Kindergarten - Gateway 3

The materials reviewed for STEMScopes Math Kindergarten 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. 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: Compare Numbers to 10, Explain, Show What You Know–Part 1: Generate a Number That is One More or One Less, Procedure and Facilitation Points, provides teacher guidance. “1. Reading assistance may be needed for some students to complete this activity. 2. Students should individually complete the Show What You Know activity that correlates with the Explore activity already completed. 3. Provide manipulatives as needed, especially those manipulatives used in the Explore. 4. This element can be used to assess whether intervention is needed for each student.”

• Scope 8: Three-Dimensional Solids, Elaborate, Spiraled Review–The Airplane Trip, Procedure and Facilitation Points, guides the teacher when using materials during this activity. “1. You may need to provide reading assistance in order for some students to complete this activity. 2. Read the story on the first page to engage student interest before moving on to the questions. 3. Use this spiraled review as a warm-up in class, or send it home for homework, but be sure to discuss answers and strategies with the class as a whole group. 4. Refer to the standard in the lower right-hand corner of each question box to assess the students’ content knowledge or need for further intervention.”

• Scope 11: Data Analysis, Explore, Explore 2–Labeling a Sort and Drawing Conclusions, Preparation, guides the teacher as they prepare for the lesson. “1. Plan to have students work in 5 groups to complete this activity.  Gather baskets for the stations. The scenario suggests using small baskets to sort the objects. If baskets are not readily available, use a different type of container and explain to students during the lesson that these containers represent the baskets. Tape one index card to the front of each basket to represent the labels. If possible, laminate the index cards before attaching them to the baskets, and provide a dry-erase marker at each station so students can write on the labels. Prepare baskets for each station as listed below: Station 1: 3 large rubber bands in one basket, 7 small rubber bands in one basket, Station 2: 3 crayons in one basket, 2 markers in one basket, 5 colored pencils in one basket, Station 3: 4 pennies in one basket, 1 nickel/3 dimes/2 quarters in one basket, Station 4: 2 blue chenille stems in one basket, 1 red chenille stem in one basket, 4 black chenille stems in one basket, 3 green chenille stems in one basket, Station 5: 3 square attribute blocks in one basket, 5 triangle attribute blocks in one basket, 2 circle attribute blocks in one basket, Print the Student Journal and Exit Ticket for each student.”

The materials reviewed for STEMScopes Math Kindergarten 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: Represent Numbers to 10, Home, Content Overview, Teacher Guide, Scope Summary.  It states “Within this Scope, students focus on expectations and concepts surrounding how to represent numbers to 10. Specifically, students will participate in various activities and explorations to master how to count from a given number going forward; write a specific set of numbers and represent objects provided as a written numeral; count and tell the number of objects counted based on the last number said or the order the objects are counted or arranged. Finally, students will learn how to add and subtract numbers that make 10, use various methods to aid in solving addition and subtraction problems, and record answers appropriately.”

• Scope 5: Join and Separate, Home, Content Support, Coming Attractions. It states, “In first grade, students develop an understanding that a unit called a ten is composed of ten ones. They learn to efficiently compose and decompose tens. First-grade students use this knowledge to develop base-ten methods to solve problems involving addition and subtraction within 20.”

• Scope 9: Create and Compose 2-D Shapes and 3-D Solids, Home, Content Support, Coming Attractions. It states, “In second grade, students continue to recognize attributes of triangles, quadrilaterals, pentagons, hexagons, and cubes. Second-grade students partition a rectangle into rows and columns of same-size squares and determine the total amount of unit squares, and they partition circles and rectangles into halves, thirds, and fourths.”

• Scope 10: Measurement, Content Support, Misconceptions and Obstacles. It states, “Students may not recognize 0 as a number. Zero represents the number of items left when all items have been taken away. Avoid using the word none to represent this situation. Students may write numbers backward. Students may have difficulty counting forward from a number that is not 1. Students may struggle with one-to-one correspondence, the concept that a number represents a quantity. Students may need practice with understanding that the last number said while counting objects represents the number of objects. Students may find it easier to count real objects and may struggle when counting pictures. When counting real objects, students can move and touch them, but the pictures are stagnant, and students may need to develop strategies such as crossing out while counting. Students need to develop strategies for counting objects: not counting them more than once and not leaving some out. Initially, students might think of counting as a string of words, but gradually they will transition to using counting as a tool to describe amounts in their world.”

The materials reviewed for STEMScopes Math Kindergarten 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 6: Represent Numbers to at Least 20, Home, Scope Overview, Teacher Guide, Scope Summary. It states, “For this Scope, students focus on expectations to help them understand how to represent numbers to at least 20. Students will participate in the activities and explorations within to gain mastery in: counting from a number within a sequence; writing and representing numbers from 0 to 20; understanding that when counting out loud the last number said is the total counted; and lastly, understanding using various methods how to compose, decompose, and record responses to equations with the numbers 11 to 19.”

• Scope 10: Measurement, Home, Content Unwrapped, Standards. It states, “Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.”

The materials reviewed for STEMscopes Math Kindergarten 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, “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 Kindergarten 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 2: Count Objects, Elaborate, Fluency Builder–Count Objects to Ten, Materials, “Printed 1 Instruction Sheet (per pair), 1 Set of Match Cards (per pair), 1 Student Recording Sheet (per student), Reusable, 1 Envelope or resealable bag (per pair).”

• Scope 5: Join and Separate, Explore, Explore 4–Writing Equations and Explaining Strategies, Materials, “Printed, 1 Student Journal (per student), 1 Task Cards (per teacher) (optional), 1 Exit Ticket (per student), Reusable, 8 Red trapezoid pattern blocks (per student), 5 Blue rhombus pattern blocks (per student), 2 Yellow hexagon pattern blocks (per student), 6 Orange square pattern blocks (per student), 3 Green triangle pattern blocks (per student), 1 Quart-size resealable bag (per student) , 1 Box of crayons (per student or group), 1 Projector or document camera (per teacher)” 

• Scope 10: Measurement, Explore, Explore 2–Comparing Length, Materials, “Printed, 1 Student Journal (per student), 1 Evidence Footprint (per group), 1 Suspect Footprints (per group), 1 Exit Ticket (per student), Reusable, 1 Large resealable bag (per group), 25 Linking cubes (per group), Consumable, 2 Different colors of cardstock (per group)”

The materials reviewed for STEMScopes Math Kindergarten 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 Kindergarten, an Observation Checklist is provided for teachers to utilize as students complete work within the Explore activities of each Scope. Each Scope provides a Show What You Know, Procedure and Facilitation Points, “This element can be used to assess whether intervention is needed for each student.” In addition, students complete Show and Tell assessments, and an Interview Rubric for the teacher to use with each student. 

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 4: Compare Numbers to 10, Evaluate, Observation Checklist, Procedure and Facilitation Points, states the following: “1. As students are working through the Explores for each Scope, take note of what you observe for each standard breakout. 2. This is a good place to document accommodations/modifications used during the Explores, as well as documentation for standards-based report cards.” An Observation Checklist provides a table with the headings, Skill, Where to Observe, and Notes, “Skill, Where to Observe, Notes, Understand that each successive number name refers to a quantity that is one larger. Explore 1, Explore 2, Explore 3 Identify whether the number of objects in one group is greater than the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to 10 objects). Explore 2, Explore 3, Identify whether the number of objects in one group is less than the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to 10 objects). Explore 2, Explore 3, Identify whether the number of objects in one group is equal to the number of objects in another group, e.g., by using matching and counting strategies (include groups with up to 10 objects). Explore 2, Explore 3, Compare two numbers between 1 and 10 presented as written numerals. Explore 3” (K.CC.4c)

• Scope 10: Measurement, Evaluate, Show and Tell, Procedure and Facilitation Points and Interview Rubric, provide teachers with opportunities to evaluate student learning. In Procedure and Facilitation Points, the following is stated:  “1. Meet with each student or group of students at a table separate from the class. 2. Read each Teacher Prompt card, and observe each student as they follow the directions. 3. Ask students to record their thinking on the Student Cards if applicable. 4. Evaluate each student’s performance of the task using the rubric.” The Interview Rubric provides the teacher with a checklist of the work students are to complete as well as points assigned to each item students complete. For example, it states, “1. Identify attribute being measured with modeling clay and balance. Student responds orally with weight (3 points). OR Student responds orally with synonym or explanation (2 points). 2. Identify attribute being measured with scissors and teddy bear counters. Student responds orally with length (3 points). OR Student responds orally with synonym or explanation (2 points). 3. Identify attribute being measured with water and cups. Student responds orally with capacity (3 points). OR  Student responds orally with synonym or explanation (2 points). 4. Describe measurable attributes of an object. Student responds orally with weight, height, and length (3 points). Score: ____/ 12” (K.MD.1)

• Scope 11: Data Analysis, Intervention, Small-Group Intervention, Procedure and Facilitation Points states, “Part I, 1. Have students work in pairs. 2. Distribute bags of manipulatives to pairs of students, and instruct students to discuss the similarities and differences between the objects (size, color, type). 3. Ask students to sort the items in the bag in 3 different ways. Watch and listen to each pair as they sort.”

The materials reviewed for STEMscopes Math Kindergarten 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, Observation Checklists, Show What You Know, Skills Quiz, Technology-Enhanced Questions, and Show-and-Tell Assessments. 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: Compare Numbers to 10, Explore, Explore 2–Compare Sets, Exit Ticket, allows students to demonstrate the full intent of K.CC.6., “Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.” “Count the (linking cubes) in each set. Write the number. Compare the numbers.” Given pictures of 5 linking cubes and 6 linking cubes. “Circle the number that is greater. ___, ___. ___ is greater than ___.” Given pictures for 7 linking cubes and 3 linking cubes, “Circle the number that is less.___, ___. ___ is less than ___.”

• Scope 6: Represent Numbers to at Least 20, Explore 2–Counting Objects and Organizing Counts, allows students to demonstrate the full intent of MP2, “Reason abstractly and quantitatively: Students recognize that a number represents a specific quantity. Then they represent that quantity using the written numeral.” Explain, Show What You Know–Part 2: Counting Objects and Organizing Counts, Procedure and Facilitation Points, “1. Reading assistance may be needed for some students to complete this activity. 2. Students should individually complete the Show What You Know activity that correlates with the Explore activity already completed. 3. Provide manipulatives as needed, especially those manipulatives used in the Explore. 4. This element can be used to assess whether intervention is needed for each student.” Question 1, given pictures of 12 shirts organized into 10 frames, “Count the objects. Write the number of each object. I counted ____ (picture of shirt).”

• Scope 10: Measurement, Evaluate, Observation Checklist, allows students to demonstrate the full intent of K.MD.1, “Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. Description, “The teacher is provided a breakdown of the scope to use as a formative assessment for each student.” Preparation, “Print a copy of the Observation Checklist for each student.” Procedure and Facilitation Points, “1. As students are working through the Explores for each scope, take note of what you observe for each standard breakout. 2. This is a good place to document accommodations/modifications used during the Explores, as well as documentation for standards-based report cards.” Observation Checklist has a table with columns labeled, Skill,  Where to Observe, and Notes. “Describe measurable attributes of objects, such as length or weight. Explore 1, Explore 2, Explore 3, Explore 4, Explore 5. ____”

The materials reviewed for STEMscopes Kindergarten 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 7: Two-Dimensional Shapes, Intervention, Small-Group Intervention provides “a reteach activity that supports student understanding of the concept by reviewing a past skill or reteaching the current skill. It states,  “Description: Students sort regular and irregular two-dimensional shapes into groups; name two-dimensional shapes, including circles, triangles, squares, rectangles, and hexagons; classify and identify attributes of two-dimensional shapes by using informal and formal geometric language interchangeably, regardless of orientation or size; distinguish between examples and nonexamples of two-dimensional shapes based on their attributes; and describe objects in the environment by using shape names and their relative positions.”

• Scope 10: Measurement, Explore, Explore 5–Comparing Weight, Instructional Supports provides the following: ”1. Review key terms (heaviest, heavier, lighter than, less than,etc.) from the Student Journal at the beginning of the lesson. 2. Be sure to complete the Skill Basics prior to beginning this Explore. If students are still having a difficult time using the balance scale, model for students using this tool at the beginning of the lesson, and practice as a whole group.”

The materials reviewed for STEMscopes Math Kindergarten 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 1: Count Objects, Acceleration, Connection Station–Community Helper Counting, Question 1 states, “How does a firefighter help the community? Discuss with your partner, and then count how many fires were fought in one day.” Question 2, “How does a teacher help the community? Discuss with your partner, and then count how many students are in the class.” 

• Scope 6: Represent Numbers to at Least 20, Acceleration, Math Today–Bubble Art Exhibit, Question 1, “Start at the given number and count up to find the total number of bubbles. ___ bubbles” Question 2, “Count the bubbles. ___ bubbles ___ bubbles.” 

• Scope 11: Data Analysis, Acceleration, Math Today–World’s Largest Easter Egg Hunt states, “At the world’s largest Easter egg hunt, which is in Illinois, children hurried around trying to find as many eggs as possible because prizes included a $1,000 US savings bond, a cruise to the Bahamas, and candy! The Easter eggs were all different sizes. Here are the eggs Emily found. Question 1, Sort the different sizes of eggs into groups from smallest to largest. Draw a picture and include the number of eggs in each category.”

The materials reviewed for STEMscopes Math Kindergarten 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: Compare Numbers to 10, Explore, Explore 3–Compare Numerals, Language Acquisition Strategy, provides guidance for students using a different language. “The following Language Acquisition Strategy is supported in this Explore activity. See the strategies below for ways to support a student's language development. Students will share information with their peers while participating in a cooperative learning activity. Beginner: Model correct pronunciation of words used in the scenario and have students repeat. Read each sentence stem and have students fill in or repeat the correct number.”

• Scope 7: Two-Dimensional Shapes, Explain, Picture Vocabulary, provides key mathematical words in Spanish. A picture of a circle is shown, “Circulo.”

• Scope 11: Data Analysis, Explore, Explore 1–Sorting Objects, Exit Ticket, is provided in Spanish. Students sorting clothes. “Clasificar objetos Boleto de salida Recorta las imágenes. Clasifica la ropa en tres secciones. Coloca la ropa que clasificaste en uno de los estantes. Escribe nombres en los estantes para explicar cómo clasificaste la ropa.”

The materials reviewed for STEMscopes Math Kindergarten 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 3: Represent Numbers to 10, Explore, Virtual Manipulative–Color Tiles, provides a virtual set of manipulatives of different color tiles to use for counting. 

• Scope 7: Two-Dimensional Shapes, Intervention, Supplemental Aids–Math Shapes, Procedure and Facilitation Points states,  “This Student Handout contains a variety of two-dimensional shapes. It can be used to reinforce the following geometry concepts: Classifying and sorting, Identifying attributes that define shapes, Identifying shapes, Identifying lines of symmetry, Identifying angles within shapes, Identifying parallel and perpendicular lines, If possible, provide a laminated copy of the assorted shapes for each student. The students may then use dry-erase markers to classify and identify properties in a variety of situations.”

• Scope 10: Measurement, Explore, Skills Basics–How to Use a Balance Scale, Procedural and Facilitation Points states,  “1. Gather students in a whole-group seating arrangement, ensuring that all students can see you and an assortment of school supplies. 2. Hold up the balance scale, and ask students to share what they know about the balance scale. Guide the conversation by asking the following questions: a. What can a balance scale be used for? A balance scale is used to weigh items. b. How do you think this scale works? The scale moves when you put stuff in the buckets. c. What movement does the scale make? The scale moves up and down. 3. Tell students they will be voting on which items they think are heavier or lighter. 4. Distribute one Balance Ballot to each student. 5. Explain to students that scale balances work by moving up and down. (Demonstrate the movement using the scale.) 6. Inform students that when one side is heavier, that side will go down and the lighter side will stay in the air. If the sides weigh the same amount, then the sides will be even. Explain that this movement can tell us about an object’s weight. If an object is on the side that goes down, that means it is heavier than the other object. If an object is on the side that goes up, that means it is lighter than the other object. 7. Chant, “Heavy plops down, and light stays off the ground.” Encourage students to chorally say the chant.”