3rd Grade - Gateway 3

The materials reviewed for STEMScopes Math Grade 3 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 4: Multiplication Models, Explore, Explore 1–Equal Groups, Procedure and Facilitation Points. Teachers do the following:  “1. Begin by projecting counters in a few groups with an equal number of counters in each group (Example: four groups of three counters). 2. DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means. 3. Give students 1 or 2 minutes to discuss among themselves, and then invite them to share with the class. 4. Ask students to write a sentence that describes what they see.” 

• Scope 9: Multiplication and Division Problem Solving, Home, Scope Overview, Teacher Guide, Engage Activities, Assessing Prior Knowledge.  Teachers will keep in mind that “to assess student understanding of multiplication and division problem solving, students will be presented with a scenario in which they have to decide if multiplication or division is the way to a solution. After discussing their decisions in small groups or partners, students justify their answer and explain why they were either right or wrong. If your students are struggling with previously taught concepts, use the Foundation Builder activity in this Scope to reinforce ideas presented in the APK.” 

• Scope 17: Equivalent Fractions, Explore, Explore 2–Modeling Equivalence with Number Lines, Procedure and Facilitation Points. Teachers will do the following: “Part I 1. Distribute the number line and 5 parchment paper strips to each student. Students will put the number line handout under each piece of parchment paper. 2. Ask students to lay the strip on top of the number lines and trace it onto each piece of parchment paper, each with a different color. 3. Explain that each piece will be folded into a different number of equal parts. 4. Model folding the number lines in the following ways: a. Halves, b. Thirds, c. Fourths, d. Sixths, e. Eighths.”

The materials reviewed for STEMScopes Math Grade 3 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: Addition and Subtraction Fluency, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states,  “In grade four, students extend their work with the base-ten system to become fluent and efficient with computation. Fourth-grade students begin to incorporate the standard algorithm as a representation for the processes of addition and subtraction. Fourth-grade students also use their understanding of place value and properties of operations to represent multiplication and division of multi-digit numbers.”

• Scope 8: Arithmetic Patterns, Home, Content Support, Current Scope. It states,  “Students identify patterns involving addition and multiplication and explain them using properties of operations. Students examine patterns within even numbers and multiples of even numbers. Students examine patterns within sums and products along the rows and columns of addition and multiplication charts. They observe that the order of two addends or factors does not affect the sum or product (Commutative Property).”

• Scope 11: Area in Square Units, Content Support, Misconceptions, and Obstacles. It states “When measuring, the properties of area and perimeter are confused. Students may not cover/construct the complete area with no gaps or overlaps. Area is misunderstood as the length of a line rather than the size of a surface. Students may have difficulty understanding that area is counted in square units.”

• Scope 17: Equivalent Fractions, Content Support, Coming Attractions. It states,  “Fifth grade continues the progression of equivalent fractions, using equivalent fractions as a strategy to add and subtract fractions. Students will solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators. Visual models or equations will represent the problem. Benchmark fractions, as well as number sense of fractions to estimate and assess the reasonableness of answers, will be utilized.”

The materials reviewed for STEMScopes Math Grade 3 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, states, “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 2: Addition and Subtraction Fluency, Home, Content Unwrapped, states to “Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.” Dissecting the Standard, “Verbs: What should students be doing? Add: To combine two or more numbers to calculate the total (sum) Subtract: To take away a number from another number to calculate the difference Nouns: What concrete words should students know? Algorithm: A step-by-step solution Strategy: A plan of action to find a solution Place value: The numerical value a number has, based on its position within a number Properties of operations: Attributes or characteristics of mathematical processes. Relationship (between addition and subtraction): The way two or more concepts or objects are connectedImplications for InstructionIn the past, students worked on a similar standard of adding and subtracting within 1,000 but were not expected to be fluent. Students have been asked to fluently add and subtract within 100 in the previous year. They have used place value understanding (including partial sums and differences), properties of operations, and the relationship between addition and subtraction. Adding and subtracting fluently implies that students are able to carry out the operations using written methods without relying on concrete objects. However, these can be used as part of an explanation and to continue to build understanding.”

• Scope 10: Problem Solve Using the Four Operations, Home, Scope Overview, Teacher Guide, Scope Summary, Vertical Alignment, Background Knowledge, Future Expectations, states the following information: “In this Scope, students will explore problem solving using the four operations, and identifying and explaining patterns in arithmetic. In this Scope, students will master how to solve multi-step word problems using the four operations; represent word problems solved using letters within equations to represent the unknown quantity; and use mental computation and estimation strategies to determine the reasonableness of answers.” Background Knowledge: “Kindergarten students lay the conceptual foundation of the meaning of addition and subtraction: to compose or decompose numbers. First grade develops multiple strategies for adding and subtracting whole numbers. Second grade develops fluency with addition and subtraction, solving one and two-step problems within 100 by applying their understanding of place value and the properties of operations.” Future Expectations: “This acts as the conceptual foundation for third grade, extending problem solving to all four operations. Fourth Grade expands the conceptual development of problem-solving to include multi-step problems using the four operations with whole numbers. Modeling how to interpret remainders is vital as students apply the academic concepts to real-world scenarios. They learn how to multiply or divide word problems involving multiplicative comparisons using drawings and equations with variables to represent the problem. Additionally, problem-solving is extended to the addition and subtraction of fractions and multiplication of fractions by a whole number. They use all four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and measurement conversions.”

The materials reviewed for STEMscopes Math Grade 3 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 3 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 3: Rounding, Elaborate, Fluency Builder–Guess My Number, Materials, “Printed, 1 Instruction Sheet (per pair), 1 Guess My Number Chart (per pair), 1 Number Line Sheet (per pair), 1 Student Recording Sheet (per player), Reusable, 1 Dry-erase marker (per pair)”

• Scope 9: Multiplication and Division Problem Solving, Explore, Explore 3-Model and Solve One- and Two-Step Problems, Materials, “Printed, 1 Student Journal (per student), 1 Set of Math Hunt Posters (per class), 1 Exit Ticket (per student), Reusable, Manipulatives: Counters, Tiles, Base ten blocks”

• Scope 16: Compose and Decompose Fractions into Units, Explore 1–Unit Fractions in a Whole, Materials, “Printed, 1 Student Journal (per student), 1 Exit Ticket (per student), 1 Set of Mystery Units (per group), Reusable, 1 Resealable plastic bag (per group)”

The materials reviewed for STEMScopes Math Grade 3 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 3, 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 4, provides a possible way a student might complete the problem. Students see a number line with 100, 157, and 200 labeled. “The number line shows the location of 157. What is 157 rounded to the nearest 100? Use the number line to explain your reasoning. (DOK-3), 200 Sample reasoning: 157 rounds to 200 because it is closer to 200 than it is to 100.” (3.NBT.1)

• Scope 14: Geometry, Standards-Based Assessment, Answer Key, Question 9 provides a possible solution a student might provide. Students see five shapes labeled A-E. In order, trapezoid, pentagon, rectangle, rhombus, and pentagon. “A group of figures is shown below. Sort the shapes into two groups, Group 1 and Group 2, based on their attributes. List the shapes that are in each group. Explain your reasoning. Write your answers in the box. (DOK-3), Answers vary. Sample response: Group 1: Shapes A, C, and D Group 2: Shapes B and E Shapes in Group 1 are quadrilaterals because they have 4 sides. Shapes in Group 2 are not quadrilaterals because they have 5 sides.”  (3.G.1)

• Scope 18: Compare Fractions, Intervention, Small-Group Intervention, Procedure and Facilitation Points states,  “3. Present different fraction combinations to the students and have them practice writing them in fraction notation. 4. Distribute the Fraction Card Sort. Have the students sort them into three groups: halves, thirds, and fourths. 5. Observe as students work. If students place the non-equal parts into the groups, explain that fractions are made up of equal parts. It would only be considered a half if both pieces are the same size. If they don’t put the non-equal parts into the group, ask them why.”

The materials reviewed for STEMscopes Math Grade 3 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: Multiplication Models, Evaluate, Standards-Based Assessment, Print Files, Student Handout, provides opportunities for students to demonstrate the full intent of the standard 3.OA.1, “Interpret products of whole numbers, e.g., interpret 5\times7 as the total number of objects in 5 groups of 7 objects each…” Item 2: “Charlie saw six flamingos at the zoo. Each flamingo has two legs, as shown below.” Picture of six flamingos shown. “Which expression can be used to find the total number of legs on the six flamingos? A. 6\div2 B. 6-2 C. 6+2 D. 6\times2.” Item 5: “This rectangular array represents multiplication.” A 6 by 5 array is shown. “Which expression corresponds with this array?  A. 5\times6;  B. 5\times5; C. 6\times6;  D. 6\times7”. Item 6: “The Sweet Candy Shop has 4 display shelves. Each shelf features 6 candies. Which two statements are true? A. The Sweet Candy Shop displays 6 groups of 4 candies.; B. The Sweet Candy Shop displays 4 groups of 6 candies.; C. The Sweet Candy Shop has a total of 24 candies.; D. The Sweet Candy Shop has a total of 10 candies.”

• Scope 12: Perimeter, Evaluate, Standards-Based Assessment, Question 8, provides students with an opportunity to demonstrate full intent of MP2, “Reason abstractly and quantitatively, as they reason abstractly and relate perimeter and area and the differences in their measurements.” “Arnav drew a rectangle with a perimeter of 18 inches. Which two answers could be possible areas for his rectangle? A. 20 square inches, B. 16 square inches, C. 18 square inches, D. 21 square inches”

• Scope 19: Time, Evaluate, Skills Quiz, Print Files, Student Handout, provides opportunities for students to demonstrate the full intent of the grade level standard, 3.MD.1, “Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.” Item two provides a clock and a digital time of 7:18 and asks students to draw the hands of the clock. Item 6 shows an analog clock with the time 3:47 and students are asked to write the digital time. Item 9, “Steven has to set up his project at the science fair by 11:30 a.m. If it takes him 15 minutes to check in and find his table and 30 minutes to set up his display, what time does he need to arrive at the science fair?” Following this question is a number line iterated and labeled every 15 minutes beginning at 9:45 and ending at 11:45.

The materials reviewed for STEMscopes Grade 3 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 2: Addition and Subtraction Fluency, Explore, Explore 4–Subtracting Using Number Line Strategies, Instructional Supports, “1. 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. 2.Students might benefit from using alternate models to show their thinking, such as drawing a base ten model. 3. Allow students to use manipulatives, base ten blocks, and place value disks as necessary.”

• Scope 18: Compare Fractions, Explore, Explore 2–Compare Fractions with Like Numerators, Instructional Supports, “1. If students are struggling to compare the given fractions, have students explain what they notice about the size of the pieces, such as comparing a third to an eighth. Encourage them to place their models on top of one another. They should notice that even though there are the same number of pieces (numerator), one model will be greater because each piece is larger. 2. Students may have a difficult time understanding that as the denominator gets bigger, the pieces get smaller. Model an example of this inverse relationship using manipulatives, such as \frac{2}{4} and \frac{2}{6}, pointing out the size of the pieces with each denominator. 3. It may be necessary to review key vocabulary, such as ‘numerator’ and ‘denominator’. 4. Some students may have difficulty completing number lines over the given fractions, and may find it helpful to draw a different model or use manipulatives to explain their thinking. 5. It may be necessary to remind students what each comparison symbol represents.”

The materials reviewed for STEMscopes Math Grade 3 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

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

• Scope 7: Multiply by Multiples of 10, Acceleration, Math Today–Bear Cub Recovery, Question 2 states, “This little cub weighed 8 pounds when she was born. If she will grow to weigh 40 times as much when she is an adult bear, how much will she weigh when fully grown? If 8\times4=32, then 8\times40= ___ pounds” 

• Scope 15: Fractions on a Number Line, Acceleration, Math Today–Concerns About Baby Food, Question 1 states,  “Six out of eight toddlers prefer foods that are high in sodium. Locate this quantity on the number line below.” Question 2, “One in four kids is overweight. Locate this quantity on the number line below.” Question 3, “One toddler ate a part of a sugar cookie as shown on the number line below. What fraction of the cookie did the child eat?  

• Scope 19: Time, Acceleration, Math Today–Ice Swimming, Question 1 states, “Lui Xialong arrived at the ice swimming hole at 8:15. Draw the hands on the clock below to show this time.” Question 2, “If Lui waited for his turn for 30 minutes, what time did he get in the pool? Show your work on the number line below.” Question 3, “Lui jogged and stretched for 15 minutes before getting into the pool. What time did he start jogging and stretching? Show your work on the number line below.”

The materials reviewed for STEMscopes Math Grade 3 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 material states, “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: Addition and Subtraction Fluency, Explore, Explore 2–Adding Using Number Line Strategies, Print Files, Printable Math Chat(Spanish) provides support for students who read, write, speak a different language than English to engage in the content. The following questions are written in Spanish on the Math Chat (Spanish) cards: “How did you decide how many jumps to use on the number line? Notice our number lines always started with the first number in our equation. Does it have to be done that way? How would you lead someone else through using this strategy to add?

• Scope 6: Multiplication and Division Strategies, Explain, Picture Vocabulary, Student Handout provides support for students who read, write, speak a different language than English to engage in the content. The handout provides visuals and explanations on the meaning of operations such as division where an equation is given, 15\div5=3 is shown along with a model of 3 circles with 5 dogs in each one and the explanation “To share or separate into equal groups or equal parts”.

• Scope 8: Arithmetic Patterns, Explore, Explore 1–Addition Patterns, 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 utilize personal backgrounds to comprehend English meanings.Ask students to describe three things that they have encountered that are arranged in a pattern. Have them discuss with a partner. Possible questions include the following: What is the item? What does the pattern look like? What math operation is the pattern using?”

The materials reviewed for STEMscopes Math Grade 3 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: Multiplication Models, Explore, Explore One–Equal Groups, Procedure and Facilitation Points states, “Begin by projecting counters in a few groups with an equal number of counters in each group (Example: four groups of three counters).DOK-1 Ask students to talk to their shoulder partners about what they see and what they think it means.Give students 1 or 2 minutes to discuss among themselves, and then invite them to share with the class.Student answers will vary but may include the following: We see four groups. Each group has three counters. All groups are equal. If we add all the counters together, we can get 12 counters.Distribute dry-erase markers and erasers to students.Ask students to write a sentence that describes what they see.Give students a few minutes to write their sentences. Walk around, looking out for students who are struggling.Ask students to share how they described the groups on the screen.Ask students to share their sentences and emphasize how each time a group is added, the total increases by the same number.”

• Scope 11: Area in Square Units, Explore, Explore 2–Counting Area in Square Units, Preparation and Print Files, Student Journal, provides for students’ active participation in content through the use of manipulatives. The journal contains 12 rectangles and rectilinear shapes along with square tiles that represent a given square measurement for students to use to find the area of figures by counting. The Preparation section states: “Make one copy of the Student Journal and an Exit Ticket for each student. Make one copy of Task Cards, on card stock if possible. Make one copy of Station Printouts, and laminate or put in a sheet protector for durability. Place the Task Cards around the room in the form of a gallery walk.Place Station Printouts in an accessible place for students to tile.Place a set of square tiles at each station.Group students into pairs. Go Digital! Have students explore or present their solutions using virtual manipulatives! The manipulatives used in this lesson can be found in the Explore drop-down menu and can be digitally assigned to students.”

• Scope 16: Compose and Decompose Fractions Into Units, Intervention, Procedure and Facilitation Points and Supplemental Aids–Fraction Strips, Print Files, Student Handout, Fraction Strips (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 fractions, Explaining fractional parts, Counting fractional parts, Representing fractions, Composing and decomposing fractions, Finding equivalent fractions, Comparing fractions, Adding and subtracting fractions, Multiplying and dividing fractions. If 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.”