7th Grade - Gateway 3

The materials reviewed for STEMScopes Math Grade 7 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 6: Percent Application, Engage, Accessing Prior Knowledge–Two Truths and a Lie, Procedure and Facilitation Points provides guidance on how to execute the suggested instructional strategy. “1. Read the prompt aloud to the class. Allow 2 minutes of thinking time for the students to read the three statements and determine which two statements are truths and which one is a lie. 2. Ask students to share with a shoulder partner how they marked their sheets and why. 3. Allow 2–5 minutes of discussion. 4. Ask students to justify their choice for the lie. 5. Statement C is the lie because 32.4 is 40% of 81, not 37.4. 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 10: Scaling, Home, Content Unwrapped, Implications for Instruction gives teachers guidance on what students should already know and a description of what they should learn throughout the Scope. “In grade 6, students have identified ratios and rates in real-world and mathematical problems. Students have found missing values in ratio tables and used proportions to solve for missing values of ratios. Additionally, students have graphed proportional relationships on a coordinate plane indicating the relationship between the terms in a ratio. Students have also found the area of special quadrilaterals, triangles, and other polygons through decomposing the figure into triangles/rectangles.In this grade level, students are expected to use their knowledge of ratios and rates to solve real-world and mathematical problems involving scale drawings. Students compare similar figures (polygons) and identify the rate at which the figures grow or shrink. Students find the missing side lengths of similar figures represented as scale drawings. Students use their knowledge of attributes of geometric figures to identify actual lengths of the geometric figures. Students solve for actual lengths of the scale drawings as well as actual areas of the scale drawings. Students overall identify scale drawings as a visual representation of proportional relationships between the side lengths of the figures. Students produce/reproduce figures based on given information.”

• Scope 16: Probability, Explore, Explore 3–Probability Models, Preparation, instructs teachers on how to get ready for the lesson. “Plan to divide the class into student groups of 4. Print the Student Journal and Exit Ticket for each student. Print a set of the Probability Model Cards for each group. Cut out and place each set of cards in a resealable bag for each group. If desired, print the cards on card stock, and laminate them for future use. Print a page of Spinners for every 2 groups. (There are 2 spinners on a page, enough for two groups.) Cut out the spinners, and place one in a resealable bag with a paperclip and pencil for each group. If desired, print them on card stock, and laminate them for future use. Gather the color counters and brown paper bags for each group. Place 10 red counters and 10 yellow counters in a bag.”

The materials reviewed for STEMScopes Math Grade 7 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 2: Adding and Subtraction with Rational Numbers, Content Overview, Teacher Guide, Future Expectations. It states, “By understanding how to properly add and subtract rational numbers, students can then explore the existence of irrational numbers in 8th grade. The idea of rational versus irrational numbers will be seen more as students begin to study the different types of functions.”

• Scope 7: Percent Application, Home, Content Support, Current Scope. It states, “In this Scope, students will use their prior knowledge of proportional relationships to solve mathematical problems involving percentages. By the end of the Scope, students will feel comfortable solving many different types of multistep ratio problems such as interest, tax, gratuities and commissions.”

• Scope 10: Scaling, Home, Content Overview, Teacher Guide, Future Expectations. It states, “Computing scale drawings and the ratios of the scales will be important as the students begin rigid motions and congruences in 8th grade. Determining if two figures are the same size and shape based on scaling will help reinforce the concept of determining congruent versus similar figures. As the students enter high school, these ideas will be used to prove theorems and definitions.”

• Scope 14: Circles, Home, Content Support, Misconceptions and Obstacles. It states, “Students may misunderstand the difference between a radius and a diameter when given the wrong measurement needed for a specific formula. For example, when asked to find the area of a circle, given a diameter, they may accidentally use the measure of the diameter rather than cutting it in half. Students need to have a full understanding of the formulas for the circumference and the area as they are commonly mixed up.”

The materials reviewed for STEMScopes Math Grade 7 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: Solve Equations and Inequalities, Home, Scope Overview, Teacher Guide, Background Knowledge, states  “In Grade 6, students expanded their knowledge of expressions with variables as equations and inequalities. They began to solve these problems using one-step equations and mathematical reasoning. These arithmetic solutions lead to understanding the concepts behind equations and how to find the values that will make each equation true.”

• Scope 18: Compound Events, Home, Content Unwrapped, Implications for Instruction, states, “In this Scope, students are expected to compare compound events to simple events. Students create and interpret sample spaces using organized lists, tables, and tree diagrams. They determine the fraction of outcomes in the sample space for which the compound event occurs, and they design use simulations to generate frequencies for compound events.”

The materials reviewed for STEMscopes Math Grade 7 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 7 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 5: Proportional Relationships, Elaborate, Fluency Builder–Constant Rate of Change, Materials, “Printed, 1 Concentration Instruction Sheet (per pair), 1 Set of Concentration Cards (per pair), Reusable, 1 Envelope or bag (per pair)”

• Scope 12: Angle Relationships, Explore, Explore 3–Multi-Step Angle Problems, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), 1 Redwood Park Map (per group, optional),1 Redwood Park Map for display (per class), Reusable, 1 Straightedge (per student), 1 Projector or document camera (per teacher)”

• Scope 18: Compound Events, Explore, Explore 3–Represent Sample Space, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), 1 Set of Snack Cards (per group), Reusable, 1 Resealable bag (per group)”

The materials reviewed for STEMScopes Math Grade7 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 7, 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 7: Percent Application, Evaluate, Standards-Based Assessment, Answer Key, Question 6, provides a possible way a student might complete the problem. “ Atticus bought a vintage vinyl record for $64. Three years later he sold the record online for $72. What was the percent increase of the record value? Explain your reasoning. Enter your answer in the box. (DOK-3) 12.5% The record value increased by $8. $64 represents 100% of the cost. The $8 increase is 12.5% of 100 because 100\div8=12,5%”  (7.RP.3)

• Scope 13: Triangle Properties, Evaluate, Standards-Based Assessment, Answer Key, Question 4 provides a possible solution a student might provide.  “Sarah wants to know whether it is possible to draw a triangle with two 60° angles and a side length of 3 centimeters. Is it possible? Explain your reasoning. Enter your answer in the box. (DOK-3) Yes. The sum of angles in a triangle is 180°. If 2 angles are 60°, then so is the third one because 60\times3=180. It is an equilateral triangle.” (7.G.2)

• Scope 18: Compound Events, Intervention, Skill Review and Practice, Review states,  “Try It, Determine whether the challenge results in a simple or compound event.”  Given a table labeled Challenge Event and Type, “Drawing two red-faced cards from a standard deck of playing cards, Throwing a dart toward a target.”

The materials reviewed for STEMscopes Math Grade 7 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 4: Rational Number Operations, Evaluate, Standards-Based Assessment, provides opportunities for students to demonstrate the full intent of 7.NS.3, “Solve real world and mathematical problems involving the four operations with rational numbers (extend the rules for manipulating fractions to complex fractions).” Question 2, “Jayden and his 4 friends were going to split the travel costs of a short trip. The total cost was $16. Part A: What is the cost for each person? $____; Part B: Two friends are unable to go. What is the new cost per person? $____” Question 3, “Mike is training for a race and runs 3\frac{5}{8} miles. What is this distance as a decimal? 3.5 miles; 3.625 miles; 3.725 miles; 3.8 miles” Question 6 is a discussion and also a constructed response question. “Byron states that \frac{3}{19} is not a repeating decimal. Is this correct? Explain your reasoning. Enter your answer below. ____”

• Scope 11: Scaling, Evaluate, Standards-Based Assessment, Question 3, provides students an opportunity to demonstrate the full intent of MP1, “Make sense of problems and persevere in solving them, as they use the information provided and their understanding of area to find the amount of paint needed to cover a wall.” “A scale drawing uses a scale of 1 inch = 1 foot. The drawing shows a wall that is 12 inches by 30 inches. There are 2 windows on the wall that are each 2 inches by 4 inches. The room needs 2 coats of paint, but the windows do not need to be painted. If a quart of paint covers 100 square feet, how many quarts are needed for the wall? Enter your answer in the box. ____ quarts.”

• Scope 17: Probability, Evaluate, Standards-Based Assessment, provides opportunities for students to demonstrate the full intent of 7.SP.7, “Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.” Question 1, “There are 16 aisle seats and 10 window seats left on a plane. The next passenger will be randomly assigned to a seat. What is the probability that the next passenger will be assigned to a window seat? \frac{1}{10}; \frac{5}{13}; \frac{1}{2}; \frac{8}{13}” Question 6, “A spinner has 10 equal-spaced sections numbered 1 to 10. Part A: If the spinner is spun 800 times, approximately how many times will the spinner land on 3? ____ times; Part B: If the spinner is spun 2,500 times, what is the percent probability of it landing on a 7? ____%; Part C: The spinner was spun 20 times, and it never landed on 10. Does this mean the spinner is unfair? Explain your reasoning. Enter your answer below. ____” Question 10, “A standard six-sided number cube is rolled. Part A: Is the probability of rolling a 7 unlikely, neither likely nor unlikely, or likely. Enter your answer below. ____; Part B: What is the probability of rolling an even number? Write the probability as a fraction, and describe the event as certain, equally likely, likely, unlikely, or impossible. Explain your reasoning. Enter your answer below. ____”

The materials reviewed for STEMscopes Grade 7 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 5: Proportional Relationships, Explore, Explore 2–Unit Rates, Instructional Supports states, “1. Struggling students may need to review the concept of unit rate. Have students determine the unit rate for three to four examples of proportions. Ask these students what they notice about the unit rates (i.e., for each example, it's the rate per 1). 2. Struggling students may have difficulty determining whether to multiply or divide to find the unit rate. Guide these students through the first three examples. Ask if they notice any patterns (i.e., when converting from a smaller quantity of time like minutes to hours, multiply; or when converting from a larger quantity of hours to one hour, divide).”

• Scope 10: Solve Equations and Inequalities, Explore, Explore 3–Construct Inequalities, Instructional Supports states, “1. Struggling students may confuse the greater than and less than signs. The more exposure students have to these symbols, the more likely they will be to remember their meanings. When students write each symbol, it is important to hear and say greater than or less than to help them internalize the meanings. Students can relate the symbols to arrows that point to the direction on a number line. A number to the left (<) of another number has a lesser value, and a number to the right (>) has a greater value. 2. Encourage students to use specific language as they become acquainted with variables, especially in the context of word problems. For example, if a student says or writes, "c equals cupcakes," have them instead specify that c equals the cost of cupcakes. Such specificity in language will be beneficial as their knowledge and practice of Algebra grows.”

The materials reviewed for STEMscopes Math Grade 7 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 5: Proportional Relationships, Acceleration, Would You Rather–The Price of Apples states, “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Kendra needs help with shopping for the best apples. She is at Food City and is looking at the prices of Fuji apples and Granny Smith apples. Fuji apples are $5.49 for a 3 lb. bag, and Granny Smith apples are $6.00 for a 5 lb. bag. Would You Rather purchase Fuji apples or Granny  Smith apples? Justify your reasoning with mathematics. Calculate the unit rate. Fuji Apples $5.49/3 lb. bag Granny Smith Apples $6.00/5 lb. bag” 

• Scope 13: Triangle Properties, Acceleration, Would You Rather–Garden Fencing states,“Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. The Student Council members and National Honor Society members are working together to plant flowers in two gardens. The Student Council members have purchased fencing for the first garden bed, and the National Honor Society members have purchased fencing for the second garden bed. Would you rather plant flowers with the Student Council or the National Honor Society? Justify your reasoning with mathematics. Include the properties of triangles. Fence 1: 74 feet available; Garden Bed 1: Side length 1: 18 feet, Side Length 2: 20 feet, Side Length 3: 36 feet; Fence 2: 75 feet available; Garden Bed 2: Side Length 1: 27 feet; Side Length 2: 18 feet; Side Length 3: 22 feet” 

• Scope 17: Probability, Acceleration, Would You Rather–The Candy Store states, “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Devin and Samuel are going to the candy store to get some candy. Devin wants a lollipop, and Samuel wants a chocolate candy bar. They have decided to play a game and get candy from the shelf blindfolded to determine the probability of selecting the candy they want. Would you rather buy a lollipop or chocolate candy bar? Justify your reasoning with mathematics. Determine the theoretical probability.”

The materials reviewed for STEMscopes Math Grade 7 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 7: Percent Application, Explore, Explore 2–Percent Change where Students will solve problems involving percent increase and percent decrease that will also include understanding how to calculate markups and markdowns in prices using proportional reasoning. 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 a vocabulary square for the term percent. 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 percent. 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 percent. 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.”

• Scope 11: Scaling, Explore, Explore 2–Perimeter and Area where students will determine a scale factor when given original dimensions and revised dimensions for a rectangular figure. Students will find the area and perimeter of real-life rectangular locations by employing proportions and formulas for area and perimeter of a rectangle. 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 have students create vocabulary squares for the terms perimeter and area. 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 each term.Intermediate: As a pre-lesson activity have students create vocabulary squares for the terms perimeter and area. Vocabulary squares should include the following sections: Definition, Example (math problem), Non-example, and Image. Provide students with the definitions and examples, but encourage students to rewrite the definitions in their own words. Advanced:As a pre-lesson activity have students create vocabulary squares for the terms perimeter and area. Vocabulary squares should include the following sections: Definition, Example (math problem), Non-example, and Image. Provide students with the definitions, but encourage students to rewrite the definitions in their own words.”

• Scope 17: Probability, Explore, Explore 2–Predicting Probability where students will predict the probability of an outcome and collect data by conducting repeated trials, understanding the similarities and differences between theoretical and experimental probability. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will be provided with pre-reading supports (graphic organizers, shape diagrams, and pre-taught vocabulary) to assist with reading comprehension. Beginner:Prior to the lesson, provide students with a list of new vocabulary they will encounter in the lesson along with images that signify the terms' meanings. Encourage students to highlight the terms and reread their definitions as they encounter them in their Student Journals. Some new terms to include are: theoretical probability, experimental probability, frequency, relative frequency,etc. Intermediate: Prior to the lesson, provide students with guided notes that include images and diagrams, along with incomplete definitions for new terms they will encounter in the Explore. As they go through the lesson, encourage students to complete the definitions. Some of the new terms to include are: theoretical probability, experimental probability, frequency, relative frequency,etc. Advanced: Prior to the lesson, provide students with guided notes that include images and diagrams, along with incomplete definitions for new terms they will encounter in the Explore. As they go through the lesson, encourage students to complete the definitions. Some of the new terms to include are: theoretical probability, experimental probability, frequency, relative frequency, etc.”

The materials reviewed for STEMscopes Math Grade 7 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 5: Proportional Relationships, Explore, Explore 3–Proportional Relationships with Equations, Description states,  “Students will find the equations of proportional relationships from tables, graphs, and verbal descriptions.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Camp Flyers (per group); 1 Set of Camp Fee Cards (per group); 1 Exit Ticket (per student). Reusable: 1 Resealable bag (per group).” Preparation, “Print a set of the Camp Flyers for each group. If desired, print them on card stock, and laminate them for future use.Print a set of the Camp Fee Cards for each group. Cut them out and place them 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 Camp Flyers to each group.”

• Scope 10: Solve Equations and Inequalities, Explore, Explore 3–Construct Inequalities, Description states,  “Students will create models of inequalities using algebra tiles and an Algebra Inequality Mat.” Materials, “Printed: 1 Student Journal (per student); 1 Exit Ticket (per student); 1 Algebra Inequality Mat (per group); 1 Set of Cupcake Booth Cards (per group). Reusable: 1 Set of algebra tiles (per group); 1 Resealable bag (per group); 1 Set of colored pencils (per group).” Preparation, “Print one two-sided Algebra Inequality Mat for each group. If desired, print it on card stock, and laminate it for future use. Print one set of Cupcake Booth Cards for each group. Cut out and place each set of cards in a resealable bag. If desired, print the cards on card stock, and laminate them for future use. In the Procedure and Facilitation Points section it states “Give one set of Cupcake Booth Cards, one set of algebra tiles, and one Algebra Inequality Mat to each group.”

• Scope 17: Probability, Explore, Explore 1–Probability, Description states, “Students will investigate chance events, find the probability of events, and evaluate the likelihood of events.” Materials, “Printed: 1 Student Journal (per student); 1 Exit Ticket (per student); 1 Set of Probability Task Cards (per group). Reusable: 1 Resealable bag (per group); 1 Set of marbles (per teacher); 10 Red marbles; 5 Blue marbles; 4 Green marbles; 1 Yellow marble. Consumable: 1 Brown paper bag (per teacher).” Preparation, “Print a set of the Probability Task Cards for each group. Cut out and place each set of Task Cards in a resealable bag. If desired, print on card stock and laminate for future use. Gather 20 marbles (10 red marbles, 5 blue marbles, 4 green marbles, and 1 yellow marble), and place them in a brown bag. This is the teacher’s Mystery Bag. In the Procedure and Facilitation Points section it statesDirect the students’ attention to the Mystery Bag with marbles and the Mystery Bag model on the Student Journal. While pulling different marbles out of the bag.”