3rd Grade - Gateway 3

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that underlying design of the materials distinguishes between problems and exercises.

The Solve & Share, Look Back, Visual Learning Bridge, and Convince Me! sections contain problem sets that connect prior learning and/or engage students with a problem in which new math concepts are taught. The Guided Practice, Independent Practice, and Problem Solving sections provide problem sets for students to build on their understanding of the new concept. Assessment Practice problems at the end of each lesson provide opportunities for students to apply what they have learned and can be used to determine differentiation. Additional Practice problems are found in the Additional Practice Workbook that accompanies each lesson and support students in developing mastery of the current lesson and topic concepts.

Examples include, but are not limited to:

• In Lesson 2-2, the Solve & Share states, “Each chicken has 2 legs. How many legs are there in a group of 9 chickens? Show how you decided." The authors state the purpose of this problem as, “Students continue using their knowledge of multiplication to see the patterns that exist in products with whole numbers when 2 or 5 is a factor. Their work shows prior and emerging understandings you can build on during the Visual Learning Bridge."
• In Lesson 14-2, Independent Practice, students apply what they have learned about elapsed time in the lesson to solve problems independently. The directions for this section of the lesson state, “Use clocks or number lines to find the elapsed or end time." 

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that design of assignments is not haphazard and exercises are given in intentional sequences.

Lessons are structured to build mastery. First, students are introduced to concepts and procedures with a problem-solving experience in the Solve & Share section. Next, the important mathematics are explicitly explained with visual direct instruction and connected to the problem-solving experience in the Visual Learning Bridge. Finally students are assessed at the end of each lesson so appropriate differentiation can be provided in the Assessment Practice section.

The following is an example of sequential learning from Lesson 9-1: Add two 3-digit numbers by breaking apart problems into smaller problems:

• Step 1: Solve & Share: “There are 2 bins of oranges. One bin has 378 oranges. The other bin has 243 oranges. Find the sum of 378 + 243. Think about place value.” The authors state the purpose of this lesson as, “Students use what they know about place value and breaking apart numbers to add two 3-digit numbers. Their work shows prior and emerging understandings you can build on during the Visual Learning Bridge." 
• Step 2: Visual Learning Bridge: “Margot counted 243 manatees one year and 179 manatees the next. How many manatees did Margot count all together?” Students are explicitly taught how to break apart numbers using place value to add.
• Step 3: Assessment Practice: “Which shows breaking 622 + 247 apart by place value to find the sum?”

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide variety in what students are asked to produce.

The instructional materials prompt students to produce answers and solutions within the Solve & Share, Guided Practice, Independent Practice, Problem Solving, and 3-Act Math sections. Students are also given opportunities to produce oral arguments and explanations during lesson discussions. Additionally students critique fictional student work. Finally, students are often prompted to solve problems “any way they choose” which provides opportunities for students to create diagrams and mathematical models. Examples include, but are not limited to:

• In Lesson 1-3, Question 10, students are shown the equation 8 x 5 = 5 x ____ and then asked to, “Use the Commutative Property of Multiplication to find the missing factor." 
• In Lesson 4-8, Question 17 states, “Rosi and Karen are trying to solve 4 = ? ÷ 8. Rosi says the value of the unknown is 32. Karen says the value of the unknown is 2. Is Rosi or Karen correct? Explain."
• In Lesson 12-3, Question 11 states, “Jenna and Jamal are making rugs. They have the finished parts shown. Draw pictures to show each whole rug. Whose rug will be longer when it is finished? Explain." 

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

Manipulatives and other mathematical representations are aligned to expectations and concepts in the standards. Visual manipulatives are embedded within the problem sets to represent ideas and build conceptual understanding. Students and teachers have access to digital manipulatives to build conceptual understanding and solve problems.

Examples include, but are not limited to:

• Students have access to two color counters, number lines, centimeter grid paper, 1-inch grid paper, cubes, paper cups, place value blocks, string/yarn, multiplication table, two color tiles, rulers, fraction strips, egg cartons, clock faces, 1 liter bowls, containers and pans, gram and kilogram weights, metric weights, quadrilaterals, and triangles.

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains an overview with discussion questions to increase classroom discourse, support for the teacher of what to look for, and ways to ensure understanding of the concept. Essential questions found at the beginning of each topic are revisited throughout the topic and teaching strategies for answering the Topic Essential Questions are provided in the Topic Assessment pages. Examples include, but are not limited to:

• In Topic 4, Essential Questions, students are asked, “How can you use known multiplication facts to find unknown division facts? How are multiplication and division related?”
• In Lesson 6-2, Solve & Share, Discussion Questions,  students are asked, “How are the unit squares in each grid different? What information do you need to know about the size of each unit square to solve the problem? How does the size of one unit square in the top of the grid compare to the size of one unit square in the bottom grid? How do the sizes of the unit squares change the area measurement?”
• In Lesson 11-3, Visual Learning Bridge, Discussion Questions, students are asked,“What is the hidden question in the problem? When you estimate to check your answer, what will you round $325 to? Why do you need two operations to solve this problem?”

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.

Each topic contains a Topic Planner providing an overview of every lesson, which includes: Lesson Objectives, Essential Understanding, Vocabulary, Materials Needed, Technology and Activity Centers, and Math Standards. The Topic Planner also includes lesson resources such as the Digital Student Edition, Additional Practice Workbook, available print materials, Digital Lesson Courseware, and lesson support for teachers. Examples include, but are not limited to:

• Visual Learning Bridge lessons include a Visual Learning Animation Plus for each lesson. 
• Digital math tools and games, technology resources, and PDF work pages available for each lesson are noted.
• Each Lesson Overview includes an Objective and an Essential Understanding, “I can” learning target statements written in student language, CCSSM that are either being “built upon” or “addressed” for the lesson, Cross-Cluster Connections, the aspect(s) of rigor addressed, support for English Language Learners, and possible Daily Review pages with Today’s Challenge to be implemented.
• Each lesson activity contains an overview, guidance for teachers, student-facing materials, anticipated misconceptions, extensions, differentiation support based on Quick Checks, and opportunities for further practice in the online materials. 
• Annotations and suggestions on how to present the content within the lesson structure of: Step 1: Engage and Explore; Step 2: Explain, Elaborate, and Evaluate; and Step 3: Assess and Differentiate are provided. The corresponding Launch section explains how to set up the activity and what to tell students. 

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials contain a teacher’s edition that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

Materials explain how mathematical concepts are built from previous grade levels or topics and lessons as well as how the grade-level concepts fit into future grade-level work. Additionally, Look Back, This Lesson, Look Ahead, and Cross-Cluster Connections are found in the Coherence Section for each lesson. Examples include, but are not limited to:

• In Topic 3, Math Background: Coherence, the Look Back states, “Grade 2: Even Numbers and Arrays: In Topic 2, students explored even and odd numbers. They also wrote equations for arrays using rows or columns.”  The authors explain how this is connected to use known facts, equal groups, and multiply with three factors.  
• In Lesson 12-2, Lesson Overview, the Look Back states, “In the previous lesson, students learned that when a region is partitioned into a nonzero number of equal parts, each equal part can be named using a unit fraction. This Lesson: Students continue their study of fractions by learning that a fraction represents multiple copies of a unit fraction.  Look Ahead: Students use what they learned about fractions to determine and draw whole (unit) shapes given one part (unit fraction) of a shape."

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

The Program Overview provides information about using assessments to gather information about students’ prior knowledge. The authors state, “Readiness assessments help you find out what students already know. Formative instruction in lessons inform instruction. Various summative assessments help you determine what students have learned. Rubrics are provided for assessing math practices. Auto-scored online assessments can be customized.” The Readiness Test can be printed or distributed digitally. In this assessment, prerequisite skills from the prior grade necessary for understanding the grade-level mathematics are assessed. The Daily Review is designed to engage students in thinking about the upcoming lesson and/or to revisit previous grades' concepts or skills. Review What You Know, found in the Topic Opener, gathers information about prior knowledge and provides an Item Analysis for Diagnosis and Intervention. Examples include, but are not limited to:

• In Grade 3 Readiness Assessment, Question 5 states, “Tanika has 16 tulips. She gives 7 tulips to friends. How many tulips does she have left?" Four multiple choice answers are provided (2.OA.1 and 2.OA.2).
• In Topic 8, Review What You Know, Question 11 states, “Atif puts 45 rocks in a display box. He has 54 rocks in all. Which expression can be used to find how many rocks are not in the display box?” (3.NBT.2)

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide strategies for teachers to identify and address common student errors and misconceptions.

Lessons include an Error Intervention section identifying where students may make a mistake or have misconceptions and how to provide support. Additionally, lessons contain side matter in the Teacher Edition that identifies possible misconceptions and ways for teachers to prevent them.  Examples include, but are not limited to:

• In Lesson 9-2, Error Intervention states, “If students are having difficulty estimating to the nearest hundred, then say Look at 538.  What digit is in the tens place? Since the digit in the tens place is less than 5, what is 538 rounded to the nearest hundred? Look at 429.  What digit is in the tens place? Since the tens digit is less than 5, what is 429 rounded to the nearest hundred? What is the sum of 500 and 400?”
• In Lesson 5-3, Visual Learning Bridge, teacher side matter prompts teachers to prevent misconceptions: “Remind students that these two ways of multiplying are strategies for finding products.  Point out that both strategies result in the same answer." 

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The lesson structure, consisting of Solve & Share, Visual Learning Bridge, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice, provides students with opportunities to connect prior knowledge to new learning, engage with content, and synthesize their learning. Throughout the lesson, students have opportunities to work independently, with partners, and in groups, and review, practice, and feedback are embedded into the instructional routine. In addition, practice problems for each lesson activity reinforce learning concepts and skills, and enable students to engage with the content and receive timely feedback. Discussion prompts in the Teacher Edition provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

Examples include, but are not limited to:

• Each Topic includes a “Review What You Know/Concept and Skills Review” that includes a Vocabulary Review and Practice Problems. This section includes review and practice on concepts that are related to the new topic. 
• The Cumulative/Benchmark Assessments, found at the end of Topics 4, 8, 12, and 16, provide review of prior topics as an assessment. Students can take the assessment online, with differentiated intervention automatically assigned to students based on their scores. 
• Different games online at Pearson Realize support students in practice and review of procedural skills and fluency.

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials offer ongoing formative and summative assessments that clearly denote which standards are being emphasized. 

Assessments are located in the Assessment Book or online portion of the program and can be accessed at any time. For each topic there is a Practice Assessment, an End-Unit Assessment, and a Performance task. Assessments in the Teacher Edition provide a scoring guide and standards alignment for each question. Examples include, but are not limited to:

• In Topic 7, Performance Task, Question 2 states, “How many fewer blue balloons were used than all of the other colors combined? Explain." This question is noted as being DOK Level 2 and addresses 3.MD.3 and MP2.
• In Topic 14, Assessment, Question 4 states, “Name the metric unit that could be used to measure the capacity of a kitchen sink. Then, using that unit, write a reasonable estimate for the capacity of a kitchen sink." This question is noted as DOK Level 2 and addresses 3.MD.2.

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials provide a detailed Scope and Sequence and the Topic Overview identifies prerequisite skills. Each lesson contains a Daily Review and a Solve & Share Activity that reviews prior knowledge and/or prepares students for the activities that follow. Each lesson contains explicit instructional support for sequencing and scaffolding. Lesson side matter provides guidance on discussion questions, sample student work, and look fors. Step 3: Assess and Differentiate, contains optional activities that can be used for additional practice or support before moving on to the next activity or lesson. Examples include, but are not limited to:

• In Lesson 6-3, Error Intervention, students are counting shaded unit squares and writing the area. The materials state, “If students do not write the correct unit for the area of the sticker, then remind them that an area measurement consists of two parts: the number of square units and the name of the square units. ‘Compare the sticker on the previous page with the sticker described in Item 1. Are they the same? How are the two stickers different? What units are used to describe the area of each sticker?’” 
• In Topic 3, Math Background: Coherence, students apply properties of multiplication facts for 3, 4, 6, 7, and 8. In the Look Back section, the materials note the Grade 2 standards needed: “In Topic 2, students explored even and odd numbers. They also wrote equations for arrays using rows or columns."

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide teachers with strategies for meeting the needs of a range of learners.

Additional Practice Materials include a lesson for each topic that includes specific questions for the leveled assignment for all learning ranges, Intervention, On-Level, and Advanced with verbal, visual, and symbolic representations. Response to Intervention strategies for each lesson give teachers “look fors,” suggestions to address the needs of struggling students, and discussion questions. Additional examples within the lesson help students extend their understanding of the concept being taught and include extra problems for the teacher to use. Differentiated Interventions, Reteach to Build Understanding, and Enrichment sections provide reteach scaffolding and concept extensions. Examples include, but are not limited to:

• In Lesson 11-2, Reteach to Build Understanding, students are presented with vocabulary and then guided through a series of problems that have partially completed portions: “Jill is in charge of scheduling fields for the youth soccer leagues. There are 4 leagues with 6 teams in each league. An equal number of teams will play on each of the 3 fields. How many teams will play on each field?” Next, students fill in the following to solve, “Step 1: Find and answer the hidden question. Hidden question: How many _____ are there in all? There are ____ leagues. There are ____ teams in each league. A= 4 x 6. A = _____. There are _____ teams in all."
• In Lesson 11-2, Enrichment, students guess a number based on the following clues: “I am thinking of a 2-digit number. Both of the number’s digits are the same. When you double the number, the resulting product is greater than 50 and less than 80. What number am I thinking of?”

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The Solve & Share, Visual Learning Bridge, Guided and Independent Practice, and Quick Check/Assessment Practice sections provide opportunities for students to apply mathematics from multiple entry points. Materials sometimes ask students to use a specific strategy, but questions within the lesson allow students to use a variety of strategies. Lesson and task narratives provided for teachers offer possible solution paths and presentation strategies for various levels. Examples include, but are not limited to:

• Lesson 3-2, Solve & Share, “There are 3 rows of pictures on a wall. Each row has 7 pictures. How many pictures are on the wall?” The helping character in the text states, “You can use appropriate tools. You can draw arrays or make arrays with counters to help solve the problem." (3.OA.5)
• Lesson 7-5 Convince Me!, “Bella has a bakery. She will use the bakery items at the right to make a gift basket worth $40. Bella wants the basket to have more than one of each bakery item. Show one way to make a gift basket." (3.OA.3)

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics.

The ELL Design is highlighted in the Teacher Edition Program Overview and describes support based on the student’s level of language proficiency: emerging, expanding, or bridging, as identified in the WIDA (World-Class Instructional Design and Assessment) assessment. An ELL Toolkit provides additional support for English Language Learners. ELL suggestions are provided in Solve & Share and Visual Learning Bridge activities. Visual Learning support is also embedded in every lesson to support ELL learners. 

Support for other special populations is also provided in the Teacher Edition Program Overview. Resources and a key are provided for Ongoing Intervention during a lesson, Strategic Intervention at the end of the lesson, and Intensive Intervention as needed at anytime. The Math Diagnosis and Intervention System (MDIS) supports teachers in diagnosing students' needs and providing more effective instruction for on- or below-grade-level students. Diagnosis, Intervention Lessons, and Teacher Support are provided through teachers' notes to conduct a short lesson where vocabulary, concept development, and practice can be supported. Online Auto Design Differentiation is also included, and supports the program after a lesson, a topic, assessments, or groups of topics. Teachers can track student progress using Assignment Reports and analyzing Usage Data. Examples include, but are not limited to:

• In Lesson 2-2, Solve & Share, English Language Learner support states, “Review the terms data, array, and patterns. Use the terms as you discuss how to find how many bottles of water Maria bought.” Support for Entering ELL students states, “Ask students to read aloud and complete the sentence stem. ‘To find the product of 2 x 9 is to group 9s ____ times.’"
• In Lesson 3-5, Visual Learning Bridge, English Language Learner support states, “Read the problem and point to the dragon. ‘How many sections are there in the dragon’s body? How long is each section?’” Support for Emerging ELL students states, “Draw a dragon on the board and draw lines between each section and write 4 under each section. ‘How many sections? How many feet in each section?’” 

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide opportunities for advanced students to investigate mathematics content at greater depth.

Materials provide extension activities for each Solve & Share activity. Also, Independent Practice problems contain Higher Order Thinking items. Additionally, Enrichment activities follow the Quick Check Assessment in each lesson which can be used for differentiation. STEM activities are provided in the Activity Center. Finally, Additional Practice contains Advanced problems for students. However, teacher guidance is not provided for advanced students activities. Examples include, but are not limited to:

• In Lesson 6-7, Solve & Share states, “Mr. Anderson is tiling his kitchen floor. He will not need tiles for the areas covered by the kitchen island or the counter. How many square meters of tiles does Mr. Andersen need?” Extension problem states, “Mr. Anderson is changing the counter to 4 meters by 1 meter. How many square meters of tiles will Mr. Anderson need now?” 
• In Lesson 12-5, Enrichment Activity: What’s in a Name? states, “Each point on the number line has more than one name. Write some of the names for each point on the number line. Label fourths, label halves, and label whole numbers.”

The instructional materials for enVision Mathematics Common Core Grade 3 meet expectations that materials provide a balanced portrayal of various demographic and personal characteristics.

Lessons contain tasks including various demographic and personal characteristics. All names and wording are chosen with diversity in mind, and the materials do not contain gender biases. Materials include a set number of names used throughout the problems and examples (e.g., Jessie, Debra, Salvatore, Clara, Lois, Delbert, Marcus, Ramon, Li, Yolanda, Hakeem, Jerome, Forest, Chico, and June). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity. Characters are often presented in pairs with different solution strategies and a pattern of one character using more/less sophisticated strategies does not occur. When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways that do not express gender, race, or ethnic bias.