8th Grade - Gateway 3

The materials reviewed for Fishtank Plus Math Grade 8 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 6, Systems of Linear Equations, Unit Summary provides an overview of content and expectations for the unit. Within Unit Prep, View Unit Launch, there is a video detailing the content for teachers. The materials state, “Welcome to the Unit Launch for 8th Grade Math, Unit 6 Systems of Linear Equations. Please watch the video below to get started.” Additionally, the Unit Summary contains Intellectual Prep and Unit Launch with Standards Review, Big ideas, and Content connections. The Standards Review provides teachers an “opportunity to reflect on select standards from the unit. [...] In this section you will examine the language of these standards and reflect on how several problems on the end-of-unit assessment relate to the standard.”  Then, Big Ideas help teachers “understand how these ideas develop throughout the unit by analyzing lessons and problems from the unit, and finally, have the chance to reflect on how you will address your students’ needs around these concepts.” Finally, Content Connections states, “In this final section of the unit launch, you’ll have the chance to zoom out and look at the related content that students study before and after this unit.” This information is included for units 1-5 in Grade 8.

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, Exponents and Scientific Notation, Lesson 6, Tips of Teachers provide guidance so teachers are prepared to support students in discovering a general rule for operations with exponents. The materials state, “Similar to Lesson 5, these Anchor Problems can be used in a variety of ways, including having students lead the discovery and seek out a general rule. Once students have experimented with the problems and found a generalization, then provide them with the name of the rule and the general form.”

• In Unit 5, Linear Relationships, Lesson 5, Anchor Problem 1 Notes provide guidance to connect students' prior knowledge to new concepts. The materials state, “Use this Anchor Problem to graph a linear graph outside of the first quadrant, as compared to the proportional graphs students saw in the beginning of this unit. This example is similar to problems that students saw in Lessons 1–4 in that the graph passes through the origin and is linear; however, the rate of the change is negative, which places the graph in the 4th quadrant in the coordinate plane.”

• In Unit 8, Bivariate Data, Lesson 2, Tips for Teachers include guidance for teachers to address common misconceptions as students create scatter plots for given data. The materials state, “A common misconception is to confuse causality with association. For example, students may misunderstand a relationship between two variables to imply that one variable causes another to change, when there is only evidence to show an association between the two variables. As students describe relationships between variables, ensure they use language to imply an association rather than a casual relationship.”

The materials reviewed for Fishtank Plus Math Grade 8 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 8th 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 8th Grade Math, Unit 7, Pythagorean Theorem and Volume, Lesson Map outlines lessons, aligned standards, and the lesson objective for each unit lesson. This is present for all units and allows teachers to identify targeted standards for any lesson.

• In Unit 4, Functions, Lesson 3, the Core Standards are identified as 8.F.A.1, 8.F.A.2, 8.F.B.4. The Foundational Standards are identified as 6.EE.A.2.C, 6.RP.A.2, 7.RP.A.2.B. Lessons contain a consistent structure that includes an Objective, Common Core Standards, Criteria for Success, Tips for Teachers, Anchor Problems, Problem Set, and Target Task. 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, Exponents and Scientific Notation, Unit Summary includes an overview of how the content in 8th grade connects to mathematics students will learn in high school. The materials state, “In high school, students will need a strong understanding of exponents and exponent properties. They will apply the properties of exponents to exponential equations in order to reveal new understandings of the relationship. They will work with fractional exponents and discover the properties of rational exponents and rational numbers. In general, students’ ability to see the structure in an expression will support them in manipulating quadratic functions, operating with polynomials, and making connections between various relationships.”

• In Unit 3, Transformations and Angle Relationships, Unit Summary includes an overview of how the math of this unit builds from previous work in math. The materials state, “Prior to eighth grade, students developed their understanding of geometric figures and learned how to draw them, calculate measurements, and model real-world situations. In seventh grade, students were introduced to the concept of scaling through scale drawings, and they solved for various measurements using proportional reasoning. Students will draw on these prior skills when they investigate dilations and similar triangles.”

• In Unit 6, Systems of Linear Equations, Unit Summary includes an overview of the Math Practices that are most strongly connected to the content in the unit. The materials state, “Using the structure of the equations in a system, students will determine if systems have one, no, or infinite solutions without solving the system (MP.7). Students also explore the many rich applications that can be modeled with systems of linear equations in two variables (MP.4).”

The materials reviewed for Fishtank Plus Math Grade 8 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. 8th Grade, 8.EE.7, 8.G.9.”

• 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 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The 8th Grade Course Summary, Course Material Overview, Course Material List 8th Grade Mathematics states, “The list below includes the materials used in the 8th 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:

• Scientific calculators are used in Units 1, 2, 3 7, and 8, one per student. 

• Graph paper is used in Units 3, 5, 7, and 8, one ream. 

• Patty paper is used in Units 3 and 5, one box of 1000 sheets. 

• Protractors are used in Unit 3, one per student. In Unit 3, Transformations and Angle Relationships, Lesson 11, students define a dilation as a non-rigid transformation, and understand the impact of scale factor (8.G.A.4 ). Anchor Problem 2 states, “Triangle ABC is dilated to create similar triangle DEF. a.) Indicate the corresponding angles in the diagram. What is the relationship between corresponding angles? b.) Name the corresponding sides in the diagram. What is the relationship between corresponding side lengths?” Notes state, “To prove that the corresponding angle measures are congruent, students may use patty paper to copy and transfer one triangle over the other, or they may use protractors to measure (MP.5).”

• Wikisticks (or raw spaghetti) are used in Unit 8, one per student. In Unit 8, Bivariate Data, Lesson 4, Tips for Teachers states, “Manipulatives that represent a line that can be maneuvered on paper are a valuable tool for this lesson; for example, wikisticks, raw spaghetti, thin pencils, etc.”

The materials reviewed for Fishtank Plus Math Grade 8 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 2, Solving One-Variable Equations, Expanded Assessment Package, Post-Unit Assessment Analysis denotes content standards addressed for each problem. Problem 1 is aligned to 8.EE.7b and states, “What is the solution to the equation below? \frac{2}{3}x+5=1 a. x= -6 b. x=4  c. x= -4.5  d.$$x=9$$.”

• In Unit 4, Functions, Unit Summary, Unit Assessment, Answer Key denotes standards addressed for each question. Question 5 is aligned to 8.F.1 and states, “Which sets of ordered pairs represent a function? Select two correct answers. a. {(1, 0), (2,1), (2, 3)} b. {(1, 3), (1, 4), (1, 5)} c. {(1, 5), (2, 5), (3, 5)} d. {(3, 1), (2, 2), (3, 3)} e. {(3, 2), (5, 1), (4, 0)}.”

• In Unit 5, Linear Relationships, Unit Summary, Post-Unit Assessment, Answer Key denotes Standards for Mathematical Practice addressed for each question. Question 1 is aligned to MP1 and states, “At a local market, the cost of apples is directly proportional to the weight of the apples. Carlos bought 10 pounds of apples for a cost of $15.00. Which graph shows the relationship between the weight of the apples, in pounds, and the cost of the apples, in dollars?” 

• In Unit 7, Pythagorean Theorem and Volume, Unit Summary, Mid-Unit Assessment, Answer Key denotes Standards for Mathematical Practice addressed for each question. Question 2 is aligned to MP3 and states, “Dr. Professor built a math robot to help her with her research. The first thing Dr. Professor asks her robot to do is to find the exact decimal value of \sqrt{5}. Can the robot do it? Explain why or why not.”

• In Unit 8, Bivariate Data, Unit Assessment Answer Key includes a constructive response and 2-point rubric with the aligned grade-level standard. Questions 3a & 3b are aligned to 8.SP.1 and state, “In a city, there are several office spaces of different sizes that businesses can rent on a yearly basis. The scatter plot below shows the sizes of some office spaces and their yearly rent in this city. Part A: Does there appear to be a relationship between the size of an office space and the rent? If so, then describe if the relationship is linear or non-linear, positive or negative. If not, then explain why there is no relationship. Part B: Are there any clusters or outliers in the scatter plot? If so, explain what they mean in context of the situation.”

The materials reviewed for Fishtank Plus Math Grade 8 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 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.” Each Mid-Unit Assessment provides an answer key and a 1-, 2-, 3-, or 4-point rubric. Each Pre-Unit Assessment provides an answer key and guide with a potential course of action to support teacher response to data. 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.” Examples from the assessment system include:

• In Unit 1, Exponents and Scientific Notation, Post-Unit Assessment Analysis, Problem 5 states, “The population of California is approximately 4×10^7 people. The population of South Dakota is approximately 800,000 people. The population of California is about how many times the population of South Dakota? a. 20 b. 50 c. 200 d. 500. Commentary: In this problem, students are given two large numbers, one of which is written in scientific notation, and are asked to compare the values. In order to compare the values, students will need to change one of the numbers into a form that matches the other. Some students may do this efficiently by writing 800,000 in scientific notation, and then using properties of exponents when dividing the two numbers.”

• In Unit 2, Solving One-Variable Equations, Lesson 5, Target Task, students model multi-step equations. The materials state, “Sequel: You want to put up 25 pictures using the same spacing; however, these pictures have been rotated 90 degrees to be in a portrait orientation. How long of a wall, in feet, do you need? How long of a wall would you need for n pictures in portrait orientation using the same spacing?” The Mastery Response states, “2(4.5) + 25(8.5) + 24(5) = ? 9 + 212.5 + 120 = 341.5 inches or 28 ft 5\frac{1}{2} in. For n pictures, 9 + 8.5n + 5(n - 1) inches.” 

• In Unit 5, Linear Relationships, Pre-Unit Assessment, Teacher Answer Key & Guide, Problem 1 states, “A photocopier can print 40 pages in 16 seconds. Which equation represents the relationship between 𝑝, the number of pages printed, and 𝑠, the amount of time in seconds? a. 𝑝=\frac{1}{16}s, b. 𝑝=\frac{2}{5}s, c. 𝑝=2\frac{1}{2}s, d. 𝑝 = 24𝑠 Potential Course of Action, If needed, this concept should be addressed early on in the unit, as students study and compare proportional relationships in Lessons 1 – 4, and again later in the unit when students focus on writing linear equations starting in Lesson 10. For example, include a multiple choice problem similar to the one above as a warm-up for Lesson 1 or Lesson 2; or include a problem without multiple choice options as a warm-up for Lesson 10 or Lesson 15. Find problems and other resources in these Fishtank lessons: Grade 7 Unit 1 Lessons 4 – 5. Grade 8 Unit 4 Lesson 4.”

• In Unit 6, System of Linear Equations, Mid-Unit Assessment, Answer Key, Problem 7 states, “Solve the system of equations algebraically. Use the substitution method. Show all your work. 4𝑥 + 2𝑦 = 9; −3𝑥 + 𝑦 = 4.” The Answer Key provides the correct answers and a 3-point rubric for teachers to follow. It states, “3 points. Student response demonstrates an exemplary understanding of the concepts in the task. The student points 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 points may be incorrect, unrelated, illogical, or a correct solution obtained by chance.”

The materials reviewed for Fishtank Plus Math Grade 8 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, Solving One-Variable Equations, Post-Unit Assessment problems support the full intent of MP5 (Choose tools strategically) as students select strategies for reasoning about linear relationships. Problem 11 states, “The perimeter of a given rectangle is 40 inches. The length of the rectangle is two inches more than three times the width. What are the dimensions of the rectangle?” Problem 15 states, “Denzel has saved $75 in his bank account and saves an additional $12.50 every week. Halle has saved $339 in her bank account, but spends $20.50 each week. After how many weeks will Denzel and Halle have the same amount of money in their bank accounts?” 

• In Unit 4, Functions, Mid-Unit Assessment Problems 4 and 5 and Post-Unit Assessment Problem 12 develop the full intent of 8.F.4 (Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table, or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values). Mid-Unit Problem 4 states, “A health club charges an up-front, joining fee to its members as well as a monthly fee. The table below shows the total cost of being a member at this health club for different numbers of months. Part A: What is the monthly fee for this health club? a. $40, b. $70, c. $80, d. $110. Part B: What is the annual fee for this health club? a. $30, b. $40, c. $70, d. $110.” Mid-Unit Problem 5 states, “Mr. Johnson is an art teacher and is buying tee-shirts online for an art project at school. The graph below shows the total cost of his order as a function of the number of tee-shirts he buys. a. Mr. Johnson’s online order includes a shipping cost. What is the shipping cost? b. What is the rate of change? What does it mean in context of the situation? c. Write an equation to represent the total cost of Mr. Johnson’s order, y, for x tee-shirts.” Post-Unit Problem 12 Part b states, “Write an equation to represent Function F.” A table is provided with x values as 0, 4, 6, 10 and y values as 6, 18, 24, 36.

• In Unit 5, Linear Relationships, Mid-Unit Assessment Problem 2 and Post-Unit Assessment Problem 6 develop the full intent of 8.EE.5 (Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways). Mid-Unit Problem 2 states, “Dawn is filling three buckets using three different faucets at her house. The water flows from each faucet at a different constant rate, as shown in each representation below. Assuming each bucket is the same size and they all start out empty, which bucket will be filled first? Justify your response with specific rates of change.” Post-Unit Problem 6 states, “Grace and Jackie are both accountants. They each charge their customers an hourly fee for their service, as described below. Grace charges $540 for 18 hours of service. Jackie charges $40 per hour. a. Draw two graphs in the grid below to show the relationship between cost, 𝑦, and hours of service 𝑥, for Grace and for Jackie. Label each line with the accountant’s name. b. Who charges more per hour? Explain your answer using your graph.” 

• In Unit 8, Bivariate Data, Post-Unit Assessment problems support the full intent of MP1 (Make sense of problems and persevere in solving them) as students make sense of bivariate data in real world contexts. Problem 5 states, “The scatter plot below shows the numbers of customers in a restaurant for four hours of the dinner service on two different Saturday nights. The line shown models this relationship, and  𝑥 = 0 represents 7 p.m. What does the value of the 𝑦-intercept represent? a. The average number of customers at 7 p.m. b. The average number of customers at 11 p.m. c. The average change in the number of customers each hour. d. The average change in the number of customers during four hours of the dinner service. Problem 7 states, “Colton is heating a pot of water. He records the temperature of the water in the pot every minute. This equation models Colton’s data, where 𝑥 represents the number of minutes the water has been heated, and 𝑦 represents the temperature of the water in degrees Fahrenheit. 𝑦 = 7.5𝑥 + 40. Part A. What does the coefficient 7.5 in the equation represent in the context of this situation? Part B. What does the value 40 in the equation represent in the context of this situation? Part C. What is the temperature, in degrees Fahrenheit, of Colton’s pot of water after 16 minutes? Show or explain how you got your answer.”

The materials reviewed for Fishtank Plus Math Grade 8 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

There are opportunities for students to investigate grade-level mathematics at a higher level of complexity. Often, “Challenge” is written within a Problem Set or Anchor Problem Guiding Questions/ Notes to identify these extensions. According to Math Teacher Tools, Preparing to Teach Fishtank Math, Components of a Math Lesson, “Each Anchor Task/Anchor Problem is followed by a set of Guiding Questions. The Guiding Questions can serve different purposes, including: scaffolding the problem, more deeply engaging students in the content of the problem, and extending on the problem. Not all Anchor Tasks/Problems include Guiding Questions that cover all three purposes. Also, not all Guiding 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.” As such, teachers determine how, when, or which students might engage with higher levels of complexity. Examples include:

• In Unit 2, Solving One-Variable Equations, Lesson 11 and 12, Tips for Teachers state, “Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.” Standard A.REI.3 is covered in both lessons.

• In Unit 3, Transformations and Angle Relationships, Lesson 12, Anchor Problem 2 Guiding Questions state, “Challenge: Is it possible for rectangle ABCD to be dilated such that its image, A′B′C′D′ was in the third quadrant? If so, describe the dilation. If not, explain why not.”

• In Unit 7, Pythagorean Theorem and Volume, Lesson 7, Problem Set states, “MARS Summative Assessment Tasks for High School Proofs of the Pythagorean Theorem? — This can be used as a challenge as it is slightly beyond the 8th grade standard. This problem can be adapted to have students explain how each proof demonstrates the Pythagorean Theorem and any limitations each proof may or may not have.”

The materials reviewed for Fishtank Plus Math Grade 8 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 3, Transformations and Angle Relationships, Lesson 1, Anchor Problem 2, students use shapes to investigate congruent/non-congruent shapes. The materials state, “Students should have access to different tools for their investigations, including rulers, scissors, tape, tracing or patty paper, etc. It may be helpful to give students the shapes on a separate sheet of paper.”

• In Unit 4, Functions, Lesson 1, Anchor Problem 1 uses survey questions and letter cards to introduce the “concept of a function by juxtaposing the clarity of a function next to the confusion of a non-function.”

• In Unit 7, Pythagorean Theorem and Volume, Lesson 5, Problem Set Guidance: MARS Formative Assessment Lesson for Grade 8 Translating between Repeating Decimals and Fractions. This includes a card matching activity to build procedural fluency in converting between decimals and fractions. The materials state, “Each small group of students will need Card Sets A: Decimals, B: Equations, C: Fractions, a large sheet of paper for making a poster, and a glue stick.”