Kindergarten - Gateway 3

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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.” “In kindergarten, most lessons do not include cool-downs. During these lessons, checkpoints are used to formatively assess understanding of the lesson. Since activities are shorter, each lesson includes 15–25 minutes of time for centers.”

• 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 Kindergarten 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 the unit and lesson in which the definition is found. 

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 2, Numbers 1-10, Section B, Lesson 8, Warm-up, Instructional Routine, “This warm-up focuses on cardinality, or knowing that the last number tells us how many, and keeping track of which images have been counted.” Suggestions to maximize preparation of the materials include: “For example, if there are 23 students in the class, cut out four 5-frames and 3 squares out of a fifth 5-frame. Consider laminating the display and using a dry erase marker to write the two choices and record students’ responses. If available, the provided images can also be enlarged.” Each step of the Warm-up includes what to ask/say, time to wait, and expectations of student responses. 

• Unit 4, Understanding Addition and Subtraction, Overview, outlines procedures and vocabulary use. “Previously, students built their counting skills and represented quantities in a group with their fingers, objects, drawings, and numbers. Here, they relate counting to the result of two actions: putting objects together or taking objects away. Students enact addition by counting the total number of objects in two groups, and subtraction by counting what remains after some objects are taken away. (The word “total” is used here instead of “sum” to reduce potential confusion with the word “some” or part of a whole.)”

• Unit 6, Numbers 0-20, Lesson 8, Lesson Narrative, "In previous lessons, students saw numbers 11–19 as ten ones and some more ones as they counted, composed, and represented these numbers. The purpose of this lesson is for students to use the understanding that a full 10-frame contains 10 ones to compose numbers 11–19. Using a 10-frame encourages students to count on from 10. While this lesson highlights counting on as a strategy, students need significant practice working with 10-frames before they are able to count on to determine the total with understanding. Students can complete the activities by counting all. Counting on to determine the total is not an expectation in kindergarten."

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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, Numbers 1-10, Section B, Lesson 10, Activity 2, “The purpose of this activity is for students to learn stage 2 of the Less, Same, More center. Students compare groups of images in different arrangements. The activity synthesis highlights that numbers that are fewer than 5 come before 5 in the count sequence and numbers that are more than 5 come after 5 in the count sequence. This idea will be revisited in future sections and units. Students need repeated experiences comparing groups of objects, images, and numbers to be able to notice, articulate, and use the connection between the counting sequence and comparing the size of numbers (MP7, MP8).”

• Unit 3, Flat Shapes All Around Us, Overview, “Students explore differences in shapes and use informal language to describe, compare, and sort them. Circle, triangle, rectangle, and square are four shapes that students study and name here. (They will not describe what makes each shape so until grade 1.) Students also learn a key idea, that congruent shapes are still “the same” even if they are in different orientations.”

• Unit 7, Solid Shapes All Around Us, Section B, Lesson 9, Compare Capacity, Lesson Narrative, “In previous units and lessons, students compared the lengths and weights of objects. Students learned that three-dimensional shapes are solid. In this lesson, students learn about an attribute of solid shapes: capacity. Initially students compare two containers where it is visually obvious which one holds more. After this initial discussion, the cups or containers that students are comparing should have capacities that are not obviously different. For example, a shorter, wider cup and a taller, thinner cup.”

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 Kindergarten 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 7, Solid Shapes All Around Us, Section A, Lesson 4, Standards, “Addressing: K.G.B.6 Compose simple shapes to form larger shapes. For example, ‘Can you join these two triangles with full sides touching to make a rectangle?’ K.OA.A.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. Building Towards: K.G.B.6.”

 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 recognize numbers and quantities in their world.” Additionally, each Unit Section provides Section Learning Goals, “Explore and use math tools. Share mathematical ideas with a partner.”

• Unit 3, Flat Shapes All Around Us, Overview, “This unit introduces students to the foundational concepts of geometry, with a focus on familiar flat (two-dimensional) shapes. Students may initially associate names of shapes with everyday objects. For example, a rectangle is a shape that looks like a door. Students need to see and interact with many examples of a shape to accurately relate what’s in their environment to the geometric term. For instance, students may say that only one of these two shapes is a triangle—the isosceles triangle sitting on its base—because they have seen examples like it being referred to as triangles. They may not consider a scalene triangle sitting on a vertex as a part of the same shape category because, in their experience, a shape like it hasn’t been associated with the term “triangle.” 

• Unit 4, Understanding Addition and Subtraction, Section C, Lesson 16, Lesson Narrative, “In previous lessons, students interpreted expressions and connected expressions to story problems and drawings. This is the first lesson where students begin by working with only expressions. Because students have matched expressions to drawings in previous lessons, students may create a drawing to find the value of the expression. Students may also use their fingers or objects to represent the expression and count to find the total or difference.”

• Unit 5, Composing and Decomposing Numbers to 10, Section B, Overview, “In this section, students represent and solve Put Together/Take Apart story problems—first where the total is unknown, and later where both addends are unknown. Students also see equations and learn the term for the first time. Jada made 6 paletas with her brother. They made two flavors, lime and coconut. How many of the paletas were lime? Then how many of the paletas were coconut? Problems where both addends are unknown may be more challenging because there is no action in the story and more than one solution is possible. Students work to find multiple solutions but are not expected to find all the solutions in kindergarten. To represent and solve story problems, students continue to use math tools and drawings, and to explain how their representation shows the story. They may use methods such as clearly separating the groups, using 2 colors, or using letter, word, and number labels to make their drawings easier for others to understand. Students also write expressions independently to record the solutions to the story problems.”

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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 state, “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 Kindergarten 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 2, Lesson 22 - Gather: Colored pencils or crayons; Copy: Pizza Orders.”

• Unit 6, Section B, Lesson 6, Preparation, Materials Needed, “Activities: 10-frames (Activity 2), Counters (Activity 2), Colored pencils, crayons, or markers (Activity 3), Connecting cubes (Activity 3), Materials from previous centers (Activity 3).”

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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 4, Understanding Addition and Subtraction, Assessments, End-of-Unit Assessment, Problem 2, “K.OA.A.2: Students solve an Add To, Results Unknown story problem. Students may use objects to represent and solve the problem or they may make a drawing. The provided drawing distinguishes the 3 stickers that were first on the book and the 2 more that Jada put on the book by using different colors. Students may distinguish them by physically separating them or they might not distinguish them, that is, they might draw 3 circles and 2 more that are altogether.” Problem 2, “There are 3 stickers on the book. Then Jada puts 2 more stickers on the book. How many stickers are on the book now? Show your thinking using drawings, numbers, words, or objects.”  

• Unit 7, Solid Shapes All Around Us, Section B, Lesson 8, Cool-down, “Assessing K.MD.A, Which is lighter: your workbook or your pencil? Select the one that is lighter.” Images of a workbook and pencil are shown.

• Unit 8, Putting It All Together, Assessments, Section D Checkpoint, Teacher Instructions, “For this Checkpoint Assessment, the content assessed is listed below for reference. Use understanding of 10 to work with numbers to 20. Given a number, find how many more are needed to make 10; Use 10 as a benchmark to estimate and count; Use 10 as a benchmark to compose and decompose numbers in different ways; Relate equations to compositions and decompositions of numbers.” (K.OA.3)

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 K, MP2 is found in Unit 4, Lessons 7, 9, and 12. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade K, MP4 is found in Unit 7, Lessons 3, 13, and 16. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP1: I Can Make Sense of Problems and Persevere in Solving Them. I can ask questions to make sure I understand the problem. I can say the problem in my own words. I can keep working when things are going well and try again. I can show at least one attempt to figure out or solve the problem. I can check that my solution makes sense.”

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, Numbers 1-10, Assessments, End-of-Unit Assessment, Problem 3, K.CC.6, “a.) Circle the group that has more things.” Two images are shown: one 5-frame with 5 dots plus one more and two hands with 8 fingers raised. “b.) Circle the group that has fewer things.” Two images are shown, 7 dots in a line and 9 dots in a circular pattern.

• Unit 3, Understanding Addition and Subtraction, Assessments, End-of-Unit Assessment, Problem 3, K.OA.2, “Students represent and solve a Take From, Result Unknown story problem. Students may use objects to represent and solve the problem. The drawing provided shows the 6 circles representing the kids playing in the park and then two of them are crossed out representing the two kids who go home. Students may represent the kids going home by using color or separating them from the others. Unlike the previous item where the picture solves the problem even if it is not organized, in this case an appropriate picture needs to distinguish the two kids who are going home from the 4 who are staying in order to help solve the problem. It won’t always be possible, from the written student work, to determine how a student envisions their drawing representing the story. In these cases, a personal interview may be needed. There are 6 kids playing in the park. 2 of the kids leave the park to go home. How many kids are playing in the park now? Show your thinking using drawings, numbers, words, or objects.”

• Unit 7, Solid Shapes All Around Us, Assessments, Section A Checkpoint, Problem 1, K.OA.A.1, K.OA.A.2, “Clare used 10 pattern blocks to make a puzzle. She used trapezoids and triangles. How many trapezoids did Clare use? Then how many triangles did Clare use?”

• Unit 8, Putting It All Together, Assessments, Section A Checkpoint, supports the full intent of MP2 (Reason abstractly and quantitatively) as students connect objects to written numbers. “Represent and write quantities and numbers up to 20. Count, read, and write numbers up to 20. Use objects, drawings, numbers, words, and expressions or equations to represent quantities up to 20.”

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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 5, Composing and Decomposing Numbers to 10, Section C, Lesson 10, Activity 2, Access for Students with Disabilities, “Representation: Language and Symbols, Synthesis: Make connections between the 5-frame representation that can be seen in the 10-frame that is being used. For example “Do you see a 5-frame in the 10-frame we are using here?” Reiterate the fact that when we use the 10-frame we will fill the top row first and then move from left to right. If time allows, show a non-example of what a 10-frame could look like. Provides accessibility for: Visual-Spatial Processing, Conceptual Processing.”

• Unit 6, Numbers 0-20, Section B, Lesson 7, Activity 2, Access for Students with Disabilities, “Action and Expression: Expression and Communication, Synthesis: Identify connections between the strategy of counting starting at 1 and counting on from 10. For example: ‘Since I know that this 10-frame is full I can start counting at 11. I do not need to count all the dots in the 10-frame again.’ Provides accessibility for: Conceptual Processing”

• Unit 7, Solid Shapes All Around Us, Section B, Lesson 12, Activity 1, Access for Students with Disabilities, “Representation: Language and Symbols, Synthesis: Make connections between the rectangular prism and the shape that is not a rectangular prism. For example, hold them side by side so students can visually see the differences. Provides accessibility for: Conceptual Processing.”

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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 2, Numbers 1-10, Section B, Practice Problems, Problem 6 (Exploration), “Make a set of cards with images. Some cards can have the same number of images and some cards can have different numbers of images. Trade your cards with a partner. Turn over two cards and decide if they have the same number or if one has fewer and one has more.”

• Unit 4, Understanding Addition and Subtraction, Section A, Practice Problems, Problem 5 (Exploration), “Start with a full 5-frame. Player 1 rolls a cube on the number mat and takes away or adds that number of counters while player 2 is not looking. Then player 2 figures out what player 1 did. Players take turns switching roles.”

• Unit 7, Solid Shapes All Around Us, Section B, Practice Problems, Problem 5 (Exploration), “a. Count out 18 connecting cubes. Can you build a box with your cubes?; b. Count out 20 connecting cubes. Can you build a box with your cubes?”

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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, Flat Shapes All Around Us, Section B, Lesson 13, Activity 2, “Students use positional words to describe the location of pattern blocks within a larger shape. Access for English Learners - Listening, Speaking: MLR8 Discussion Supports. For each description that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language, specifically position words.”

• Unit 4, Understanding Addition and Subtraction, Lesson 13, Activity 1, “Access for English Learners - Representing, Listening: MLR2 Collect and Display. Circulate, listen for and collect the language students use as they create story problems. On visible display, record words and phrases such as: ‘more,’ ‘joined,’ ‘went away,’ ‘take away,’ and ‘less.’ Review the language on the display, then ask, ‘Which of these words tell you the story is about addition?’ and ‘Which of these words tell you the story about subtraction?’”

• Unit 7, Solid Shapes All Around Us, Lesson 3, Warm-up, Instructional Routine, MLR7: Compare and Connect, Notice and Wonder, "The purpose of this warm-up is to elicit the mathematical questions that students produce about shapes composed of pattern blocks, which will be useful when students create and ask questions about shapes in a later activity. While students may notice and wonder many things about the shape, the questions that students can answer about the image are the important discussion points. As students discuss and justify their questions and answers, they share a mathematical claim and the thinking behind it (MP3)."

The materials reviewed for Open Up Resources K-5 Math Kindergarten 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, Numbers 1-10, Section A, Lesson 3, Activity 1, Student Work Time, “Give each group of students a bag of pattern blocks. ‘Take the pattern blocks out of your bag. Are there more orange squares or green triangles?’ 30 seconds: quiet think time. 30 seconds: partner discussion. ‘How do you know if there are more orange squares or more green triangles?’ Share responses. ‘Figure out and tell your partner how many orange squares you have. Then figure out how many green triangles you have.’ 2 minutes: partner work time. ‘Switch your bag of objects with another group.’ Repeat the steps above, asking ‘Are there fewer …?’ instead of ‘Are there more …?’”

• Unit 4, Understanding Addition and Subtraction, Section B, Lesson 9, Activity 1, “Groups of 2. Give students access to two-color counters, connecting cubes, and markers. Read and display the task statement. ‘Tell your partner what happened in the story.’ 30 seconds: quiet think time. 1 minute: partner discussion. Monitor for students who accurately retell the story. Choose at least one student to share with the class. Reread the task statement. ‘Show your thinking using drawings, numbers, words, or objects.’”

• Unit 6, Numbers 0-20, Section A, Lesson 3, Activity 3, “The purpose of this activity is for students to learn stage 1 of the Find the Pair center. Students develop fluency with addition and subtraction within 5 as they find the number that makes 5 when added to a given number. Each student draws a hand of 5 cards. Students take turns asking their partner for a card that goes with one of their cards to make 5. When students receive a match, they write an expression. Students draw a new card when they do not receive a match. Students may use math tools such as 5-frames or draw a picture to make 5.”