 1.9 is greater than 1.21. Why? How would #2 be different if given area models to use to represent the values? Which is easier to use to model the values? Which is easier to use to compare? Why? Would you rather have 2.7 pounds of strawberries or 2.34 pounds? Why? If you didn’t like strawberries, how might your answer change?”

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 4 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 3, Lesson 6, Tips for Teachers states, “As noted in Lesson 5 Anchor Task #2, because many of the computations in this lesson involve a remainder when computing the partial quotient in the ones place, the computation has been recorded using the partial quotients algorithm to avoid writing the ‘R’ notation after an equal sign. If you’d like to postpone the introduction of the partial quotient notation, you could either record the computation in a way that is similar to Lesson 5 Anchor Task #1 but in such a way to avoid confusion regarding the equality of a computation with its quotient and remainder. (See the Tips for Teachers section of Lesson 1 to read more.)”
  • In Unit 8, Lesson 3, Tips for Teachers states, “This lesson is optional. It does, however, make a connection across domains between the work of metric measurement conversion (4.MD.1) and students’ place value understanding (4.NBT.A), since ‘expressing larger measurements in smaller units within the metric system is an opportunity to reinforce notions of place value’ (GM Progression, p. 20).”

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 4 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 4 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 4 Course Summary states, “Grade 4 focuses on three key advancements from previous years: (1) developing understanding with multi-digit multiplication and division; (2) developing an understanding of fraction equivalence, and certain cases of fraction addition, subtraction, and multiplication; and (3) understanding that geometric figures can be analyzed and classified based on their properties, including their angle measure and symmetry.” An explanation about how the units are sequenced is also provided.
  • Each unit opens with a Unit Summary, which details the specific grade level content to be taught, as well as connections to previous and future grades.
  • Each lesson provides current standards addressed in the lesson, as well as foundational standards taught in previous units or grades that are important background for the current lesson.

Indicator 3j

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

The instructional materials for Match Fishtank Grade 4 provide a list of lessons in the Teacher's Edition, cross-referencing the standards addressed, and a pacing guide.

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

Indicator 3k

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

The instructional materials for Match Fishtank Grade 4 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.
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grade 4 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 4 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 4 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 4 meet expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Examples include: 

  • In Unit 3, Lesson 5, Anchor Task, the Problem 1 Notes state, "Students may need base ten blocks for this task (optional: see note below). For those students who are still developing their place value understanding, it may be beneficial for students to see the division with base ten blocks themselves, as shown in the diagram. Otherwise, you could draw the base ten block model or even just use an area model.”
  • In Unit 4, Lesson 5, Tips for Teachers states, “John A. Van de Walle notes, ‘angle measurement can be a challenge for two reasons: the attribute of angle size is often misunderstood, and protractors are commonly introduced and used without understanding how they work’ (Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3-5 (Volume II). Pearson, 2nd edition, 2013. Page 335). Thus, this lesson serves to help students understand angle measure as the spread of an angle’s rays, which can be measured with smaller angles.”

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 4 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, Anchor Tasks, the Problem 3 Notes state, “As students develop their fluency with reading number names, they can default to read numbers in unit form first and then practice reading them the usual way after hearing the teacher say it.”
  • In Unit 7, Lesson 5, Anchor Tasks, the Problem 1 Notes state, “Students don’t need to use models here, but as in Lesson 3, they may help students reason abstractly and quantitatively (MP.2). An example of how to draw pictorial base ten blocks to hundredths is shown below:”

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

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

The instructional materials for Match Fishtank Grade 4 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, Rounding, Addition and Subtraction, Assessment Item 4a correlates with 4.OA.3 and 4.NBT.4. 
  • In Unit 3, Multi-Digit Division, Assessment Item 5 correlates with 4.OA.5.
  • In Unit 6, Fraction Operations, Assessment Item 3c correlates with 4.NF.3.a. 

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 4 do not meet expectations for including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

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

  • In Unit 2, Decimal Fractions, Unit Assessment, Item 3, “$3.50. 1 point – modeling component – student shows or explains how to find the amount of change. 1 point – computation component – student gets correct answer of $3.50.”

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

Indicator 3q

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

The instructional materials for Match Fishtank Grades 4 do not provide any strategies or resources for students to monitor their own progress.

Criterion 3r - 3y

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

The instructional materials for Match Fishtank Grade 4 do not meet expectations for supporting teachers in differentiating instruction for diverse learners. The instructional materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners and strategies for meeting the needs of a range of learners. The materials embed tasks with multiple entry points that can be solved using a variety of solution strategies or representations and include extension activities for advanced students, but do not present advanced students with opportunities for problem solving and investigation of mathematics at a deeper level. The instructional materials also suggest support, accommodations, and modifications for English Language Learners and other special populations and provide a balanced portrayal of various demographic and personal characteristics.

Indicator 3r

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

The instructional materials for Match Fishtank Grade 4 partially meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. For example:

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

Indicator 3s

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

The instructional materials for Match Fishtank Grade 4 partially meet the expectations for providing teachers with strategies for meeting the needs of a range of learners. For example: 

  • The units do not provide materials or a plan for differentiated instruction with teacher-guided, small-group options.
  • The materials do provide some guidance on reteaching or modifying the lesson for struggling learners in teacher notes or tips for teachers. For example: 
    • In Unit 2, Lesson 6, Anchor Task, Problem 1, the Teacher Notes suggests, “Students may need square tiles or other counters for this task,” to solve a multiplication word problem. 
    • In Unit 5, Lesson 2, Anchor Task, Problem 2, the Teacher Notes state, “Students may want to draw a tape diagram or an area model but should be encouraged to draw a number line. Depending on students’ comfort level with using number lines to represent a fraction, it may help to draw tape diagrams that represent each fraction, then construct a number line beneath the tape diagram.”
  • The materials do not provide guidance or materials to extend learning for those students mastering lesson content.

Indicator 3t

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

The instructional materials reviewed for Match Fishtank Grade 4 meet expectations for embedding tasks with multiple entry points that can be solved using a variety of solution strategies or representations.

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

  • In Unit 2, Lesson 12, Anchor Task, Problems 1-3 students explore the use of area models when multiplying a two-digit number by a one-digit number. In the Target Task, Problem 2, students “Solve. Show or explain your work: $$35\times7$$.” Students may choose to use the area model strategy or choose another method to solve.
  • In Unit 3, Lesson 4, the Anchor Tasks provide students opportunities to divide two-, three- and four-digit numbers by one-digit numbers using area models. In the Target Task, Problems 1-3, students “Solve. Show or explain your work.” Each student may independently choose a strategy that works for them.
  • In Unit 5, Lesson 2, the Anchor Tasks provide students the opportunity to find equivalent fractions using number lines. In the Problem Set, Problem 3, students can choose any strategy to determine if two fractions are equivalent.

Indicator 3u

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

The instructional materials for Match Fishtank Grades 4 partially meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. In the Teacher Tools section, “A Guide to Supporting English Learners,” features the use of scaffolds, oral language protocols, and graphic organizers. However, there are no features on providing support or accommodations to English Language Learners and other special populations throughout the materials.

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

Specific strategies for support, accommodations, and/or modifications are mentioned in “A Guide to Supporting English Learner” that include sensory, graphic, and interactive scaffolding; oral language protocols which include many cooperative learning strategies, some of which mentioned in teacher notes; and using graphic organizers with empathize on lighter or heavier scaffolding. For example, Oral Language Protocols provide structured routines to allow students to master opportunities and acquire academic language. Several structures are provided with an explanation on ways to incorporation them that include turn and talk, simultaneous round table, rally coach, talking chips, number heads together, and take a stand. Ways to adapt the lessons or suggestions to incorporate them are not included within lessons, units, or summaries.

There is no support provided for special populations.

Indicator 3v

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

The instructional materials reviewed for Match Fishtank Grade 4 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. For example: 

  • Unit 6, Lesson 17, Problem Set, Problem 9, “CHALLENGE: Make the smallest product by filling in the boxes using the whole numbers 1-9 no more than one each time.”


Indicator 3w

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

The instructional materials reviewed for Match Fishtank Grade 4 meet expectations for providing a balanced portrayal of various demographic and personal characteristics. The lessons contain students that have a variety of demographic and personal characteristics that do not illustrate gender bias, lack of racial or ethnic diversity, or racial or naming stereotyping. For example:  

  • Different cultural names and situations are represented in the materials, for example: Ms. Roll, Ayana, Jada, Damon, Molly, Andre, Andrea, Yasmin, and Osvaldo.
  • In Unit 3, Lesson 11, Anchor Task, Problem 2 states, “Now Edris wants to retile the rectangular patio in his backyard. He uses 128 tiles that are each one square foot. His patio is 8 feet wide. He wants to edge the patio with metal tape to make sure the tiles don’t move or shift at all. How many feet of metal tape should Edris buy?"

Indicator 3x

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

The instructional materials for Match Fishtank Grades 4 provide limited opportunities for teachers to use a variety of grouping strategies.

The Guide to Supporting English Learners provides cooperative learning and grouping strategies which can be used with all students. However, there are very few strategies mentioned in the instructional materials, and there are no directions or examples for teachers to adapt the lessons or suggestions on when and how to incorporate then are not included in the teacher materials. For example:

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

Indicator 3y

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

The instructional materials for Match Fishtank Grades 4 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 3z - 3ad

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 4 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 3z

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

The instructional materials reviewed for Match Fishtank Grade 4 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 Factor Game and Partial Product Finder Applet.

Indicator 3aa

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

The instructional materials reviewed for Match Fishtank Grade 4 are web-based and compatible with multiple internet browsers. Print resources may be downloaded from the website as teacher edition pages and PDF files for student resources.

The materials are platform neutral (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, Safari, etc.).

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

Indicator 3ab

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

The instructional materials reviewed for Match Fishtank Grades 4 do not include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology.

Indicator 3ac

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

The instructional materials reviewed for Match Fishtank Grade 4 do not include opportunities for teachers to personalize learning, including the use of adaptive technologies.

The instructional materials reviewed for Match Fishtank Grade 4 are not customizable for individual learners or users. Suggestions and methods of customization are not provided.

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
0/0
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Indicator Rating Details

The instructional materials for Match Fishtank Grades 4 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.

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Additional Publication Details

Report Published Date: 01/14/2020

Report Edition: 2019

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

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

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. 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).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, 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.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric 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 rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric 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.

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.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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