2nd Grade - Gateway 3

The materials reviewed for Open Up Resources K-5 Math Grade 2 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 2 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 4, Addition and Subtraction on a Number Line, Lesson 5, Lesson Narrative, "In previous lessons, students estimated the length of objects using what they know about the size of standard length units and the tools used to measure them. Students have located numbers on number lines using what they know about the structure of a number line and the labeled tick marks. The purpose of this lesson is for students to extend this understanding by estimating numbers on number lines that do not have tick marks to represent each consecutive whole number. Students use their understanding of length and unit intervals on the number line to estimate. Students should be encouraged throughout the lesson to explain why their estimates are reasonable using what they know about number, length, and the structure of the number line."

• Unit 6, Geometry, Time and Money, Section D, Lesson 15, Activity 1, Launch, provides teachers guidance on how to represent coins. "Display the pre-made poster to show front and back images of pennies, nickels, and dimes. 'Each coin has a value in cents. Does anyone know the names or values of these coins?' Share and record responses, Write the name and value of each coin on the poster. 'When we write the total value we use the cent symbol after the number to show that it represents cents.' Demonstrate writing the ¢ symbol next to the amount."

• Unit 9, Putting It All Together, Section A, Lesson 1, Activity 1, “The purpose of this activity is for students to identify the addition facts within 20 that they do not yet know from memory. They write these sums on index cards which can be used to help students build fluency throughout the section. Students should store these cards to use again in an upcoming lesson. The number choices in this activity include some of the facts that students may still be working to recall from memory at this point in the school year. If desired, the inventory of sums that students complete at the beginning of the activity could be replaced with a list of all sums within 20 or a smaller set of sums that best fit the needs of your students.”

The materials reviewed for Open Up Resources K-5 Math Grade 2 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 4, The Structure of the Number Line, Section A, Lesson 4, Compare Numbers on a Number Line, Lesson Narrative, “In previous lessons, students learned how to locate a number on the number line and represent numbers with labeled tick marks and points. They used multiples of 5 and 10 to help them locate numbers up to 100 on a number line. In this lesson, students recognize that as you move to the right on the number line, numbers increase in value because they are a greater distance from 0. Students also use the relative position of numbers and generalize that a number that is greater than a given number if it is farther to the right on the number line. To demonstrate this understanding, students compare numbers within 100 (a skill from grade 1) and use the number line to explain their comparison (MP7).”

• Unit 5, Numbers to 1,000, Section B, Lesson 12, Warm-up, Instructional Routine, “The purpose of this Number Talk is to elicit strategies and understandings students have for mentally subtracting a multiple of 10 from a number. Building on their understanding of place value, students subtract tens from tens. These understandings help students develop fluency and will be helpful in later lessons when students will need to be able to subtract using strategies based on place value.”

• Unit 8, Equal Groups, Overview, “Later, students transition from working with arrays containing discrete objects to equal-size squares within a rectangle. They build rectangular arrays using inch tiles and partition rectangles into rows and columns of equal-size squares. The work here sets the stage for the concept of area in grade 3.”

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, K-2, “Units, a Unifying Idea in Measurement, Fractions, and Base Ten. In this blog post, Zimba illustrates how units ‘make the uncountable countable’ and discusses how the foundation built in K-2 measurement and geometry around structuring space allows for the development of fractional units and beyond to irrational units.”

• 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 2 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 1, Adding, Subtracting, and Working With Data, Section B, Lesson 8, Standards, “Building On: 1.OA.C.5, 2.MD.D.10, Addressing: 2.MD.D.10 Draw a picture graph and a bar graph (single-unit scale) to represent data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.”

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 measure and estimate lengths in standard units and solve measurement story problems within 100.” Additionally, each Unit Section provides Section Learning Goals, “measure length in centimeters and meters.”

• Unit 3, Measuring Length, Unit Overview, "Students relate the structure of a line plot to the tools they used to measure lengths. This prepares students for the work in the next unit, where they interpret numbers on the number line as lengths from 0. The number line is an essential representation that will be used in future grades and throughout students’ mathematical experiences."

• Unit 5, Numbers to 1,000, Section A, Lesson 2, Lesson Narrative, "In a previous lesson, students learned that a hundred is composed of 10 tens or 100 ones. In this lesson, students deepen their understanding of a hundred as a unit. They learn that for every 10 tens, they can compose 1 hundred. Students notice that it may be easier to count the hundreds rather than count the tens to find a total value. Students begin to recognize and describe the patterns in the structure of the base-ten system (MP7, MP8). They recognize that 10 tens make 1 hundred, 30 tens make 3 hundreds, 60 tens make 6 hundreds, etc. as they build numbers with tens and exchange them for hundreds. Students identify the multiples of 100 written as numerals and begin to make connections between base-ten blocks and the value of each digit in a three-digit number."

• Unit 6, Geometry, Time, and Money, Section C, Section C Overview, "In this section, students use their understanding of fourths and quarters to tell time. In grade 1, students learned to tell time to the hour and half-hour. Here, they make a connection between the analog clock and circles partitioned into halves or fourths."

The materials reviewed for Open Up Resources K-5 Math Grade 2 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 2 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. “5-frame and 10-frame (K-2): 5- and 10-frames provide students with a way of seeing the numbers 5 and 10 as units and also combinations that make these units. Because we use a base-ten number system, it is critical for students to have a robust mental representation of the numbers 5 and 10. Students learn that when the frame is full of ten individual counters, we have what we call a ten, and when we cannot fill another full ten, the ‘extra’ counters are ones, supporting a foundational understanding of the base-ten number system. The use of multiple 10-frames supports students in extending the base-ten number system to larger numbers.”

• 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 5, Lesson 4 - Gather: Base-ten blocks, Number cards 0-10; Copy: Greatest of Them All Stage 1 Recording Sheet, Mystery Number Stage 1 Directions.”

• Unit 6, Geometry, Time and Money, Section D, Lesson 15, Materials Needed, “Activities: Scissors (Activity 2); Centers: Paper (How Are They the Same?, Stage 2), Picture books (Picture Books, Stage 3).”

The materials reviewed for Open Up Resources Math Grade 2 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 3, Measuring Length, Assessments, Section A Checkpoint, Problem “1, 2.MD.A.1 Find the length of the rectangle with a centimeter ruler.” A 1cm x 12cm picture of a rectangle is provided for students. 

• Unit 7, Adding and Subtracting Within 1,000, Assessments, End-Of-Unit Assessment, Problem 1, “2.NBT.B.8: Students add and subtract multiples of 10 and 100 from three-digit numbers.”

• Unit 8, Equal Groups, Section B, Lesson 8, Cool-down, Make Rows and Columns, “Assessing 2.OA.C.4: Show an array with 4 rows and 2 objects in each row. How many columns are there? How many objects are in each column? How many objects are there in all?”

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 2, MP3 is found in Unit 3, Lessons 4, 8, 9, 12, 16. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 2, MP7 is found in Unit 5, Lessons 1, 2, 3, 5, 8. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP3: I can Construct Viable Arguments and Critique the Reasoning of Others. I can explain or show my reasoning in a way that makes sense to others. I can listen to and read the work of others and offer feedback to help clarify or improve the work. I can come up with an idea and explain whether that idea is true.”

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, Adding, Subtracting, and Working with Data, Assessments, End-of-Unit Assessment, Problem 5, 2.OA.1, “Students solve a Compare Smaller Unknown story problem. They may subtract by place value without decomposing a ten. Students may find the sum 48+26 instead of the difference if they do not read the problem carefully.” Problem 5, “A farmer has 48 chickens on her farm. There are 26 more chickens than there are pigs. How many pigs are there on the farm? Show your thinking using diagrams, numbers, words, or equations.”

• Unit 3, Measuring Length, Section B, Lesson 9, Cool-down, supports the full intent of MP3 (Construct viable arguments and critique the reasoning of others) as students support their thinking related to length measurements. “Tyler told Han that a great white shark is about 16 inches long, but Han disagrees. Han believes it would be about 16 feet long. Who do you agree with? Explain.” 

• Unit 6, Geometry, Time, and Money, Assessments, Section A Checkpoint, Problem 2, 2.G.1, "Draw a triangle that has 1 square corner and 2 sides that have the same length."

• Unit 9, Putting it All Together, Assessments, End-of-Course Assessment, Problem 3, 2.NBT.2, “Students identify numbers that appear on a list when counting from 0 by tens. Students who select B may be thinking of counting by fives. Students who select E have likely not read the question carefully as 540 would appear on a list of numbers counting by tens but it is larger than 500. If you skip count from 0 to 500 by 10s, which of these numbers will you say as you count? a. 150; b. 275; c. 300; d. 480; e. 540”

The materials reviewed for Open Up Resources K-5 Math 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/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, Measuring Length, Section B, Lesson 10, Activity 1, Access for Students with Disabilities, “Action and Expression: Expression and Communication. Give students access to inch tiles to double check their measurement. Reiterate how the measurement is the same regardless of the whole inch they start at on the ruler. Provides accessibility for: Conceptual Processing, Visual-Spatial Processing.”

• Unit 7, Adding and Subtracting Within 1000, Section C, Lesson 13, Activity 2, Access for Students with Disabilities, “Action and Expression: Expression and Communication. Provide students with alternatives to writing on paper. Students can share their learning by creating a video using the base-ten blocks, or writing out their steps and explaining on video. Provides accessibility for: Language, Attention, Social-Emotional Functioning.”

• Unit 8, Equal Groups, Section B, Lesson 12, Activity 2, Access for Students with Disabilities, “Action and Expression: Expression and Communication. Give students access to 1-inch grid paper to get their thinking started, and create an array with the inch tiles. Have students transfer what they made on the grid paper to the open rectangles given. The concrete image transferred to the more abstract image may help some students visually. Provides accessibility for: Visual-Spatial Processing, Organization.”

The materials reviewed for Open Up Resources K-5 Math Grade 2 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, Measuring Length, Section B, Practice Problems, Problem 7 (Exploration), “If you and all of your classmates stand side to side with your arms stretched out, about how long of a line do you think you can make? Explain your reasoning including the unit of measure you choose.”

• Unit 5, Numbers to 1,000, Section A, Practice Problems, Problem 10 (Exploration), “a. Can you represent the number 218 without using any hundreds? Explain your reasoning.; b. Can you represent the number 218 without using any tens? Explain your reasoning.; c. Can you represent the number 218 without using any ones? Explain your reasoning.“

• Unit 7, Adding and Subtracting Within 1,000, Section A, Practice Problems, Problem 11 (Exploration), “Tyler says he can find the value of 438-275 using what he knows about differences of two-digit numbers. “First I find 43-27 and then I find 8-5 and that gives me the answer.” Use Tyler’s reasoning to find the value of 438-275.”

The materials reviewed for Open Up Resources K-5 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.

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 2, Adding and Subtracting Within 100, Section C, Lesson 14, Activity 1, “Access for English Learners - Convesing, Representing: MLR8 Discussion Supports. To support both students with an opportunity to produce language, display a question starter ‘How did you do the problem?’ and sentence frames ‘First, I  because _____ because… My method is like yours because …Our methods are different because …’”

• Unit 3, Measuring Length, Lesson 5, Activity 2, Access for English Learners, "Conversing, Reading: MLR2 Collect and Display. Direct attention to words collected and displayed from the previous lesson. Add “meter stick” to the collection. Invite students to borrow language from the display as needed, and update it throughout the lesson."

• Unit 5, Numbers to 1,000, Section A, Lesson 6, Activity 2, "Access for English Learners, Representing, Conversing: MLR7 Compare and Connect, Synthesis: After the Gallery Walk, lead a discussion comparing, contrasting, and connecting the different representations of numbers. To amplify student language and illustrate connections, follow along and point to the relevant parts of the displays as students speak."

The materials reviewed for Open Up Resources K-5 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.

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

• Unit 2, Adding and Subtracting Within 100, Section B, Lesson 5, Activity 1, “The purpose of this activity is for students to subtract in a way that makes sense to them. Students use a method of their choice and share their methods with one another. This can serve as a formative assessment of how students approach finding the value of a difference when a ten must be decomposed when subtracting by place. Although students may use many methods to subtract, including those based on counting or compensation, the synthesis focuses on connecting these methods to those based on place value where a ten is decomposed. Monitor and select students with the following methods to share in the synthesis:  Uses connecting cubes to make 82 and removes 9 blocks. Counts back or counts all to find the difference. Subtracts 2 from 82 to get to a ten, 80, and then subtracts 7 from 80 by counting back (with or without blocks). Uses base-ten blocks to show 82 and decomposes a ten to get 12 ones. Subtracts 9 ones from 12 ones and counts the remaining blocks.”

• Unit 6, Geometry, Time, Money, Lesson 8, Activity 2, “Groups of 2. Give students access to colored pencils. ‘You are going to read some stories with a partner about students sharing pies. Then you will partition and color shapes on your own.’ 5 minutes: partner work time. As students work, encourage them to use precise language when talking with their partners. Consider asking: ‘Is there another way you could say how much of the circle is shaded?’ 10 minutes: independent work time. Monitor for students who accurately shade the circles to share in the synthesis.”

• Unit 8, Equal Groups, Section B, Lesson 7, Activity 1, “The purpose of this activity is for students to create arrays with counters. Students get sets of 6, 7, and 9 counters. Based on their experiences with images that show an even number of objects arranged in 2 equal groups, they may make an array with 3 rows and 2 columns or 2 rows and 3 columns with 6 counters. They may wonder if 7 or 9 counters can be arranged in an array since they are not even numbers.  Encourage students to experiment with other ways of arranging the counters that include more than 2 rows or columns. They may also make an array with 1 row. Arrays with 1 row or 1 column will be studied in future grades, so for the rest of this unit, students should be encouraged to make arrays with more than 1 row and more than 1 column.”