3rd-5th Grade - Gateway 3

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for providing teacher 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.

Materials provide comprehensive guidance that assists teachers in presenting the student and ancillary materials. Each unit contains a Unit Overview that provides a summary of the unit, a vocabulary list, the materials needed, and the Common Core State Standards taught throughout the unit. Each Unit Overview also includes resources, such as the Unit Teacher Edition, Unit Glossary, Routine Facilitation Guide, and Unit Math Language Development Resources, to support teachers. The Unit Teacher Edition provides guidance on the Math of the Unit, Unit at a Glance, Lesson Material and Prep, Assessments, Differentiation, Accessibility, Math Identity and Community, Language Development, Technology, Professional Learning, Connections to Future Learning, Unit Story, and Assess and Respond Pre-Unit Check. This comprehensive document also outlines each sub-unit and lesson.

A Grade 3 example is:

• Unit 2: Area and Multiplication, Unit Overview states,“Explore area concepts and relate area to multiplication using rectangles and rectilinear shapes. Sub-Unit 1: Describe area as the number of unit squares that cover a plane figure without gaps and overlaps. Measure the areas of rectangles by counting unit squares. Sub-Unit 2: Explain why the area of a rectangle can be determined by multiplying the side lengths. Solve problems involving the areas of rectangles. Sub-Unit 3: Determine the areas of figures composed of rectangles.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of specific learning objectives. The Course Overview, Navigating This Program, describes support for facilitation throughout the program. Materials state, “Throughout this Teacher Edition, lesson guidance for teachers is organized clearly and consistently so that they have all of the information they need at their fingertips.” In the Lesson at a Glance section, materials explain, “The Lesson at a Glance page describes the purpose of the Warm-Up, Activities, Synthesis, and Show What You Know. Teachers will find suggested timing for each part of the lesson, as well as guidance on whether students should work individually, in pairs, in small groups, or with the whole class.” In the Teacher Edition, each activity includes a Purpose statement: “The Purpose of each activity is highlighted here, as well as suggestions for the student grouping, time frame, and screen pacing for the activity.” Each lesson contains one, two, or three activities, described as “the heart of each lesson.” Materials explain, “Students notice, wonder, explore, calculate, predict, measure, explain their thinking, settle disputes, create challenges for their classmates, and more. Guidance is provided to help teachers Launch, Monitor, and Connect students’ thinking over the course of each activity. Teachers will also find suggestions for pacing, facilitation moves, discussion questions, examples of early student thinking, ideas for students who may enjoy a challenge, ways to increase access to the language and content, as well as opportunities to build and develop the math community in your classroom. The suggestions for facilitation provide comprehensive support for teachers as they prepare for and teach lessons.”

Amplify Desmos Math PD Library, Getting Started, Grades K–5, Program Guide, page 48, Student Activity Screens state, “To make planning and teaching seamless, tips for instruction are available in both the print Teacher Edition and digitally at point of use. At the bottom of Activity Screens, the teacher will see suggestions for facilitation to support great classroom conversations:

• Teacher Moves: Suggestions for pacing, facilitation moves, discussion questions, examples of early student thinking, and ideas for early finishers, as well as opportunities to build and develop the math community in your classroom.

• Sample Responses: One or more examples of a possible student response to the problem.

• Student Supports: Facilitation suggestions to support students with disabilities and multilingual students.”

The Teacher Edition also offers facilitation notes with Launch, Monitor, and Connect suggestions.

Grade 5 examples include:

• Unit 2: Fractions as Quotients and Fraction Multiplication, Lesson 4, Teacher Edition, Activity 2, the materials state, “Purpose: Students use the relationship between division expressions and their fractional quotients to write story problems when given a division equation or a fraction. Launch: Read aloud the directions from the Student Edition. Ask: ‘What information has been provided in the division story problems we have solved so far?’ ‘What information has been unknown or missing?’ Say, ‘Complete Problems 1 and 2 with your partner. Join another pair to complete Problem 3.’ Monitor: After students have completed Problem 2, refer to the D Differentiation Teacher Moves table on the following page. If students need help getting started . . . Ask, ‘What do you know about this equation?’ Ask, ‘How could you use our list of things that can be shared or divided to get started?’ Connect: Invite students to share their story problems from Problem 2 by displaying student work. Ask, ‘How are these problems similar? How are they different?’ Ask (if not yet mentioned during discussion), ‘Why were you able to write a story problem when only given a fraction?’ Key Takeaway: Say, ‘You can use what you know about the relationships between the dividend and numerator and the divisor and denominator to write equal-sharing story problems.’”

• Unit 5: Place Value Patterns and Decimal Operations, Lesson 11, Screen 4, Activity 1, the materials state, “Complete Problems 1–3 (pg. 448) with your partner.” Teacher Moves, “Launch: Read aloud the introduction and Problem 1 from the Student Edition. Say, ‘Complete Problems 1–3 with your partner.’ Monitor: After students have completed Problem 1, refer to the Differentiation table. If students need help getting started . . . Ask, ‘What does it mean to determine the difference between 2 different-length scarves?’”

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for containing explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.

Materials contain adult-level explanations and examples of the more complex grade-level concepts so that teachers can improve their own knowledge of the subject. Each Unit Overview includes three teacher-facing pages: Math of the Unit, Professional Learning, and Connections to Future Learning that explain grade-level concepts, standards, and their progression across grade levels. The Math of the Unit page explains how the unit content aligns with standards, coherence across grade levels, and aspects of rigor, while also pointing out connections to both prior and future learning. The Professional Learning page provides explanations of the mathematics in the unit and describes instructional approaches connected to that content. The Connections to Future Learning page identifies how the unit’s mathematical ideas link to concepts that students will encounter in later grades or courses. Each Unit Overview also includes at least one Unit Overview Video that provides an overview of the content and key features of the unit, telling the story of the unit and showing how the sub-units fit together. When possible, the video highlights key interactions, models, and strategies used within the unit. For example, in Grade 4, Unit 3: Extending Operations to Fractions, the video describes what students will be able to do by the end of the unit, identifies what might be tricky for students, and explains the progression of learning in each sub-unit while manipulating online tools to show key mathematical understandings.

Evidence demonstrates that units provide resources to support teachers in understanding the progression of mathematics across the course. For example, the Grade 5 Overview states, “Each unit includes a range of resources designed to support teachers in thinking through the progression of mathematics that students will engage with over the course of the unit. These resources can support teachers in their unit planning, as well as choices they make in response to students’ thinking, strengths, and needs that arise over the course of the unit.”

Materials also provide sub-unit– and lesson-level explanations and examples to support teacher knowledge. Each sub-unit contains Math That Matters Most and Sub-Unit Summary pages. The Math That Matters Most page outlines how specific strategies, skills, and language develop across the sub-unit, while the Sub-Unit Summary page provides a Student Edition excerpt that presents the key mathematical learning in student-friendly language. The Grade 5 Overview further explains how lessons are structured to support teachers: “Each lesson includes one or two activities. These activities are the heart of each lesson. Students notice, wonder, explore, calculate, predict, measure, explain their thinking, settle disputes, create challenges for their classmates, and more. Guidance is provided to help teachers Launch, Monitor, and Connect students’ thinking over the course of each activity. Teachers will also find suggestions for pacing, facilitation moves, discussion questions, examples of early student thinking, and ideas for students who may enjoy a challenge, as well as opportunities to build and develop the math community in their classroom.” These supports help teachers understand both the mathematical development across the sub-unit and how students will engage with the content.

Materials contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject. The Scope and Sequence in each grade overview shows how concepts are taught across the 3-5 grade span, helping teachers understand the progression of learning across multiple grades. At the lesson level, each Lesson Overview identifies relevant prior knowledge in the Prior Learning section, with “Building On” tags that connect to standards from earlier grades or units, and highlights future concepts in the Future Learning section, with “Building Toward” tags that identify related standards in later grades. For example, in Grade 3, Unit 2: Area and Multiplication, the Math of the Unit, Professional Learning, and Connections to Future Learning explain that students encounter the concept of area as a measure of how much space a shape covers. They relate the areas of rectangles to multiplication and solve problems involving area, seeing that area is additive when working with rectilinear shapes. This work includes determining the areas and unknown side lengths of figures composed of non-overlapping rectangles. For more information about this unit, prior learning, and future learning, see the Unit Overview Video. Connections include Grade 3, Unit 4, applying equal groups and multiplication to division; Grade 3, Unit 7, analyzing similarities and differences between area and perimeter; and Grade 4, Unit 6, multiplying two-digit numbers using area diagrams and algorithms and applying the four operations to solve multi-step problems involving area and perimeter.

The Connections to Future Learning section also provides adult-level explanations that bridge across grade levels. For example, in Grade 3, Unit 3: Wrapping Up Addition and Subtraction Within 1,000, the Teacher Edition states, “In this unit, students fluently add and subtract within 1,000 using algorithms based on place value, properties of operations, and the relationship between addition and subtraction. In Grade 4, Unit 4, they will fluently add and subtract multi-digit whole numbers using the standard algorithm.”

Professional development resources also support teachers in building adult-level understanding of grade-level and future concepts. The Program Guide states, “The Unit Overview for each unit includes a Professional Development page, which lists opportunities for teachers to deepen their understanding of the math in the unit and how to teach it.

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for including a year-long scope and sequence with standards correlation information.

A Course Overview for each grade level includes a Grade Level Overview with a table of contents listing lesson titles and the standards addressed. A lesson list with standards correlation outlines alignment to grade-level standards and the Standards for Mathematical Practice. From the landing page, teachers can access a Grade Standards and Routines document that identifies which standards are addressed in each lesson. Each unit and lesson includes an overview page, in both digital and print formats, that identifies prior learning, the standards addressed, and the standards students are building toward. The Scope and Sequence outlines instructional and assessment days and shows connections across grade levels. Correlation tables for both Mathematical Content and Practice standards identify where each standard is addressed within units and lessons.

This structure is consistent across Grades 3-5. Examples from Grade 3 include:

• Unit 4: Relating Multiplication to Division, Lesson 7 landing page identifies the standards as Addressing MP7, MP8, 3.OA.B.6, and 3.OA.B.7.

• Unit 5: Fractions as Numbers, Unit Overview (Teacher Edition) lists the focus content standards, including, “Students develop an understanding of fractions as numbers, explore equivalence of fractions, and compare fractions by reasoning about their size. (3.NF.A MAJOR WORK, 3.G.A SUPPORTING WORK)” The overview also identifies the Standards for Mathematical Practice such as MP1, MP2, MP3, MP4, MP6, MP7 and MP8 with descriptions of how students engage with them. For example, “Students describe and represent fractions. They use the structure of fractions as they explore equivalence and fraction comparisons. (MP7, MP8)”

• Grade 3 Overview, Scope and Sequence, Unit 6: Measuring Length, Time, Liquid Volume, and Weight includes 17 instructional days and 5 assessment days, for a total of 22 days.

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for explaining the program’s instructional approaches, identifying research-based strategies, and explaining the role of the standards.

Materials explain the instructional approaches of the program.

• The Program Guide, Our Philosophy, describes four core tenets of the curriculum: Math that Motivates, A Structured Approach to Problem-Based Learning, Student Thinking is Valuable and Can Be Made Evident, and Access to Grade-Level Math for Every Student, Every Day. For example, lessons are “designed around what we call the Proficiency Progression, a model that systematically builds on students' curiosity to develop lasting grade-level understanding.” 

Materials include and reference research-based strategies.

• Program guidance cites frameworks and studies that informed design. For example, lessons embed the 5 Practices for Orchestrating Productive Classroom Discussions (Smith & Stein) to structure discourse. Universal Design for Learning guidelines (Engagement, Representation, Action & Expression) and Mathematical Language Routines (Zwiers et al., 2017) are integrated into lesson supports. NCTM’s Principles to Action (2014) are referenced directly and published research on student engagement, feedback, and differentiation is cited.

Materials include and reference the role of the standards in the program.

• The Grade Overview includes a Standards document that maps content and practice standards by unit and lesson. Lesson pages mark standards as “Building On,” “Addressing,” and “Building Toward,” clarifying how learning progresses across grades. For example, in Grade 5, Unit 5: Place Value Patterns and Decimal Operations, prior learning is identified from Grade 4, Unit 4 (understanding of tenths and hundredths; describing the relationship between digits using ten times as much language; adding and subtracting whole numbers using the standard algorithm) and from Grade 5, Unit 3 (interpreting multiplication as resizing and comparing the size of products to factors; dividing whole numbers by unit fractions and unit fractions by whole numbers). Future learning is identified in Grade 5, Unit 6 (converting metric measurements, including decimal measurements, by multiplying and dividing by powers of 10) and in Grade 6, Unit 5 (performing all four operations with decimals to any place).

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Course Overview Year-long Materials List provides the materials needed throughout the year along with the lessons they correspond to. Each Unit Teacher Edition includes a Lesson Materials and Prep section with a list of materials for the lessons in the unit. Additionally, each Lesson at a Glance Prep Checklist lists the materials needed for that specific lesson.

Examples in Grade 3 include the following; however, each grade has its own set of examples.

• Grade Overview, Year-Long Materials List, butcher paper, chart paper, coloring tools, containers, dry-erase markers, folders, markers, metersticks, objects, paper clips, paper, scissors, sticky notes, straightedges, tape, and yardsticks. 

• Unit 1: Introducing Multiplication, Unit Overview, Unit Teacher Edition, Lesson Materials and Prep, lists the following: Lesson 2 – chart paper, markers, Ways to Represent Multiplication Situations Chart; Lesson 7 – Manipulative Kit: number cubes (1 per pair), colored pencils or crayons, paper clip, Ways to Represent Multiplication Situations Chart; Lesson 8 – chart paper, makers, Arrays Chart; Lesson 11 – tools to create a visual display. Manipulative Kit: base-ten units (2 per pair), two-color counters (25 per pair).

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for providing consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance and determining instructional next steps.

The assessment system includes multiple components across the school year. The mCLASS Beginning-of-Year Screener is a digital, norm-referenced assessment that uncovers students’ mathematical thinking and provides insight into their knowledge, strengths, and areas for support. At the start of each unit, Pre-Unit Checks help teachers identify key concepts and skills from previous grades that may need reinforcement. Each includes an Assess and Respond document with item-level details and follow-up recommendations. At the lesson level, a Show What You Know is included at the end of every lesson, with Beyond the Lesson Differentiation Tables providing suggestions for future learning.

Sub-Unit Quizzes and End-of-Unit Assessments include digital and paper answer keys, rubrics on a four-point scale (Meeting, Approaching, Developing, Beginning), and Assess and Respond documents. These resources provide correct answers, sample responses, item analyses aligned to standards and lessons, DOK levels, and differentiated guidance. End-of-Unit Assessments also include Form A and Form B versions to allow for reassessment opportunities.

Examples from Grade 4 include:

• Unit 1: Factors and Multiples, Sub-Unit Quiz, Problem 6 states, “Is 17 a prime number or a composite number?” The Assess and Respond resource identifies the concept identifying a number as prime or composite (DOK 1) and aligns the problem to standards 4.OA.B.4 and MP7. Differentiation guidance connects the problem to Sub-Unit goals, such as generating and extending shape and number patterns, determining whether a number is prime or composite, and relating the side lengths and areas of a rectangle to factors and multiples. Examples include completing Identifying Prime and Composite Numbers as a mini-lesson and asking students to explain the similarities and differences in counting on by tens and by hundreds.

• Unit 3: Extending Operations to Fractions, End-of-Unit Assessment: Form A, Problem 4 states, “Jada needs 2 pounds of walnuts for a trail mix. She has 3 packages of walnuts that each weigh 3443​ pounds. Does Jada have enough walnuts to make the trail mix? Show or explain your thinking.” The accompanying rubric aligns the problem to standards 4.NF.B.3.C, 4.NF.A.2, MP6, and MP7 and provides scoring guidance on a four-point scale (Meeting, Approaching, Developing, Beginning). For example, a “Meeting” response includes the correct choice with conceptualIn Lesson 12, Activity 1, begin with a review of the terms prime and composite. understanding shown. “Approaching” responses may include the correct choice with minor flaws in reasoning or an incorrect choice with a logical explanation. “Developing” and “Beginning” levels show incomplete understanding with significant errors. For example, a student who answers “no” and writes 112121​ or 6446​ may have multiplied by 2 pounds instead of 3 packages. Another student may attempt to multiply 3×343×43​ but make a calculation error. Assess and Respond guidance directs teachers to revisit Unit 3, Lesson 12 to support students who need additional help with this concept.

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for providing strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.

The Program Guide within the Grades K-5 Math PD Library states the following about the materials: “An excellent mathematics program requires that all students have access to a high-quality mathematics curriculum, effective teaching and learning, high expectations, and the support and resources needed to maximize their learning potential. This commitment reflects a broader push within the educational community to foster a culture of equity, ensuring that every student has the opportunity to thrive as a learner and practitioner of mathematics. The differentiation of Amplify Desmos Math extends beyond academic differences to encompass variations in student motivation, interests, and identity. Understanding and addressing these aspects are essential for creating inclusive learning environments where all students feel valued and empowered to succeed. We incorporated Universal Design for Learning guidelines (Engagement, Representation, Action & Expression) into each lesson and developed a platform that is intuitive and easy-to-use for all learners. Amplify Desmos Math incorporates research-based Mathematical Language Routines (MLRs) by providing language modality strategies like sentence frames where appropriate, both in the teacher language provided for each task and in the differentiation support section found throughout the program.”

Each grade’s Course Overview describes ways to support all students in accessing and participating in meaningful and challenging tasks. The materials state, “Lesson Facilitation Supports: Every lesson includes at least one specific suggestion that teachers can use to increase access to the lesson without reducing the mathematical demand of the tasks. These suggestions address the following areas: conceptual processing, visual-spatial processing, executive functioning, memory and attention, fine motor skills, and affective functioning.” Throughout the Teacher Edition, these accessibility supports are marked by a small circle with an “A.”

The materials also provide “Accessibility Tools: Students have the ability to control accessibility tools so that each learning experience is customized to their individual needs. In many instances, these tools can be turned on or off at any point of instruction.” These tools include text-to-speech, enlarged font, braille mode, and language selection.

In addition, the Grade-Level Overview (p. xxxi) highlights opportunities for differentiation. The materials state, “Within every lesson activity, teachers can use the Differentiation Teacher Moves suggestions to provide in-the-moment instructional support to learners as they engage in the work of the lesson. Teachers are provided with clear student actions and understandings to look for, each matched with immediately usable suggestions for how to respond to the student thinking illustrated in each row of the table. In addition to using these suggestions in the moment as teachers monitor student work, teachers can review the Differentiation table in advance to help them anticipate how students are likely to approach the activity.” Throughout the Teacher Edition, these differentiation supports are marked by a small orange circle with a “D.”

The Teacher Edition lists accessibility supports for every lesson. Each lesson includes a differentiation table with explicit next steps based on student responses to Show What You Know. Each sub-unit provides Support Mini-Lessons that “provide targeted intervention for students by using these resources.” Assess and Respond guidance is also included for each Pre-Unit Check, Sub-Unit Quiz, and End-of-Unit Assessment.

An example from Grade 3 includes:

• Grade 3, Unit 6: Measuring Length, Time, Liquid Volume, and Weight, Lesson 12, Activity 1, Launch, Accessibility: Visual-Spatial processing states, “Provide access to learning clocks, or a virtual equivalent, to support students in telling time.”

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 meet expectations for regularly providing extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.

The Program Guide within the Grades K-5 Math PD Library describes resources for extending student learning. In Beyond the Lesson, materials state, “The learning goal of each lesson is broken down for teachers into what it looks like for students to need support in the lesson goal, for students to need to keep strengthening their understanding of the lesson goal, and for students to be ready to stretch their learning. Teachers are provided with recommendations for resources to use with each group of students.” Assess and Respond states, “At each Assessment point in a unit, teachers have the opportunity to respond to student understanding…Students who are ready to strengthen or stretch their learning based on the assessment can access any of the strengthen or stretch resources aligned to the content of the assessment.” Within lessons, Differentiation Teacher Moves include “Stretch” suggestions. The materials state, “Within every lesson activity, teachers can use the Differentiation Teacher Moves suggestions to provide in-the-moment instructional support…Teachers are provided with clear student actions and understanding to look for, each matched with immediately usable suggestions.”

In addition to in-lesson supports, Amplify Desmos Math provides Sub-Unit Extensions. The Intervention and Extension Resources provides Sub-Unit Extensions that allow students to explore mathematical concepts from the sub-unit in greater depth. For example, in Grade 3, Unit 7: Two-Dimensional Shapes and Perimeter, Sub-Unit 1, students determine the quantities of groups of up to 10 objects. Students make a group with fewer objects than a given group. Students make a group with the same number of objects as a given group. Students make a group with more objects than a given group.

Challenge Creators also extend student learning. In Grade 4, Unit 5: Multiplicative Comparison and Measurement, Lesson 16, Screen 8, the student-facing prompt is “Make My Challenge,” where students design mathematical challenges and then solve those created by classmates. Students create a challenge for classmates by selecting ingredients for a recipe and calculating the total time required for all steps.

Lesson-level Stretch opportunities are consistently embedded. In Grade 5, Unit 6: More Decimal and Fraction Operations, Lesson 6, Activity 1, Differentiation table states, “Stretch, Ask, ‘Would this strategy still work if you were converting to centimeters? Why or why not?’”

The materials reviewed for Amplify Desmos Math Grades 3 through Grade 5 include manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Virtual and physical manipulatives support students’ understanding throughout the curriculum. Each unit’s Materials and Prep section identifies the manipulatives needed, and lesson-specific materials are listed in the Lesson Prep Checklist on the Lesson at a Glance page. Virtual manipulatives are integrated into many lessons, often embedded within student digital screens that provide Responsive Feedback. 

Examples include:

• Grade 3, Unit 2: Area and Multiplication, Lesson 6, Activity 1, students draw rectangles representing multiplication expressions on square grid paper to connect area and multiplication expressions. Launch states, “Say, ‘Today you will play a new center called Rectangle Rumble.’ Display the Center materials and read aloud the Directions from the Student Edition. Demonstrate how to play Rectangle Rumble, Stage 1 by inviting a student to act as a partner. Say, ‘Take turns until the grid cannot fit any more rectangles. The player with the greater total area wins.’” Connect states, “Invite students to share numbers they spun and rolled and how they made the rectangle based on the product. Select and sequence their responses in the order shown in the Differentiation table. Ask, ‘What is similar and different about the strategies that were shared?’ Key Takeaway: Say, ‘To create a rectangle with a given area, you can use strategies such as counting square units, thinking about equal groups, or using the structure of arrays.’”

• Grade 4, Unit 7: Angles and Properties of Shapes, Lesson 3, Activity 2, students use rulers/straightedges and a dot grid to draw and identify intersecting, perpendicular, and parallel lines and line segments then connect the drawing to strategies they can use to determine whether lines or line segments are parallel. Launch states, “Say, ‘Let’s look at a dot grid. Each dot represents a point.’ Demonstrate drawing a line on the dot grid, including arrows on both ends. Label 2 points on the line with the letters X and Y. Say: ‘The letters in a figure like this name points, which are often on line segments or lines. The line segments and lines in a figure can also be named using letters, so this would be line XY. You could also call it line YX.’ Complete Problems 5–9 with your partner.” Student Edition states, “Here is a dot grid. Each dot represents a point.” Problem 5 says, “Draw a line through at least two points. Label the line JK.” Problem 6 says, “Draw another line that goes through at least two points and intersects your first line. Label the line LM.” Problem 7 says, “Draw a line that goes through at least two points and is perpendicular to line JK. Label the line NO.” Problem 8 says, “Draw a line that you think would be parallel to line LM. Label the line PQ. If a line cannot be drawn, be prepared to explain why.” Connect states, “Ask, ‘Which sides of the quadrilateral did you think were parallel? Why?’ ‘What strategies can you use to help you determine whether lines or line segments are parallel?’ Annotate the quadrilateral as students share, and then play the animation.” Key Takeaway states, “Say, ‘To determine whether lines or line segments are parallel, you can extend the lines to see whether they intersect. You can also measure whether the distance is the same between the lines in more than one location.’”

• Grade 5, Unit 1: Volume, Lesson 4, Activity 1, students connect their work with building three-dimensional rectangular prisms with cubes to determine the volumes of rectangular prisms shown in two-dimensional images. Launch states, “Ask, ‘How is this image of a rectangular prism related to a rectangular prism built with unit cubes?’ Read aloud the introduction and Problems 1 and 2 from the Student Edition. Say, ‘Complete Problems 1 and 2 with your partner.’” Student Edition states, “Each image on the next page shows how different households arranged their garbage cubes for collection on trash day.” Problem 1 says, “Record the volume of trash that each household produced. Be prepared to explain your thinking.” Problem 2 says, “Find 2 prisms that are related. Explain how they are related. Find another 2 prisms that are related. Explain how they are related. What other relationships do you see among the trash arrangements?” Connect states, “Invite students to share their strategies for Problem 1 Households A, B, and D. Record students’ thinking by annotating the images of the rectangular prisms. Ask (if not yet mentioned during discussion), ‘How was determining the volume of a figure shown as a two-dimensional image similar to determining the volume of a three-dimensional figure? Different?’”Key Takeaway states, “Say, ‘You can determine the volume of a rectangular prism shown in a two-dimensional image by using your understanding of layers composed of equal groups of unit cubes.’”