5th Grade - Gateway 3

The materials reviewed for Open Up Resources K-5 Math Grade 5 meet expectations for providing teachers 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. 

Within the Course Guide, several sections (Design Principles, A Typical Lesson, How to Use the Materials, and Key Structures in This Course) provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include but are not limited to:

• Resources, Course Guide, Design Principles, Learning Mathematics by Doing Mathematics, “A problem-based instructional framework supports teachers in structuring lessons so students are the ones doing the problem solving to learn the mathematics. The activities and routines are designed to give teachers opportunities to see what students already know and what they can notice and figure out before having concepts and procedures explained to them. The teacher has many roles in this framework: listener, facilitator, questioner, synthesizer, and more.”

• Resources, Course Guide, A Typical Lesson, “A typical lesson has four phases: 1. a warm-up; 2. one or more instructional activities; 3. the lesson synthesis; 4. a cool-down.” “A warm-up either: helps students get ready for the day’s lesson, or gives students an opportunity to strengthen their number sense or procedural fluency.” An instructional activity can serve one or many purposes: provide experience with new content or an opportunity to apply mathematics; introduce a new concept and associated language or a new representation; identify and resolve common mistakes; etc. The lesson synthesis “assists the teacher with ways to help students incorporate new insights gained during the activities into their big-picture understanding.” Cool-downs serve “as a brief formative assessment to determine whether students understood the lesson.”

• Resources, Course Guide, How to Use the Materials, “The story of each grade is told in eight or nine units. Each unit has a narrative that describes the mathematical work that will unfold in that unit. Each lesson in the unit also has a narrative. Lesson narratives explain: the mathematical content of the lesson and its place in the learning sequence; the meaning of any new terms introduced in the lesson; how the mathematical practices come into play, as appropriate. Activities within lessons also have narratives, which explain: the mathematical purpose of the activity and its place in the learning sequence, what students are doing during the activity, what the teacher needs to look for while students are working on an activity to orchestrate an effective synthesis, connections to the mathematical practices, when appropriate.”

• Resources, Course Guide, Scope and Sequence lists each of the nine units, a Pacing Guide to plan instruction, and Dependency Diagrams. These Dependency Diagrams show the interconnectedness between lessons and units within Grade 5 and across all grades.

• Resources, Course Guide, Course Glossary provides a visual glossary for teachers that includes both definitions and illustrations. Some images use examples and nonexamples, and all have citations referencing what unit and lesson the definition is from.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Several components focus specifically on the content of the lesson. Examples include:

• Unit 1, Finding Volume, Section A, Lesson 1, Preparation, Math Community guides teachers in developing a Math Community. “Prepare a space, such as a piece of poster paper, titled “Mathematical Community”​ ​and a T-chart with the headers “Doing Math”​ ​and “Norms.” Partition each of the columns into two sections: students and teacher. The two sections encourage the students and teacher to be mindful that both respective parties are responsible for the way math is done in the classroom.”

• Unit 3, Multiplying and Dividing Fractions, Section C, Lesson 19, Preparation, Lesson Narrative, explains how students will apply knowledge and work together to solve problems. “Students work together with expressions involving a unit fraction divided by a whole number and a whole number divided by a unit fraction. In both activities, students write multiplication and division expressions, given specific digits to choose from. In Activity 1, students are applying what they learned to strategically write expressions that represent the greatest product or quotient. In Activity 2, they are trying to write expressions that represent the smallest product or quotient.”

• Unit 6, More Decimal and Fraction Operations, Overview, Throughout this Unit, “The Number Talk routine is used throughout the unit to support students’ developing fluency and to see multiplicative structures present in the base-ten system, adding and subtracting of fractions, and multiplication of fractions. Students use benchmark fractions and equivalent fractions to reason about the value of the expressions.” It then gives a sampling of the Number Talk Warm-ups. It also explains how students will use this routine to reason values of expressions.

The materials reviewed for Open Up Resources K-5 Math Grade 5 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject. 

Unit Overviews and sections within lessons include adult-level explanations and examples of the more complex grade-level concepts. Within the Course Guide, How to Use the Materials states, “Activities within lessons also have narratives, which explain: the mathematical purpose of the activity and its place in the learning sequence, what students are doing during the activity, what the teacher needs to look for while students are working on an activity to orchestrate an effective synthesis, connections to the mathematical practices, when appropriate.” Examples include:

• Unit 2, Fractions as Quotients and Fraction Multiplication, Section B, Lesson 6, Relate Division and Multiplication, Lesson Narrative, “In previous lessons, students interpreted a fraction as division of the numerator by the denominator, and equivalently, as a whole number divided into equal sized pieces. In this lesson, students relate division of two whole numbers to multiplying a whole number by a unit fraction. In the first activity, students are given an opportunity to solve a division problem using any strategy and, in the synthesis, they examine how the solution can be interpreted in terms of multiplication or division.  In the second activity, students continue to explore the relationship between a fraction, a division expression, and a multiplication expression. In grade 4, students multiplied a unit fraction by a whole number and in this lesson they begin to explore how to interpret a whole number multiplied by a unit fraction.”

• Unit 5, Place Value Patterns and Decimal Operations, Section D, Lesson 22, Preparation, Lesson Narrative, “In prior lessons, students represented decimals to the thousandths with diagrams, words, numbers, and expressions. They also added, subtracted and multiplied decimals using place value understanding, properties of operations, and relationships between operations. In this lesson, students begin to work with decimals and division. They divide whole numbers by one tenth and one hundredth and notice and explain patterns they observe. Students apply their understanding of division as ‘how many groups’ to hundredths grids where the entire grid represents one whole. This allows them to visualize how many tenths or hundredths are in one or several wholes while also preparing students to find quotients of more complex decimals in future lessons.” 

• Unit 7, Shapes on the Coordinate Plane, Overview, “In this unit, students learn about the coordinate grid, deepen their knowledge of two-dimensional shapes, and use the coordinate grid to study relationships of pairs of numbers in various situations. Here, students learn about grids that are numbered in two directions. They see that the structure of a coordinate grid allows us to precisely communicate the location of points and shapes. Students also continue to study two-dimensional shapes and their attributes. In grade 3, they classified triangles and quadrilaterals by the presence of right angles and sides of equal length. In grade 4, they learned about angles and parallel and perpendicular lines, which allowed them to further distinguish shapes. In this unit, students use these insights to make sense of the hierarchy of shapes.”

Also within the Course Guide, About These Materials, Further Reading states, “The curriculum team at Open Up Resources has curated some articles that contain adult-level explanations and examples of where concepts lead beyond the indicated grade level. These are recommendations that can be used as resources for study to renew and fortify the knowledge of elementary mathematics teachers and other educators.” Examples include:

• Resources, Course Guide, About These Materials, Further Reading, 3-5, “Fraction Division Parts 1–4. In this four-part blog post, McCallum and Umland discuss fraction division. They consider connections between whole-number division and fraction division and how the two interpretations of division play out with fractions with an emphasis on diagrams, including a justification for the rule to invert and multiply. In Part 4, they discuss the limitations of diagrams for solving fraction division problems.”

• Resources, Course Guide, About These Materials, Further Reading, Entire Series, “The Number Line: Unifying the Evolving Definition of Number in K-12 Mathematics. In this article, the authors (Lahme, McLeman, Nakamaye, and Umland) focus their attention on the selection of definitions, notation, and graphical conventions surrounding the development of the real numbers from kindergarten to grade 12, and address the work that students might do in later years.”

The materials reviewed for Open Up Resources K-5 Mathematics 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 can be found within different sections of the Course Guide and within the Standards section of each lesson. Examples include:

• Resources, Course Guide, About These Materials, CCSS Progressions Documents, “The Progressions for the Common Core State Standards describe the progression of a topic across grade levels, note key connections among standards, and discuss challenging mathematical concepts. This table provides a mapping of the particular progressions documents that align with each unit in the K–5 materials for further reading.”

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress in the Mathematical Practices, The Standards for Mathematical Practices Chart, “The unit-level Mathematical Practice chart is meant to highlight a handful of lessons in each unit that showcase certain Mathematical Practices. Some units, due to their size or the nature of their content, may have fewer predicted chances for students to engage in a particular Mathematical Practice. A dash in the chart indicates that there may not be enough opportunities to reliably look for this Mathematical Practice in the unit. One primary place Mathematical Practice 4 is tagged is the optional modeling lesson at the end of each unit. Aside from these lessons, optional activities and lessons are not included in this chart.”

• Resources, Course Guide, Scope and Sequence, Dependency Diagrams, All Grades Unit Dependency Diagram identifies connections between the units in grades K-5. Additionally, a “Section Dependency Diagram” identifies specific connections within the grade level.

• Resources, Course Guide, Lesson and Standards, provides two tables: a Standards by Lesson table, and a Lessons by Standard table. Teachers can utilize these tables to identify standard/lesson alignment.

• Unit 4, Wrapping Up Multiplication and Division with Multi-Digit Numbers, Section A, Lesson 4, Warm Up, “Addressing 5.NBT.B.5. The purpose of this Number Talk is to highlight the calculations that students will make when they use the standard algorithm. The first three calculations are partial products. The fourth calculation is the sum of the first three and this is the number that is recorded when performing the standard multiplication algorithm to which students will be introduced in this lesson.”

Explanations of the role of specific grade-level mathematics can be found within different sections of the Resources, Course Guide, Unit Overviews, Section Overviews, and Lesson Narratives. Examples include:

• Resources, Course Guide, Scope and Sequence, each Unit provides Unit Learning Goals, for example, “Students find the volume of right rectangular prisms and solid figures composed of two right rectangular prisms.” Additionally, each Unit Section provides Section Learning Goals, “Describe volume as the space taken up by a solid object.”

• Unit 3, Multiplying and Dividing Fractions, Overview, “In this unit, students find the product of two fractions, divide a whole number by a unit fraction, and divide a unit fraction by a whole number. Previously, students made sense of multiplication of a whole number and a fraction in terms of the side lengths and area of a rectangle. Here, they make sense of multiplication of two fractions the same way. Students interpret area diagrams with two unit fractions for their side lengths, then a unit fraction and a non-unit fraction, and then two non-unit fractions.”

• Unit 5, Place Value Patterns and Decimal Operations, Section B, Section Overview, "In this section, students add and subtract decimals to the hundredths. They begin by adding and subtracting in ways that make sense to them, which prompts them to relate the operations to those on whole numbers. It also allows the teacher to take note of the strategies and algorithms they choose, including the standard algorithm and those that use expanded form. Adding and subtracting decimals using the standard algorithm brings up a new question in terms of how the digits should be aligned. To highlight this consideration, students analyze a common error. Before using the standard algorithm, students use place-value reasoning to decide whether sums and differences are reasonable and to ensure that the digits in the numbers are aligned correctly. As they take care to align tenths with tenths and hundredths with hundredths, students practice attending to precision (MP6)."

• Unit 7, Shapes on the Coordinate Plane, Lesson 6, Lesson Narrative, "The purpose of this lesson is for students to first relate squares and rhombuses and then relate rectangles and parallelograms. They see that if a shape is a square then it is also a rhombus and if a shape is a rectangle then it is also a parallelogram. But there are rhombuses that are not squares and there are parallelograms that are not rectangles. Students record these observations on the anchor chart from previous lessons. This gives students a chance to organize the quadrilaterals in a hierarchy and highlight the relationships they see between the properties of the shapes they worked with in this lesson. Students should have access to straight edges, protractors, and patty paper throughout this lesson. When students define shapes and make explicit connections between shapes and categories, they reason abstractly and quantitatively (MP2)."

The materials reviewed for Open Up Resources K-5 Math Grade 5 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. 

The materials explain and provide examples of instructional approaches of the program and include and reference research-based strategies. Both the instructional approaches and the research-based strategies are included in the Course Guide under the Resources tab for each unit. Design Principles describe that, “It is our intent to create a problem-based curriculum that fosters the development of mathematics learning communities in classrooms, gives students access to mathematics through a coherent progression, and provides teachers the opportunity to deepen their knowledge of mathematics, student thinking, and their own teaching practice.” Examples include:

• Resources, Course Guide, Design Principles, “In order to design curriculum and professional learning materials that support student and teacher learning, we need to be explicit about the principles that guide our understanding of mathematics teaching and learning. This document outlines how the components of the curriculum are designed to support teaching and learning aligning with this belief.” Principles that guide mathematics teaching and learning include: All Students are Capable Learners of Mathematics, Learning Mathematics by Doing Mathematics, Coherent Progression, Balancing Rigor, Community Building, Instructional Routines, Using the 5 Practices for Orchestrating Productive Discussions, Task Complexity, Purposeful Representations, Teacher Learning Through Curriculum Materials, and Model with Mathematics K-5.

• Resources, Course Guide, Design Principles, Community Building, “Students learn math by doing math both individually and collectively. Community is central to learning and identity development (Vygotsky, 1978) within this collective learning. To support students in developing a productive disposition about mathematics and to help them engage in the mathematical practices, it is important for teachers to start off the school year establishing norms and building a mathematical community. In a mathematical community, all students have the opportunity to express their mathematical ideas and discuss them with others, which encourages collective learning. ‘In culturally responsive pedagogy, the classroom is a critical container for empowering marginalized students. It serves as a space that reflects the values of trust, partnership, and academic mindset that are at its core’ (Hammond, 2015).”

• Resources, Course Guide, Design Principles, Instructional Routines, “Instructional routines provide opportunities for all students to engage and contribute to mathematical conversations. Instructional routines are invitational, promote discourse, and are predictable in nature. They are ‘enacted in classrooms to structure the relationship between the teacher and the students around content in ways that consistently maintain high expectations of student learning while adapting to the contingencies of particular instructional interactions.’ (Kazemi, Franke, & Lampert, 2009)”

• Resources, Course Guide, Key Structures in This Course, Student Journal Prompts, Paragraph 3, “Writing can be a useful catalyst in learning mathematics because it not only supplies students with an opportunity to describe their feelings, thinking, and ideas clearly, but it also serves as a means of communicating with other people (Baxter, Woodward, Olson & Robyns, 2002; Liedke & Sales, 2001; NCTM, 2000).”

The materials reviewed for Open Up Resources K-5 Math Grade 5 meet expectations for including a comprehensive list of supplies needed to support the instructional activities.

In the Course Guide, Materials, there is a list of materials needed for each unit and each lesson. Lessons that do not have materials are indicated by none; lessons that need materials have a list of all the materials needed. Examples include:

• Resources, Course Guide, Key Structures in This Course, Representations in the Curriculum, provides images and explanations of representations for the grade level. “Base-ten Blocks (2-5): Base-ten blocks are used after students have had the physical experience of composing and decomposing towers of 10 cubes. The blocks offer students a way to physically represent concepts of place value and operations of whole numbers and decimals. Because the blocks cannot be broken apart, as the connecting cube towers can, students must focus on the unit. As students regroup, or trade, the blocks, they are able to develop a visual representation of the algorithms. The size of relationships among the place value blocks and the continuous nature of the larger blocks allow students to investigate number concepts more deeply. The blocks are used to represent whole numbers and, in grades 4 and 5, decimals, by defining different size blocks as the whole.” 

• Resources, Course Guide, Materials, includes a comprehensive list of materials needed for each unit and lesson. The list includes both materials to gather and hyperlinks to documents to copy. “Unit 2, Lesson 11 - Gather: Number cards 0-10; Copy: How Close? Stage 6 Recording Sheet, How Close? Stage 7 Recording Sheet.”

• Unit 1, Finding Volume, Section A, Lesson 3, Materials Needed, “Activities: Connecting cubes (Activity 1); Centers: Connecting cubes (Can You Build It?, Stage 3), Folders (Can You Build It?, Stage 3), Paper clips (Five in a Row: Multiplication, Stage 3), Two-color counters (Five in a Row: Multiplication, Stage 3).”

The materials reviewed for Open Up Resources Math Grade 5 meet expectations for having assessment information in the materials to indicate which standards are assessed. 

The materials consistently and accurately identify grade-level content standards for formal assessments for the Section Checkpoints and End-of-Unit Assessments within each assessment answer key. Examples from formal assessments include:

• Resources, Course Guide, Summative Assessments, End-of-Unit Assessments, “All summative assessment problems include a complete solution and standard alignment. Multiple choice and multiple response problems often include a reason for each potential error a student might make.”

• Unit 5, Place Value Patterns and Decimal Operations, Assessments, End-of-Unit Assessment, Problem 3, “5.NBT.A.4. What is 1.357 rounded to the nearest hundredth? What about to the nearest tenth? To the nearest whole number? Explain or show your reasoning.”

• Unit 3, Multiplying and Dividing Fractions, Section C, Lesson 17, Cool-down, "Assessing 5.NF.B.6: a. A container has 2 cups of milk in it. How many \frac{1}{4} cups of milk are in the container? Explain or show your reasoning. b. A container has 2 cups of milk in it. The container is \frac{1}{3} full. How many cups does the container hold? Explain or show your reasoning."

• Unit 6, More Decimal and Fraction Operations, Section A Checkpoint, Problem 3, “5.MD.A.1, 5.NBT.A.1: It is 325 meters around a track. Jada ran around the track 12 times. How many kilometers did Jada run?”

Guidance for assessing progress of the Mathematical Practices can be found within the Resources, Course Guide, How to Use These Materials, Noticing and Assessing Student Progress in Mathematical Practices, How to Use the Mathematical Practices Chart, “Because using the mathematical practices is part of a process for engaging with mathematical content, we suggest assessing the Mathematical Practices formatively. For example, if you notice that most students do not use appropriate tools strategically (MP5), plan in future lessons to select and highlight work from students who have chosen different tools.” In addition, “...a list of learning targets for each Mathematical Practice is provided to support teachers and students in recognizing when engagement with a particular Mathematical Practice is happening…the ‘I can’ statements are examples of types of actions students could do if they are engaging with a particular Mathematical Practice.” Examples include:

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 5, MP2 is found in Unit 3, Lessons 1, 4, 11, 14, 18. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 5, MP5 is found in Unit 5, Lessons 5, 11, 14. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “9: I Can Look for and Express Regularity in Repeated Reasoning. I can identify and describe patterns and things that repeat. I can notice what changes and what stays the same when working with shapes, diagrams, or grinding the value of expressions. I can use patterns to come up with a general rule.” (MP8)

The materials reviewed for Open Up Resources K-5 Math Kindergarten meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

Formative assessments include instructional activities, Practice Problems and Section Checkpoints in each section of each unit. Summative assessments include End-of-Unit Assessments and End-of-Course 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, short answer, restricted constructed response, and extended response. Examples include:

• Unit 1, Finding Volume, Assessments, End-of-Unit Assessment, Problem 2, 5.MD.5c, “Students find the volume of a figure. No strategy is suggested but students will likely cut the figure into two rectangular prisms and add the volumes of those prisms. But they may decompose the figure in any way that allows them to count the total number of cubes that make the figure.” Problem 2, “Find the volume of the figure. Explain or show your reasoning.”

• Unit 3, Multiplying and Dividing Fractions, Assessments, Section B, Lesson 16, Cool-Down, 5.NF.7, students respond to the question, ”Which is greater 5\div\frac{1}{3}  is greater than \frac{1}{3}\div{5}. Explain or show your reasoning.”

• Unit 6, More Decimal and Fraction Operations, Assessments, Section C Checkpoint, Problem 1, 5.NF.4, 5.NF.5, “Write <, =, or > in the blanks to make each statement true. a. \frac{9}{7}\times197 ____ 187; b. \frac{19}{19}\times\frac{11}{13} ____ \frac{11}{13}; c. \frac{19}{19}\times\frac{11}{13} ____ \frac{19}{19}.”

• Unit 7, Shapes on the Coordinate Plane, Assessments, Section A Checkpoint, Problem 1, supports the full intent of MP6 (Attend to precision) as students locate points on a coordinate plane. Three points are on a coordinate plane. “Write the coordinates for each point on the grid. Locate the point (3,0) on the grid and label it D. Locate the point (0,5) on the grid and label it E.”

The materials reviewed for Open Up Resources K-5 Math 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/series mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics as suggestions are outlined within each lesson. According to the Resources, Course Guide, Universal Design for Learning and Access for Students with Disabilities, “Supplemental instructional strategies that can be used to increase access, reduce barriers and maximize learning are included in each lesson, listed in the activity narratives under ‘Access for Students with Disabilities.’ Each support is aligned to the Universal Design for Learning Guidelines (udlguidelines.cast.org), and based on one of the three principles of UDL, to provide alternative means of engagement, representation, or action and expression. These supports provide teachers with additional ways to adjust the learning environment so that students can access activities, engage in content, and communicate their understanding.” Examples of supports for special populations include: 

• Unit 3, Multiplying and Dividing Fractions, Section B, Lesson 13, Activity 2, Access for Students with Disabilities, “Representation: Perception. Provide access to strips of paper for students to cut and fold. Ask students to identify correspondences between the number of pieces/folds and the fraction they represent. Provides accessibility for: Conceptual Processing, Memory.”

• Unit 5, Place Value Patterns and Decimal Operations, Section D, Lesson 22, Activity 1, Access for Students with Disabilities, “Representation: Comprehension. Begin by asking, “Does this problem/situation remind anyone of something we have seen/read/done before?” Provides accessibility for: Memory, Attention.”

• Unit 7, Shapes on the Coordinate Plane, Section B, Lesson 5, Activity 2, Access for Students with Disabilities, “Engagement: Recruiting Interest. Synthesis: Optimize meaning and value. Invite students to share the meaning of a trapezoid and the similarities and differences in the two definitions of a trapezoid with a classmate who missed the lesson. Provides accessibility for: Conceptual Processing, Language.”

The materials reviewed for Open Up Resources K-5 Math Grade 5 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

While there are no instances where advanced students do more assignments than classmates, materials do provide multiple opportunities for students to investigate grade-level content at a higher level of complexity. These are found where problems are labeled as “Exploration” at the end of practice problem sets within sections, where appropriate. According to the Resources, Course Guide, How To Use The Materials, Exploration Problems, “Each practice problem set also includes exploration questions that provide an opportunity for differentiation for students ready for more of a challenge. There are two types of exploration questions. One type is a hands-on activity directly related to the material of the unit that students can do either in class if they have free time, or at home. The second type of exploration is more open-ended and challenging. These problems go deeper into grade-level mathematics. They are not routine or procedural, and they are not just “the same thing again but with harder numbers. Exploration questions are intended to be used on an opt-in basis by students if they finish a main class activity early or want to do more mathematics on their own. It is not expected that an entire class engages in exploration problems, and it is not expected that any student works on all of them. Exploration problems may also be good fodder for a Problem of the Week or similar structure.” Examples include:

• Unit 3, Multiplying and Dividing Fractions, Section B, Practice Problems, Problem 9 (Exploration), “It takes Earth 1 year to go around the Sun. a. During the time it takes Earth to go around the Sun, Mercury goes around the Sun about 4 times. How many years does it take Mercury to make 1 full orbit of the Sun? Write an equation showing your answer. b. During the time it takes Earth to go around the Sun, Saturn goes 1⁄29 of the way around the Sun. How many years does it take Saturn to go around the Sun? Write an equation showing your answer.“

• Unit 5, Place Value Patterns and Decimal Operations, Section B, Practice Problems, Problem 8 (Exploration), “Lin is trying to use the digits 1, 3, 4, 2, 5, and 6 to make 2 two-digit decimals whose sum is equal to 1. a. Explain why Lin can not make 1 by adding together 2 two-digit decimal numbers made with these digits. b. What is the closest Lin can get to 1? Explain how you know.”

• Unit 7, Shapes on the Coordinate Plane, Section C, Practice Problems, Problem 7 (Exploration), “Andre starts from 2 and counts by 6s. Clare starts at 1,000 and counts back by 7s. a. List the first 6 numbers Andre and Clare say. b. Do Andre and Clare ever say the same number in the same spot on their lists? Explain or show your reasoning.”

The materials reviewed for Open Up Resources K-5 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.

Guidance is consistently provided to teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. According to the Resources, Course Guide, Mathematical Language Development and Access for English Learners, “In an effort to advance the mathematics and language learning of all students, the materials purposefully engage students in sense-making and using language to negotiate meaning with their peers. To support students who are learning English in their development of language, this curriculum includes instruction devoted to fostering language development alongside mathematics learning, fostering language-rich environments where there is space for all students to participate.” Examples include:

• Unit 3, Multiplying and Dividing Fractions, Section A, Lesson 4, Activity 1, “Access for English Learners - Speaking, Conversing, Representing: MLR8 Discussion Supports. Synthesis: At the appropriate time, give groups 2–3 minutes to plan what they will say when they present to the class. ‘Practice what you will say when you share your drawing with the class. Talk about what is important to say, and decide who will share each part.’”

• Unit 4, Wrapping Up Multiplication and Division with Multi-Digit Numbers, Section A, Lesson 9, Activity 2, "Access for English Learners - Writing, Speaking, Listening: MLR1 Stronger and Clearer. Synthesis: Before the whole-class discussion, give students time to meet with 2–3 partners to share and get feedback on their response to What is the possible range of volumes for each type of birdhouse? Invite listeners to ask questions, to press for details, and to suggest mathematical language. Give students 2–3 minutes to revise their written explanation based on the feedback they receive."

• Unit 6, More Decimal And Fraction Operations, Section A, Lesson 2, Activity 1, “Access for English Learners - Conversing, Reading: MLR2 Collect and Display. Circulate, listen for and collect the language students use as they use exponential notation to represent large numbers. On a visible display, record words and phrases such as: million, thousands, billion, powers of 10, exponential notation, represent, times, multiply by ten, number of zeros. Invite students to borrow language from the display as needed, and update it throughout the lesson.”

The materials reviewed for Open Up Resources K-5 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.

Suggestions and/or links to manipulatives are consistently included within materials to support the understanding of grade-level math concepts. Examples include:

• Unit 3, Multiplying and Dividing Fractions, Section A, Lesson 9, students use paper, rulers, markers, crayons or colored pencils to use the principles of flag design from the North American Vexillological Association to design their own flag. “The purpose of this activity is for students to make their own flags and analyze them. Students will use their experience with multiplying fractions to answer area questions related to their flag. Some students may include non-rectangular designs. Encourage them to relate the area of their shape to a rectangle and estimate.” Launch “Give each student white paper. ‘Use the design principles we discussed in the last activity to make your own flag. As you make the design, think about the meaning of each symbol and color you use.’ Student Work Time “15 minutes: independent work time. 5 minutes: partner discussion. a.) Design your flag; b.) Imagine you are making your flag with fabric. About how much of each color fabric will you need in square inches? c.) Switch flags with a partner. Describe the meaning of each symbol and color you used ; d.) How do you see each of the design principles in your partner’s flag?”

• Unit 4, Wrapping Up Multiplication and Division with Multi-Digit Numbers, Section C, Lesson 19, Activity 1, “Groups of 2. Lay a meter stick on the ground. ‘Tyler walked from his classroom to the cafeteria. He said, ‘I think that’s about a kilometer.’ Do you agree with Tyler?’ (No, a kilometer is a long distance, it’s 1,000 meters, and it is not that far from a classroom to the cafeteria.). 1 minute: quiet think time. 1–2 minutes: partner discussion. Give students access to meter sticks.”

• Unit 6, More Decimal and Fraction Operations, Section A, Lesson 7, Activity 1, “Groups of 2. Give each group of students one set of pre-cut cards. Display a yardstick. ‘What do you notice? What do you wonder?’ (It shows feet and inches. It shows 36 inches. I wonder if it’s the same length as a meter stick.). ‘In this activity, you will sort some cards into categories of your choosing. When you sort the measurements, you should work with your partner to come up with categories.’ 4 minutes: partner work time. Select groups to share their categories and how they sorted their cards. Choose as many different types of categories as time allows, but ensure that one set of categories identifies the way the quantity is written (whole number, mixed number, fraction). ‘Now work with your partner to match the cards with equal measurements. Then, list the groups of matching measurements in increasing order.’ 3 minutes: partner work time.”