1st Grade - Gateway 3

The materials reviewed for Open Up Resources K-5 Math Grade 1 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 eight units, a Pacing Guide to plan instruction, and Dependency Diagrams. These Dependency Diagrams show the interconnectedness between lessons and units within Grade 1 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 3, Adding and Subtracting Within 20, Overview, describes how subtraction correlates with addition. “Subtraction work occurs throughout the unit and becomes the focus in the last section. Students consider taking away and counting on as methods for subtracting. They understand subtraction as an unknown-addend problem and use their knowledge of addition to find the difference of two numbers.”

• Unit 4, Numbers to 99, Section C, Lesson 14, Activity 1, Launch, provides prompts for the teacher to start the lesson. “Groups of 2: Give each group two paper clips and access to connecting cubes in towers of 10 and singles. Display 35 and 52. “Which number is more? Show your thinking using math tools. Be ready to explain your thinking to your partner.” 2 minutes: independent work time 2 minutes: partner discussion “Which is more and how do you know?” (53 is more because it has more tens than 35.)”

• Unit 8, Putting It All Together, Lesson 6, Activity 1, "The purpose of this activity is for students to practice solving Compare, Difference Unknown story problems (MP2). In the synthesis, students revisit a representation of a Compare problem that was introduced in a previous unit. This representation lays the foundation for working with tape diagrams in grade 2.The teacher may want to incorporate movement into this activity by writing each problem on a piece of chart paper and placing each one in a different location around the classroom. Students can solve the problem at one location, discuss the problem with their partner, then move on to a new problem at a new location."

The materials reviewed for Open Up Resources K-5 Math Grade 1 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 1, Adding, Subtracting, and Working With Data, Section B, Lesson 7, Activity 1, “The purpose of this activity is for students to sort math tools, name the groups they used to sort, and tell the number of objects in each group. Students identify attributes of the objects and sort them into two or more groups. Students may choose to use one of the blackline masters to organize as they sort. When students share how they sorted with their partner, they use their own mathematical vocabulary and listen to and understand their partner’s thinking (MP3, MP6). Students may describe the objects’ attributes by referring to shape names, number of sides, color, or other attributes. Encourage students to tell how many tools are in each category. During the synthesis, students are introduced to the term category. They discuss different categories that were used to sort the math tools.”

• Unit 5, Adding Within 100, Section B, Lesson 6, Activity 2, “The purpose of this activity is for students to add one-digit and two-digit numbers with composing a ten and deepen their understanding of place value. In this activity, students make sense of two different addition methods where an addend is decomposed to make a ten. Students then determine the next step needed to find the value of the original sum. Invite students to use different representations to make sense of these methods including connecting cubes and base-ten drawings. Completing the start of a calculation as students do here requires critically analyzing, understanding, and expressing different strategies (MP3).”

• Unit 6, Length Measurements Within 120 Units, Section A, Lesson 1, Lesson Narrative, “In kindergarten, students compared the length of two objects directly by lining up the endpoints. They described the objects using language such as longer and shorter. In this unit the words “longer than” and “shorter than” are encouraged, although students may use “taller than” in certain contexts related to height. In this lesson, students compare the length of objects and consider how they know which is longer or shorter. Then, they order three objects by length.”

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 1 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: K.CC.B.4, Addressing: 1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. Building Towards: 1.MD.C.4.”

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 add and subtract within 10, and represent and interpret categorical data.” Additionally, each Unit Section provides Section Learning Goals, “organize and represent data.”

• Unit 2, Addition and Subtraction Story Problems, Overview, “In kindergarten, students solved a limited number of types of story problems within 10 (Add To/Take From, Result Unknown, and Put Together/Take Apart, Total Unknown, and Both Addends Unknown). They represented their thinking using objects, fingers, mental images, and drawings. Students saw equations and may have used them to represent their thinking, but were not required to do so. Here, students encounter most of the problem types introduced in grade 1: Add to/Take From, Change Unknown, Put Together/Take Apart, Unknowns in All Positions, and Compare, Difference Unknown. The numbers are kept within 10 so students can focus on interpreting each problem and the relationship between counting and addition and subtraction. This also allows students to continue developing fluency with addition and subtraction within 10.”

• Unit 4, Numbers to 99, Section D, Section D Overview, "In this section, students deepen their understanding of the base-ten structure by representing two-digit numbers with different amounts of tens and ones. They also extend their comparison work by comparing numbers expressed in different ways."

• Unit 6, Length Measurements Within 120 Units, Section C, Lesson 14, Lesson Narrative, "In previous lessons, students solved Take From, Start Unknown, Compare, Bigger Unknown, and Compare, Smaller Unknown problems. They showed their thinking using drawings, numbers, or words. Throughout the year, students solved all types of story problems with unknowns in all positions. In this lesson, students learn that they can use equations to make sense of story problems in different ways."

The materials reviewed for Open Up Resources K-5 Math Grade 1 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 1 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 1, Lesson 13 - Gather: Connecting cubes, Materials from a previous activity; Copy: Favorite Special Class Data.”

• Unit 8, Putting it All Together, Section B, Lesson 5, Materials Needed, “Activities: Connecting cubes in towers of 10 and singles (Activity 1).”

The materials reviewed for Open Up Resources Math Grade 1 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 2, Addition and Subtraction Story Problems, Section A, Lesson 2, Cool-down, “Assessing 1.OA.A.1, Mai put 5 books on the shelf. Then Noah put 4 books on the shelf. How many books are on the shelf now? Show your thinking using drawings, numbers or words."

• Unit 4, Numbers to 99, Assessments, Section D Checkpoint, “For this Checkpoint Assessment, the content assessed is listed below for reference. Represent two-digit numbers in different ways, using different amounts of tens and ones (for example 52=50+2=40+12). Represent a number with tens and ones in more than one way. Recognize when the same number is represented with different amounts of tens and ones. Compare two-digit numbers represented in different ways.” (1.NBT.3)

• Unit 7, Geometry and Time, Assessments, End-Of-Unit Assessment, Problem 4, “1.G.A.3:  Students identify whether or not the same amount of a square is shaded. They are given two images of the same size square with half of one square shaded and a quarter of the other square shaded. Students should note that the size of the pieces is smaller when the (same) whole is divided into more pieces.”

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 1, MP3 is found in Unit 6, Lessons 1 and 5. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 1, MP6 is found in Unit 6, Lessons 1-3, 6, and 7. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP2: I can Reason Abstractly and Quantitatively. I can think about and show numbers in many ways. I can identify the things that can be counted in a problem. I can think about what the numbers in a problem mean and how to use them to solve the problem. I can make connections between real-world situations and objects, diagrams, numbers, expressions, or equations.”

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 2, Addition and Subtraction Story Problems, Assessments, End-of-Unit Assessment, Problem 2, 1.OA.1, 1.OA.6, “After recess, Tyler collected 6 footballs. Then he collected some baseballs. Altogether, Tyler collected 10 balls. How many baseballs did Tyler collect? Show your thinking with drawings, numbers, or words. Write an equation to match the story problem.”

• Unit 3, Adding and Subtracting Within 20, Assessments, Section C Checkpoint, Practice Problems, Problem 1, 1.OA.2, “There are 5 bananas, 6 oranges, and 4 apples in a bowl. How many pieces of fruit are in the bowl? Show your thinking using objects, drawings, numbers, or words. Equation: _____.”

• Unit 6, Length Measurements Within 120 Units, Assessments, End-of-Unit Assessment, Problem 1, 1.MD.1, three images of rectangles of varying orientations and lengths are provided. “a. Write a sentence comparing the length of Rectangle A and the length of Rectangle B”; and ” b. Write a sentence comparing the length of Rectangle A and the length of Rectangle C.”

• Unit 8, Putting It All Together, Section B, Lesson 4, Cool-down, supports the full intent of MP4 (Model with mathematics) as students solve an unknown addend problem. “Clare counted 8 sharks swimming in a tank. Then some more sharks swam by. Clare counted 13 sharks all together. How many more sharks swam by? Show your thinking using drawings, numbers, or words.”

The materials reviewed for Open Up Resources K-5 Math Grade 1 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 4, Numbers to 99, Section D, Lesson 19, Activity 2, Access for Students with Disabilities, “Action and Expression: Executive Functions. Invite students to plan a method with their partners, including the tools they will use, for decomposing 37 in multiple ways. Provides accessibility for: Organization, Attention”

• Unit 7, Geometry and Time, Section A, Lesson 5, Access for Students with Disabilities, “Representation: Comprehension. Synthesis: Provide more examples and non-examples to reinforce the defining attributes of triangles. Provides accessibility for: Conceptual Processing, Visual-Spatial Processing”

• Unit 8, Putting It All Together, Section B, Lesson 4, Activity 1, Access for Students with Disabilities, “Representation: Perception. Provide appropriate reading accommodations and supports to ensure student access to word problems and other text-based content. Provides accessibility for: Language, Visual-Spatial Processing, Attention.”

The materials reviewed for Open Up Resources K-5 Math Grade 1 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 1, Adding Subtracting, and Working With Data, Section A, Practice Problems, Problem 10 (Exploration), “Materials needed: Number cards 2–10; Two dot cubes. Directions: a. Choose a number card. Show 2 numbers on the dot cubes that add to make your number. b. Can you show another way?”

• Unit 3, Adding and Subtracting Within 20, Section D, Practice Problems, Problem 6 (Exploration), “Mai was playing Number Card Subtraction. She started with a teen number. Then she drew a card and subtracted. Mai’s answer was the same as the number she subtracted. What could Mai’s teen number and card have been?”

• Unit 6, Length Measurements within 120 Units, Section B, Practice Problems, Problem 6 (Exploration), “Priya and Noah want to measure their classroom in steps. Priya takes 28 steps to cross the room and Noah takes 26 steps. a. How could Priya and Noah get different measurements?; b. Measure the length of your classroom in steps.”

The materials reviewed for Open Up Resources K-5 Math Grade 1 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 1, Adding, Subtracting, and Working With Data, Section C, Lesson 11, Activity 1, “Access for English Learners - Reading, Representing: MLR6 Three Reads. To launch this activity, display the task statement. ‘We are going to read this statement 3 times.’ After the 1st Read, ask: ‘What is this situation about?’ Listen for and clarify any questions about the context. After the 2nd Read: ‘What are all the things we can count?’ (number of votes for each pet, number of classmates who took the survey). After the 3rd Read: ‘How can we know if a statement is true or false?’”

• Unit 2, Addition and Subtraction Story Problems, Section A, Lesson 3, Activity 1, "Access for English Learners - Representing, Conversing: MLR7 Compare and Connect. Synthesis: After all methods have been presented, lead a discussion comparing, contrasting, and connecting the different approaches. Ask, ‘How were the different methods the same?’ and ‘How were they different?’”

• Unit 4, Numbers to 99, Lesson 1, Activity 1, Access for English Learners, "Conversing, Reading: MLR2 Collect and Display. Circulate, listen for, and collect the language students use as they work with their partners. On a visible display, record words and phrases such as: count, represent, representation, my representation shows … 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 1 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 1, Adding, Subtracting, and Working With Data, Section A, Lesson 4, Activity 1, students use number cards, a game board, two-color counters, and access to 10-frames to subtract one or two from a number within 10. Launch, “Groups of 2. ‘We are going to learn a new way to play, Five in a Row. Last time we played, we added one or two to the number on our card. This time, you will take turns flipping over a card and choosing whether to subtract one or two from the number. Then put a counter on the number on the game board, The first person to get five counters in a row wins. Remember, your counters can be in a row across, up and down, or diagonally.’” Student Work Time, “10 minutes: partner work time. As students work, consider asking: ‘How did your subtract? How did you decide whether to subtract 1 or 2?’”

• Unit 4, Numbers to 99, Section A, Lesson 4, Activity 1, “The purpose of this activity is for students to solve two story problems involving adding or subtracting multiples of 10. Students are presented with a familiar context from a previous lesson in which students counted cubes in different bags. The quantities of cubes are described using representations that students are familiar with, and students add or subtract in a way that makes sense to them. The familiar context and representations are used to help students make sense of adding and subtracting tens. In the synthesis, students compare and connect the different representations used for each problem (MP2).”

• Unit 6, Length Measurements Within 120 Units, Section B, Lesson 3, Activity 1, “Students choose from a variety of objects: connecting cubes towers, pieces of string, and unsharpened pencils. As students compare the length of the paths, students may use a single tool, such as a piece of string to compare the two paths. They may mark or cut the string. Some students may choose the tower of connecting cubes and determine that breaking off or counting the cubes is a way to determine whether one length is shorter or longer than the other. Others may select and try different tools until they find one that has a length that is in between the length of the two paths.”