6th Grade - Gateway 3

The materials reviewed for STEMScopes Math Grade 6 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 10: Percents, Engage, Accessing Prior Knowledge–Four Corners, Identifying Misconceptions, provides guidance on how to identify student misconceptions. “Slide 1: Students who choose slide 1 think that a product is always greater than the multiplicands. They don’t understand that multiplying a whole number with a fraction less than 1 will result in a product less than the whole number. Slide 2: This is the correct slide. Slide 3: The students who choose this slide don’t understand that is actually equal to 1, and the product of a whole number and 1 is the same whole number. Slide 4: The students who choose this slide are multiplying the whole number with both the numerator and the denominator, which is an incorrect way of multiplying whole numbers and fractions.”

• Scope 12: Dependent and Independent Variables, Engage, Accessing Prior Knowledge–Fact or Fiction, Description provides an instructional strategy and the purpose of the strategy. “Students will listen to prompts about the prior standard and communicate whether they feel the prompts are fact or fiction by walking to the designated sides of the classroom. This element is designed to uncover student misconceptions; it should not be taken for a grade.”

• Scope 15: Understand Variability, Explore, Explore 1–Variability in Data, Procedure and Facilitation Points provides the teacher with guiding questions to ask students as students work. “6. Monitor and assess each group’s understanding of the task by asking the following guiding questions: a. DOK-1 What survey question will you be asking your classmates? Answers will vary. b. DOK-2 What does it mean when it says your question will be answered with data? Answers may vary. Data is information collected from individuals. c. Explain to the class: The information collected can be numerical or categorical. Numerical data is responses that are numbers. Categorical data includes responses such as favorite pizza toppings. d. DOK-3 How can you organize the data collected on the table provided on the survey document? Answers may vary depending on the survey question. I can list the classmate responses on the left side of the table and mark a tally for each classmate who responds with that response on the right side of the table. e. DOK-3 How can you use the data collected to create a dot plot? Answers may vary. I can split the dot plot into equal parts for each response and label each line with the student response. Then, for each tally represented in the table, we can place a dot above that response on the dot plot. If there are a lot of responses, we can create a key that shows that each dot on the dot plot equals 2, 3, 4, 5, etc. responses. f. DOK-1 Using the data provided by your classmates, what is the answer to your survey question? Answers will vary based on data.”

The materials reviewed for STEMScopes Math Grade 6 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: Integers, Home, Content Support, Current Scope. It states, “Students will extend their knowledge of the number line to represent positive and negative numbers. Students reason about the relationship between a number and its opposite as points that are equidistant from zero. Both horizontal and vertical numbers will be used, as experience with both types facilitate students’ movement from number lines to coordinate grids. Students use integers to represent real-world contexts and to understand the meaning of zero in each situation. Students learn the absolute value symbol and that absolute value measures the distance from an integer to zero, and can be used to determine the distance between two numbers. Contextual problem solving, such as temperature, elevation, and banking help students relate their understanding of positive and negative values, opposites, and absolute value.”

• Scope 6: Positive Rational Number Operations, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states,  “Effective strategies for computation with positive rational numbers relate to a series of other sixth grade Scopes. Sixth graders will apply computation strategies when exploring measurement conversions, equations and inequalities, area, surface area, volume, and ratios. In Grade 7, students will extend operations to include negative numbers. Proficiency of number operations will effectively allow seventh-grade students to study repeating decimals, proportional relationships and scale drawings, equations and inequalities, circle measurement, and probability and sampling.”

• Scope 12: Measurement Conversions, Home, Content Overview, Teacher Guide, Scope Summary. It states, “Within this Scope, students will grow their knowledge about measurement through using their understanding of ratio concepts and ratio reasoning to solve real-world and mathematical problems. As students progress through this Scope, they will also learn how to use ratio reasoning to convert measurement units through the manipulation and transformation of units when it is appropriate for multiplying and dividing quantities.”

• Scope 18: Summarize Numerical Data, Home, Content Support, Coming Attractions. It states, “Students in seventh grade use random sampling to draw inferences about populations, and they investigate chance processes. They develop, use, and evaluate probability models. In eighth grade, students investigate patterns of association in bivariate data. This work extends into high school, where students continue to interpret categorical and quantitative data, and then explore conditional probability and the rules of probability.”

The materials reviewed for STEMScopes Math Grade 6 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 8: Algebraic Expressions, Home, Scope Overview, Teacher Guide, Scope Summary, states, “As students participate in this Scope, they will extend their previous knowledge and understanding of arithmetic to algebraic expressions. By participating in the explorations within the Scope, students will learn how to read and identify parts of expressions using mathematical terms; write expressions that contain letters; and evaluate and perform expressions and arithmetic operations at specific values for their variables. Students will also learn how to apply properties of operations to create equivalent expressions and identify if two expressions are equivalent or not.”

• Scope 15: Surface Area, Home, Content Unwrapped, Implications for Instruction, states “In this grade level, students extend their reasoning about area to include figures composed of both rectangles and triangles. Students explore properties of nets that form three-dimensional figures. They determine the surface area of a three-dimensional figure by finding the area of each face in reference to its corresponding net.”

The materials reviewed for STEMscopes Math Grade 6 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 6 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: Integers, Elaborate, Fluency Builder–Integers, 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 6: Positive Rational Number Operations, Explore, Explore 3–Division of Fractions, Materials, “Printed, 1 Student Journal (per student), 1 Set of Tablecloth Fabric Cards (per group), 1 Exit Ticket (per student), Reusable, 1 Resealable bag (per group), 1 Set of colored pencils (per student, optional)”

• Scope 11: Percents, Explore, Explore 3–Finding the Price and Discount, Materials, “Printed, 1 Student Journal (per student), 1 Percent Model Work Mat (per station), 1 Set of Sale Cards (per class), 1 Exit Ticket (per student), Reusable, 1 Dry-erase marker (per station), 1 Clear sheet protector (per station)”

The materials reviewed for STEMScopes Math Grade 6 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 6, 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: Equivalent Numerical Expressions, Evaluate, Standards-Based Assessment, Answer Key, Question 6, provides a possible way a student might complete the problem. “There are 90 apples and 75 bananas available to make fruit baskets. Each basket has the same number of pieces of fruit. What is the greatest amount of fruit baskets that can be made with no fruit left over? How many pieces of fruit are in each basket? Write an expression using the distributive property. Explain your reasoning. Enter your answer in the box. (DOK-3) 15 baskets with 6 apples and 5 bananas. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The factors of 75 are 1, 3, 5, 15, 25, and 75. The greatest common factor for 90 and 75 is 15, so the greatest number of baskets that can be made is 15. 15(6+5), so there will be 15 baskets and each basket will have 6 apples and 5 bananas.”(6.NS.4)

• Scope 13: Dependent and Independent Variables, Evaluate, Standards-Based Assessment, Answer Key, Question 4, Part C, provides a possible solution a student might provide. “Which variable, t or d, is the independent variable, and which variable is the dependent variable? Is there more than one answer? Explain your reasoning. Enter your answer in the box. (DOK-3) The independent variable is t. Time, t, is the independent variable, and distance, d, is the dependent variable because the distance depends on the number of hours traveled” (6.EE.9)

• Scope 16: Understand Variability, Intervention, Skill Review and Practice, Review, “Try It, Prices for candy bars at a local store are as follows: $1.00, $0.75, $1.75, $1.50, $1.50, $2.00, $1.00, $0.50, $1.50, $1.25, $1.50. Make a frequency table by listing the responses in order and make tally marks for each time the price occurs. Make a dot plot below to represent the data in the table.”

The materials reviewed for STEMscopes Math Grade 6 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: Compare and Order Rational Numbers, Evaluate, provides opportunities for students to demonstrate the full intent of 6.NS.7b, “Write, interpret, and explain statements of order for rational numbers in real-world contexts.” Question 1, “A proton has a charge of +1, and an electron has a charge of -1. Which statement is true about the values of the charges? −1>+1 because -1 is to the right of +1.; -1<+1 because -1 is to the right of +1.; -1>+1 because -1 is to the left of +1.; -1<+1 because -1 is to the left of +1.” Question 2, “The temperature on the weekend was -2\degreeC on Friday, -8\degreeC on Saturday, and -4\degreeC on Sunday. Which statements are true? Select all that apply. Saturday was the warmest day.; Sunday was colder than Friday.; Friday was warmer than Saturday.; Friday was the coldest day.” Question 3, “A diver starts at sea level. He dives down to 65 feet below sea level and then swims up to 25 feet below sea level. After a few minutes, he dives back down to a depth of 55 feet below sea level. What is the greatest depth of the diver? Enter your answer below. ____”

• Scope 8: Algebraic Expressions, Evaluate, Standards-Based Assessment, provides opportunities for students to demonstrate the full intent of 6.EE.2, “Write, read, and evaluate expressions in which letters stand for numbers.” Question 1, “A company rents bicycles for $25 per hour. There is also a $40 fee for required insurance. Which expression represents the total cost of renting a bicycle for h hours? 25h+40; h\div25+40;  40h+25; h\div40+25” Question 7, “Five days a week, Mack runs m minutes on a treadmill and lifts weights for 20 minutes. The expression 5(m+20) represents the weekly length of Mack’s workout. Write an equivalent expression for this time. Enter your answer below. ____” Mathematical Modeling Task - Who Is Correct?, Question 1, “The first expression they have is 6g+12m-2g+8t+2t. Juan says this expression simplified is 16g+10t. Carlos says the equivalent expression is 4g+12m+10t. Explain who is correct. ____”

• Scope 18: Summarize Numerical Date, Evaluate, Skills Quiz, Question 1, provides students with an opportunity to demonstrate MP5, “Use appropriate tools strategically, as they decide and explain which model they would use to display data collected.” “1. Jillian collected data to find out the leg span of each student in her class. She wants to display the data so that each student can see how their individual measurement compared with the others in the class. Should she choose to represent the data using a dot plot, box plot, or histogram? Explain your reasoning.”

The materials reviewed for STEMscopes Grade 6 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 9: Equations and Inequalities, Explore, Explore 2–Write and Solve Equations, Instructional Supports states, “1. Struggling students may grasp the concept of the problem but have difficulty computing with decimals. Have students break down the decimals into smaller steps to solve. 2. Struggling students may have difficulty grasping why we multiply by the reciprocal when a variable is multiplied by a fraction. Use manipulatives to help them grasp the concept. For example, have students line up beans 4 by 5 making a total of 20 beans. Ask students to then isolate one-fourth of the beans (5 beans). Help students see that to get back to 20 beans they have to multiply the 5 beans 4 times (the reciprocal) making 4 sets of 5 beans, which is 20 beans.”

• Scope 14: Area and Volume, Explore, Explore 2–Finding the Area of Quadrilaterals, Instructional Supports states,  “1. To ensure understanding of the concept of area over the mechanical application of the formula, point out that the unit squares can be used to determine area as well since area is the space covered by a closed flat shape and it takes x unit squares to cover the space. 2. Struggling students may have difficulty conceptualizing the height of the parallelogram and the triangle. As a rule of thumb, tell them that the base and height are always perpendicular to one another, and allow them to identify and mark with a highlighter the base and height of the figure to ensure that they are perpendicular to one another.”

The materials reviewed for STEMscopes Math Grade 6 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 6: Positive Rational Number Operations, Acceleration, Would You Rather–Forest Scout Fundraiser states, “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Thomas and Ayaan are Forest Scouts and are raising money for the Scouts’ annual camping trip. They are working in teams selling chocolate bars. You have the option to join Team Oak or Team Spruce to sell Chocolate bars. Would you rather join Team Oak or Team Spruce? Justify your reasoning with mathematics. Team Oak Sold \frac{4}{5} of 18 boxes of milk chocolate bars Cost: $2.00 per box  Team Spruce Sold \frac{1}{3} of 12 boxes of milk chocolate bars with almonds Cost: $3.00 per box”

• Scope 9: Equations and Inequalities, Acceleration, Would You Rather–Magazine Subscriptions states,  “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Crazy Sports Car Magazine is offering different subscription plans to potential customers. They are offering potential customers the opportunity to pay $99.00 for a yearly subscription that comes with one magazine per month.  Their other plan allows potential customers to pay $9.00/month to receive one magazine per month with the option to cancel anytime. Would you rather pay for a yearly subscription or pay a monthly fee for a Crazy Sports Car Magazine subscription? Justify your reasoning with mathematics.” 

• Scope 17: Represent and Interpret Data, Acceleration, Would You Rather–Shopping for New TVs states,  “Use mathematical reasoning and creativity to justify your answer to the Would You Rather question. Amari is interested in purchasing TVs that measure at least 50 inches for his new home. He is looking at TVs at Pete’s Electronics store and the Shop Smart store and is trying to determine which store offers the best selection of TVs by size. Would you rather recommend that Amari shops at Pete’s Electronics store or the Shop Smart store? Justify your answer by describing the distribution data.”

The materials reviewed for STEMscopes Math Grade 6 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 2: Integers, Explore, Explore 2–Absolute Value where students will use their knowledge of number lines to recognize that the absolute value of a positive or negative integer is the distance that number is away from zero. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will enhance language attainment as they acquire knowledge from a variety of multimedia instructional formats. Beginner: Before the lesson, display images of different sports, including football, and have students repeat the sports names after you. Then share that they will create a football field on paper. Intermediate: Before the lesson, show students a clip from a football game to help them visualize the context for the Explore. Pause the clip intermittently to point out important features such as the football, the football field, helmets, etc. Advanced: Before the lesson, allow students to play a virtual football game to help them understand the sport mentioned in the Explore.”

• Scope 12: Measurement Conversions, Explore, Explore 2–Two-Step Measurement Conversions where students will solve two-step word problems using ratio reasoning to convert measurement units within the standard measurement system or within the metric measurement system. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use support from visual cues, peers, and teachers to develop vocabulary, language structure, and background knowledge needed to comprehend written text. Beginner: Prior to the lesson, use the word convert in several sentences along with diagrams or images. Then explain to students that today they will continue to convert one unit of measurement to another. Intermediate: As a pre-lesson activity, use the word convert in several sentences along with diagrams or images. Explain to students that today they will continue to convert one unit of measurement to another. Have students create a vocabulary square for the word convert. The four sections of the square should include, Definition, Sentence, Image, and Non-example. Provide the definitions for students and encourage them to rewrite the definition in their own words underneath. Advanced: As a pre-lesson activity, use the word convert in several sentences along with diagrams or images. Then explain to students that today they will continue to convert one unit of measurement to another. Have students create a vocabulary square for conversions. The four sections of the square should include, Definition, Sentence, Image, and Non-example.”

• Scope 16: Understand Variability, Explore, Explore 1–Variability in Data where Students will determine the difference between a statistical and a non-statistical question and explain that both require data but a statistical question has data that varies. There lies a Language Acquisition Supports segment that provides strategies for fostering students' language development. For example “Students will use support from visual cues, peers, and teachers to develop vocabulary, language structure, and background knowledge needed to comprehend written text. Beginner: As a pre-lesson activity, teach students the word survey by conducting a survey as a class. The question could be: What's your favorite color? Create a dot plot on the board as students share their responses. Explain that we're going to learn more about surveys as part of today's lesson. Intermediate: As a pre-lesson activity, read a short blurb about surveys to students then ask them how many times they heard the word survey read. Create a dot plot based on the range of guesses, then reveal the actual number. Advanced: As a post-lesson activity, give students two differently colored index cards. On one color index card will be written the word statistical and on the other color index card will be written the word nonstatistical. Show students a series of questions; students will choose which card to raise for each question. If there are discrepancies in cards raised, have students defend their answers.”

The materials reviewed for STEMscopes Math Grade 6 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 4: Coordinate Planes, Explore, Explore 2–Reflections on a Coordinate Plane, Description states,  “Students will work with a city map and find locations of buildings to determine the relationship between the signs of numbers and locations in quadrants. Students will determine ordered pairs that show reflections across one of the axes.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Building Location Cards (per group); 1 Exit Ticket (per student). Reusable: 2 Quart-sized resealable bags (per group); 1 Permanent marker (per class); 1 Set of colored pencils (per group). Consumable: 3 Card stock pages (per group, optional); 1 Large piece of white butcher paper (per group).” Preparation, “Print a set of the Building Location Cards for each group. Optionally, print on card stock and laminate for durability. Cut out Building Location Cards Part I, and place in a resealable bag labeled “Part I” for each group. Cut out Building Location Cards Part II, and place in a resealable bag labeled “Part II” for each group.” Procedure and Facilitation Points, “Give a set of colored pencils, the coordinate plane on butcher paper, and a Part I bag of the Building Location Cards Part I to each group.”

• Scope 9: Equations and Inequalities, Explore, Explore 2–Write and Solve Equations, Description states,  “Students will write and solve equations using properties to find the value of the variable.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Daily Deals Cards (per group); 1 Exit Ticket (per student). Reusable: 1 Projector or document camera (per class); 1 Resealable bag (per group).” Preparation, “Print one copy of the Daily Deals Cards per group. If desired, print on card stock and laminate for future use. Cut out the Daily Deals Cards, and place them in a resealable bag for each group. In the Procedure and Facilitation Points section it states “Give a set of Daily Deals Cards to each group.”

• Scope 10: Ratios, Rates, and Unit Rates, Explore, Explore 2–Ratio Tables and Graphs, Description states, “Students will reason, analyze, and create tables and graphs of ratios.” Materials, “Printed: 1 Student Journal (per student); 1 Set of Purchasing Fruit Bushes Cards (per group); 1 Exit Ticket (per student).” Preparation, “Print one set of Purchasing Fruit Bushes Cards for each group. If desired, print on card stock and laminate for future use. In the Procedure and Facilitation Points section it states "Give a Student Journal to each student and the Purchasing Fruit Bushes Cards – Part I to each group.”