4th Grade - Gateway 3

The materials reviewed for STEMScopes Math Grade 4 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 3: Rounding, Explore, Explore 1–Money in the Bank!, Procedure and Facilitation Points, provides teacher guidance. “Part I 1. Have students gather around the number line with multiples of 1,000. Ask the following question: DOK-1 What multiples does this number line show? 2. Read the following scenario: You and your group have started a toy business. The number on which your beanbag lands is the amount you will report as your estimated savings each week from the sales of your toys. You need an estimate of your business’s profit - how much money you are able to save each week–in order to be able to buy more materials to make new toys. 3. Ask the following questions: DOK-2 When we want an estimate, what can we do? DOK-2 When is rounding numbers useful? 4. Choose one student from each group to demonstrate how to toss the beanbag onto the 1,000 number line.” 

• Scope 10: Multiply Fractions by Whole Numbers, Home, Scope Overview, Teacher Guide, Engage Activities, Assessing Prior Knowledge. Teachers, “Before beginning the lesson, students’ prior knowledge is assessed. The teacher assesses using visual models to represent multiplication. Students will choose a visual model such as an area model, array, or bar model to solve a real-world problem.” 

• Scope 17: Problem Solve Using the Four Operations, Explore, Explore 4–Problem Solve Using the Four Operations (Level 3), Procedure and Facilitation Points. Teachers follow these steps:  “1. Distribute a resealable bag of Scenario Cards to each pair. 2. Distribute a Student Journal, a whiteboard, and a dry erase marker to each student. 3. Tell students that for every problem, they will need to draw a strip diagram on their whiteboards, build an equation using a letter for an unknown quantity (maybe even two letters for two unknown quantities!), estimate the solution, and then solve. 4. Remind students to take their time and do one step at a time.”

The materials reviewed for STEMScopes Math Grade 4 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: Rounding, Home, Content Overview, Teacher Guide, Scope Summary. It states, “In this Scope, students learn how to use place value understanding to round multi-digit whole numbers to any place collaboratively with real-world scenarios.”

• Scope 8: Equivalent Fractions, Home, Content Support, Current Scope. It states, “Students will use visual models such as area models and number lines as they generate and explain equivalent fractions. Fractions include denominators of 2, 3, 4, 5, 6, 8, 10, and 100. Students will express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100. This is used in a problem-solving context.”

• Scope 14: Division Models and Strategies, Home, Content Support, Coming Attractions. It states, “Grade five extends division to two-digit divisors and includes dividends with decimals to hundredths. They continue using concrete models or drawings based on place value and the properties of operations. Students relate a division strategy to a written method, consistently checking the reasonableness of their solutions. Sixth grade applies and extends students’ understanding of division to divide fractions by fractions. They fluently divide multi-digit numbers and decimals using the standard algorithm.”

• Scope 22: Generating Patterns, Content Overview, Future Expectations. It states,  “In fifth grade, students generate two numerical patterns using two given rules, and they identify relationships between the corresponding terms. Fifth-grade students form ordered pairs of the corresponding terms and graph them on a coordinate plane.”

The materials reviewed for STEMScopes Math Grade 4 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 K-5, 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 3: Rounding, Home, Content Unwrapped, Implications for Instruction, states that “Learners often confuse estimation with guessing. Estimation involves reasoning and thought. When possible, include real-world situations in which estimation would be used. Prior to this grade level, students have rounded to the nearest 10 or 100 to estimate solutions to addition and subtraction problems.Students often try to memorize “rounding rules” to know when to round. However, this often does not provide them with a purpose for rounding. Rounding should be presented in contextual situations with an emphasis on the reasoning skills associated with it. It would be beneficial to identify conceptual misunderstandings of place value.Students will be rounding numbers up to 1,000,000 to any place value. Typically, they have an easier time rounding to place values in the outermost left and often struggle when rounding to place values in the middle of a number.”

• Scope 15: Prime and Composite, Home, Key Concepts, Key Concepts, states “I can demonstrate an understanding of the relationship between factors and multiples of whole numbers. I can distinguish between a prime number and a composite number. I can use a variety of strategies and tools (build rectangular arrays and area models, use a hundreds chart, use counters) to find all the factor pairs of a number in the range 1–100, and I can use the number of factor pairs to determine if the number is prime or composite. I can notice patterns within the multiples of numbers on a hundreds chart. I can generate multiples by skip counting by each factor, and I can keep track of the number of factors within the number. I can recognize that a whole number is a multiple of each of its factors.”

The materials reviewed for STEMscopes Math Grade 4 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The Teacher Toolbox contains an Elementary 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 4 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Teacher Toolbox provides an Elementary Materials List that provides a spreadsheet with tabs for each grade level, K-5. Each tab lists the materials needed for each activity. 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: Represent and Compare Decimals, Elaborate, Fluency Builder–Who is the Greatest?, Materials, “Printed, 1 Instruction Sheet (per pair), 1 Set of Digit Cards (per pair), 1 Work Mat and Recording Sheet (per student), Consumable, 1 Bag or envelope (per group)”

• Scope 10: Multiply Fractions by Whole Numbers, Explore, Explore 2–Multiplying Multiples of Unit Fractions, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), 2 Sets of Station Cards (per class), Reusable, 18 Sets of fraction tiles (per class), 10 Sets of fraction circles (per class), 8 Rulers (per class),Consumable, 2 Strips of manila paper, measuring 3 x 18 inches (per student), 2 Dispensers with clear tape (per class)”

• Scope 15: Prime and Composite Numbers, Explore, Explore1–Finding Factor Pairs, Materials, “Printed, 1 Student Journal (per student), 1 Set of Scenario Cards (per group), 1 Exit Ticket (per student), Reusable, 100 Color tiles (per station)”

The materials reviewed for STEMScopes Math Grade 4 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 4, 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: Rounding, Evaluate, Standards-Based Assessment, Answer Key, Question 2, provides a possible way a student might complete the problem. “What is 323 rounded to the nearest ten? Use the number line to explain your thinking. (DOK-3) 323 rounded to the nearest ten is 320, because it is closer to that value than it is to 330.”  (4.NBT.3)

• Scope 12: Represent Measurements with Line Plots, Evaluate, Standards-Based Assessment, Answer Key, Question 8, Part B, provides a possible solution a student might provide. “How many textbooks weigh less than one pound? Write your answer in the box. Use equations or text to justify your answer. (DOK-3), 7 textbooks Sample reasoning: There are two dots above one-fourth, one dot above three-eights, three dots above one-half, and one dot above three-fourths. 2+1+3+1=7.” (4.MD.4)

• Scope 17: Problem Solving Using the Four Operations, Intervention, Small-Group Intervention states, “Part I: Addition and Subtraction, 1. Read the following word problem to the group: a. Jasmine has a goal to read 345 pages in a chapter book over a four-day period. She reads 50 pages on Monday, 66 pages on Tuesday, and 140 pages on Wednesday. How many pages will Jasmine need to read on Thursday to reach her goal of 355 pages? 2. Allow time for students to discuss the word problem in their pairs. 3. Ask the following questions: a. What is the question asking us to find? It’s asking how many pages Jasmine needs to read on Thursday to reach her goal of 345 pages. B. What information is needed to solve the problem? She read 50 pages on Monday, 66 pages on Tuesday, and 140 pages on Wednesday. 4. Distribute the whiteboard materials to the students and prompt them to draw a long rectangle on their board…”

The materials reviewed for STEMscopes Math Grade 4 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 5: Represent and Compare Decimals, Evaluate, Skills Quiz, Question 3 and 6, provides opportunities for students to demonstrate the full intent of MP7, “Look for and make use of structure, as they look for patterns when converting decimals to fractions noting the tenths and hundredths.” “Convert each decimal to a fraction. 3. 0.1 = ___, 6. 0.85 = ___”

• Scope 16: Multiplicative Comparisons in Multiplication and Division, Evaluate, Standards- Based Assessment, Print Files, Student Handout, provides opportunities for students to demonstrate the full intent of the standard, 4.OA.2, “Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.” “Read each question. Then follow the directions to answer each question. Mark your answers by circling the correct answer choices. If a question asks you to show or explain your work, you must do so to receive full credit.” Question one: “1. Atticus and Nina kept track of how many text messages they each received in one day. Atticus received 20 text messages, while Nina received 5. Which two statements are correct? A. Atticus received 4 times as many messages as Nina. B. Atticus received 15 times as many messages as Nina. C. Atticus received 15 more messages than Nina. D. Nina received one-fifth of the number of messages as Atticus.” Question 2: “ Scott has 2 surfboards. His son has 3 more than he has. Which equation represents the number of surfboards Scott’s son has? A. 2\times3=n B. n+3=2 C. n+2=3 D. 2+3=n”. Question 5, “A multiplicative comparison is shown below.” A bar model with 4 equal size boxes with 7 labeled in each one and a second bar below that with one 7 labeled in the box. “Which three statements describe this comparison? A. 28 is 4 times as much as 7. B. There are 5 sevens in 28. C. 7 is one-fourth of the value of 28. D. 7\times4=28”.

• Scope 19: Angles, Explore, Explore 1, Print Files, Exit ticket, provides opportunities for students to demonstrate the full intent of the standard 4.MD.5a, An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through \frac{1}{360} of a circle is called a "one-degree angle," and can be used to measure angles. “Design your best dance moves by using at least one whole-circle turn, one straight-angle turn, and one right-angle turn! Draw each angle and label it with its name, degree measure, and fraction of a circle.” Below the directions are 6 boxes connected with arrows for students to complete.

The materials reviewed for STEMscopes Grade 4 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: Represent and Compare Decimals, Explore, Explore 3–Represent and Compare Decimals, Instructional Supports states, “1. If students are struggling with the process of comparing decimals, remind students that the instructions ask them to cover each place value with a sheet of paper, working from left to right. It may be necessary to provide examples with smaller numbers, starting with whole-number examples first and working toward the tenths place, to ensure they understand the process. Ensure students understand that the decimal points must always be aligned vertically so that each place value is in line properly. 2. If students are struggling with writing a comparison statement using symbols, revisit the prerequisite skill of comparing only one decimal. Then have them try comparing two decimals. 3. If students are struggling with the greater-than and less-than symbols, it might be helpful to present the concept in multiple ways. First, draw pictures of two groups of objects on the board with space between them. Have three sticky notes available on which you’ve drawn <, >, and =. Ask students which group has more (greater than), and put the appropriate sticky note between the groups. Repeat for less than and equal to. Explain that the symbol always opens to the number that is greater. You could also make a game by writing two numbers on the board and asking students to write the correct symbol on their personal whiteboards and hold them up. 4. If a student is struggling with creating his or her own number line, provide the student with a premade number line with benchmark numbers labeled.”

• Scope 19: Angles,  Explore, Explore 4–Additive Angles, Instructions Supports states, “1. If students are struggling to understand the concept of adjacent angles, it might be helpful to demonstrate using the cut paper plates from Explore 1. 2. Some students may benefit from using the 90-degree and 180-degree paper plate cutouts when determining angles. The frame decorations could be laid on top of the paper plate pieces. 3. Remind students that it might be easier to rotate their cutouts while they measure the angles, rather than try to read a protractor that’s at an awkward angle. 4. For Part II, some students may find it beneficial to use base ten blocks or other manipulatives to help them add and subtract the angle measurements.”

The materials reviewed for STEMscopes Math Grade 4 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 9: Add and Subtract Fractions and Mixed Numbers, Acceleration, Math Today–Winbot, Question 3 states,  “A company bought a Winbot for their office building. The company has two buildings that have eight windows each that need window cleaning. On Day 1 the Winbot cleaned 1\frac{3}{8} of the windows on the buildings. How much of the windows does the Winbot still need to clean?”

• Scope 15: Prime and Composite Numbers, Acceleration, Math Today–Melting Away,  Question 1 states, “One of the lakes the melting glaciers feeds into in Peru is Lake Palcacocha. The volume of this lake is 34 times what it was in 1947. Is 34 a prime or composite number? Explain your reasoning.”  Question 2, “Rising water levels in places such as Lake Palcacocha have increased the size of lakes and decreased the amount of land. The lake covers the land at a rate of 25 square feet per year. Is 25 a prime or composite number? Explain your reasoning.” 

• Scope 21: Properties of Two-Dimensional Figures, Acceleration, Math Today–Washington Monument, Question 1 states, “What type of angle is formed by two adjacent blades of the helicopter?” Question 2, Can a line of symmetry be drawn in the shape that makes up the top section of the monument? If so, draw the shape and the line of symmetry.” Question 3, “The tall, non triangular shape that makes up most of the monument has vertical edges. Are these edges parallel? Explain your answer?” Question 4, “A structure is being built to honor you! Draw and label a blueprint of your structure below. You must include one quadrilateral with at least one set of parallel sides, one acute angle, and one obtuse angle. Your structure must have symmetry. Your structure must also include a right triangle.”

The materials reviewed for STEMscopes Math Grade 4 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 4: Addition and Subtraction Algorithms, Explore, Explore 1–Multi-Digit Addition, Language Acquisition Strategy provides support for students who read, write, speak a different language than English to engage in the content. “The following Language Acquisition Strategy is supported in this Explore activity. See below for ways to support a student's English language development. Students apply a variety of different learning strategies, such as asking for assistance, interpreting nonverbal cues, and using context clues to derive and describe the meaning of unknown words.During discussion, check for understanding of the following words: modeling, strategy, algorithm, sum, and difference. Challenge students to come up with their own definitions and descriptions of these terms in their groups.Teach students the self-advocacy skills of requesting assistance, learning how to interpret body language or facial expressions that aren't necessarily spoken, and having students repeat back to you or each other what they understand a word or phrase to mean. This allows you to check for understanding. It also gives the students an opportunity to use the new words in sentences and receive specific feedback.”

• Scope 6: Compose and Decompose Fractions and Mixed Numbers, Explore, Explore 1–Joining and Separating Parts of a Whole, Language Acquisition Strategy provides support for students who read, write, speak a different language than English to engage in the content. “The following Language Acquisition Strategy is supported in this Explore activity. See below for ways to support a student's English language development. Students learn to spell English words correctly using patterns and English rules with continued accuracy and improvement. After the lesson, have students create a word cloud of the most commonly used terms in the lesson. The more they used the word in their answers, the bigger the word will be in the cloud. Say the words fourths, sixths, eighths, etc. to the class. Let the students listen to the sounds in the word. Have the students practice speaking the words with a partner and take turns listening and speaking.”

• Scope 15: Prime and Composite Numbers, Explain, Picture Vocabulary, Flash Cards, Student Handout provides support for students who read, write, speak a different language than English to engage in the content. The student handout provides models and explanations in terms such as factors and multiples for students to understand. This resource is also available in Spanish.

The materials reviewed for STEMscopes Math Grade 4 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: Represent and Compare Decimals, Explore, Virtual Manipulatives–Base Ten Blocks  provides virtual base ten block manipulatives to support students as they represent and compare decimals. 

• Scope 8: Division Models and Strategies, Explore, Skills Basics–Ways to Represent Division, Procedure and Facilitation Points provides for students’ active participation in content through the use of manipulatives. “Give one Strategy Work Mat, a set of counters, one dry-erase marker, and one dry-erase eraser to each student.Read the following scenario to the class: Tyra baked 48 delicious sugar cookies for the school bake sale. When she got ready to put an equal number of cookies in bags, she realized she only had 8 bags. How many cookies must she be able to put in each bag?.... The first strategy is the equal groups and shares strategy. Instruct students to count out 48 counters. Explain that in order to use the equal groups and shares strategy, we need to equally share the dividend amount of 48 counters among 8 groups.Under “Division Models” on the Strategy Work Mat, instruct students to draw 8 large circles to represent the groups. Place one counter in each of the 8 circles. Instruct students to repeat this process until all 48 counters have been placed in the circles.Discuss the following questions:(Point to a circle.) How many counters are in this circle? 6 (Point to another circle.) How many counters are in this circle? 6 Continue pointing to the remaining circles and asking students how many counters are in each circle.Point out that each circle contains an equal number of counters. Explain that when dividing an amount into groups, the amounts in each group have to be equal.Discuss the following question:How many cookies will Tyra need to put in each bag? 6”

• Scope 10: Multiplying Fractions by Whole Numbers, Intervention, Supplemental Aids, Procedure and Facilitation Points along with Print Files, Student Handout–1,2,3,4,6,8 provides for students’ active participation in content through the use of manipulatives. Procedure and Facilitation Points: “The Student Handouts contain a variety of fraction strips. These can be used to reinforce the following fraction concepts:Identifying fractionsExplaining fractional partsCounting fractional partsRepresenting fractionsComposing and decomposing fractionsFinding equivalent fractionsComparing fractionsAdding and subtracting fractionsMultiplying and dividing fractionsIf possible, provide a laminated copy of the fraction strips for each student. The students may then use dry-erase markers to shade and identify various fractions.Encourage students to draw fraction strips at the top of their paper or assessment as a reminder when working with fractions.” These instructions are used in conjunction with the Student Handout - 1,2,3,4,6,8 where fraction strips are provided for halves, thirds, fourths, sixths and eighths are provided but not labeled.”