2nd Grade - Gateway 3

The materials reviewed for STEMScopes Math Grade 2 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: Compare Numbers to 1,000, Engage, Foundation Builder, Preparation. Teachers “plan to have students work with partners to complete this activity. Prepare to project the Slideshow for students. Print the Student Handout for each pair of students. Gather a set of base ten blocks for each pair, and place them in a resealable bag: 1 flat, 20 rods, and 20 units.”

• Scope 9: Arrays, Explore, Explore 1–Arrays with Concrete Objects, Procedure and Facilitation Points. Teachers will do the following:  “Part I, 1. Read the following scenario: The STEMScopes Toy Factory needs to package up the toys to distribute to all the local toy stores in the next week. The Toy Factory noticed that some of the packages don’t have labels that tell the customer how many toys are in each package. Can you help the toy factory prepare to distribute all the toys and meet its deadline? 2. Divide students into groups of 3 to 4, and place each group at a station. 3. Direct students’ attention to the array at their station. Allow students a few moments to discuss the manipulatives without touching or moving the array. 4. Instruct students to count the objects in the array. Encourage students to discuss the different counting strategies that can be used with their group. 5. Monitor and talk with students as needed to check for understanding using guided questions. Ask the following questions: a. DOK-1 How many objects make up your array? Answers will vary. For example, there are 10 buttons. B. DOK-2 How did you count the objects? Answers will vary. For example, we skip counted by twos. C. DOK-3 Is there another way to count the objects? Answers will vary. For example, we could add 5+5 to get 10. 6. Give each student a copy of the Student Journal, and direct students' attention to Part I. Ask students to write an equation to represent how many total objects are in the array. Remind students to label the package of toys with the total on the Student Journal. 7. Rotate students through each station, and remind students to complete their copy of the Student Journal for Part I.”

• Scope 14: Time, Explore, Skill Basics–How to Use a Geared Clock, Procedure and Facilitation Points. Teachers do the following: “1. Give a small geared clock to each student. 2. Gather students into a whole-class group, and discuss the basics of using a geared clock. Show students your large geared clock. Identify the parts of the geared clock: the face of the clock, the red numbers (hours), the blue numbers (minutes), the red hand (hour), and the blue hand (minute). Ask the following questions: a. How should I move the hour hand on the clock? By moving the blue (minute) hand to the right, b. What happens to the hour hand as I move the minute hand? (demonstrate) The hour hand is slowly moving to the next number, the next hour. 3. Divide the class into pairs. 4. Model showing various times to the nearest hour and half hour using your large geared clock. Have students show the same times on their small geared clocks. Practice saying a time and then modeling it, while students show the same times on their clocks. Then model a time and see if students can say the time shown. 5. Once students have practiced as a whole-class group with your guidance, tell them that you will ask students questions and they must show their answers to their partners. Remind students to demonstrate a time to the closest hour or half hour. Explain that if they are not sure, they can make their best guesses. 6. Demonstrate a question and answer. Say: What time do we eat lunch? For us, it is close to 11 o’clock. (Show 11 o’clock on your large clock.) Let’s say it’s the weekend and you eat lunch at 11:30. (Show 11:30 on your large clock.) Now listen to the questions and then share your answers with your partners. 7. Ask the following questions. Check for understanding. Randomly ask students to show what time it would be 30 minutes later. This is to make sure they are practicing time to both the hour and half hour. a. What time do you go to bed? b. What time do you eat dinner? c. What time do you wake up during the week? d.What time do you wake up on the weekend? e. What time do you have to be at school? f. What time do you get out of school?  g. What is the latest time you have ever stayed up? h. What is the earliest time you have woken up? 8. When this activity is complete, move on to Explore 2 for students to apply their knowledge of the skills just learned.”

The materials reviewed for STEMScopes Math Grade 2 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 4: Compare Numbers to 1,000, Content Support, Current Scope. It states, “Students use their understanding of place value to compare numbers within 1,000 and record these comparisons using the >, =, and < symbols. In addition, students use mental math strategies to add 10 or 100 to a given number 100–900, and to subtract 10 or 100 from a given number 100–900.”

• Scope 7: Addition and Subtraction Problem Solving, Content Overview, Future Expectations. It states,  “In third grade, students find efficient strategies for adding and subtracting within 1,000. They apply strategies based on place value, properties of operations, and the relationship between addition and subtraction. Third-grade students solve multistep problems involving all four operations, and they represent the problems using an equation with a variable. Students assess the reasonableness of answers using mental computation and estimation strategies, including rounding.”

• Scope 8: Money, Content Overview, Teacher Guide, Scope Summary. It states,  “Within this Scope, students will master concepts revolving around working with money. Students learn how to solve real-world problems that involve dollar bills, quarters, dimes, nickels, and pennies and record answers using the appropriate money symbols for dollars and cents.” 

• Scope 12: Length, Content Support, Coming Attractions. It states,  “In fourth grade, students use all four operations to solve measurement problems (including distance, time, liquid volume, mass, and money). Conversions within one system of units are required to express larger units of measure to smaller units of measure.”

The materials reviewed for STEMScopes Math Grade 2 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. It contains 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: Numbers on a Number Line, Home, Scope Overview, Teacher Guide,provides the following information:  “Vertical Alignment, Background Knowledge, First-grade students explored relationships within the place value system. Students gained oral proficiency in counting up from any number to 120, used a written numeral to represent the total amount, and used concrete and pictorial models to develop strategies to add within 100. First-grade students also investigated that the length is the number of same-sized units of length that, when laid end to end with no gaps or overlaps, reach from one end of the object to the other. Prior to second grade, students have been introduced to number lines as a  strategy, and they may have also experienced using a number path to find sums and differences. Future Expectations, In third grade, students will represent and interpret data within several categories using scaled picture graphs, bar graphs, line plots, and number lines. Third grade students measure lengths using rulers marked with halves and fourths of an inch.”

• Scope 9: Arrays, Home, Home, Content Unwrapped, Vertical Alignment, Grade 1, Standard, states to “Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.” Grade 2, “Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.” Grade 3, “Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.”

The materials reviewed for STEMscopes Math Grade 2 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, “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 2 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 4: Compare Numbers to 1,000, Explore, Explore 2–Comparing Numbers, Materials, “Printed, 1 Student Journal (per student), 1 Set of Spelling Bee Scorecards (per pair), 1 Exit Ticket (per student), Reusable, 1 Set of base ten blocks (per pair), 1 Resealable bag (per pair)”

• Scope 8: Money, Elaborate, Fluency Builder–Money Match, Materials, “1 Instruction Sheet (per pair), 1 Set of Money Match Cards (per pair), 1 Student Recording Sheet (per student), Reusable, 1 Envelope or resealable bag (per pair)”

• Scope 14: Time, Explore, Skills Basics–How to Use a Geared Clock, Materials, “Reusable, 1 Small geared clock (per student), 1 Large geared clock (per teacher)”

The materials reviewed for STEMScopes Math Grade 2 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 2, the Assessment section of 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 6: Addition and Subtraction Strategies, Evaluate, Standards-Based Assessment, Answer Key, Question 2, provides a possible way a student might complete the problem. “2. Miguel needs help solving the problem below. 87-53= ___ How can Miguel solve this problem using strategies based on place value? Explain your reasoning and write your answer in the box. (DOK 3) 34, Sample reasoning: I used base ten blocks and placed 8 tens in the tens section of the place value chart and 7 ones in the ones section of the place value chart. First I subtracted the ones: 7 ones − 3 ones = 4 ones. Then I subtracted the tens: 8 tens − 5 tens = 3 tens. 30 + 4 = 34, so 87 - 53 = 34.” (2.NBT.7)

• Scope 14: Time, Evaluate, Standards-Based Assessment, Answer Key, Question 10 provides a possible solution a student might provide. Students see an analog clock with 10:15 displayed. “10. Read the time on the clock. None of these Write the time on the clock in the box below. Explain the steps that you use to tell time on a clock. (DOK 3) It is 10:15. I looked at the hour hand first. It is right past the ten, but not yet 11. I looked at the minute hand next. I counted by fives until I got to the 3, which is 15 minutes.” (2.MD.7)

• Scope 15: Data Analysis, Intervention, Small-Group Intervention, Procedure and Facilitation Points states, “Part I, 1. Prior to beginning the activity, ask students to tell you everything they know about data and graphs. As students answer, check to see if they understand the definitions of data, picture graphs, bar graphs, and line plots. Identify student misconceptions. 2. Display Our Favorite Pet Data. Share with students that you’ve collected some data on students’ favorite pets. You have organized your data in a chart. 3. Explain that you’d like some help creating a picture graph using the data from the chart.”

The materials reviewed for STEMscopes Math Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

Assessment opportunities are included in the Exit Tickets, Show What You Know, Skills Quiz, Technology-Enhanced Questions, Standards-Based Assessment, and Decide and Defend situations. Assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types, including multiple choice, multiple response, and short answer. While the MPs are not identified within the assessments, MPs are described within the Explore sections in relation to the Scope. Examples include:

• Scope 3: Numbers on a Number Line, Evaluate, Decide and Defend, allows students to demonstrate the full intent of 2.MD.6, “Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.” “How Many to Feed? There were 52 students in line to get their lunches from the cafeteria. They were later joined by 20 more students whose class was running late. How many students are in the cafeteria line now? Draw and label a number line that shows your thinking. Describe your reasoning below.”

• Scope 10: Two-Dimensional Shapes, Explore, Explore 3–Drawing 2-D Shapes, Exit Ticket, allows students to demonstrate the full intent of MP6, “Attend to precision: Students use geometric language to identify and describe the attributes of given shapes.” “Draw a shape with 5 sides, 5 angles, and 5 vertices. It is called a ___. Draw a shape with 4 equal sides, 4 right angles, and 4 vertices. It is called a ___. Draw a shape with 4 sides, 4 angles, and 4 vertices with opposite sides that are equal. It is called a ___. Draw a quadrilateral with 1 set of parallel sides. It is called a ___.”

• Scope 15: Data Analysis, Show What You Know, allows students to demonstrate the full intent of 2.MD.9, “Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.” “Data Analysis, Part 4: Organizing Data Using Line Plots, Below are the measurements of sticks that were found in a pile outside the school. Use the data to create a line plot and answer the questions.” Given a table with columns labeled, “Length of Sticks, Number of Sticks” and the number of sticks as tally marks, “11 inches \vert\vert\vert, 13 inches \vert\vert\vert\vert\vert, 16 inches \vert\vert, 17 inches \vert\vert\vert, 20 inches \vert\vert\vert\vert, How many sticks were found outside the school? ___ What size stick did most students find outside the school? ___ What size was the longest stick found outside the school? ___”

The materials reviewed for STEMscopes Grade 2 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 6: Addition and Subtraction Strategies, 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.” Procedure and Facilitation Points, “Part I,1.  Prior to beginning the activity, ask students to tell you everything they know about different strategies that can be used to add and subtract two-digit numbers. As students answer, check to see if they understand how to use the strategies appropriately. Identify student misconceptions. 2. Give a whiteboard, a dry-erase marker, and a set of base ten blocks to each student. 3. Give the students the equation 42+27. 4. Discuss first how you can estimate a solution before solving the problem. a. What strategy can we use to estimate a solution? Answers will vary. We can use friendly numbers. We can change 42 to 40, and we can change 27 to 30. Then we can mentally  add 40 and 30 to get 70. 5. Instruct students to build each number. Discuss how many rods (tens) and units (ones) there are for each number. Ask the following questions: a. How many tens are in your model of 42? 4 b. What is the value of the group of tens? 40 c. How many ones are in your model of 42? 2 d. What is the  value of the group of ones? 2 e. How many tens are in your model of 27? 2 f. What is the value of the group of tens? 20 g. How  many ones are in your model of 27? 7 h. What is the value of  the group of ones? 7 6. Ask students to write the value of each group of tens and ones under their blocks on the table. Encourage students to group the tens and ones together to  solve the equation. 7. Instruct students to write a number sentence to find the sum of the group of tens and then a  number sentence to find the sum of the group of ones. Add the  two sums to find the total sum. 8. Discuss whether the estimated solution is close to the actual solution.”

• Scope 13: Area, Explore, Explore 1–Covering Rectangles with Squares, Instructional Supports, ”1. Students will need to use their understanding of addition to find the total area. Provide support for adding multi digit numbers as needed or review the skill if necessary. 2. When working, provide short, explicit feedback on errors before misconceptions are developed.”

The materials reviewed for STEMscopes Math Grade 2 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 3: Numbers on a Number Line, Acceleration, Math Today–Dinosaur Recycled, Question 1 states, “On the number line below, point A shows how many bottles were collected on Saturday, and point B shows how many were collected on Sunday during one weekend. Label the number line to show how many bottles were picked up on Saturday and how many were [picked up on Sunday.”

• Scope  5: Fractions, Acceleration, Math Today–A Cat’s New Leg states, “Sgt. Stubbs lived a hard life as a stray cat before Adam Schofield of Oak Creek, Wisconsin, adopted him. Sgt. Stubbs got an infection in his two back legs, and they had to be amputated, or removed. Engineering students at the University of Wisconsin–Madison used a 3-D printer to create prosthetic legs with strong straps for Sgt. Stubbs. Now he can use his back legs once again! The students used a rectangular piece of fabric to make the straps for Sgt. Stubbs’s new legs. Question 1, The first strap needs a piece that is one-half of the rectangle. Use your pencil to partition the rectangle into two equal shares. Each piece is one-(half, third, fourth) Question 2, The second strap needs a piece that is one-fourth of the rectangle. Use your pencil to partition the rectangle into four equal shares. Each piece is one- (half, third, fourth)” 

• Scope 10: Two-Dimensional Shapes, Acceleration, Math Today–The Shape of Art states, “Tanya created some mosaic-style art pieces of her own. Mosaic art is created using different shapes that eventually become a picture. Question 1, What shapes did Tanya use to create the pictures above? Question 3, Draw and label the shapes in your own piece of art below. You should include two shapes with 4 vertices.”

The materials reviewed for STEMscopes Math Grade 2 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 5: Fractions, Engage, Foundation Builder, Possible Preconceptions, provides the teacher with guidance on challenging words. “The English language has many words that have multiple meanings. Suggested Solution, To eliminate any confusion, ensure that students understand the following words. Word, Possible Student Thinking, Our Intention, In Context, Fair, A gathering where products are sold, Dividing or separating equally, Each person got a fair share of the cake because all the pieces were the same size and shape, Fair, According to the rules, Dividing or separating equally, Each person got a fair share of the cake because all the pieces were the same size and shape. Part, A role, as in a play or movie, A separate piece or section of a whole, James got one part of the cookie cake.”

• Scope 10: Two-Dimensional Shapes, Explore, Explore 3–Drawing 2-D Shapes, Language Acquisition Strategy, provides guidance for the teacher.  “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 connect printed text that is routinely used in classroom materials to basic sight vocabulary. Beginner: Provide an illustrated word wall and preview the words being used in the Explore. Model referencing the word wall while completing the Student Journal and Exit Ticket. Allow students to point to the words/visuals in order to answer the questions.”

• Scope 15: Data Analysis, Elaborate, Fluency Builder–Data Analysis Match, Student Recording Sheet, is provided for students that read, write or speak Spanish. “Pareo de Análisis de datos Hoja de registro del estudiante Al final del juego, escoge dos pareos que hayas hecho. Escribe las letras del pareo. Luego, dibuja una gráfica diferente para representar los mismos datos. Por ejemplo, si los datos en la tarjeta están representados en una gráfica pictográfica, dibuja una gráfica de barras para representar los datos.”

The materials reviewed for STEMscopes Math Grade 2 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: Numbers on a Number Line, Intervention, Supplemental Aids–Open Number Line, Procedure and Facilitation Points states,  “Number lines are a tool that can be used for a variety of mathematical concepts, including the following: Addition and subtraction, Fractions, Comparing numbers, Ordering numbers, Estimation, Rational numbers, A blank number line can be used as a supplemental aid for students who need assistance visualizing numerical concepts. Display the number line provided on the Student Handout that is applicable to the concepts being taught. Model how to add hash marks and numbers to the number line as needed. You may also cut the Student Handout into strips so that students may write on their own number line. If possible, provide a laminated copy of a number line for each student. The students may then use dry-erase markers to utilize the number line in a variety of problems. During assessment, encourage students to draw a number line at the top of their paper or notebook as a strategy to solve problems.”

• Scope 9; Arrays, Explore, Virtual Manipulative–Linking Cubes, provides a variety of colors of cubes that can be linked to one another in preparation for arrays and multiplication.

• Scope 12: Length, Explore, Skills Basics–How to Use Measuring Tools, Procedural and Facilitation Points states,  “1. Share with students that they will be working to measure two items (a pencil and a notebook) using a ruler and measuring tape. 2. Explain to students that there are rules to using measurement tools by saying: When you use a measurement tool to measure the length of an object, you have to keep the measurement tool straight and close to the edge. Line the measurement tool up evenly with one end and measure to the other end. 3. Tell students that they can draw a start line and stop line to help them. 4. Distribute materials to each group. Instruct students to use their rulers and measuring tapes to measure the length of their notebooks and pencils. 5. Support groups and facilitate discussions as they work to measure a pencil by asking the following questions: a. Where did you start measuring? Where did you stop measuring? Encourage students to identify the starting and ending points. Students can be encouraged to draw start and stop lines. b. How do you know you measured correctly? Answers will vary. Allow students to share the rules that they used to measure their objects.  c. Can you explain to me how your group is using the measurement tool? Answers will vary. Allow students to elaborate on the steps to use a measurement tool.”