The materials reviewed for STEMscopes Math Grade 8 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The curriculum is divided into 19 Scopes, and each Scope contains a Standards-Based Assessment used to assess what students have learned throughout the Scope. Examples from Standards-Based Assessments include:

• Scope 4: Irrational Numbers, Evaluate, Standards-Based Assessment, Question 5, “The diagonal length of a right triangle for a piece of fabric is $\sqrt{72}$ inches. Part A What are the perfect squares that 72 is between? The perfect squares are ____ and ____. Part B Where is $\sqrt{72}$ located on a number line? Plot the point on the number line below.” Students see a number line that extends from 7 to 10 with tick marks at every tenth of each number. (8.NS.2)

• Scope 7: Solving Linear Equations, Evaluate, Standards-Based Assessment, Question 3, “Eric says the correct solution to the $\frac{8}{3}$. Explain the error in his reasoning. Find the correct solution. Enter your answers below.” (8.EE.7b)

• Scope 12: Rate of Change, Evaluate, Standards-Based Assessment, Question 2, “The equation $h=100-4t$ represents the height, h, from the location on a sledding hill after t seconds. What is the meaning of the rate of change and the initial value? Enter your answers below.” (8.F.4)

• Scope 14: Transformations, Evaluate, Standards-Based Assessment, Question 2, “Figure ABCDE is dilated to create figure A’B’C’D’E’ on the coordinate plane below. What is the scale factor for the dilation?” Two figures are shown on a coordinate plane. (8.G.3) 

• Scope 19: Patterns in Bivariate Data, Evaluate, Standards-Based Assessment, Question 5, “The line of fit for a scatterplot is $y=-1.1x+14$. Predict the value of y when $x=30$. -14.5; -42.9; 13.27; -19.” (8.SP.3)

The materials reviewed for STEMscopes Math Grade 8 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Grade 8 as students engage with all CCSSM standards within a consistent daily lesson structure, including Engage, Explore, Explain, Elaborate, and Evaluate. Intervention and Acceleration sections are also included in every lesson. Examples of extensive work to meet the full intent of standards include:

• Scope 2: Integer Expressions, Explore, Explore 4 - Exponential Powers, Procedure and Facilitation Points and Exit Ticket, engage students with the full intent of 8.EE.1 (Know and apply the properties of integer exponents to generate equivalent numerical expressions…) In the previous three Explores, students worked on multiplying and dividing with exponential powers. Explore 4 focuses on putting everything together. In Procedure and Facilitation Points, students work in small groups to use the properties of exponents to make equivalent and simplified equations. “1. Read the following scenario to the students: It’s the day before the test, and Ms. Taylor has provided one final review activity for you. She has given you six expressions that include an exponential term raised to a power. Not only do you have to create an equivalent expression, but you also need to explain the steps that you take to make that expression. Show Ms. Taylor that you’re ready for the test by completing her test review. 2. Give a Student Journal to each student. 3. Explain to students that they will collaborate with their groups to use the properties of exponents to determine equivalent expressions they can use for each of the given expressions in the table. 4. As students collaborate, monitor their work and use the following guiding questions to assess student understanding: a. DOK–1 What do the properties of integer exponents teach us about when an exponential term is raised to a power? b. DOK–1 What happens to the exponents when you multiply numbers with like bases? c. DOK–1 What happens to the exponents when you multiply numbers with unlike bases but common exponents? d. DOK–1 What happens when the bases are the same when dividing exponents? e. DOK–1 What happens when the exponents are the same when dividing exponents? 5. After the Explore, invite the class to a Math Chat to share their observations and learning.” On the Exit Ticket, students are given a complex equation to apply what they have learned. Students see the expression and work space to simplify and make an equivalent expression. “The test is finally here! You feel like you’ve done really well, but Ms. Taylor threw in a bonus question that encompasses everything you’ve learned so far. Find an equivalent expression for the expression below. Ms. Taylor’s Expression, $(8^{5+3}\div(4\times2)^5)^3$, Workspace, Equivalent Expression”

• Scope 4: Irrational Numbers, Explore, Explore 1 - Irrational Numbers vs. Rational Numbers, Procedure and Facilitation Points, engages students in extensive work to meet the full intent of 8.NS.1 (Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.) “Part I, 1. Read the scenario aloud: You are looking for an internship to improve your job skills. You’ve applied to a local builder, Team Builders, to plan and build youth sporting areas throughout the city. The hiring manager has called you in for an interview. She feels you have great potential, but you will need to prove that you can learn new math skills and apply your new knowledge before she can offer you the job. Help Team Builders sort their numbers by their classifications. 2. Discuss the following questions with the class: a. DOK–1 What types of numbers have we discovered so far? b. DOK–1 What is an example of a whole number? c. DOK–1 What is an example of an integer? d. DOK–1 What is an example of a rational number? 3. Display the Real Numbers Venn Diagram. 4. Discuss the following with the class: This is called a Venn diagram. Venn diagrams help to show information based on relationships. Ask the class the following questions: a. DOK–1 What does this Venn diagram illustrate? b. DOK–1 What set of numbers is within the integers set? c. DOK–1 What are the names of the type of numbers that include integers as subsets? … 8. Monitor and assess students as they work. Use the Real Numbers Classification Explanation Cards to provide hints and guidance as appropriate for each group. Ask students the following guiding questions: a. DOK–2 What are some key words on this classification card that were helpful? How did the key word help? b. DOK–2 What are some key numbers in the examples on this classification card that were helpful? How did the key numbers help? c. DOK–3 How can the Venn diagram help you?... Part II, 1. Read the scenario aloud: The hiring manager for Team Builders was impressed with your ability to sort each classification of real numbers! But can you apply this knowledge? Help determine if each number is rational or irrational. Then, show proof of your decision. 2. Explain to students that they will collaborate with their groups to determine if each of the numbers provided is a rational number or an irrational number. Then they will need to use the Venn diagram to help prove their decisions are correct. 3. Students will collaborate to apply their knowledge of real number classification to a variety of numbers provided. Students should use the Venn diagram completed in Part I to help prove their thinking is correct. Allow students to use a calculator to assist in determining if a number is a repeating decimal or not. 4. Monitor and assess students as they work. Ask guided questioning as needed: a. DOK–1 Why do you think 0.5 is rational? b. DOK–2 Can a decimal that does not repeat be written as a fraction?”

• Scope 5: Scientific Notation, Explain, Show What You Know-Part 3: Comparing Numbers in Scientific Notation, engages students in extensive work to meet the full intent of 8.EE.3 (Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other…) In previous Explores, students have multiplied, divided, and compared numbers with scientific notation. In Show What You Know, they apply their knowledge. Students see a table with the following information: City, Population, Duncanville, $2.4\times10^5$, Lumber City, $1.2\times10^7$, Parkerton, $4.8\times10^4$.  “A tech company is planning to build a new manufacturing complex in a new city. The executive board needs to decide where the new complex will be built. They have narrowed their decision down to three cities. The final decision will be based on the city’s population. The population of the three cities is shown in the table below. 1. Which city has the greatest population? What is that city’s population? 2. Which city has the smallest population? What is that city’s population? 3. How many times greater is the population of Duncanville than the population of Parkerton? 4. How many times greater is the population of Lumber City than the population of Duncanville?”

• Scope 18: Volume, Explore 1 and 2, and Show What You Know–Part 3, engages students in extensive work to meet the full intent of 8.G.9 (Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.) Explore 1-Cylinders, Procedure and Facilitation Points, students work in pairs to understand the formula for the volume of a cylinder. “Part I: Understanding the Volume of a Cylinder Formula, 1. Read the following scenario: One of your friends and classmates is named Madeline Dupont. Madeline’s family owns a food processing plant. One branch of the plant involves canning foods. Because a large number of employees are absent today, Madeline’s mom has asked if she has any friends that are good at math who could help with the canning process. Your job today is to show that you understand the volume of cylinders and can determine the volume of cans (cylinders) with a variety of bases, sizes, and heights. 2. Give a Cylinder Net, a dry-erase marker, a glue stick, and a pair of scissors to each partnership. 3. Review students’ prior knowledge of finding the volume of a rectangular prism by asking the following questions: a. DOK–1 How do you find the volume of a rectangular prism? b. DOK–1 When you use the formula $V=lwh$, what formula is being used when you multiply the length times the width? Explain why the formula is being used. c. DOK–2 What is the formula that is used to find the volume of a rectangular prism? $V=Bh$ where B = area of the base So V = B$$\times$$height, or length$$\times$$width$$\times$$height. d. DOK–2 What is the volume of this rectangular prism?...6. Instruct students to arrange the centimeter cubes in a single layer at the bottom of the cylinder and to fit as many cubes into the layer as possible. They will also need to find how many layers of cubes fit in the cylinder and will need to make a stack of cubes along the inside of the cylinder. Students will use page 2 of the Cylinder Net/Volume of a Cylinder Work Mat to calculate the area of the base and the volume of the cylinder. (Note that you should show the students how to use the base to determine the radius and how to determine the height of the cylinder using the formula.) Monitor and assess student understanding as each group collaborates by asking the following guiding questions: a. DOK–1 What shapes are in a cylinder? b. DOK–1 What is the shape of the bases on a rectangular prism and cylinder? c. DOK–2 How might finding the volume of a cylinder be similar to finding the volume of a rectangular prism? d. DOK–2 How might finding the volume of a cylinder be different from finding the volume of a rectangular prism? e. DOK–2 How many layers of cubes did it take to fill the cylinder? f. DOK–2 What is the area of the cylinder’s base? Express your answer in terms of $\pi$. $4\pi$, g. DOK–2 What is the volume of the cylinder? Express your answer in terms of $\pi$. $48\pi$, h. DOK–2 How can you determine the approximate number of cubes that will fit in the cylinder? Why is this an approximate number of cubes? i. DOK–2 How can you calculate the volume of the cylinder?... Explore 2-Cones, Exit Ticket, students use what they have learned to find a cone’s volume. Students see a cone with a radius of 15cm and a height of 25 cm. There is also work space to complete the work to find the volume. “The Duponts want to add a new cone to their menu. It’s called the Family Sundae Cone. Look at its dimensions in the model, use the workspace to represent the area of the base expressed in terms of $\pi$, and then find the volume. Use 3.14 as an approximation for $\pi$. Round to the nearest hundredth, if necessary.” Show What You Know-Part 3: Spheres, Student Handout, students apply what they have learned about the formula for finding the volume of a sphere. “Mr. Kennedy is a physical education teacher at the neighborhood elementary school. He keeps several different kinds of balls in a bin so the students can play sports during their gym time. Use the information provided to determine the volume of each ball. Use 3.14 as an approximation for $\pi$. Round your answer to the nearest hundredth. There are several baseballs in Mr. Kennedy’s bin. Each baseball has a radius of 3.7 cm. What is the volume of each baseball? Volume: ___, The girls really enjoy playing volleyball during gym class. A volleyball has a diameter of 8 inches. What is the volume of a volleyball? Volume: ___, Most of the boys like to play basketball during gym class. Each basketball has a radius of 4.7 inches. What is the volume of each basketball? Volume: ___, Mr. Kennedy has several beach balls that he uses for his lessons. He keeps them deflated until he needs to use them. When inflated, each beach ball has a diameter of 11 inches. What is the volume of one beach ball? Volume: ___”

• Scope 19: Patterns in Bivariate Data, Explore, Explore 2 - Lines of Fit, Procedure and Facilitation Points and Exit Ticket, engages students in extensive work to meet the full intent of 8.SP.2 (Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.)  In Procedure and Facilitation Points, “1. Read the scenario to the class: Due to a viral outbreak, increased safety measures are imposed in Woodville Hospital. Doctors are not happy as the new shipment of latex gloves are all the wrong size. The staff at Woodville Hospital need to know the hand length and hand width of each doctor to ensure the glove order gets corrected. The hospital needs you to analyze the relationship between the length and width of the hand to help determine the missing dimensions for the glove order. 2. Project the Class Data Table on the front board, or hang a printed Class Data Table on the front board. 3. Explain to students that they will work in their groups to measure each member’s hand in centimeters. Groups will record each person’s data on the Class Data Table on the front board. 4. Give a Student Journal and hard spaghetti noodle to each student. 5. Once all data is collected for the class, have students create a scatterplot of the data on the Student Journal. Instruct students to work with their groups to analyze the scatterplot to complete the glove order for the hospital. 6. As students collaborate, monitor their work and use the following guiding questions to assess student understanding: a. DOK–2 How would you describe the association between the two variables? b. DOK–2 Why would it be useful to draw a line through the data points? c. DOK–2 How do you determine if your line fits the data well? d. DOK–2 Will outliers affect the line that best represents the data? Explain… Students then apply their knowledge on the Exit Ticket.  Data is provided in a graph and students select the line of three given that best represents the data given. “Lines of Fit Exit Ticket In each of the questions below, circle the label of the line that best fits each set of data.”

The materials reviewed for STEMscopes Math Grade 8 meet expectations that, when implemented as designed, the majority of the materials address the major cluster of each grade.

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

• The approximate number of scopes devoted to major work of the grade (including assessments and supporting work connected to the major work) is 15 out of 19, approximately 79%.

• The number of lesson days and review days devoted to major work of the grade (including supporting work connected to the major work) is 122 out of 154, approximately 79%.

• The number of instructional days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 139 out of 180, approximately 77%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of lesson days, all assessment days, and review days. As a result, approximately 77% of the instructional materials focus on the major work of the grade.

The materials reviewed for STEMscopes Math Grade 8 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Examples of connections include:

• Scope 4: Irrational Numbers, Explore, Explore 2–Decimal Expansion, Exit Ticket, connects the supporting work of 8.NS.1 (Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually…) to the major work of 8.EE.2 (Use square roots and cube root symbols to represent solutions to equations in the form $x^2=p$ and $x^3=p$, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that $\sqrt{2}$ is irrational). Students convert fractions to decimals and decimals to fractions to determine if each number is rational or irrational. “Convert the decimals to fractions and the fractions to decimals. Classify each number as rational or irrational. Decimal, Fraction, Rational or Irrational?, $0.75,0.3⁻,\frac{1}{8},\pi,\frac{6}{9},\sqrt{4}$”.

• Scope 17: Pythagorean Theorem, Explain, Show What You Know-Part 3: The Pythagorean Theorem in Rectangular Prisms, connects the supporting work of 8.G.9 (Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.) to the major work of 8.G.7 (Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.) Students are given cones with missing measurements.  “The Pythagorean Theorem in Rectangular Prisms, Use the measurements provided to determine the slant height of each 3-dimensional figure. Round to the nearest tenth if necessary. (1) height = 16 cm radius = 9 cm slant height =, (4) height = 13 inches diameter = 11 inches slant height = ”

• Scope 19: Patterns in Bivariate Data, Explore, Explore 3–Linear Equations, Procedure and Facilitation Points, connects the supporting work of 8.SP.2 (Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line…) to the major work of 8.EE.6 (Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation $y=mx$ for a line through the origin and the equation $y=mx+b$ for a line intercepting the vertical axis at  b). Students work in groups to create a scatter plot and linear equation to represent that data. “Part I, 1. Read the scenario to the class: The Tanaka High School Student Council decided to do a massive 20-week fundraiser to raise money for hurricane relief for a neighboring county. Each grade level chose a different fundraiser and set the goal of raising at least $500 per class. Some of the classes started off with big donations from parents, while the others started at $0. The 9th-grade class chose to sell cookies during lunch periods, and the data for the first 8 weeks has been collected. Based on the data, are they on track to meet the goal of at least $500? 2. Give a Student Journal and ruler to each student. 3. Explain to students that they will work in their groups to create a scatter plot to represent the funds raised by the 9th-grade class over the first 8 weeks of the fundraiser. Instruct them to use the ruler as a straightedge to draw the line of fit. Have students work with their groups to answer the questions to determine whether the 9th-grade class is on track to meet their fundraising goal...” 

The materials for STEMscopes Math Grade 8 meet expectations that materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade. 

Materials are coherent and consistent with the Standards. These connections are sometimes listed for teachers in one or more of the three sections of the materials: Engage, Explore and Explain. Examples of connections include:

• Scope 12: Rate of Change, Explain, Show What You Know–Part 3: Interpret the Rate of Change and Y-Intercept, connects the Expressions & Equations domain to the Functions domain. Students create equations, find rate of change and y-intercept based on the given scenario. For example, “Interpret the following scenario, and complete the corresponding information. Bike Rental RatesIt costs  $20 to rent a bike and an additional $5 per hour. Equation: ___; Rate of Change: ___; Y-intercept: ___.”

• Scope 13: Model Function Relationships, Explore, Explore 2–Sketching Graphs, Procedure and Facilitation Points connects the major work of 8.F.A (Define, evaluate, and compare functions.) to the major work of 8.F.B (Use functions to model relationships between quantities.). Students sketch a graph that shows the qualitative features of a function that can be described as linear or nonlinear and increasing or decreasing. “1. Read the following scenario: Lashawn and Diego are going to the beach for another vacation. They will use their software tracking program to keep track of the speed, distance, and time traveled using graphs. Help Lashawn and Diego sketch and analyze the graphs from their software tracking program. 2. Give a Student Journal to each student. 3. Give a set of Beach Cards to each group. 4. Explain to students that they will sketch graphs and will describe the graphs as linear or nonlinear and increasing or decreasing.”

• Scope 17: Pythagorean Theorem, Explain, Show What You Know–Part 2: Finding an Unknown Side Length in Right Triangles, connects the Expressions & Equations domain to the Geometry domain. Students are given a diagram of a right triangle with side lengths and are asked to find the length of a hypotenuse. For example, “Kevin is a carpenter and enjoys building things for his neighbors. One of his neighbors uses a wheelchair to get around. Kevin wants to help his neighbor move around the outside of his home more easily by building a few wheelchair ramps around his house. The neighbor’s home is elevated, and it has a long front porch and a porch to get to the backyard. Kevin decides to build three ramps: two for the front porch and one for the back porch. Determine the missing side length of each of Kevin’s ramps. Kevin is a carpenter and enjoys building things for his neighbors. One of his neighbors uses a wheelchair to get around. Kevin wants to help his neighbor move around the outside of his home more easily by building a few wheelchair ramps around his house. The neighbor’s home is elevated, and it has a long front porch and a porch to get to the backyard. Kevin decides to build three ramps: two for the front porch and one for the back porch. Determine the missing side length of each of Kevin’s ramps. Given a diagram of a right triangle with side lengths of legs 1.5 ft and 4.8 ft. and labeled x for the hypotenuse. ___”

• Scope 18: Volume, Explain, Show What You Know–Part 1: Cylinders, Student Handout, connects The Number System domain to the Geometry domain. Students solve real-life problems working with cylinders. “One of the main methods that a fruit company uses to distribute its fruit is in cans. Because the fruit company sells its canned fruit in different forms, it distributes its fruit in cans of different sizes. Label each can with the measurements described. Use those measurements to determine the volume. Use 3.14 as an approximation for $\pi$. Round to the nearest hundredth, if necessary. A can of pineapple pieces has a radius of 9 cm and a height of 4 cm. What is the volume of the can of pineapple pieces? Volume = ___, A small can of orange juice has a diameter of 3 inches and a height of 5 inches. What is the volume of the can of orange juice? Volume = ___”

The materials reviewed for STEMscopes Math Grade 8 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Prior and future connections are identified within materials in the Home, Content Support, Background Knowledge, as well as Coming Attractions sections. Information can also be found in the Home, Scope Overview, Teacher Guide, Background Knowledge and Future Expectations sections. 

Examples of connections to future grades include:

• Scope 6: Operations with Scientific Notation, Home, Scope Overview, Teacher Guide, Future Expectations connects 8.EE.A (Expressions and Equations Work with radicals and integer exponents.) to work that will be done in upcoming grades. “In high school, students will be working with various scales on all numerical levels including very large whole numbers and very small decimals. Students will be using numerical conversions to change the values in order to understand and guide the completion of multistep real-world or mathematical problems.”

• Scope 7: Solving Linear Equations, Home, Content Support, Background Knowledge, connects 8.EE.7b (Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.) to future grades. “Students will be continuing to solve linear equations using the distributive property and combining like terms and inverse operations throughout all levels of high school. Students will be using the various steps to evaluate systems of equations, inequalities, and linear functions, as well as factoring and solving for zeros when working with polynomials.”

• Scope 10: Functions, Home, Content Support, Background Knowledge, connect 8.F.1 (Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.) to future grades. “In the coming years, students will continue their work with linear and nonlinear functions. They will expand this thinking into quadratic, exponential, logarithmic, and other types of functions. Students will learn how to express the inputs and outputs of functions in function notation as well as how to build and interpret all types of functions and their rules.”

Examples of connections to prior grades include:

• Scope 7: Solving Linear Equations, Home, Content Support, Background Knowledge, connect 8.EE.7b (Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.) to prior grades. “In Grade 6, students began to identify and apply properties of operations in order to develop equivalent expressions that may be written in different forms. As students developed an understanding of equivalent expressions, students started to use variables to represent unknown values in real-life and mathematical problems. Students then used one inverse operation to solve for the appropriate value that the variable is representing. In Grade 7, students applied properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients in order to develop equivalent expressions. Students included more than 1 inverse operation or property in order to solve for the missing variable value when working with a single variable.”

• Scope 10: Functions, Home, Content Support, Background Knowledge, connect 8.F.1 (Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.) to prior grades. “In previous grades, students learned how to plot points on a graph. They learned about the relationship between the x- and y-coordinates and how to analyze tables and graphs. In Grade 7, they discovered proportional relationships between quantities. All of these concepts will tie together in order for students to understand the basics of functions.”

• Scope 14: Transformations, Home, Scope Overview, Teacher Guide, Background Knowledge, connects 8.G.A (Understand congruence and similarity using physical models, transparencies, or geometry software.) to learning done in prior grades. “In previous grades, students developed an understanding of congruence and similarity. They created scale drawings and discussed the relationship between geometrical figures. Being able to determine these relationships will be the foundation of transformations as students discover how images map onto one another.”

The materials reviewed for STEMScopes 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. Within each Scope, there is a Home dropdown menu, where the teacher will find several sections for guidance about the Scope. Under this menu, the Scope Overview has the teacher guide which leads the teacher through the Scope’s fundamental activities while providing facilitation tips, guidance, reminders, and a place to record notes on the various elements within the Scope. Content Support includes Background Knowledge; Misconceptions and Obstacles, which identifies potential student misunderstandings; Current Scope, listing the main points of the lesson, as well as the terms to know. There is also a section that gives examples of the problems that the students will see in this Scope, and the last section is the Coming Attractions which will describe what the students will be doing in the next grade level. Content Unwrapped provides teacher guidance for developing the lesson, dissecting the standards, including verbs that the students should be doing and nouns that the students should know, as well as information on vertical alignment. Also with each Explore, there is a Preparation list for the teacher with instructions for preparing the lesson and Procedure and Facilitation Points which lists step-by-step guidance for the lesson. Examples include:

• Scope 9: Functions, Engage, Accessing Prior Knowledge–Two Truths and a Lie, Procedure and Facilitation Points, gives teachers guidance about executing the recommended instructional strategy. “1. Read the prompt aloud to the class. 2. Allow 2 minutes of thinking time for the students to read the three statements and determine the two truths and one lie. 3. Ask students to share with a shoulder partner how they marked their sheet and why. 4. Allow 2–5 minutes of discussion. 5. Ask students to justify their choice for the lie. a. The second statement is the lie. The x and y values should be switched in the statement.  6. If students are struggling to complete this task, move on to do the Foundation Builder in order to fill this gap in prior knowledge before moving on to other parts of the Scope.”

• Scope 13: Transformations, Explore, Explore 3 - Dilations, Procedure and Facilitation Points provides teachers with guiding questions to ask struggling students. “1. If students have difficulty understanding the dilations, ask the following guiding questions: a. DOK-1 What is a dilation? A process that changes the size of a figure b. DOK-1 Does a dilation make a figure smaller or larger? It can be either one. A scale factor greater than 1 results in a larger figure, while a scale factor less than one results in a smaller figure. c. DOK-1 What is a scale factor? A scale factor is the ratio of any two corresponding lengths of a figure. It tells whether a figure being dilated will result in a larger or a smaller figure. d. DOK-1 What does it mean when the center is around the origin? It means the origin is the starting point from which distances are measured in a dilation.”

• Scope 16: Pythagorean Theorem, Home, Content Unwrapped, Dissecting the Standards provides guidance on what students should be doing and saying as they work through the Scope. “Verbs: What should students be doing? Apply: to use, determine: to solve for; to figure out, explain: to account for actions or occurrences by telling reasons why, find: to discover; to solve, understand: to grasp the meaning of. Nouns: What concrete words should students know? coordinate system: a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points, converse of the Pythagorean Theorem: theorem which states that if the squares of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle; if $c^2=a^2+b^2$, then it is a right triangle. distance: a measurement of the length between two points…”

The materials reviewed for STEMScopes Math Grade 8 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

Each Scope has a Content Overview with a Teacher Guide. Within the Teacher Guide, information is given about the current Scope and its skills and concepts. Additionally, each Scope has a Content Support which includes sections entitled: Misconceptions and Obstacles, Current Scope, and Coming Attractions. These resources provide explanations and guidance for teachers. Examples include:

• Scope 3: Square Roots and Cube Roots, Home, Scope Overview, Teacher Guide, Future Expectations. It states, “In high school, students will expand their knowledge of radicals as they begin to expand and simplify radicals within equations. Students will be focusing on properties of rational exponents to find roots of various expressions through polynomials, Pythagorean theorem, and complex area and volume questions..”

• Scope 8: Proportional Relationships, Home, Concept Support, Misconceptions and Obstacles. It states,  “Students must recognize that slopes (average rate of change) can be both positive and negative. Students may believe that all graphs of straight lines represent a proportional relationship when only those that pass through the origin are proportional. Students may mistakenly graph points on a coordinate graph. They need to be confident about the direction of the x- and y-axis. Students may mistake a slope of 5 as just a rise or run of 5 units rather than a rise of 5 units vertically and a run of 1 unit horizontally.”

• Scope 12: Rate of Change, Home, Scope Overview, Teacher Guide, Scope Summary. It states, “In this Scope, students will build on their skills of how to construct a function to model a linear relationship between two quantities; calculate the rate of change and initial value of a function from tables, graphs, equations, and verbal descriptions; and interpret slope and initial value from real-world situations.”

• Scope 15: Congruence and Similarity, Home, Content Support, Coming Attractions. It states, “In the coming years, students will use their understanding of transformations to continue the expansion of rigid motions. Students will grow their thinking beyond the basics of transformation rules such as rotations beyond that of 90° and 180° and reflections over lines other than the axes. In high school, students will use these ideas to create constructions and series of rigid motions.”

The materials reviewed for STEMScopes 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 and can be found in several places including a drop-down Standards link on the main home page, within teacher resources, and within each Scope. Explanations of the role and progressions of the grade-level mathematics are present. Examples include:

• In each Scope, the Scope Overview, Scope Content, and Content Unwrapped provides opportunities for teachers to view content correlation in regards to the standards for the grade level as well as the math practices practiced within the Scope. The Scope Overview has a section entitled Student Expectations listing the standards covered in the Scope. It also provides a Scope Summary. In the Scope Content, the standards are listed at the beginning. This section also identifies math practices covered within the Scope. Misconceptions and Obstacles, Current Scope, and Background Knowledge make connections between the work done by students within the Scope as well as strategies and concepts covered within the Scope. Content Unwrapped again identifies the standards covered in the Scope as well as a section entitled, Dissecting the Standard. This section provides ideas of what the students are doing in the Scope as well as the important words they need to know to be successful.

• Teacher Toolbox, Essentials, Vertical Alignment Charts, Vertical Alignment Chart Grade 5-8, provides the following information:  “How are the Standards organized? Standards that are vertically aligned show what students learn one grade level to prepare them for the next level. The standards in grades K-5 are organized around six domains. A domain is a larger group of related standards spanning multiple grade levels shown in the colored strip below: Counting and Cardinality, Operations and Algebraic Thinking,  Number and Operations in Base Ten, Number and Operations–Fractions, Measurement and Data, Geometry.” Tables are provided showing the vertical alignment of standards across grade levels.

• Scope 10: Functions, Home, Scope Overview, Teacher Guide, Scope Summary, states, “In this Scope, students will build on their skills and learn how to define a function as every input having exactly one output; define a function on a table or graph as having not repeating x-values; text a graph using the vertical line test to determine if the graph is a function; and identify functions from tables, graphs, and equations.”

• Scope 19: Patterns in Bivariate Data, Home, Content Unwrapped, Implications for Instruction, states, “In previous grade levels, students have solved real-world problems by graphing points in all four quadrants. Students have determined frequency and outliers. Students have also modeled linear relationships on graphs.”

The materials reviewed for STEMscopes Math Grade 8 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The Teacher Toolbox contains a Secondary STEMscopes Math Philosophy document that provides relevant research as it relates to components for the program. Examples include:

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Learning within Real-World, Relevant Context, Research Summaries and Excerpts, states, “One of the major issues within mathematics classrooms is the disconnect between performing procedural skills and knowing when to use them in everyday situations. Students should develop a deeper understanding of the mathematics in order to reason through a situation, collect the necessary information, and use the mechanics of math to develop a reasonable answer. Providing multiple experiences within real-world contexts can help students see when certain skills are useful. “If the problem context makes sense to students and they know what they might do to start on a solution, they will be able to engage in problem solving.” (Carpenter, Fennema, Loef Franke, Levi, and Empson, 2015).

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, CRA Approach, Research Summaries and Excerpts, states, “CRA stands for Concrete–Representational –Abstract. When first learning a new skill, students should use carefully selected concrete materials to develop their understanding of the new concept or skill. As students gain understanding with the physical models, they start to draw a variety of pictorial representations that mirror their work with the concrete objects. Students are then taught to translate these models into abstract representations using symbols and algorithms. “The overarching purpose of the CRA instructional approach is to ensure students develop a tangible understanding of the math concepts/skills they learn.” (Special Connections, 2005) “Using their concrete level of understanding of mathematics concepts and skills, students are able to later use this foundation and add/link their conceptual understanding to abstract problems and learning. Having students go through these three steps provides students with a deeper understanding of mathematical concepts and ideas and provides an excellent foundational strategy for problem solving in other areas in the future.” (Special Connections, 2005).” STEMscopes Math Elements states, “As students progress through the Explore activities, they will transition from hands-on experiences with concrete objects to representational, pictorial models, and ultimately arrive at symbolic representations, using only numbers, notations, and mathematical symbols. If students begin to struggle after transitioning to pictorial or abstract, more hands-on experience with concrete objects is included in the Small Group Intervention activities.”

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Collaborative Exploration, Research Summaries and Excerpts, states, “Our curriculum allows students to work together and learn from each other, with the teacher as the facilitator of their learning. As students work together, they begin to reason mathematically as they discuss their ideas and debate about what will or will not work to solve a problem. Listening to the thinking and reasoning of others allows students to see multiple ways a problem can be solved. In order for students to communicate their own ideas, they must be able to reflect on their knowledge and learn how to communicate this knowledge. Working collaboratively is more reflective of the real-world situations that students will experience outside of school. Incorporate communication into mathematics instruction to help students organize and consolidate their thinking, communicate coherently and clearly, analyze and evaluate the thinking and strategies of others, and use the language of mathematics.” (NCTM, 2000)

• Teacher Toolbox, Essentials, STEMscopes Math Philosophy, Elementary, Promoting Equity, Research Summaries and Excerpts, states, “Teachers are encouraged throughout our curriculum to allow students to work together as they make sense of mathematics concepts. Allowing groups of students to work together to solve real-world tasks creates a sense of community and sets a common goal for learning for all students. Curriculum tasks are accessible to students of all ability levels, while giving all students opportunities to explore more complex mathematics. They remove the polar separation of being a math person or not, and give opportunities for all students to engage in math and make sense of it. “Teachers can build equity within the classroom community by employing complex instruction, which uses the following practices (Boaler and Staples, 2008): Modifying expectations of success/failure through the use of tasks requiring different abilities, Assigning group roles so students are responsible for each other and contribute equally to tasks, Using group assessments to encourage students' responsibility for each other's learning and appreciation of diversity” “A clear way of improving achievement and promoting equity is to broaden the number of students who are given high-level opportunities.” (Boaler, 2016) “All students should have the opportunity to receive high-quality mathematics instruction, learn challenging grade-level content, and receive the support necessary to be successful. Much of what has been typically referred to as the "achievement gap" in mathematics is a function of differential instructional opportunities.” (NCTM, 2012).” STEMscopes Math Elements states, “Implementing STEMscopes Math in the classroom provides access to high quality, challenging learning opportunities for every student. The activities within the program are scaffolded and differentiated so that all students find the content accessible and challenging. The emphasis on collaborative learning within the STEMscopes program promotes a sense of community in the classroom where students can learn from each other.”

The materials reviewed for STEMScopes Math Grade 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Teacher Toolbox provides a Secondary Materials List that has a spreadsheet with tabs for each grade level, 6-8. Each tab lists the materials needed for each activity within each Scope for the grade level. Within each Scope, the Home Tab also provides a material list for all activities.  It allows the teacher to input the number of students, groups, and stations, and then calculates how many of each item is needed.  Finally, each activity within a Scope has a list of any materials that are needed for that activity. Examples include:

• Scope 2: Integer Exponents, Elaborate, Fluency Builder–Integer Exponents, Materials, “Printed, 1 Go Fish! Instruction Sheet (per pair), 1 Set of Go Fish! Cards (per pair), Reusable, 1 Envelope or bag (per pair)”

• Scope 10: Functions, Explore, Explore 1–Understand Functions on a Graph, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per 2 students), 1 Set of Monthly Deposits Cards (per group), Reusable, 1 Gallon-sized resealable bag (per group), 1 Quart-size resealable bag (per group)”

• Scope 16: Angles, Explore, Explore 3–Traversals, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), 1 Parallel Lines and Transversals Work Mat (per group), 1 Parallel Lines and Transversals Card (per class), 1 Set of Camp Map Cards (per group), Reusable, 1 Dry-erase marker (per group), 1 Clear sheet protector (per group), 1 Ruler (per group), 1 Projector or document camera (per teacher), Consumable, 1 Sheet of tracing paper (per group)”

The materials reviewed for STEMScopes 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. 

In Grade 8, each Scope has an activity called Decide and Defend, an assessment that requires students to show their mathematical reasoning and provide evidence to support their claim. A rubric is provided to score Understanding, Computation, and Reasoning. Answer keys are provided for all assessments including Skills Quizzes and Technology-Enhanced Questions. Standards-Based Assessment answer keys provide answers, potential student responses to short answer questions, and identifies the Depth Of Knowledge (DOK) for each question. 

After students complete assessments, the teacher can utilize the Intervention Tab to review concepts presented within the Scopes’ Explore lessons. There are Small-Group Intervention activities that the teacher can use with small groups or all students. Within the Intervention, the lesson is broken into parts that coincide with the number of Explores within the Scope. The teacher can provide targeted instruction in areas where students, or the class, need additional practice. The program also provides a document in the Teacher Guide for each Scope to help group students based on their understanding of the concepts covered in the Scope. The teacher can use this visual aide to make sure to meet the needs of each student. Examples include:

• Scope 3, Square Roots and Cube Roots, Evaluate, Standards-Based Assessment, Answer Key, Question 6, provides a possible way a student might complete the problem. “Josh has a square tabletop. The area of the tabletop is 12 square feet. He says the side length of the table top is irrational. Is Josh correct? Explain your reasoning. Enter your answer in the box. (DOK-2) Josh is correct. To find the side length, the equation $s^2=12$ is solved. The side length is $\sqrt{12}$, which is between $\sqrt{9}$ and $\sqrt{16}$. Therefore, the side length is irrational.” (8.EE.2)

• Scope 8: Proportional Relationships, Evaluate, Standards-Based Assessment, Answer Key, Question 3, Part C, provides a possible solution a student might provide. “What conclusion can be drawn from the slopes and the triangles? Enter your answer in the box. (DOK-2) The slope is the same between any two points on the same line. Similar right triangles show this relationship because the rate of change will be the same for each right triangle.” (8.EE.6)

• Scope 17: Pythagorean Theorem, Intervention, Skill Review and Practice, Review provides the following information:  given a 3D rectangular prism with length labeled 12cm and height labeled 10 cm, “Try It, Determine the length of the diagonal from the upper-left corner and the lower-left corner of the rectangular prism to the nearest tenth.”

The materials reviewed for STEMscopes 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.

Assessment opportunities are included in the Exit Tickets, Show What You Know, Skills Quiz, Technology-Enhanced Questions, Standards-Based Assessment, and Decide and Defend situations. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, and short answer. While the MPs are not identified within the assessments, MPs are described within the Explore sections in relation to the Scope. Examples include:

• Scope 3: Square Roots and Cube Roots, Skills Quiz, Question 1 and 5, provide students with opportunities to demonstrate the full intent of MP2, “Reason abstractly and quantitatively, as they explain their reasoning for solutions to problems involving square roots and cube roots.” “Directions: Solve each problem and show the steps you took to get your answer. 1. $\sqrt{225}$, 5. $4^3$ A. $12$ B. $16$ C. $64$ D. $81$”

• Scope 7: Solving Linear Equations, Evaluate, Standards-Based Assessment, provides opportunities for students to demonstrate the full intent of 8.EE.7b, “Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.” Question 1, “Which equation has a solution of 0? $4(2x+3)=8(x + 1)$; $3(2x-4)=6(x-2)$; $0.3(2-3x)=0.6(x+1)$; $0.2(4-3x)=-0.6(x-2)$” Question 2 is a constructed response question. “What value of x makes the equation $\frac{3}{4}(x-4)=3x$ true? Enter your answer below. ____” Question 8, “Marcos solves the equation $\frac{1}{2}(4-2x)-2=-x$. He says the equation has no solutions because the last step results in 0 = 0. Explain if his reasoning is correct. Enter your answer below. ____”

• Scope 12: Rate of Change, Evaluate, Standards-Based Assessment, provides opportunities for students to demonstrate 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.” Question 1, “Arthur started with 24 cards and added 48 cards each year to his collection. What equation models the relationship between c, cards and t,years? $c=48t$; $c=24t$; $c=48t+24$; $c=24t+48$ Question 2, “The equation $h=100-4t$ represents the height, h, from the location on a sledding hill after t, seconds. What is the meaning of the rate of change and the initial value? Enter your answers below. ____” Mathematical Modeling Task - Eli’s Video Games Manual, “Eli loves the Astro’s Space Adventure Video game and wants to teach others how to play the game. He is creating an instruction manual on how to play Astro’s Space Adventure. Players will need to use equations to represent the topics that will be included in the manual. Part I: Astro’s Space Adventure allows you several customizable features: A new avatar costs 250 points. Each space suit costs 25 points. An avatar must be purchased before a new space suit can be bought.” Question 1, “Write the linear equation that represents the customizable features in Astro’s Space Adventure. ____” Question 2, “What is the rate of change? ____” Question 3, “What does the rate of change represent in this scenario? ____” Question 4, “What are the independent and dependent variables in this scenario? ____”

The materials reviewed for STEMscopes Grade 8 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Within the Teacher Toolbox, under Interventions, materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Within each Explore section of the Scopes there are Instructional Supports and Language Acquisition Strategy suggestions specific to the Explore activity. Additionally, each Scope has an Intervention tab that provides support specific to the Scope. Examples include:

• Teacher Toolbox, Interventions, Interventions–Adaptive Development, Generalizes Information between Situations, supplies teachers with teaching strategies to support students with difficulty generalizing information. “Unable to Generalize: Alike and different–Ask students to make a list of similarities and differences between two concrete objects. Move to abstract ideas once students have mastered this process. Analogies–Play analogy games related to the scope with students. This will help create relationships between words and their application. Different setting–Call attention to vocabulary or concepts that are seen in various settings. For example, highlight vocabulary used in a math problem. Ask students why that word was used in that setting. Multiple modalities–Present concepts in a variety of ways to provide more opportunities for processing. Include a visual or hands-on component with any verbal information.”

• Scope 10: Functions, Explore, Explore 2–Understand Functions, Instructional Supports states, “2. Given the specific representation of functions in this and the next Explore, students may develop the misconception that functions can only be depicted graphically, by diagram, or by table. Emphasize that functions can be represented in a variety of ways. While we'll focus on two of them in this Explore, we'll also look at three other representations (tables, equations, and verbal descriptions) in future Explores. 2. Some students may limit the concept of function to its representation without understanding the essence of the definition. For example, a student might mistakenly think, "A function is a mapping diagram," versus a situation in which every input has only one output. Discuss real-world examples of functions and nonfunctions such as a username to password situation (function) versus a student to hair color scenario (not a function).”

• Scope 18: Volume, Explore, Explore 2–Cones, Instructional Supports states,  “1. If students struggle to visualize the dimensions of a model, encourage them to draw the model and label its dimensions. This practice will help them properly visualize the model and give them insight into how to apply the given information. 2. Students who are rushing through the work and plugging in values for radius by rote, may mistakenly plug in the value of diameter for the radius. Encourage students to read the problem carefully, draw and label their diagrams accordingly, and then solve.”

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

Within each Scope, Scope Overview, Teacher Guide, a STEMscopes Tip is provided. It states,  “The acceleration section of each Scope, located along the Scope menu, provides resources for students who have mastered the concepts from the Scope to extend their mathematical knowledge. The Acceleration section offers real-world activities to help students further explore concepts, reinforce their learning, and demonstrate math concepts creatively.” Examples include:

• Scope 7: Solving Linear Equations, Acceleration, Would You Rather–Blue and Green Marbles states,  “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Melissa has some marbles, 25 more than 4 times the number of blue marbles is the same number as 15 less than 6 times the number of green marbles. How many marbles does Melissa have? Would you rather have the blue marbles or the green marbles? Justify your reasoning with mathematics.”

• Scope 9: Solving Pairs of Linear Equations, Acceleration, Would You Rather–Cupcakes and Hot Chocolate states, “Use mathematical reasoning and creativity to justify your answer to the Would You Rather questions. Shanaya and Tomas are going to the cupcake shop to get cupcakes and hot chocolate. Shanaya purchased Combo 1 and got three hot chocolates and a cupcake that cost a total of $7. Tomas purchased Combo 2 and got two hot chocolates and four cupcakes that cost a total of $8. What is the individual price for a single hot chocolate and a single cupcake? Would you rather purchase Shanaya’s combo or Tomas’s combo? Justify your reasoning with mathematics. Use the coordinate plane below to create a linear equation to represent each combo, and then determine where the lines intersect.”

• Scope 14: Transformations, Acceleration,  Would You Rather–Redecorating a Bedroom states, “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Arturo is redecorating his bedroom and is having trouble deciding where he should move his bed. He is considering either leaving his bed by the window or moving his bed next to the closet? Justify your reasoning with mathematics. Explain the effect that is applied to the 2-D shape in the coordinate plane using an algebraic representation.”

The materials reviewed for STEMscopes Math Grade 8 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. 

Within the Teacher Toolbox, the program provides resources to assist MLLs when using the materials. The materials state, “In the curriculum, we have integrated resources to support teachers and families. Below are a few features and elements that can be used to support students at their level and provide an opportunity for families and caregivers to engage in student learning.” Examples include but are not limited to:

• “Proficiency Levels by Domain – In this section, you will find a snapshot of language application across domains at different proficiency levels. Teachers can use this tool to help identify a student’s English proficiency level by analyzing how students are able to interpret and produce language.”  

• “Working on Words – This open-ended activity allows students to take agency and accountability for their growing vocabulary. This activity also encourages making relevant, personal connections to new terms in different ways, such as identifying cognates.” 

• “Sentence Stems/Frames – Students are able to practice engaging in purposeful discussion. These sentence stems and sentence frames can be used for different intents, such as asking for clarification, defending their thinking, and explaining their responses.” 

• “Integrated Accessibility Features – Across the curriculum, we have embedded tools that allow students to listen to text being read, find the definition of words in the moment, make notes, and highlight words and phrases.” 

• “Parent Letters – Each scope includes a letter tailored to caregivers in which the content of a scope, including its vocabulary, is explained in simplified terms. Within the Parent Letters, we have included an activities section called Tic-Tac-Toe–Try This at Home that students can engage in along with their families. This letter is written in two languages.” 

• “Tiered Supports – Within each Explore lesson, we have included tiered supports and strategies that can be applied during the lesson for students at each proficiency level. These range in focus across all domains.” 

• “Language Connections – Every scope has three Language Connection activities, one at each proficiency level. Language Connections meets the students at their proficiency level by providing teachers with prompts to support students in demonstrating their understanding in each language domain.” 

• “Virtual Manipulatives – Students are able to use these across the curriculum to help them justify their answers when expressive language may be limited. These can also be used as tools for creating meaningful connections to vocabulary terms and skills.” 

• “Visual Glossary/Picture Vocabulary – Students are able to combine visual representations and mathematical terms using student-friendly language.” 

• “Distance Learning Videos – Major skills and concepts are broken down in these student- facing videos. Students and caregivers alike can engage in the activities at home at their own pace and incorporate familiar objects. In this way, students can apply their own language to math.” 

• “My Math Thoughts/Math Story – These literary elements give students the opportunity to practice reading and writing about math. Students can apply reading strategies to aid with comprehension and practice not just math vocabulary, but situational vocabulary as well.”

Guidance is also provided throughout the scopes to guide the teacher. Examples include:

• Scope 3: Square Roots and Cube Roots, Explore, Explore 1–Square Roots and Perfect Squares where students will find patterns to recognize that solutions to perfect squares can never be negative. Students will apply their knowledge of squaring numbers being inverses to square roots to calculate solutions to problems containing either a perfect square or a square root. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use learning techniques such as concept mapping, drawing, comparing, contrasting, memorizing, and reviewing to acquire basic and grade-level vocabulary. Beginner: As a pre-lesson activity to review area, place square and rectangle blocks made of snap cubes around the classroom (each block of cubes should be made of one color). Provide students a sheet that lists different areas in the first column and have them write the block color in the second column. For example, if students find a 3 by 5 block of yellow snap cubes, they will write yellow next to the area that states 15 units squared. Intermediate: As a pre-lesson activity to review area, place square and rectangle blocks made of snap cubes around the classroom (each block of cubes should be made of one color). Students are on a scavenger hunt to find all blocks of cubes and their areas. Provide students with a sheet with two columns. Some block colors or areas may be pre-identified in the columns and students will have to determine the missing block color or area. Advanced: As a pre-lesson activity to review area, place square and rectangle blocks made of snap cubes around the classroom (each block of cubes should be made of one color). Students are on a scavenger hunt to find all blocks of cubes and their areas. Provide students with a sheet with two columns. Some block colors or areas may be pre-identified in the columns and students will have to determine the missing block color or area.”

• Scope 8: Proportional Relationships, Explore, Explore 2–Compare Proportional Relationships where students will compare proportional relationships shown in graphs, tables, and equations. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use visual cues, peers, and teachers to develop vocabulary, language structure, and background knowledge needed to comprehend written text. Beginner: As a pre-lesson activity, students will work with a partner to put a series of pictures in chronological order. The pictures will detail a person's experience from the airport to inside the plane to their destination. Intermediate: As a pre-lesson activity, divide students into groups of two to three students. Have students perform pre-scripted dialogue between a flight attendant and passenger, two passengers, or a Transportation Security Officer and passenger. Advanced: As a pre-lesson activity, students in groups of two to three will write and perform skits about a bad travel experience via plane.”

• Scope 15: Congruence and Similarity, Explore, Explore 2–Similarity where students will describe the scale factor that produces similar figures and will determine whether it represents a reduction or an enlargement. They will also perform transformations that represent similarity and prove that figures are similar. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use learning techniques such as concept mapping, drawing, comparing, contrasting, memorizing, and reviewing to acquire basic and grade-level vocabulary. Beginner: As a post-lesson activity, have students create vocabulary squares for the term similarity. Complete the following sections of the vocabulary square as a class: Definition, Example (math problem), Non-example, and have students create their own image for the term. Intermediate: As a post-lesson activity, have students create vocabulary squares for the term similarity. Vocabulary squares should include the following sections: Definition, Example (math problem), Non-example, and Image. Provide students with the definition and example, but encourage students to rewrite the definition in their own words. Advanced: As a post-lesson activity, have students create vocabulary squares for the term similarity. Vocabulary squares should include the following sections: Definition, Example (math problem), Non-example, and Image. Provide students with the definition, but encourage students to rewrite the definition in their own words.”

The materials reviewed for STEMscopes 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. Examples include:

• Scope 2: Integer Exponents, Explore, Explore 2–Multiplying with Exponents, Description states,  “Students will match equivalent multiplication expressions and show how one expression can be simplified to generate another.” Materials, “Printed 1 Student Journal (per student); 1 Set of Matching Cards (per partnership); 1 Exit Ticket (per 2 students). Reusable: 1 Resealable bag (per partnership).” Preparation: “Print a set of Matching Cards for each partnership. Cut out and place cards in a resealable bag. If desired, print them on card stock, and laminate them for future use. In the Procedure and Facilitation Points section it states “Give a set of Matching Cards to each partnership.”

• Scope 8: Proportional Relationships, Explore, Explore 2–Compare Proportional Relationships, Description states, “Students will compare proportional relationships shown in graphs, tables, and equations.” Materials, “Printed: 1 Student Journal (per student); 1 Exit Ticket (per student); 1 Set of Flight Prices by Season Cards (per group); 1 Set of Flight Prices by Day Cards (per group). Reusable: 2 Resealable bags (per group).” Preparation, “Print a set of the Flight Prices by Season Cards for each group. Cut out the cards, and place each set in a resealable bag labeled “Part I.” If desired, print them on card stock, and laminate them for future use. Print a set of Flight Prices by Day Cards for each group. Cut out the cards, and place each set in a resealable bag labeled “Part II.” If desired, print them on card stock, and laminate them for future use. In the Procedure and Facilitation Points section it states give a set of Flight Prices by Season Cards to each group.”

• Scope 18: Volume, Explore, Explore 2–Cones, Description states,  “Students will discover the formula for the volume of a cone and solve mathematical and real-world problems to find the volume of a cone.” Materials, “Printed 1 Student Journal (per student); 1 Set of Cone It Cards (per group) 1 Cylinder and Cone Nets (per group) 1 Exit Ticket (per student) Reusable 1 Resealable bag (per group); 1 Pair of scissors (per teacher); 1 Glue stick (per group). Consumable: 1 Bag of rice (per group).” Preparation, “Print one Cylinder and Cone Nets for each group of students. If desired, print them on cardstock. Print a set of Cone It Cards for each group of students. If desired, print them on card stock and laminate for future use. Cut out the cards, and put them in a resealable bag for each group. In the Procedure and Facilitation Points section it states "Give one copy of the Cylinder and Cone Nets, a pair of scissors, a glue stick, and a bag of rice to each group.”