5th Grade - Gateway 3

The materials reviewed for Fishtank Plus Math Grade 5 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 4, Addition and Subtraction of Fractions/Decimals, 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, “When referred to fractions and decimals throughout Units 4-6, use unit language as opposed to ‘out of’ or ‘point’ language (e.g.,$$\frac{3}{4}$$ should be described as ‘3 fourths’ rather than ‘3 out of 4’ and 0.8 should be described as ‘8 tenths’ rather than ‘zero point eight’). To understand why this is important for fractions (which can be extrapolated to decimals), read the following blog post: Say What You Mean and Mean What You Say by William McCallum on Illustrative Mathematics. Read the following table that includes models used in this unit.” Additionally, the Unit Summary contains Essential Understandings. It states, “Quantities cannot be added or subtracted if they do not have like units. Just like one cannot add 4 pencils and 3 bananas to have 7 of anything of meaning (unless one changes the unit of both to ‘objects’), the same applies for the units of fractions (their denominators) and the units of decimals (their place values). This explains why one must find a common denominator to be able to add fractions with unlike denominators and why one must align corresponding places correctly (which in turn aligns the decimal points) when adding and subtracting decimals. ‘It is not necessary to find a least common denominator to calculate sums of fractions, and in fact the effort of finding a least common denominator is a distraction from understanding algorithms for adding fractions’ (NF Progressions, p. 11). Similar to computational estimates with whole numbers, some computational estimates with fractions can be better than others, depending on what numbers are chosen to use in place of the actual values. Computational estimates can be too high or too low, depending on how the numbers were originally estimated, what computation is being performed, and where in the number sentence it’s located. ‘Because of the uniformity of the structure of the base-ten system, students use the same place value understanding for adding and subtracting decimals that they used for adding and subtracting whole numbers’ (NBT Progression, p. 19).”  

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 With Decimals, Lesson 8, Tips for Teachers include guidance to address common misconceptions with decimal patterns. The materials state, “A common misconception when multiplying decimals by 10 is that one just ‘adds a zero’ to the end of the number, which with decimals does not change the value of the number. If you notice this misconception come up, address it directly with the whole class, using various models and arguments to dispute it. The Target Task should give the teacher helpful feedback on whether this misconception persists by the end of the lesson.”

• In Unit 4, Addition and Subtraction of Fractions/Decimals, Lesson 2, Anchor Tasks Problem 1 Notes provide teachers guidance about how to set students up to solve the problems. The materials state, “The contexts for the problems were intentionally chosen to encourage students to use one type of model—an area model for part (a) and a number line for part (b). Students, of course, can use them interchangeably. Since students relied more heavily on tape diagrams and number lines for fraction addition and subtraction in Grade 4, they may gravitate towards those, in which case you can decide whether to introduce the area model here or wait for Lesson 4 when they become more useful to find a common unit. An area model and number line for Parts (a) and (b), respectively, are shown below. If students struggle to see why the numerators are added and the denominators stay the same, relate it to the idea of the denominators being the units of the fractions. Just like 3 bananas and 4 bananas together are 7 bananas, 3 eighths and 4 eighths together are 7 eighths.”

• In Unit 6, Multiplication and Division of Decimals, Lesson 9, Tips for Teachers provide context when students divide decimals by a single-digit whole number. The materials state, “Because students will encounter cases of decimal division for which they have not seen the equivalent fraction division, students cannot use fraction division to reason about where to place the decimal point in all cases of decimal division that students will encounter. Thus, it is not included in this lesson since students have not yet performed the corresponding fraction division related to today’s cases. This lesson is analogous to Lessons 1 and 2 but with decimal division. It has been consolidated into one lesson, assuming that students are more easily able to use reasoning about the placement of the decimal point. However, if students would benefit from this lesson being broken up into two days, including if they may benefit from it based on students’ reasoning skills when placing the decimal point in a decimal quotient or based on their procedural comfort with multi-digit division, it can be split into two lessons.”

The materials reviewed for Fishtank Plus Math Grade 5 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 5th 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 5th Grade Math, Unit 2, Multiplication and Division of Whole Numbers, 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 3, Shapes and Volume, Lesson 1, the Core Standard is identified as 5.MD.C.3 and 5.MD.C.4. The Foundational Standard is identified as 3.MD.C.5. 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 with Decimals, Unit Summary includes an overview of how the math of this unit builds from previous work in math. The materials state, “In Grade 4, students developed the understanding that a digit in any place represents ten times as much as it represents in the place to its right (4.NBT.1). With this deepened understanding of the place value system, students read and wrote multi-digit whole numbers in various forms, compared them, and rounded them (4.NBT.2—3).”

• In Unit 3, Shapes and Volume, Unit Summary includes an overview of the Math Practices that are connected to the content in the unit. The materials state, “Throughout Topic A, students have an opportunity to use appropriate tools strategically (MP.5) and make use of structure of three-dimensional figures (MP.7) to draw conclusions about how to find the volume of a figure.”

• In Unit 7, Patterns and the Coordinate Plane, Unit Summary includes an overview of how the content in 5th grade connects to mathematics students will learn in middle grades. The materials state, “This work is an important part of “the progression that leads toward middle-school algebra” (6—7.RP, 6—8.EE, 8.F) (K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, p. 7). This then deeply informs students’ work in all high school courses. Thus, Grade 5 ends with additional cluster content, but that designation should not diminish its importance this year and for years to come.”

The materials reviewed for Fishtank Plus Math Grade 5 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. 5th Grade, 5.NBT.5, 5.OA.1, 5.NBT.3, 5.NBT.4, 5.NBT.5, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.4, 5.NF.7, and 5.MD.1, 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”

• 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 5 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The 5th Grade Course Summary, Course Material Overview, Course Material List 5th Grade Mathematics states, “The list below includes the materials used in the 5th 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:

• Tape or staplers are used in Units 1 and 3, one per group. In Unit 1, Place Value and Decimals, Lesson 1, students work with place value to millions. The materials state, “For this task, the teacher will need paper hundreds flats (20 count) cut to show 1 one, 1 ten, 1 hundred. Students will need a lot of copies of the paper hundreds flats (20 count), cut along the lines to make hundreds, and tape or staples to group the hundreds together.”

• Base-ten blocks are used in Unit 1, maximum of 80 ones, 70 tens, 80 hundreds, and 8 thousands per individual, pair, or group of students.

• Centimeter cubes are used in Unit 3, two hundred per pair or group of students. 

• Cardstock is used in Unit 3, three sheets per student. 

• A pair of scissors is used in Unit 5, one per student. In Unit 5, Multiplication and Division of Fractions, Lesson 1, students model fractions as division using area models. The materials state, “Students may need pieces of paper and scissors for this task (optional: see note below).”

• Markers or crayons are used in Units 3 and 7, three different colors per student. 

• Graph paper is used Unit 7, two sheets per student.

The materials reviewed for Fishtank Plus Math Grade 5 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 with Decimals, Expanded Assessment Package, Post-Unit Assessment Analysis denotes content standards addressed for each problem. Problem 10 is aligned to 5.NBT.3b and states, “Select the two correct comparisons. A. 0.057 < 0.008, B. 0.057 < 0.57, C. 0.57 = 0.570, D. 0.57 > 1.001, E. 0.057 < 0.049.”

• In Unit 2, Multiplication and Division of Whole Numbers, Unit Summary, Mid-Unit Assessment, Answer Key denotes Standards for Mathematical Practice addressed for each question. Question 5 is aligned to MP4 and states, “The ground floor of a hotel measures 74 feet long and 126 feet wide. There is 15 times as much square footage in the whole hotel as on the ground oor. What is the total square footage of the hotel? Show or explain your work.”

• In Unit 4, Addition and Subtraction of Fractions/Decimals, Unit Summary, Unit Assessment, Answer Key denotes standards addressed for each question. Problem 6 is aligned to 5.NF.1 and states, “Solve. 7\frac{5}{6} + 3\frac{4}{9}. Select the two correct answers. A. 10\frac{15}{54}, B. 10\frac{9}{15}, C. 11\frac{15}{54}, D. 10\frac{5}{18}, E. 11\frac{5}{18}, F. 10\frac{3}{5}.” 

• In Unit 6, Multiplication and Division of Decimals, Post-Unit Assessment, Answer Key denotes Standards for Mathematical Practice addressed for each question. Question 1 is aligned to MP2 and states, “At a café, the cost of a turkey sandwich is 1 less than twice the cost of a side salad. A side salad costs 3.50. Which of the following expressions can be used to find the cost, in dollars, of a turkey sandwich at the café? A. $$ 3.50\times2−1 $$, B. 3.50\times2+1, C. (3.50−1)\times2, D. (3.50+1)\times2.”

• In Unit 7, Patterns and the Coordinate Plane, Unit Assessment Answer Key includes a constructed response and 2-point rubric with the aligned grade-level standard. Problem 5d is aligned to 5.G.2 and states, “The data table below shows the height of a typical meerkat at different times during their first 20 months of life. Decide whether the meerkat grew more from month 0 to month 10 or from month 10 to month 20. Explain your answer.”

The materials reviewed for Fishtank Plus Math Grade 5 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 of Whole Numbers, Pre-Unit Assessment, Problem 2 states, “Translate the following into numbers and symbols. Do not solve. a. Six more than one; b. Five times as much as four; c. The quotient of eight and two; d. Three subtracted from seven.” The Answer Key includes the following teacher guidance, “Translating verbal statements to numeric expressions (K.OA.1, 1.OA.1, 3.OA.1, 3.OA.2, 4.OA.1). Students started to learn about addition and subtraction starting in Kindergarten, developing an understanding of how addition and subtraction situations translate to numerical expressions, and vice versa. This understanding grew to encompass additive comparison, as expressed in Part (a) above as ‘six more than one’, in 1st grade. Simultaneously, their vocabulary to describe addition and subtraction situations grew, including use of terms like ‘sum’, ‘difference’, and others. Then, in 3rd grade, students develop an understanding of how multiplication and division situations translate to numerical expressions, and vice versa. In 4th grade, students expand their understanding of multiplication to include cases of multiplicative comparison, as expressed in Part (b) above as ‘five times as much as four’, in 4th grade. As students deepened their understanding of these operations, their vocabulary to describe them grew as well, such as terms like ‘product’ and ‘quotient’, among others. Students will rely on this understanding to write simple expressions to record calculations with numbers, such as expressing the calculation ‘add 8 and 7, then multiply by two’ as ‘2×(8+7)’, among other possibilities. Notice how this skill is dependent on an understanding of the role of parentheses and the order of operations to record a numerical expression that is actually equivalent to the verbal description. Potential Course of Action If needed, this concept should be reviewed early in the unit, since students will write expressions that record calculations with numbers in Lesson 2.  For example, include a task similar to the one above as a warm-up for Lesson 2. Find problems and other resources in these Fishtank lessons: Grade 3, Unit 2, Lessons 1—5 (Note: these just encompass multiplication and division; adapt these resources for analogous tasks with addition and subtraction).”

• In Unit 6, Multiplication and Division of Decimals, Lesson 24, Target Task, Problem 2 states, “Solve. Show or explain your work. Yolanda took a bus to visit her grandmother. She brought a CD to listen to on the bus. The CD is 78 minutes long. The bus ride was 2\frac{1}{2} hours long. How many minutes longer was the bus ride than the CD?” A Mastery Response is provided, which states, “$$2\frac{1}{2}$$ x 1hr = $$2\frac{1}{2}$$ × 60 minutes =120 + 30 minutes = 150 minutes. 150 - 78 = 72. The bus ride was 72 minutes longer than the CD.” 

• In Unit 3, Shapes and Volume, Post Assessment, Problem 9 states, “An art piece is made using two rectangular prisms. The side lengths of the art piece are shown. The length of one of the sides, m, is missing. What is the length of side m? What is the volume of the art piece? Show or explain your work.” The Post-Unit Assessment Answer Key provides the answer, “m=14 feet; the volume is 1,088 cubic feet. See 4-point rubric on the last page.” The 4-Point Rubric states, “4 points - Student response demonstrates an exemplary understanding of the concepts in the task. The student correctly and completely answers all aspects of the prompt. 3 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. 2 points - 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. 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 4, Addition and Subtraction of Fractions and Decimals, Mid-Unit Assessment, Question 4 states, “Elbert is subtracting 1\frac{5}{8}-\frac{2}{3}. He thinks the answer is 1\frac{3}{8} because 5-2 is 3 and 8 is the larger denominator. Explain the error in reasoning Elbert made. Find the correct answer. Be sure to show or explain your work.” The Mid-Unit Assessment Answer Key provides scoring guidance, “Answers may vary, e.g., ‘Elbert’s mistake was that he just subtracted the numerators and used the bigger denominator for the difference. Instead, he could have computed 1\frac{5}{8}-\frac{2}{3}=1\frac{15}{24}-\frac{16}{24}=1-\frac{1}{24}=\frac{23}{24}.’” The 2-Point Scoring Rubric states, “2 points: Students' 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.”

The materials reviewed for Fishtank Plus Math Grade 5 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 1, Place Value with Decimals, Post-Unit Assessment, Problem 6, supports the full development of MP3 (Construct viable arguments and critique the reasoning of others). The materials state, “Terry made an error while finding the product 0.4 × 100. He writes, When I multiply by ten I just add a zero to the end of my number, so since multiplying by 100 is the same as multiplying by ten twice, I add two zeros to the end of my number. So, 0.4 × 100 = 0.400. Identify Terry’s mistake. Explain what he should do to get the correct answer and include the correct answer in your response.”

• In Unit 4, Addition and Subtraction of Fractions/Decimals, Post-Unit Assessment, Problems 2, 5, and 7 develop the full intent of 5.NBT.7 (Add, subtract, multiply and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction). Problem 2 states, “The decimal grids below are shaded to model and expression. What is the value of the expression modeled by the decimal grids? A. 3.29; B. 3.32; C. 4.10; D. 4.13.” Problem 5 states, “Fred is going to the movies. A movie ticket costs $15, and Fred wants to buy a bucket of popcorn for $3.50 and a candy bar for $0.89. Fred has $20. Does Fred have enough money for a movie ticket, a bucket of popcorn, and a candy bar? If so, how much change will he receive? If not, how much more money does he need? Show or explain your work.” Problem 7 states, “Solve. 14.4 - 5.63.” Additionally, in Unit 6, Multiplication and Division of Decimals, Mid-assessment, Problem 2 states, “Multiply or divide. Show or explain your work. a. 8 × 4.35 b. 3.89 ÷ 5.”

• In Unit 5, Multiplication and Division of Fractions, post assessment, Problem 12, supports the full development of MP2 (Reason abstractly and quantitatively, as students interpret multiplication as scaling). The materials state, “The students in Raul’s class were growing grass seedlings in different conditions for a science project. He noticed that Pablo’s seedlings were 1\frac{1}{2} times as tall as his own seedlings. He also saw that Celina’s seedlings were \frac{3}{4} as tall as his own. Which of the seedlings below must belong to which student? Explain your reasoning.” 

• In Unit 7, Patterns and the Coordinate Plane, Mid-Unit Assessment, Problem 2 and Post-Unit Assessment, Problems 4 and 5, meet the full intent of 5.OA.3 (Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation). Mid-unit Assessment Problem 2 states, “Sonia and Ahmal plotted the point F on the coordinate grid below. a. Sonia wants to plot a point G so that F and G form a horizontal line. Write an ordered pair that represents where Sonia could plot point G. b. Ahmal wants to plot a point H so that F and H form a vertical line. Write an ordered pair that represents where Ahmal could plot point H.” Post-Unit Assessment, Problem 4 states, “Select the three statements that correctly describe the coordinate system. A. The x- and y-axes intersect at 10. B. The x- and y-axes intersect at the origin. C. The x- and y-axes are parallel number lines. D. The x- and y-axes are perpendicular number lines. E. The x- and y-coordinates are used to locate points on a coordinate plane.” Problem 5 states, “The data table below shows the height of a typical meerkat at different times during their first 20 months of life. A. Graph the data on the grid below. B. How many inches did the meerkat grow between month 4 and month 12? C. How many months did it take for the meerkat to grow from 7 inches to 12 inches?”

The materials reviewed for Fishtank Plus Math Grade 5 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 of Whole Numbers, Lesson 1, Problem Set, Problem 7 states, “CHALLENGE: Use the digits 0 to 9 to make the equation true. You don't need to use all the digits from 0 to 9, but you can only use each digit once. 20 = ___ + (___ - ___) × ___.”

• In Unit 4, Addition and Subtraction of Fractions/Decimals, Lesson 1, Anchor Tasks, Problem 4, Notes state, “This task is optional, depending on whether you have time for it. Students saw tasks like these in Grade 4 and they are included on the Problem Set, but students’ ability to solve tasks like this are not a necessary skill for fraction addition and subtraction (since they will always know the values they are multiplying the numerator and denominator by rather than need to figure them out). But, because they are more challenging than the fractions in Anchor Task #3 and include larger numbers, they encourage students to use the algorithm rather than draw models, which will help them fluently find equivalent fractions in the context of addition and subtraction of fractions with unlike denominators.”

• In Unit 7, Patterns and the Coordinate Plane, Lesson 7, Problem Set, Problem 4e states, “CHALLENGE: i. Compare the coordinates of points Q and T. What is the difference of the x-coordinates? The y-coordinates? ii. Compare the coordinates of points Q and R. What is the difference of the x-coordinates? The y-coordinates? iii. What is the relationship of the differences you found in parts (e) and (f) to the triangles of which these two segments are a part?”

The materials reviewed for Fishtank Plus Math Grade 5 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 with Decimals, Lesson 6, Anchor Tasks, Problem 1 uses a place chart to help students explain patterns in the number of zeros of the quotient when dividing a whole number by powers of 10. The materials state, “For this task, teachers and students may need base ten blocks (about 30 ones, 30 tens, 30 hundreds, and 3 thousands per group/teacher) and a Millions Place Value Chart.”

• In Unit 5, Multiplication and Division of Fractions, Lesson 3, Anchor Tasks, Problem 1, students use two-sided counters as manipulatives to model multiplying fractions by a whole number. 

• In Unit 7, Patterns and the Coordinate Plane, Lesson 1, Anchor Tasks, Problem 2 uses Inch Grid Paper to introduce and “construct a coordinate plane and identify the coordinates of given points.”