3rd Grade - Gateway 3

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• In Teacher Tools, Math Teacher Tools, Preparing to Teach Fishtank Math, Preparing to Teach a Math Unit recommends seven steps for teachers to prepare to teach each unit as well as the questions teachers should ask themselves while preparing. For example step 1 states, “Read and annotate the Unit Summary-- Ask yourself: What content and strategies will students learn? What knowledge from previous grade levels will students bring to this unit? How does this unit connect to future units and/or grade levels?”

• In Unit 2, Multiplication and Division, Part 1, Unit Summary provides an overview of content and expectations for the unit. Within Unit Prep, Intellectual Prep, there is Unit-Specific Intellectual Prep detailing the content for teachers. The materials state, “Read the article, Modeling with Mathematics by the Teaching Channel and watch the videos about Three-Act Tasks. Read the document “Situation Types for Operations in Word Problems” by Achieve the Core for multiplication and division. Identify the word problem types of any applicable assessment questions. (Optional) Read pp. 22–28 of the Operations and Algebraic Thinking (“OA”) Progressions document about Grade 3. Read the following table that includes models used throughout the unit.” Additionally, the Unit Summary contains Essential Understandings. It states, “In the United States, the convention for how to think of the equation 3 × 6 = ◻ is as 3 groups of 6 things each: 3 sixes (as opposed to 6 groups of 3). ‘But in other countries the equation 3 × 6 = □ means how many are 3 things taken 6 times (6 groups of 3 things each): six threes. Some students bring this interpretation of multiplication equations into the classroom. So it is useful to discuss the different interpretations and allow students to use whichever is used in their home’ (OA Progression, p. 25). The equation 20÷4=◻ can be interpreted in two ways: there are 20 objects to be partitioned into groups of 4 and we want to know how many groups we can make (the measurement model of division), or there are 20 objects to be partitioned into 4 groups and we want to know how many objects are in each group (the partitive model of division). Making sense of problems and persevering to solve them is an important practice when solving word problems. Keywords do not always indicate the correct operation. Multiplication problems can be solved using a variety of strategies of increasing complexity, including making and counting all of the quantities involved in a multiplication or division (Level 1 strategy), repeated counting on by a given number (Level 2), and using the properties of operations to compose and decompose unknown facts into known ones (Level 3).”  

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Teacher Tools, Math Tools, Preparing to Teach Fishtank Math, Components of a Math Lesson, states, “Each math lesson on Fishtank consists of seven key components: Objective, Standards, Criteria for Success, Tips for Teachers, Anchor Tasks/Problems, Problem Set, and Target Task. Several components focus specifically on the content of the lesson, such as the Standards, Anchor Tasks/Problems, and Target Task, while other components, like the Tips for Teachers, serve to ensure teachers have the support and knowledge they need to successfully implement the content.” Examples include:

• In Unit 1, Place Value, Rounding, Addition, and Subtraction, Lesson 8, Tips for Teachers provide context about representations when students add two numbers within 1,000. The materials state, “When discussing how to line up numbers in order to add or subtract them vertically, emphasize that units need to be lined up because one can only add or subtract like units (ones with ones and tens with tens), as opposed to saying that numbers need to be lined up from right to left. This is an important distinction since lining numbers up from right to left no longer works when students begin working with decimals (e.g., adding 6.4 and 2.08 would result in an incorrect sum if lined up from right to left).”

• In Unit 2, Multiplication and Division, Part 1, Lesson 6, Anchor Tasks Problem 2 Notes provide teachers guidance about how to set students up to solve the problems. The materials state, “If students are not solid in their count-by for twos, fives, or tens, drawing a model of some sort may be helpful, such as equal groups, array, a number line, or a tape diagram. Both equal groups and arrays are still one-to-one models, so you may want to focus on those for the time being. Because an array is very organized, you may want to emphasize this model in particular. An example of an array for the twos count-by is shown below:” An image shows skip counting by 2’s.

• In Unit 5, Shapes and Their Perimeter, Lesson 4, Tips for Teachers include guidance to address common misconceptions as students work to find the perimeter of polygons. The materials state, “Perimeter problems for rectangles and parallelograms often give only the lengths of two adjacent sides or only show numbers for these sides in a drawing of the shape. The common error is to add just these two numbers. Having students first label the lengths of the other two sides as a reminder is helpful” (MD Progression, p. 16).”

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.  

Correlation information is present for the mathematics standards addressed throughout the grade level/series and can be found in several places, including the course summary standards map, unit summary lesson map, and within each lesson. Examples include:

• In 3rd Grade Math, Standards Map includes a table with each grade-level unit in columns and aligned grade-level standards in the rows. Teachers can easily identify a unit when each grade-level standard will be addressed. 

• In 3rd Grade Math, Unit 2, Multiplication and Division, Part 1, Lesson Map outlines lessons, aligned standards, and the objective for each lesson. This is present for all units and allows teachers to identify targeted standards for any lesson.

• In Unit 5, Shapes and their Perimeter, Lesson 7, the Core Standard is identified as 3.MD.D.8. The Foundational Standard is identified as 3.OA.D.8. Lessons contain a consistent structure that includes an Objective, Common Core Standards, Criteria for Success, Tips for Teachers, Anchor Tasks, Problem Set & Homework, Target Task, and Additional Practice. This provides an additional place to reference standards, and language of the standard, within each lesson.

Each Unit Summary includes an overview of content standards addressed within the unit as well as a narrative outlining relevant prior and future content connections for teachers. Examples include:

• In Unit 1, Place Value, Rounding, Addition, and Subtraction, Unit Summary includes an overview of how the math of this unit builds from previous work in math. The materials state, “In Grade 2, students developed an understanding of the structure of the base-ten system as based in repeated bundling in groups of 10. With this deepened understanding of the place value system, Grade 2 students ‘add and subtract within 1000, with composing and decomposing, and they understand and explain the reasoning of the processes they use’ (NBT Progressions, p. 8). These processes and strategies include concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction (2.NBT.7). As such, at the end of Grade 2, students are able to add and subtract within 1,000 but often aren’t relying on the standard algorithm to solve.”

• In Unit 4, Area, Unit Summary includes an overview of how the content in Grade 3 connects to mathematics students will learn in Grades 4 and 5. The materials state, “In future grades, students will rely on the understanding of area to solve increasingly complex problems involving area, perimeter, surface area, and volume (4.MD.3, 5.MD.3—5, 6.G.1—4). Students will also use this understanding outside of their study of geometry, as multi-digit multiplication problems in Grade 4 (4.NBT.5), fraction multiplication in Grade 5 (5.NF.4), and even polynomial multiplication problems in Algebra (A.APR.1) rely on an area model.”

• In Unit 6, Fractions, Unit Summary includes an overview of the Math Practices that are connected to the content in the unit. The materials state, “This unit affords ample opportunity for students to engage with the Standards for Mathematical Practice. Students will develop an extensive toolbox of ways to model fractions, including area models, tape diagrams, and number lines (MP.5), choosing one model over another to represent a problem based on its inherent advantages and disadvantages. Students construct viable arguments and critique the reasoning of others as they explain why fractions are equivalent and justify their conclusions of a comparison with a visual fraction model (MP.3). They attend to precision as they come to more deeply understand what is meant by equal parts, and being sure to specify the whole when discussing equivalence and comparison (MP.6).”

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. This information can be found within Our Approach and Math Teacher Tools. Examples where materials explain the instructional approaches of the program include:

• In Fishtank Mathematics, Our Approach, Guiding Principles include the mission of the program as well as a description of the core beliefs. The materials state, “Content-Rich Tasks, Practice and Feedback, Productive Struggle, Procedural Fluency Combined with Conceptual Understanding, and Communicating Mathematical Understanding.” Productive Struggle states, “We believe that students develop essential strategies for tackling complex problems, and build non-cognitive skills such as perseverance and resilience, through productive struggle. Productive struggle happens when students are asked to use multiple familiar concepts and procedures in unfamiliar applications, and the process for solving problems is not immediately apparent. Productive struggle can occur, and should occur, in multiple settings: whole class, peer-to-peer, and individual practice. Through instruction and high-quality tasks, students can develop a toolbox of strategies, such as annotating and drawing diagrams, to understand and attack complex problems. Through discussion, evaluation, and revision of problem-solving strategies and processes, students build interest, comfort, and confidence in mathematics.”

• In Math Teacher Tools, Preparing To Teach Fishtank Math, Understanding the Components of a Fishtank Math Lesson helps to outline the purpose for each lesson component. The materials state, “Each Fishtank math lesson consists of seven key components, such as the Objective, Standards, Criteria for Success, Tips for Teachers, Anchor Tasks/Problems, Problem Set, the Target Task, among others. Some of these connect directly to the content of the lesson, while others, such as Tips for Teachers, serve to ensure teachers have the support and knowledge they need to successfully implement the content.” 

• In Math Teacher Tools, Academic Discourse, Overview outlines the role discourse plays within Fishtank Math. The materials state, “Academic discourse is a key component of our mathematics curriculum. Academic discourse refers to any discussion or dialogue about an academic subject matter. During effective academic discourse, students are engaging in high-quality, productive, and authentic conversations with each other (not just the teacher) in order to build or clarify understanding of a topic.” Additional documents are provided titled, “Preparing for Academic Discourse, Tiers of Academic Discourse, and Strategies to Support Academic Discourse.” These guides further explain what a teacher can do to help students learn and communicate mathematical understanding through academic discourse.

While there are many research-based strategies cited and described within the Math Teacher Tools, they are not consistently referenced for teachers within specific lessons. Examples where materials include and describe research-based strategies:

• In Math Teacher Tools, Procedural Skill and Fluency, Fluency Expectations by Grade states, “The language of the standards explicitly states where fluency is expected. The list below outlines these standards with the full standard language. In addition to the fluency standards, Model Content Frameworks, Mathematics Grades 3-11 from the Partnership for Assessment of Readiness for College and Careers (PARCC) identify other standards that represent culminating masteries where attaining a level of fluency is important. These standards are also included below where applicable. 3rd Grade, 3.OA.7, 3.NBT.2, 3.OA.4, 3.NBT.1, 3.NBT.3, 3.NF.2, and 3.NF.3b-d, among others.”

• In Math Teacher Tools, Academic Discourse, Tiers of Academic Discourse, Overview states, “These components are inspired by the book Classroom Discussions in Math: A Teacher’s Guide for Using Talk Moves to Support the Common Core and More. (Chapin, Suzanne H., Catherine O’Connor, and Nancy Canavan Anderson. Classroom Discussions in Math: A Teacher’s Guide for Using Talk Moves to Support the Common Core and More, 3rd edition. Math Solutions, 2013.)”

• In Math Teacher Tools, Supporting English Learners, Scaffolds for English Learners, Overview states, “Scaffold categories and scaffolds adapted from ‘Essential Actions: A Handbook for Implementing WIDA’s Framework for English Language Development Standards,’ by Margo Gottlieb. © 2013 Board of Regents of the University of Wisconsin System, on behalf of the WIDA Consortium, p. 50. https://wida.wisc.edu/sites/default/files/resource/Essential-Actions-Handbook.pdf”

• In Math Teacher Tools, Assessments, Overview, Works Cited lists, “Wiliam, Dylan. 2011. Embedded formative assessment.” and “Principles to Action: Ensuring Mathematical Success for All. (2013). National Council of Teachers of Mathematics, p. 98.”

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The 3rd Grade Course Summary, Course Material Overview, Course Material List 3rd Grade Mathematics states, “The list below includes the materials used in the 3rd grade Fishtank Math course. The quantities reflect the approximate amount of each material that is needed for one class. For more detailed information about the materials, such as any specifications around sizes or colors, etc., refer to each specific unit.” The materials include information about supplies needed to support the instructional activities. Examples include:

• Markers and crayons are used in Units 1 and 5, two different colors per student. In Unit 1, Place Value, Rounding, Addition, and Subtraction, Lesson 1, teachers are informed on both essential and optional materials needed for the unit. The materials state, “Optional: markers or crayons (2 of different colors per pair of students). Students could use pen and pencil instead.”

• Square inch tiles are used in Units 4, 5, and 6, twenty-four per student. In Unit 5, Shapes and Their Perimeter, Lesson 8, Tips For Teachers states, “Students may benefit from using square tiles to find rectangles with an area of 12 square units. For this task, teachers and students may need square inch tiles (optional: see note above).”

• String and/or pipe cleaners are used in Unit 3, two per student (or about 2 feet of string per student).

• Pattern blocks are used in Units 4 and 6, six of each shape per student.

• A pair of scissors is used in Units 4 and 7, one per student.

• A balance scale is used in Unit 7, one per group of students. 

• A 1 L beaker is used in Unit 7, one per group of students.

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for having assessment information included in the materials to indicate which standards and mathematical practices are assessed. 

Mid- and Post-Unit Assessments within the program consistently and accurately reference grade-level content standards and Standards for Mathematical Practice in Answer Keys or Assessment Analysis. Mid- and Post-Unit Assessment examples include:

• In Unit 1, Place Value, Rounding, Addition, and Subtraction, Expanded Assessment Package, Post-Unit Assessment Analysis denotes content standards addressed for each problem. Problem 2 is aligned to 3.OA.8 and states, “On the first day of their trip, the Knox family drove 368 miles. On the second day, they drove 447 miles. How many miles did the Knox family drive on the two days? A. 705, B. 715, C. 805, D. 815.”

• In Unit 2, Multiplication and Division, Part 1, Unit Summary, Mid-Unit Assessment, Answer Key denotes Standards for Mathematical Practice addressed for each question. Question 1 is aligned to MP2 and states, “Which of the following situations can be represented by the expression 20\div2? A. Gerald puts 20 pens into 2 containers. B. Manny makes 2 batches of cookies with 20 cookies in each batch. C. Carol has 20 tee shirts. She buys 2 more tee shirts at the store. D. Felicia puts 2 apples in each bag. She puts 20 apples into bags in total.”

• In Unit 5, Shapes and Their Perimeters, Unit Summary, Unit Assessment, Answer Key denotes standards addressed for each problem. Problem 6 is aligned to 3.G.1 and states, “In the space below, draw a quadrilateral that is not a parallelogram.” 

• In Unit 6, Fractions, Unit Assessment Answer Key includes a constructed response and 2-point rubric with the aligned grade-level standard. Problem 12 is aligned to 3.MD.4 and states, “Diondre is helping his art teacher, Mr. Jarrett, organize the materials in his closet. Mr. Jarrett asks Diondre to measure a bunch of square tiles to see if he can use them in a mosaic he is making. Diondre measures each one to the nearest quarter-inch and records the measurements in the table below. In the space below, create a line plot to show the data in the table above. Make sure your line plot is properly labeled.” An image of a table shows “Side lengths of Square Tiles” 4\frac{1}{2}, 4\frac{1}{4}, 4\frac{1}{4}, 4\frac{2}{4}, 3\frac{3}{4}, 4\frac{1}{2}, 5, and 4.

• In Unit 7, Measurement, Unit Summary, Post-Unit Assessment, Answer Key denotes Standards for Mathematical Practice addressed for each question. Question 6 is aligned to MP6 and states, “Which is closest to the mass of the stapler? A. 15 grams, B. 25 grams, C. 65 grams, D. 75 grams.” An image shows a stapler weighing between 70 and 75 grams.

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

Each lesson provides a Target Task with a Mastery Response. According to the Math Teacher Tools, Assessment Overview, “Target Tasks offer opportunities for teachers to gather information about what students know and don’t know while they are still engaged in the content of the unit.” Each Pre-Unit Assessment provides an answer key and guide with a potential course of action to support teacher response to data. Each Mid-Unit Assessment provides an answer key and a 2-, 3-, or 4-point rubric. Each Post-Unit Assessment Analysis provides an answer key, potential rationales for incorrect answers, and a commentary to support analysis of student thinking. According to Math Teacher Tools, Assessment Resource Collection,“commentaries on each problem include clarity around student expectations, things to look for in student work, and examples of related problems elsewhere on the post-unit assessment to look at simultaneously.” Examples from the assessment system include:

• In Unit 2, Multiplication and Division, Part I, Pre-Unit Assessment, Problem 2 states, “a. Draw an array with 8 objects where each row has 2 objects in it. b. How many rows are in your array?” Pre-Unit Assessment Analysis states, “Putting objects in arrays (Approaching 3.OA.2, 2.OA.4), As mentioned above, students used addition to find the total number of objects arranged in rectangular arrays and wrote equations to express the total as a sum of equal addends. Thus, this item extends that understanding to assess whether students are able to arrange a total number of objects in an array with rows of a certain size, analogous to a division situation involving equal groups with the number of equal groups unknown. Students may struggle with the language of rows and columns despite their introduction to these terms in 2nd grade. “Problems in terms of “rows” and “columns,” e.g., ‘“The apples in the grocery window are in 3 rows and 6 columns,” are difficult because of the distinction between the number of things in a row and the number of rows. There are 3 rows but the number of columns (6) tells how many are in each row. There are 6 columns but the number of rows (3) tells how many are in each column” (OA Progression, 24). Thus, this item uses just row language as will be the case when students first work with arrays in Lesson 2, but check to see whether students struggle even with that language, such as drawing an array with 2 rows instead of rows of 2. Students will rely on this understanding to make sense of multiplication and division situations involving arrays in this unit.” Potential Course of Action states, “If needed, this concept should be reviewed before students are introduced to unknown size of group or unknown number of groups problems in Lessons 3 and 4. For example, include a task similar to the one above as a warmup for Lesson 4, or an analogous problem with an unknown group size (e.g., asking students to construct an array with a certain number of rows) as a warmup for Lesson 3. You could also adapt Lesson 3 Anchor Task #2 Part (b) and/or Lesson 4 Anchor Task #2 Part (b), in which students solve unknown group size and unknown number of group problems involving arrays, respectively, to be more in-depth or allot more time for discussion.”

• In Unit 3, Mid-Unit Assessment, Problem 6 states, “Joey decides to give away 48 pieces of Halloween candy. He distributes the candies equally to six friends. Each friend got 7 fewer pieces of candy than Joey kept for himself. How many pieces of candy did Joey keep?” Scoring guidance is provided on a 3-point rubric. It states, “3 Points - Student response demonstrates an exemplary understanding of the concepts in the task. The student correctly and completely answers all aspects of the prompt. 2 Points - Student response demonstrates a good understanding of the concepts in the task. The student arrived at an acceptable conclusion, showing evidence of understanding of the task, but some aspect of the response is flawed. 1 Point - Student response demonstrates a minimal understanding of the concepts in the task. The student arrived at an incomplete or incorrect conclusion, showing little evidence of understanding of the task, with most aspects of the task not completed correctly or containing significant errors or omissions. 0 points - Student response contains insufficient evidence of an understanding of the concepts in the task. Work may be incorrect, unrelated illogical, or a correct solution obtained by chance.”  

• In Unit 5, Shapes and Their Perimeter, Post-Unit Assessment Answer Key, Question 7, scoring guidance states, “A. 1 pt - correct answer of 26 feet, B. 2 pts - any of the following dimensions: 1 × 12, 2 × 11, 3 × 10, 4 × 9, or 5 × 8, as well as a valid explanation, e.g., “I knew the length and width has to add to 13 so that the perimeter was 26, so I thought of 10 and 3. I knew the area had to be different from 42, the area of the rug, so the length and width could be 10 feet by 3 feet. See 2-point rubric on last page. (3.MD.8).” It states, 2 points - Student response demonstrates an exemplary understanding of the concepts in the task. The student correctly and completely answers all aspects of the prompt. 1 point - Student response demonstrates a fair understanding of the concepts in the task. The student arrived at a partially acceptable conclusion, showing mixed evidence of understanding of the task, with some aspects of the task completed correctly, while others not. 0 points - Student response contains insufficient evidence of an understanding of the concepts in the task. Work may be incorrect, unrelated, illogical, or a correct solution obtained by chance.”

• In Unit 6, Lesson 20, Target Task, Problem 2 states, “Solve. Then explain how you solved: \frac{3}{2}=$$\frac{\Box}{6}$$” The Mastery Response includes a sketched solution and, ‘I solved using the area models above. The second model is split into many more pieces, so it makes sense that we need more of them to be equivalent.’”

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

The Expanded Assessment Package includes the Pre-Unit, Mid-Unit, and Post-Unit Assessments. While content standards are consistently identified for teachers within Answer Keys for each assessment, practice standards are not identified for teachers or students. Pre-Unit items may be aligned to standards from previous grades. Mid-Unit and Post-Unit Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, short answer, and constructed response. Examples include:

• In Unit 2, Multiplication and Division, Part 1, Post-Unit Assessment, Problem 11, supports the full development of MP3 (Construct viable arguments and critique the reasoning of others) as students work with multiplication and division. The materials state, “Part A - Fred has 36 stuffed animals that he will give to 4 different friends. He will give an equal number of stuffed animals to each friend. Fred uses the equation 36÷4=? to find how many stuffed animals he will give each friend. He thinks the ? equals 8. Explain why he is wrong. Part B - Find the correct answer using Fred’s equation. Part C - How would you use multiplication to find the number of stuffed animals Fred gives each friend?”

• In Unit 4, Area, Mid-Unit Assessment, Problems 3-5 and Post-Unit Assessment, Problems 2, 3, 5, and 7, develop the full intent of standard 3.MD.7 (Relate area to the operations of multiplication and addition). Mid-Unit Assessment, Problem 3 states, “Find the area of the figure below.” [A rectangle with dimensions 7 meters x 9 meters included.] Problem 4 states, “Which of the following figures has an area of 36 square units? Select the ​two​ correct answers.” [Four different figures on graph paper included.] Problem 5 states, “Kelsey buys a square-shaped dog bed that has a length of 3 feet. How much space will her dog have to sleep?” Post-Unit Assessment, Problem 2 states, “A patio is in the shape of a rectangle with a width of 8 feet and a length of 9 feet. What is the area, in square feet, of the patio?” Problem 3 states, “Tomas made a poster for his science project. The shaded part of the figure below shows the area of his poster. Which figure has the same area as the poster?” [Four quadrilateral figures, A-D with dimensions provided.] Problem 5 states, “The grid below shows a playground and a basketball court at a park. Part A - What is the area of the playground? Part B. What is the total area of both the playground and the basketball court? Part C - Fill in the blanks to show how the number sentence below can be used to find the total area of the playground and the basketball court. (4 × _) + (4 × _) = 4x(_ + _).” Problem 7 states, “A Gardener is drawing plans for a new yard. She creates the picture below to represent the size and shape of a new lawn. Part A. How can the gardener find the total area of the new lawn? Describe the process she can use with words or equations. Part B. What is the total area, in square feet, of the new lawn?”

• In Unit 5, Shapes and Their Perimeter, Post-Unit Assessment, Problem 7, supports the full development of MP2 (Reason abstractly and quantitatively, as students solve problems involving perimeter and area). The materials state, “Ms. Shaw has a quilt that is in the shape of a rectangle. The quilt is 7 feet long and 6 feet wide, as shown. Part A - What is the perimeter, in feet, of Ms. Shaw’s quilt? Part B - Ms. Garcia also has a quilt in the shape of a rectangle. Ms. Garcia’s quilt has the same perimeter as Ms. Shaw’s quilt but has a different area. What could be the length and width, in feet, of Ms. Garcia’s quilt? Show or explain how you got your answer.”

• In Unit 6, Fractions, Post-Unit Assessment, Problems 2, 6, 8, 9, and 11, develop the full intent of 3.NF.3 (Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size). Problem 2 states, “Write a fraction that is less than \frac{1}{3}using 1 as the numerator. Explain why the answer you chose is less than \frac{1}{3}.” Problem 6 states, “Angela and Jacob are learning about fractions. Jacob says that the fractions  $$\frac{1}{4}$$and \frac{2}{3} are equivalent. Angela disagrees with him, so Jacob draws a picture to prove his point: Jacob is incorrect. Explain what is wrong with Jacob’s reasoning.” Problem 11 states, “Which number goes in the box to make the comparison true? \frac{5}{8}>$$\frac{\Box}{8}$$ A. 3; B. 5; C. 7; D. 9.”

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

There are no instances within the materials when advanced students have more assignments than their classmates, and there are opportunities where students can investigate grade-level mathematics at a higher level of complexity. Often, “Challenge” is written within a Problem Set or Anchor Task Guidance/Notes to identify these extensions. Examples include:

• In Unit 2, Multiplication and Division, Part 1, Lesson 2, Problem Set, Problem 9 states, “CHALLENGE: Using the digits 1 through 9, at most one time each, fill in the blanks to make the following problem true. How many different sentences can you make? Sarah planted _ carrots in her garden. She planted them in rows. Each row had __ carrots.”

• In Unit 4, Area, Lesson 8, Problem Set, Problem 7 states, “CHALLENGE: A larger square sticky note has an area of 36 square inches. What is the side length of the larger sticky note?”

• In Unit 6, Fractions, Lesson 8, Anchor Task, Problem 3, Notes state, “This task is optional, as it goes beyond the scope of the standards. It will help prepare students for similar tasks on the number line, like Find \frac{2}{3} by Illustrative Mathematics that they will see in Lesson 14.”

The materials reviewed for Fishtank Plus Math Grade 3 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials provide suggestions and/or links for virtual and physical manipulatives that support the understanding of grade-level concepts. Manipulatives are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. Examples include: 

• In Unit 1, Place Value, Rounding, Addition, and Subtraction, Lesson 1, Anchor Tasks, Problem 2 uses a Tic-Tac-Toe Board as number grids, allowing students to work with place value understanding. 

• In Unit 3, Multiplication and Division, Part 2, Lesson 21, Anchor Tasks, Problem 1 uses a Multiplication Chart to teach students how to identify patterns in a multiplication table. The materials state, “You could discuss all of the patterns as a whole class and have them write down their observations at the end of the discussion, or you could explore just one of these relationships as a whole class (the fives, for example) and then have students notice patterns a bit more independently on the Problem Set and Homework.”

• In Unit 7, Measurement, Lesson 7, Anchor Tasks, Problem 2 uses a Balance Scale to help students develop benchmarks in 1 kilogram and 1 gram from objects they weigh. The materials state, “For this task, students will need a thumbtack, a copy of textbook, a pair of scissors, a ruler, counters or other nonstandard unit used to measure mass, and a balance scale per group.”