5th Grade - Gateway 3

The materials reviewed for STEMScopes Math Grade 5 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 5: Compare Decimals, Explore, Explore 2–Unequal Number of Decimal Places, Procedure and Facilitation Points. Teachers follow these steps:  “1. Ask students if they have ever seen a horse race. Allow them to share their experiences. 2. Prepare pictures or a video clip of the Kentucky Derby so students may have a visual picture of what a horse race is. 3. Explain that a famous race called the Kentucky Derby is run every year on a track called Churchill Downs in Louisville, Kentucky. The length of the track is 1.25 miles. Well-prepared horses race for the finish line so they can be called the champion of the Kentucky Derby! 4. Tell students they will be comparing the times it took champion horses from different years to run the track at the Kentucky Derby. Of the two horses racing, the one with the faster time would be the champion. 5. Ask students to discuss in their groups what it means to have a faster time in a race. Will the number be the greatest or least, and why?”

• Scope 12: Fractions as Division, Explore, Skill Basics–Reason with Benchmark Fractions, Procedure and Facilitation Points. Teachers will follow these instructions:  “1. Give a Student Work Mat, dry-erase marker, and dry-erase eraser to each student. 2. Tell students they will be given some fractional parts. With partners, they will decide if the fractional parts are less than, greater than, or equal to the benchmark fraction on one whole. 3. Give bag 1 to each pair. Instruct them to remove the two trapezoids and fraction card from the bag. 4. Instruct students to draw two trapezoids under Fraction Model on the Student Work Mat. 5. As you discuss the following questions, have students write the information on the Student Work Mat: a. What does the fraction card say? Write “halves” on the Student Work Mat. b. If these trapezoids represent halves, what does each trapezoid, or part, represent? Write “one-half” on the Student Work Mat. c. How many one-halves, or parts, are in a whole? Write “2” on the Student Work mat. D. How many trapezoids, or parts, are there? Write “2” on the Student Work Mat. e. What fraction do these trapezoids, or parts, represent? Write "\frac{2}{2}" on the Student Work Mat. f. Are these trapezoids, or parts, less than, equal to, or greater than one whole? Write "\frac{2}{2}=1 whole” on the Student Mat.” 

• Scope 19: Apply Volume Formulas, Explore, Skill Basics–Differentiate Square Units from Cubic Units, Procedure and Facilitation Points. Teachers perform the following steps:  “1. Project the first slide of the Square Units and Cubic Units Slideshow. 2. Distribute a Square and Cubic Units Graphic Organizer to each student. 3. Discuss the following question: a. What do you notice about these shapes? I. If students don’t mention it, lead them to understand that these unit squares are two-dimensional figures. 4. Instruct students to draw a model of a square unit in the Square Unit Model section of their Square and Cubic units Graphic Organizers. Ask the following question: a. What are the dimensions of a square unit? 5. Instruct students to write “1 unit long by 1 unit wide” in the Square Unit Dimensions section of their Square and Cubic Units Graphic Organizers. Ask the following questions: a. What does the area of a figure represent? B. How can we use these square units to find the area of a figure? C. How are the words square and area related? 6. Instruct students to remove their inch tiles from the bag and find the area of the Square Units section on the Square Units and Cubic Units Work Mat. 7 Ask the following questions: a. How many inch tiles were you able to place in the section? B. What is the area of this section? C. What are some other things you could measure using square units?”

The materials reviewed for STEMScopes Math Grade 5 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 5: Compare Decimals, Home, Content Overview, Teacher Guide, Vertical Alignment, Future Expectations. It states, “As students reach sixth grade, they are expected to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm. The use of the algebraic system of rational numbers is extended to include negative numbers. Additionally, decimals are used when reasoning and solving one variable equations and inequalities.”

• Scope 10: Model Fraction Multiplication, Home, Content Support, Current Scope. It states, “Students use area models, tape diagrams, and number lines to make sense of the process for multiplying two fractions or for multiplying a fraction by a whole number. Students create story contexts that represent the multiplication of fractions, and they write equations to represent the solutions. Students interpret multiplication as scaling or resizing. Students reason about how numbers change when they are multiplied by fractions by considering the size of a product in relation to the sizes of each factor. Students recognize that when multiplying a fraction greater than one the number increases, and when multiplying by a number less than one the number decreases.”

• Scope 15: Classify Two-Dimensional Figures, Home, Content Support, Misconception and Obstacles. It states,  “Students might think that a 2D shape can only fit into one category. For example, they may not realize that a square can also be called a quadrilateral, parallelogram, and rectangle. Using visual graphic organizers, such as Venn diagrams or T-charts can help students organize shapes into hierarchies and varying subcategories.”

• Scope 20: Graph on a Coordinate Plane, Home, Content Support, Coming Attractions. It states,  “In grade six, students use all four quadrants of the coordinate system to plot polygons and to reason about their attributes. In grades six and seven, students analyze proportional relationships by making tables of equivalent ratios and graphing them on a coordinate plane. In grade eight, students observe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Eighth-grade students describe the functional relationship between two quantities by using the coordinate system to graph and analyze functions. Students have used tables to represent and compare values since the fourth grade, but in grade eight, the domain Functions is introduced. In eighth grade, functions are formally worked with as an algorithm for slope; students define, evaluate, and compare linear functions.”

The materials reviewed for STEMScopes Math Grade 5 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 12: Fractions as Division, Home, Content Unwrapped, Implications for Instruction, states, “Implications for Instruction in previous grade levels, students have experience with number lines and evenly partitioning sections for fractions. In this grade level, students expand this knowledge to divide fractional parts evenly. Students should understand that a fraction is equivalent to the numerator divided by the denominator. For example, 12 is the same as one whole divided into two parts or 1 divided by 2. Students should understand word problems involving a whole number divided by a whole number that equals a fraction. Some answers are mixed numbers instead of just fractions or whole numbers. Students should also be able to express between what two whole numbers an answer exists. For example, \frac{3}{2}=1\frac{1}{2} which lies between the whole numbers 1 and 2 on a number line.”

• Scope 14: Numerical Expressions, Engage, Accessing Prior Knowledge, Procedure and Facilitation Points, standard 5.OA.2, states, “Read the first bullet with students, and ask students to convert the words into a number sentence, i.e., an equation. Invite students to share their equations with the class. Ask students if there is exactly one way to represent this number sentence. Repeat the process explained above with the other three bulleted word problems. Ask the students if there are any similarities among all of the word problems. Ask the students if there are any differences. Before concluding the conversation, extend student thinking to explain what operation these equations are related to and explain why. If students are struggling to complete this task, move on to the Foundation Builder to fill this gap in prior knowledge before moving on to other parts of the Scope.”

The materials reviewed for STEMscopes Math Grade 5 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 5 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: Round Decimals, Elaborate, Fluency Builder–Rounding Decimal Bingo, Materials, “Printed, 1 Instruction Sheet (per pair), 1 Set of Bingo Cards (per class), 1 Set of Rule Cards (per bingo caller), 1 Student Recording Sheet (per student), Reusable, 50 Translucent counters (per pair)”

• Scope 12: Fractions as Division, Explore, Explore 1–Fractions as Division with No Remainders, Materials, “1 Student Journal (per student), 1 Set of Ice Cream Cards (per group), 1 Exit Ticket (per student), Reusable, 4 Sets of fraction tiles (per group) OR 4 Sets of fraction circles (per group), Colored pencils or markers or crayons (per student)”

• Scope 16: Unit Conversions, Explore, Explore 4–Convert Units of Time, Materials, “Printed, 1 Student Journal (per student), 1 Task Cards (per class), 1 Exit Ticket (per student), Reusable, 1 Geared practice clock (per group), 1 Timer (per group)”

The materials reviewed for STEMScopes Math Grade 5 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 5, 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 5: Compare Decimals, Evaluate, Standards-Based Assessment, Answer Key, Question 3, Part B, provides a possible way a student might complete the problem. “Which beetle was the longest? Which beetle was the shortest? Explain your reasoning. (DOK-3) Beetle C is the longest beetle, and beetle B is the shortest beetle. Sample reasoning: All of the beetles are over 3 cm long. To determine the longest length, I compared the decimal digits from left to right. Beetles A and C both have the digit 6 in the tenths place. Beetle A has a 4 in the hundredths place, and Beetle C has a 7 in the hundredths place. Since 7 hundredths is greater than 4 hundredths, I knew that beetle C was the longest. Likewise, to find the shortest length, I saw that beetles B and D both have the smallest digit in the tenths place, but Beetle B has a 3 in the hundredths place, and Beetle D has a 4 in the hundredths place. Since 3 hundredths is less than 4 hundredths, Beetle B has the shortest length. (5.NBT.3b)

• Scope 16: Unit Conversions, Evaluate, Standards-Based Assessment, Answer Key, Question 7, Part A, provides a possible solution a student might provide. “Shawn made a large batch of punch. He used 128 fluid ounces of water. Part A How many cups were used? Explain your reasoning. (DOK-3) 8. Makayla’s dad designed a building that is 2,808 inches tall. What is the building’s height in yards? (DOK-2) A, 78 yards B, 234 yards C, 936 yards D, 8,424 yards There are 16 cups in 128 fluid ounces. Sample reasoning: There are 8 ounces in a cup. I divided 128 by 8. 128\div8=16” (5.MD.1)

• Scope 20: Graph on Coordinate Plane, Intervention, Small-Group Intervention, Procedure and Facilitation Points states,“Part II: Finding Coordinates, 1. Refer to the large coordinate plane. 2. Draw a large T-chart. Label the left side x, and the right side y. This is where you will write practice coordinates for the students to find. 3. Ask for student volunteers to do the following: (They can do this with a game piece or their finger if they are using a coordinate on a chart paper.) a. Jump three times on the origin. b. Walk on your tiptoes along the x-axis. c. Walk on your tiptoes along the y-axis. d. Walk to the location of (2, 3). e. Walk to the location of (4, 4). f. Walk to the location of (0, 1). g. Walk to the location of (5, 0).”

The materials reviewed for STEMscopes Math Grade 5 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: Read and Write Decimal Numbers, Evaluate, Standards-Based Assessment, Question 5, provides opportunities for students to demonstrate the full intent of MP6, Attend to precision, as they attend to precision when reading and comparing decimal numbers, paying close attention to the place values used. “List the following numbers in order from least to greatest. Write your answer in the box. 16.2, 16.102, 16.021” 

• Scope 11: Multiplication Problem Solving Using Fractions, Evaluate, Decide and Defend, Print Files, Student Handout and Explore, Explore 2, Print Files, Exit Ticket provide opportunities for students to demonstrate the full intent of the standard 5.NF.6, “Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.” “Franklin was doing a project on eye color. He was trying to figure out what fraction of the class was represented by brown-eyed girls. His teacher showed him the picture below to help him, but he didn’t understand it. Explain to Franklin how to use the model to find the fraction of girls with brown eyes in his class.” Below the prompt are three circles. The first is divided into fifths with three pieces shaded, the second is divided into fourths with three pieces shaded. There is a multiplication sign between these two models. Following the second model is an equal sign and a circle divided into twentieths with nine shaded pieces. “Write the equation that goes with the picture.” ”For the big field day finale, the whole class must work together to win. To win, the class must use a sponge to fill a bucket of water. The team with the most water in the bucket after every teammate has finished wins. This year, the winning team filled their gallon bucket. How much water was in the winning bucket?” This is followed by a box for a model, then a line for solution statement and equation. 

• Scope 12: Fractions as Division, Evaluate, Skills Quiz, Print Files, Student Handout, Questions 1 and 2, provide opportunities for students to demonstrate the full intent of the standard 5.NF.3, Interpret a fraction as division of the numerator by the denominator (\frac{1}{b}=a\div b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem…) “Read the word problems and solve. 1. There are 3 siblings that want to equally share 5 cookies. How much of the cookies does each sibling get? 2. The Lowells have some land that they want to divide among their 4 grandchildren. If the grandparents have 13 acres, how much land does each grandchild get?” Below question two is a bar model divided into four equal boxes with 13 on top of the model.

The materials reviewed for STEMscopes Grade 5 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 4: Round Decimals, Home, Content Support, Misconceptions and Obstacles states, “Students may think as you move to the left of the decimal point, the number increases in value. Using visual models can help students understand the magnitude between powers of ten. Students may think that the longer the number is the greater its value is, but a decimal with one decimal place may actually be greater than a number with two or three decimal places. Students should be given ample experience to reason about the size of decimal numbers.”

• Scope 14: Numerical Expressions, Explore, Explore 3–Interpreting Expressions, Instructional Supports states, “1. Review key words for all operations, including sum. Difference, product, quotient, less than, more than, double, triple, decreases, etc. 2. If students are struggling with how to set up each expression, it may be helpful to review the order of operations and when it would be necessary to use parentheses in the problem. 3. If students continue to struggle, provide them with more simplistic situations to model until they gain confidence with the process.”

The materials reviewed for STEMscopes Math Grade 5 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 10: Model Fraction Multiplication, Acceleration, Math Today–A Home for Bees, Question 1 states, “Holes will be drilled into the thin side of the house for the bees to enter and exit. What is the area of this side? Use a model and write an expression to solve.” Question 2, “What is the area of the front of the house? Use a model and write an expression to solve.” 

• Scope 13: Divide Unit Fractions, Acceleration, Math Today–Natural Energy, Question 1 states, “People took shifts riding the 20 bicycles throughout the movie. The movie was 3 hours long, and each bicycle rider rode for \frac{1}{4} of an hour. How many shifts were there throughout the movie? Show the answer using the model below.” Question 2, “The bicycle riders were so thirsty after they finished their shift! The Brazil bicycle cinema organizers had 50 liters of water. If each rider drank \frac{1}{2} liter of water, how many riders were able to drink water throughout the night?” Question 3, “The generator still needs to be \frac{1}{5} filled. 7 people are going to share the responsibility of riding the bicycle to generate the power. What fraction will each rider generate?” 

• Scope 19: Apply Volume Formulas, Acceleration, Math Today–Fighting Forest Fires, Question 1 states, “The smallest air tanker is the Single Engine Airtanker (SEAT). Below is a rectangular prism that can hold the same amount of water as a SEAT. What is the amount of water that can be sprayed from this air tanker?” Question 2, “The Lockheed EC-130Q Hercules is a medium-sized fixed-wing tanker airplane. It can hold more water or retardant than the SEATs. If the base of the container has an area of 83.5 square feet and a height of 6 feet, what is the volume?”

The materials reviewed for STEMscopes Math Grade 5 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 16: Unit Conversions, Explore, Explore 1–Convert Units of Length, Print Files, Student Journal (Spanish) provides  support for students who read, write, speak a different language than English to engage in the content. The print files contain the lesson’s task cards in Spanish.

• Scope 19: Apply Volume Formula, Explore, Explore 2–Using Three Dimensions to Measure Volume, Language Acquisition Strategy 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 practice using formal and informal spoken language at appropriate times. Students may speak formally or informally while working in their groups. Give each group a chance to present a solution to the rest of the class. Formal language should be used when presenting to the class. Allow them time to write a formal explanation on an index card before they present.”

• Scope 21: Generate and Graph Numerical Patterns, Explore, Explore 2–Generate and Graph Numerical 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 use prior experiences to understand academic concepts in math.Check for understanding of the terms rule, graph, multiplicative, additive, and numerical pattern. Working with the class, have students create a definition for each—keep this word bank in an easily accessible place. Add the following sentence strands to the Student Journal page: In an additive rule, a value is being ___ to the x-value to get the y-value. In a multiplicative rule, a value is being ___ to the x-value to get the y-value. In an additive graph, when the x-value is 0, the y-value is ___. In a multiplicative graph, when the x-value is 0, the y-value is ___.”

The materials reviewed for STEMscopes Math Grade 5 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. Examples include:

• Scope 5: Compare Decimals, Intervention, Small Group Intervention, Procedure and Facilitation Points, Part I provides for students’ active participation in content through the use of manipulatives. “Does the length of the decimal or amount of digits within the decimal determine its value? Provide an example to demonstrate your thinking. Not necessarily. It is more important to compare the values of each place value position. For example, 0.2 has fewer digits than 0.123, but it has a greater value, because two-hundredths is greater than one-hundredth and also greater than one hundred twenty-three-thousandths. Provide each pair with a Student Handout, and a zip-top bag containing a set of Number Cards, a Spinner, and a paper clip. Prompt students to generate decimal numbers to the thousandths. Each student will place the decimal point card on the table. Then, they use a paper clip anchored with a pencil to spin a number. Explain that this number indicates the amount of digit cards to draw. Draw the corresponding number of digits and place them in order after the decimal point on the table. Once the students have generated a number, they will use place value disks to represent the number on the first page of the Student Handout. Once both students have built a number, students write the word form of the decimal and compare both decimals (using two comparison statements) on the second page of the Student Handout. Students may need prompting to swap the placement of each number and to reverse the inequality sign. Invite a few pairs of students to share their results with the group. Provide each student with a sticky note and invite them to write the value of each digit of their decimal. Repeat the process as needed.Invite pairs to talk about their comparisons and how they used place value to find the greater number. Afterward, allow time for students to complete the Checkup individually.”

• Scope 8: Multiplication Problem Solving Using Fractions, Explore, Virtual Manipulative–Fraction Tiles provides for students’ active participation in content through the use of virtual manipulatives. Manipulatives may be assigned to students through the online platform and used to engage in lessons from Scope 8. 

• Scope 15: Classify Two-Dimensional Figures, Procedure and Facilitation Points, provides for students’ active participation in content through the use of manipulatives. “Distribute the geoboard, rubber band, and Geoboards handout to each student. Instruct students to use the rubber band to make a square on their geoboards. Ask the following questions: What do you notice about the sides of the square? All four side lengths are congruent. The opposite sides are parallel to each other. The sides are perpendicular to each other. What do you notice about the angles in the square? The angles are all congruent. They are all right angles formed by perpendicular sides.Instruct students to draw the square from their geoboards in the upper left geoboard on the Geoboards handout. Remind students that we use tick mark symbols to identify when attributes of a figure are congruent. Explain that arrow symbols identify sides of figures that are parallel. Ask the following question: On which sides should we draw arrows to distinguish them as being parallel? We should draw them on the top and bottom sides and the left and right sides. Remind students that the number of tick marks on congruent sides and angles must be the same. Explain the same is true for distinguishing parallel sides. If there is more than one pair of parallel sides in a figure, we draw additional arrows on the other pairs of parallel sides. Model and instruct students to draw one arrow in the middle of each of the top and bottom sides on the square and two arrows in the middle of each of the left and right sides on the square.”