3rd Grade - Gateway 3

The materials reviewed for Open Up Resources K-5 Math Grade 3 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 3 and across all grades.

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

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

• Unit 1, Introduction to Multiplication, Overview, “Students learn that multiplication can mean finding the total number of objects in a groups of b objects each, and can be represented by a\times b. They then relate the idea of equal groups and the expression a\times b to the rows and columns of an array. In working with arrays, students begin to notice the commutative property of multiplication. In all cases, students make sense of the meaning of multiplication expressions before finding their value, and before writing equations that relate two factors and a product.”

• Unit 5, Fractions as Numbers, Section B, Lesson 7, Activity 1, “The purpose of this activity is for students to practice identifying fractional intervals along a number line. This is Stage 2 of the center activity, Number Line Scoot. This activity encourages students to count by the number of intervals (the numerator). Students have to land exactly on the last tick mark, which represents 4, to encourage them to move along different number lines. While this activity does not focus on equivalence, it gives students exposure to this idea before they work more formally with it in the next section. In the synthesis, students relate counting on a number line marked off in whole numbers to their number lines marked off in fractional-sized intervals. It may be helpful to play a few rounds with the whole class to be sure students are clear on the rules of the game. Keep the number line game boards for center use.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section C, Lesson 9, Activity 2, Activity Synthesis, provides teachers guidance on student telling and writing time. "Invite students to share the times they drew the clocks. Emphasize how they distinguish between the hour and minute hands for someone else to be clear on the time they are showing. Consider asking: 'Were there any times that confused you at first or were harder to show?' (For 3:18 I had to draw the hands really close together.) 'Does anyone have suggestions for how to handle some of the times that might be hard to show? When you were drawing a time for your partner, what did you have to keep in mind?' "

The materials reviewed for Open Up Resources K-5 Math Grade 3 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, Introduction to Multiplication, Overview, Throughout this Unit, “Number Talks are likewise designed to help students build fluency with equal groups and multiplication expressions. The sequence of expressions encourages students to relate multiplication to skip-counting. For example, in the sequence 1\times10, 2\times10, 3\times10, 4\times10, students can discover that the products increase in the same way as in skip-counting by 10. Some Number Talks elicit students’ understanding of addition and subtraction within 100 in preparation for the work in an upcoming unit.”

• Unit 4, Relating Multiplication to Division, Section C, Lesson 12, Multiply Multiples of Ten, Lesson Narrative, “The work of this lesson connects to previous work because students have used strategies based on properties of operations to multiply within 100. Now, students extend this work and consider place value to multiply one-digit numbers by multiples of 10. Students complete a problem in context in which they explore how 180 can be grouped into multiples of ten in different ways. Students analyze two strategies for multiplying a single-digit number by a multiple of ten, then complete similar problems using the strategy of their choice. Throughout the lesson the associative property is used as a strategy to think of problems like 3\times60  as 18 tens or 18\times10.”

• Unit 7, Two-Dimensional Shapes and Perimeter, Section A, Lesson 1, Preparation, Lesson Narrative, “In previous grades, students sorted shapes into categories based on the attributes of the shape. In this lesson, students revisit this work and learn the terms angle in a shape and right angle in a shape to describe the corners of shapes. This will be helpful in later lessons as students further sort triangles and rectangles by additional attributes.”

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

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

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

The materials reviewed for Open Up Resources K-5 Mathematics Grade 3 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 3, Wrapping Up Addition and Subtraction Within 1,000, Section D, Lesson 17, Standards, “Addressing: 3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Building Towards: 3.OA.D.9.”

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 represent and solve multiplication problems through the context of picture and bar graphs that represent categorical data.” Additionally, each Unit Section provides Section Learning Goals, “Interpret scaled picture and bar graphs.”

• Unit 2, Area and Multiplication, Section B, Lesson 10, Lesson Narrative, “In previous lessons, students found the area of rectangles with tiles, grids, partial grids, or linear measurements marked along the sides of the rectangle.  Students also used rulers to find the area of rectangles. The problems in this lesson are about a community garden. Consider launching the lesson with a read-aloud of City Green by DyAnne DiSalvo-Ryan to get students thinking about different aspects of a community garden. Students might draw squares within rectangles, draw tick marks on side lengths, count groups, or multiply to find area in the lesson. Any reasoning that makes sense to them is acceptable. 

• Unit 5, Fractions as Numbers, Unit Overview, “Students develop an understanding of fractions as numbers and of fraction equivalence by representing fractions on a diagram and number lines, generating equivalent fractions, and comparing fractions.” 

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Section C Overview, “In this section, students learn to tell and write time to the nearest minute and to show given time on an analog clock. They also solve elapsed time problems with an unknown start time, unknown duration, or unknown end time.”

The materials reviewed for Open Up Resources K-5 Math Grade 3 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 3 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. “Fraction Strips (3-4): Fraction strips are rectangular pieces of paper or cardboard used to represent different parts of the same whole. They help students concretely visualize and explore fraction relationships. As students partition the same whole into different-size parts, they develop a sense for the relative size of fractions and for equivalence. Experience with fraction strips facilitates students’ understanding of fractions on the number line.”

• 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 13 - Gather: Paper Clips, Two-color counters; Copy: Five in a Row Addition and Subtraction Stage 8 Gameboard, Five in a Row Multiplication and Division Stage 2 Gameboard.”

• Unit 7, Two-Dimensional Shapes and Perimeter, Section D, Lesson 14, Materials Needed, “Activities: Colored pencils, crayons, or markers (Activity 1); Centers: Folders (Can You Draw It?, Stage 4), Number cards 0-10 (How Close?, Stage 5).”

The materials reviewed for Open Up Resources Math Grade 3 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, Area and Multiplication, Section A Checkpoint, Problem 2, 3.MD.C.5.b, "Andre places these squares on the rectangle and says the area of the rectangle is 10 square units. Do you agree with Andre? Explain your reasoning."

• Unit 5, Fractions as Numbers, Section A, Lesson 3, Cool-down, “Shaded Fraction Assessing 3.NF.A.1: The rectangle represents 1 whole. What fraction is shaded? Explain your reasoning.” The Cool-down includes a diagram of a rectangle divided into 6 equal parts. 5 of the 6 parts are shaded.

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Assessments, End-Of-Unit Assessment, Problem 6, “3.MD.A.2: Students subtract within 1,000 to answer a question about weights. Students may add 835 and 143 if they do not read the question carefully. This would be the total weight of the two whales in kilograms. Students may subtract by place value, as shown in the solution, or they may use a number line or other diagram. A young humpback whale weighs 835 kg. A young killer whale weighs 143 kg. How much heavier is the humpback whale than the killer whale? Explain or show your reasoning.”

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 3, MP8 is found in Unit 1, Lessons 11, 14, 15, 19. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practices Chart, Grade 3, MP4 is found in Unit 7, Lessons 3, and 15.. 

• Resources, Course Guide, How to Use the Materials, Noticing and Assessing Student Progress In Mathematical Practices, Standards for Mathematical Practice Student Facing Learning Targets, “MP5: I can Use Appropriate Tools Strategically. I can choose a tool that will help me make sense of a problem. These tolls might include counters, base-ten blocks, tiles, protractor, ruler, patty paper, graph, table, or external resources. I can use tools to help explain my thinking. I know how to use a variety of math tools to solve a problem.”

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, Area and Multiplication, Assessments, Section B Checkpoint, Problem 2, 3.MD.7c “Priya and Han are designing a tree fort with a rectangular floor. They want at least 30 square feet of floor space. The sides all have to measure less than 8 feet. What are two possible pairs of side lengths for the floor of the fort? Explain your reasoning.”

• Unit 4, Relating Multiplication to Division, Assessments, End-of Unit Assessment, Problem 1, 3.OA.7, “Students are building toward fluency with multiplication and division facts by the end of the year. This item gives students an opportunity to demonstrate fluency for multiplication facts within 100. If a student incorrectly answers several questions in this item then they may need to spend some extra time practicing multiplication. Students who select E are probably using addition instead of multiplication and students who select C are probably confusing 4\times5 with 4\times6. Students who select both C and D need more practice with single digit multiplication.” Problem 1, “Select all expressions that have a value of 24. A. 2\times12; B. 3\times8; C. 4\times5; D. 6\times4; E. 20\times4.”

• Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Assessments, End-of-Unit Assessment, Problem 2, 3.MD.2, “Students choose objects that weigh about 1 kilogram. The distractors are not close to 1 kilogram so if students select A, D, or E, they probably do not have a good understanding of weight or of the kilogram unit.” Problem 2, Select 3 items that weigh about 1 kilogram. A. pencil; B. laptop computer; C. pineapple; D. paper clip; E. car; F. dictionary.”

• Unit 7, Two-Dimensional Shapes and Perimeter, Section C, Lesson 11, Cool-down, supports the full intent of MP7 (Look for and make use of structure) as students draw rectangles with equal perimeters, but different areas. “Draw two rectangles that each have a perimeter of 18 units, but different areas. Explain or show your reasoning.”

The materials reviewed for Open Up Resources K-5 Math Grade 3 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, Relating Multiplication to Division, Section B, Lesson 8, Activity 1, Access for Students with Disabilities, “Representation: Comprehension. To support working memory, provide students with sticky notes or mini whiteboards. Provides accessibility for: Memory, Organization.”

• Unit 5, Fractions as Numbers, Section C, Lesson 13, Access for Students with Disabilities, “Engagement: Recruiting Interest. Leverage choice around perceived challenge. Invite students to select at least 3 of the 5 problems in each question to complete. Provides accessibility for: Organization, Attention, Social-Emotional Functioning.” 

• Unit 7, Two-Dimensional Shapes and Perimeters, Section A, Lesson 2, Access for Students with Disabilities, “Representation: Perception. Synthesis: Use gestures during explanation of triangle sorting to emphasize side lengths of triangles. Provides accessibility for: Visual-Spatial Processing.”

The materials reviewed for Open Up Resources K-5 Math Grade 3 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, Area and Multiplication, Section A, Problem 11 (Exploration), “How many different rectangles can you make with 36 square tiles? Describe or draw the rectangles. How are the rectangles the same? How are they different?”

• Unit 4, Relating Multiplication to Division, Section B, Practice Problems, Problem 7 (Exploration), “Noah finds 9\times8 by calculating (10\times8)-(1\times8). a. Make a drawing showing why Noah’s calculation works.; b. Use Noah’s method to calculate 9\times8.”

• Unit 7, Two-Dimensional Shapes and Perimeter, Section B, Practice Problems, Problem 6, (Exploration), “a. Draw some different shapes that you can find the perimeter of. Then find their perimeters.; b. Can you draw a rectangle whose perimeter is odd? Explain or show your reasoning.; c. Can you draw a pentagon or hexagon (or a figure with even more sides) whose perimeter is odd?”

The materials reviewed for Open Up Resources K-5 Math Grade 3 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, Wrapping Up Addition and Subtraction Within 1,000, Section B, Lesson 12, Activity 1, “Access for English Learners - Conversing, Representing: MLR8 Discussion Supports. Display sentence frames to support partner discussion: ‘Can you say more about …? and Why did you …?’”

• Unit 4, Relating Multiplication to Division, Section C, Lesson 13, 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. How did the number of chairs show up in each method? Why did the different approaches lead to the same outcome? To amplify student language, and illustrate connections, follow along and point to the relevant parts of the displays as students speak."

• Unit 7, Two-Dimensional Shapes and Perimeter, Lesson 1, Activity 1, “Access for English Learners - Conversing, Reading: MLR2 Collect and Display. Collect the language students use to sort the cards into categories. Display words and phrases such as: “equal sides,” “equal lengths,” “corners,” “diagonal,” “straight,” “curved,” “slanted,” and “shaded.” During the synthesis, invite students to suggest ways to update the display: ‘What are some other words or phrases we should include?” etc. Invite students to borrow language from the display as needed.’"

The materials reviewed for Open Up Resources K-5 Math Grade 3 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, Area and Multiplication, Section B, Lesson 9, Activity 2, “The purpose of this activity is for students to create a rectangle with a given area. Students use what they know about area and the structure of rectangles to decide on the side lengths of the rectangle. Students use tape (painter’s or masking) to create the rectangles. They should have enough tape to create square feet within the rectangle, but should be encouraged to mark the 1 foot intervals to help them visualize the square feet inside the rectangle, if needed. In the synthesis, each group shares strategies for creating a rectangle and how they know the area is the given number of square feet. When students think about the structure of a rectangle and use it to create a rectangle with a given area they are looking for and making use of structure (MP7).”

• Unit 4, Relating Multiplication to Division, Section B, Lesson 10, Activity 2, “Groups of 2. ‘Take a minute to read the directions of the activity. Then, talk to your partner about what you are asked to do.’ 1 minute: quiet think time. 1 minute: partner discussion. Answer any clarifying questions from students. Give students access to colored pencils, crayons, or markers. ‘Mark or shade each diagram to represent how each student found the area.’ 3–5 minutes: independent work time. ‘Share with your partner how you used the rectangles to show each expression.’ 3–5 minutes: partner discussion.”

• Unit 8, Putting It All Together, Section C, Lesson 10, Activity 1, “The purpose of this activity is for students to relate multiplication and division using a variety of representations. Students are given a card with a base ten diagram, tape diagram, area diagram, multiplication equation with a missing factor, or division equation. Students need to find the other student who has the card that matches their card. Each pair of cards includes a division equation. After students find the student with the matching card, they work together to create another diagram and a division situation that their cards could represent (MP2).”