8th Grade - Gateway 1

The instructional materials reviewed for Match Fishtank Grade 8 meet the expectations for assessing grade-level content and, if applicable, content from earlier grades. The materials do not assess topics before the grade level in which the topic should be introduced. Unit Assessments were examined for this indicator, and all materials are available digitally and downloadable PDFs. 

Examples of assessment items aligned to grade-level standards include:

• Unit 1 Test, Question 7, “Which expressions are equivalent to $$3^{-8}$$ / $$3^{-4}$$? Select two correct answers. Answer choices: a. $$3^2$$, b. 1/$$3^2$$, c. 1/$$3^4$$, d. 1/$$3^12$$, e. $$3^{-2}$$" (8.EE.1)
• Unit 4 Test, Question 7,  “Which functions are not linear? Select three such functions. Answer choices: a. $$y=\frac {x}{5}$$, b. $$y=5-x^2$$, c. $$-3x +2y = 4$$, d. $$y = 3x^2+ 1$$, e. $$y = -5x - 2$$, f. $$y = x^3$$" (8.F.3) 
• Unit 4 Test, Question 5, “Which set of ordered pairs represents a function?  Answer choices: a. {(2,7), (2,8), (3,8)} b. {(3,2), (3,3), (3,4)} c. {(4,1), (5,1), (4,4)} d. {(5,6), (8,6), (9,6)}” (8.F.1)
• Unit 5 Test, Question 3, “Line M passes through point A(1,7) and point B(-2,4). Determine if Line M also passes through point C(5,3). Use slope to justify your answer.” (8.F.4) 
• Unit 7 Test, Question 3, “What is the value of the expression below?  8-3$$\sqrt16$$  Answer choices:  a. −40, b. −4, c. 2, d. 20”  (8.EE.2)

The instructional materials reviewed for Match Fishtank Grade 8  meet expectations for spending a majority of instructional time on major work of the grade, using the materials as designed. 

The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is seven out of eight units, which is approximately 88%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 99 out of 112, which is approximately 88%.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 123 out of 143, which is approximately 86%. 

A lesson level analysis is most representative of the instructional materials because the units contain major work, supporting work, and assessments. As a result, approximately 88% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Match Fishtank Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are connected to the major standards/clusters of the grade, for example:

• Unit 1, Exponents and Scientific Notation, Lesson 15, Anchor Problem 2, 8.NS supports 8.EE.1, 3, and 4 as students solve multi-step applications using scientific notation and properties of exponents. “This headline appeared in a newspaper. ‘Every day 7% of Americans eat at Giantburger Restaurants.’ Decide whether this headline is true using the following information: There are about $$8 \times 10^3$$ Giantburger restaurants in America. Each restaurant serves on average $$2.5 \times 10^3$$ people every day.  There are about $$3 \times 10^8$$ Americans. Explain your reasons and show clearly how you figured it out.” 
• Unit 7, Pythagorean Theorem and Volume, Lesson 13, Anchor Problems 2 and 3 connect 8.NS.2 and 8.EE.2 as students define and evaluate cube roots. For example, Anchor Problem 2 is as follows: “Determine if there is a solution to each equation below.  If yes, then give the exact solution. If no, explain why there is no solution. a. $$x^3 = -27$$  b. $$x^2 = -9$$. Evaluate the square and cube roots below, if possible. If not possible, explain why not. a. $$-\sqrt64$$  b. $$\sqrt-64$$  c. $$-\sqrt[3]64$$  d.$$\sqrt[3]-64$$.”  Anchor Problem 3: “Compare each pair of values with <, >, or = . a. $$\sqrt200$$   $$\sqrt[3]200$$   b. $$\sqrt64$$     $$\sqrt[3]125$$    c. $$\sqrt16$$     $$\sqrt[3]64$$   d. $$\sqrt8$$     $$\sqrt[3]50$$”
• Unit 8, Bivariate Data, Lesson 3, Anchor Problem 1 connects 8.SP.1 and 8.F.3, 4, and 5 as students “identify and describe associations in scatter plots including linear/nonlinear associations, positive/negative associations, clusters, and outliers.” An example is as follows: “For the following five scatter plots, answer the following questions:  a. Does there appear to be a relationship between x and y?  b. If there is a relationship, does it appear to be linear?  c. If the relationship appears to be linear, is it a positive or negative linear relationship?  d. If applicable, circle the correct words in this sentence: There is a (positive/negative) association between x and y, because as x increases, then  y  tends to (increase/decrease).” 
• Unit 8, Bivariate Data, Lesson 5, 8.SP.3 supports 8.F.4  as students “write equations to represent lines fit to data and make predictions based on the line. For example, Anchor Problem 2 states, “Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend’s house with a full battery. The pictures below show screenshots of the battery charge indicator after he plugs in the computer at 9:11a.m.” Questions: “1. The screenshots suggest an association between two variables.  What are the two variables in this situation? 2. Make a scatterplot of the data.  3. Draw a line that fits the data and find the equation of the line.  4. When can Jerry expect to have a fully charged battery?”

Instructional materials for Match Fishtank Grade 8 meet expectations that the amount of content designated for one grade-level is viable for one year. 

The instructional materials can be completed in 143 days.  The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. Included in the 143 days are: 

• 112 lesson days
• 23 review/flex days
• 8 assessment days 

Each unit is comprised of 9 to 21 lessons that contain  a mixture of Anchor Problems, Problem Set Guidance, a Target Task, and a Mastery Response. These components align to the number of minutes needed to complete each part as provided in the Pacing Guide. Based on the Pacing Guide, the suggested lesson time frame is 60 minutes. The breakdown is as follows:

• 5 - 10 mins Warm up 
• 25 - 30 mins Anchor Problems  
• 15 - 20 mins Problem Set 
• 5-10 minutes Target Task 

The instructional materials for Match Fishtank Grade 8 meet expectations for the materials being consistent with the progressions in the standards. The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. 

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from prior or future grades is clearly identified and related to grade-level work. Prior grade knowledge is explicitly related to grade-level concepts. Each lesson provides the teacher with current standards and foundational standards which are addressed under the “Standards” tab. Through the Unit Overview, Tips for Teachers, and Unit Summary, teachers are provided explicit connections to prior and future knowledge for each standard.

The Unit Plan Summary section includes a list of foundational standards from earlier grades that are connected to the content standards addressed in that unit, as well as a list of future standards that relate. For example:

• Unit 1, Exponents and Scientific Notation, “In fourth and fifth grade, students learned the difference between multiplicative and additive comparisons and they interpreted multiplication as a way to scale. Students will access these prior concepts in this unit as they investigate patterns and structures in ratio tables and use multiplication to create equivalent ratios.”  Foundational Standards include: Numbers and Operations in Base Ten 5.NBT.1, 5.NBT.2, 4.NBT.1, Expressions and Equations 6.EE.1, 6.EE.2, 6.EE.2.c, The Number System 7.NS.2. Future Connections include: High School – Number and Quantity N.RN.1, N.RN.2, Seeing Structure in Expressions A.SSE.2, A.SSE.3.c, Arithmetic with Polynomials and Rational Expressions A.APR.6, A.APR.7. Students will use their knowledge from previous eighth-grade units, including work with single linear equations and functions from clusters 8.EE.B and 8.F.B.4. Students will continue their work with systems, working with linear, absolute value, quadratic, and exponential functions. They will also graph linear inequalities and consider what the solution of a system of linear inequalities looks like in the coordinate plane.”
• Unit 2, Solving One-Variable Equations reviews content from grades 6 and 7 in preparation for the remaining lessons in the unit. “In sixth grade, students developed the conceptual understanding of how the components of expressions and equations work. They learned how the distributive property can create equivalent forms of an expression and how combining like terms can turn an expression with three terms into an expression with one term. By the end of seventh grade, students fluently solved one- and two-step equations with rational numbers and used equations and inequalities to represent and solve word problems.” Additionally, the Unit Summary connects grade-level concepts to current and future standards. “Furthermore, these skills will be needed throughout high school as students are introduced to new types of equations involving radicals, exponents, multiple variables, and more.”
• Unit 4, Functions, “This unit introduces students to the concept of a function to describe a relationship. Though they have worked with functions prior to eighth grade with equations and proportional relationships, this is the first time they will formally define it. Through this unit and the next unit, students will explore functions in-depth; this lesson provides the basic definition of a function as a relationship of inputs and outputs where every input has exactly one output.”
• Unit 6, System of Equations Unit Summary, “Students will use their knowledge from previous eighth-grade units, including work with single linear equations and functions from clusters 8.EE.B and 8.F.B. They will also need to draw on concepts from sixth grade, where they understood solving an equation as a process of answering which values make an equation true.”
• Unit 7, Pythagorean Theorem and Volume, “Prior to this unit, students learned many skills and concepts that prepared them for this unit. Since elementary grades, students have been learning about and refining their understanding of area and volume. They have learned how to use composition and decomposition as tools to determine measurements, they have learned formulas and how to use them in problem-solving situations, and they have encountered various real-world situations. Standard 8.G.9 is a culminating standard in the Geometry progression in middle school, which will lay the foundation for much of the work they will do in high school geometry. In high school, students will more formally derive the distance formula and other principles, they will expand their work with right triangles to include trigonometric ratios, and they will solve more complex problems involving volume of cylinders, pyramids, cones, and spheres.”
• Unit 8, Bivariate Data Unit Summary, “Prior to eighth grade, students explored how and why data is collected—by thinking about statistical questions, samples, populations, and various ways to analyze data representations. Students worked with line plots, histograms, and box plots, and they considered what the shape, center, and spread of these data sets said about the data itself. In high school, students’ understanding of statistics is formalized. They analyze bivariate data using functions, design and carry out experiments, and make predictions about outcomes based on probabilities. Students use their knowledge of association between variables as a basis for correlation. They develop nonlinear models for data and formally analyze how closely the model fits the data. This unit addresses the content standards: 8.SP.1, 8.SP.2, 8.SP.3, and 8.SP.4 and identifies the foundational standards “Covered in previous units or grades that are important background for the unit”: 6.RP.3.c, 7.RP.3, 7.SP.1, 7.SP.2, 7.SP.5, 6.SP.2, and 6.SP.4 from previous grades, and 8.F.3, 8.F.4, and 8.F.5 from a previous unit.”

Lessons also include connections between grade-level work, standards from earlier grades, and future knowledge. For example:

• Unit 2, Solving One Variable Equations, Lesson 3, the Objective states, “Justify each step in solving a multi-step equation with variables on one side of the equation” (8.EE.7.a, 8.EE.7.b ). Tips for Teachers suggest this lesson may be extended over more than one day to ensure enough time for both analysis of work and procedural practice. Students will recall and apply the following Grade 7 standards that were listed on the lesson plan. (7.EE.1, 7.EE.4)
• Unit 4, Functions,  Lesson 1, the Objective states, “Define and identify functions.” (8.F.1). Tips for Teachers state "this lesson introduces students to the concept of a function to describe a relationship. Though they have worked with functions prior to eighth grade with equations and proportional relationships, this is the first time they will formally define it. Through this unit and the next unit, students will explore functions in-depth; this lesson provides the basic definition of a function as a relationship of inputs and outputs where every input has exactly one output."
• Unit 7, Pythagorean Theorem and Volume, Lesson 13 identifies Current Standards: 8.NS.2, the Number System and 8.EE.2, Expressions and Equations. Foundational Standards include: 7.NS.3, the Number System and 6.EE.5, Expressions and Equations. Tips for Teachers states, "This lesson is a parallel lesson to Lesson 1, where students investigated and learned about square roots. This lesson is placed at this point in the unit so it immediately precedes students' study of volume."

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. Anchor Problems help students make sense of the mathematics of the lesson as outlined in the Criteria for Success and Objective by providing them multiple opportunities to engage in the grade-level content in meaningful ways. The Problem Set Guidance provides students the opportunity to work with problems in a variety of formats to integrate and extend concepts and skills. Target Tasks are aligned to the Objective and designed to cover key concepts and misconceptions students might have. Target Tasks can be used as an indicator of student understanding or mastery of the Objective. For example:

• Unit 3, Transformations and Angle Relationships, Lesson 5, in the Anchor Problem, students are given two figures shown in a coordinate plane. For example, the Anchor Problem reads, “Figure 1 is reflected over the y-axis to create Figure 2, as shown in the coordinate plane below. Describe what you notice about the coordinate points of a figure when it is reflected over the y-axis. What do you think happens to coordinate points of a figure when it is reflected over the x-axis?” (8.G.3)
• Unit 3, Transformations and Angle Relationships, Lesson 20, the Objective states, “Define and use the interior angle sum theorem for triangles 8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.” Tips for Teachers has a reminder that students have experience working with triangles and angle measurements from Grade 7 when they investigated unique triangles (7.G.2) and that students may know that the angles in a triangle add up to 180°. In this lesson they have the chance to prove this fact using parallel line angle relationships using facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.5) 
• Unit 7, Pythagorean Theorem and Volume, Lesson 2,  in Target Task Problem 1, students are given a choice of rational and irrational solutions and they must identify which are irrational.  “Which of the following are irrational numbers? Select all that apply. Answer choices: a. $$\sqrt200$$, b.  $$0.005\overline{7}$$, c. $$0.0057$$…, d. $$\frac{1}{191}$$, e. $$\frac{\sqrt121}{5}$$, f. $$\frac{121}{\sqrt5}$$” (8.NS.1)

The instructional materials for Match Fishtank Grade 8 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings and problems and activities that connect two or more clusters in a domain or two or more domains, when these connections are natural and important.

 The Units are divided into Lessons focused on domains. Grade 8 standards are clearly identified in the Pacing Guide, Standard Map Document and a CCSSM Lesson Map found in the Unit Summary of each Unit. Additionally, each lesson identifies the objectives that address specific clusters. Instructional materials shaped by cluster headings include the following examples:

• Unit 1, Exponents and Scientific Notation, Lesson 6, Objective, “Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.” (8.EE.A) 
• Unit 3, Transformations and Angle Relationships, Lesson 6, Objective, “Describe and perform rotations between congruent figures” (8.G.A)
• Unit 3, Transformations and Angle Relationships, Lesson 9, Objective, “Describe multiple rigid transformations using coordinate points.” (8.G.A)
• Unit 5, Linear Relationships, Lesson 11, Objective, “Write linear equations using slope and a given point on the line.” (8.EE.B)
• Unit 6, Systems of Equations, Lesson 1, Objective, “Define a system of linear equations and its solution.” (8.EE.C)
• Unit 7, Pythagorean Theorem and Volume, Objective, “Find missing side lengths involving right triangles and apply to area and perimeter problems.” (8.G.B) 

Instructional materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important. For example:

• Unit 4, Functions, Lesson 6, 8.F.B and 8.F.A are connected when students use functions to model relationships between quantities and define, evaluate, and compare functions using multiple representations. Anchor Problem 2 reads, “In a laboratory, a scientist is tracking the temperature of a substance over time. Each hour, she takes the temperature and records it in the graph below.” Questions: a. “What is the rate of change of the substance’s temperature, in ºF per hour, between 12 PM and 3 PM?  b. What is the rate of change of the substance’s temperature in ºF per hour between 7pm and 9pm? c. What is the starting temperature of the substance? d. Does it appear that the temperature of the substance is a function of the time of day? Why or why not?”
• Unit 5, Linear Relationships, Lesson 7 connects 8.EE.B and 8.F.B as students determine slope from coordinate points. Target Task states, “Samantha found the slope of the line that passed through the points (2,6) and (-4,-8). Her work is shown below. $$\frac{8-6}{2-(-4)}= \frac{2}{2+4}= \frac{2}{6} = \frac{1}{3}$$. Samantha made an error in her work. Describe the error and then find the correct slope of the line through the two given points.”
• Unit 5, Linear Relationships, Lesson 7, connects 8.EE.6 and 8.F.4 through slope and constructing linear relationship. Anchor Problem 2 states, “Find the slope of the line in each group below.”
• Unit 6, Systems of Equations, Lesson 7, 8.F.B and 8.EE.C are connected as students use functions to model relationships between quantities and analyze and solve linear equations and pairs of simultaneous linear equations. Target Task states, “Maya buys greeting cards to give to her friends at school. She buys some greeting cards that cost $2.50 each and some greeting cards that cost $4 each. She buys 13 cards in all for a total of $40.50.  How many greeting cards that cost $2.50 did Maya buy?”
• Unit 7, Pythagorean Theorem and Volume, Lesson 13, 8.G.3 supports 8.EE.2, as students use the formula for volume of cubes to solve equations in the form: “x^2= p and x^3= p”.  For example, Anchor Problem 1 states, “Two cubes are shown below with their volume in cubic units.” Questions: “ a.  What is the side length of each cube?  b. Describe the relationship between the side length of a cube and its volume.”