The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations that they assess grade-level content. Above grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

The series is divided into topics with an assessment for each topic that can be delivered online and/or paper and pencil, and a topic performance assessment. Additional assessments include a Kindergarten Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-11, and 1-15. Assessments can be found in the Assessment Resource Book online or in print. The materials also include an ExamView Test Generator. Examples of grade-level assessment items include:

• Topic 1, Topic 1 Assessment, Item 14, “Julie has 8 fewer pears than Dan. Dan has 14 pears. How many pears does Julie have? Part A: Draw a model. Part B: Write an equation.” (2.OA.1)
• Topic 3,Topic 3 Assessment, Item 15, “Write an equation to solve each part of the two-step problem. Matt has 44 seeds. He gives away 10 seeds. Then he buys 8 more seeds. How many seeds does he have now?.” (2.OA.1)
• Topic 6, Topic 6 Assessment, Item 14, “Find 64 - 25. Use any strategy to solve. Then explain why your strategy works.” (2.NBT.5)
• Topic 9, Topic 9 Assessment, Item 9, “Mark and Sara collect shells. Mark has 362 shells. Sara has 359 shells. Who has more shells? Write <, =, or > to compare the number of shells.” (2.NBT.4)
• Topic 11 Performance Task, Item 4, “Brian has 725 stamps in his collection. 247 stamps have pictures of flags. 108 stamps have pictures of people. 213 stamps have pictures of animals. The rest have pictures of places. How many stamps have pictures of places?” (2.NBT.7)
• Topic 14,Topic 14 Assessment, Item 6, “Seth got a pet snake that was 32 cm long. Now the snake is 56 cm long. How many centimeters did the snake grow?” (2.MD.5)

Examples of above grade level assessment items that could be modified or omitted:

• Arrays with more than 5 rows and/or columns (3.OA.3): 
• Topic 2 Performance Task, Item 3, “Scott hangs animal drawings at the art show. He hangs 3 rows of animal drawings, with 6 drawings in each row. Draw an array to show how Scott hangs the drawings.”
• Topic 2 Performance Task, Item 4, “Jamar says there are other ways to make an array of 18 drawings. Show an array of 18 drawings that is different from the array Scott used.”
• Word problems with addition and subtraction greater than 100 (3.OA.8):
• Topic 10 Assessment, Item 1, “Dina has 100 red counters. She has 326 blue counters and 10 green counters. How many red and blue counters does Dina have?”
• Topic 10 Assessment, Item 2, “Ryan works at a farm stand. He sells 157 eggs. Now he has 346 eggs. How many eggs did Ryan have before he sold some?”
• Topic 11 Assessment, Item 3, “John collected 396 toy cars. Chloe collected 256 fewer toy cars than John. How many toy cars did they collect in all?” 
• Topics 1-12 Cumulative/Benchmark Assessment, Item 16, “An art museum has 658 paintings. The museum also has 569 drawings. How many more paintings than drawings does the museum have?”
• Topics 1-15 Cumulative/Benchmark Assessment, Item 7, “Mr. Hom’s students collect 438 cans. Ms. Jenson’s students collect 343 cans. How many cans do the students collect in all?”
• Knowledge of angle measurements: (4.G.2)
• Topic 13 Assessment, Item 4, “Draw a polygon with 5 angles. Make one angle a right angle. Then name the polygon.”
• Topic 13 Assessment, Item 8: “Draw the polygon described below. Then complete the sentence. I have 2 fewer angles than a hexagon. I have one more side than a triangle. I have no right angles.”

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for spending a majority of instructional time on major work of the grade. The evidence was collected from Topics, Performance Tasks, Topic Assessments, Benchmarks, Centers, and 3-Act activities.

• The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is 14 out of 15, which is 93%. 
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 102 out of 113, which is approximately 90%. 
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 136 out of 151, which is approximately 90%.

A lesson level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each topic. As a result, approximately 90% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work on the Topic Planner pages in the Teacher Edition. For example:

Topic 2 addresses supporting cluster 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends) which connects to major work of cluster 2.OA.B (add and subtract within 20).

• Lesson 2-3, Teacher Edition, Guided Practice, Item 2, students “Write two equations that match each array.” The first sentence is addition of rows and the second sentence is addition of columns. (2.OA.B)
• Lesson 2-3, Solve and Share, students solve, “Show and explain two different ways to find how many circles in all” in an array showing 3 rows of 5 circles. (2.OA.B)
• Lesson 2-4, Independent Practice, Item 3, students draw an array to show the problem and use repeated addition to solve. “Sarah bakes loaves of bread. She places them in 5 columns with 3 loaves in each column. How many loaves of bread does Sarah have in all?” (2.OA.B)

Topic 8 addresses supporting cluster 2.MD.C (Work with time and money) which connects to the major work of 2.NBT.2 (count within 1,000; skip count by 5s, 10s, 100s) and 2.OA.1 (use addition and subtraction within 100 to solve one- and two-step word problems). For example:

• Lesson 8-1, Solve and Share, students solve, “Kelsey had 10 cents in her piggy bank. She finds 5 cents more and puts it in her bank. Then Kesey’s mother gives her 20 cents to put in her bank. How many cents does Kelsey have in her bank now?” (2.NBT.2)
• Lesson 8-4, Teacher Edition, Guided Practice, Item 1, students solve “Sam had some money in his wallet. He went to the carnival and spent $12. Now Sam has $5. How much was in his wallet before the carnival?” (2.OA.1)
• Lesson 8-5, Solve and Share, page 345, students solve, “Suppose you want to buy a pencil that costs 35 cents. How many different ways can you use nickels, dimes, or quarters to make 35 cents? Show each way. Tell how you know.” (2.OA.1)
• Lesson 8-6, Teacher Edition, Guided Practice, Item 2, students view a digital clock that shows the time, 3:25. Students skip count by 5s to write the corresponding time on the analog clock. (2.NBT.2)
• Lesson 8-7, Visual Learning Bridge, students are guided “To look at the times. Count by 5s to tell the time. What are other ways to name the same times?” (2.NBT.2)

Topic 15 addresses supporting standard 2.MD.10 (draw a picture graph and a bar graph (with a single-unit scale) to represent a data set with up to four categories) which connects to the major work in 2.OA.1 (use addition and subtraction within 100 to solve one- and two-step word problems).  

• Lesson 15-3, Teacher Edition, Solve and Share, students use data from the graph, “Birthdays by Season”, to solve, “Use the graph to write the number of birthdays in the table. How many more birthdays are celebrated during spring, fall, and winter than during summer? Be ready to explain how you know.” (2.OA.1)
• Lesson 15-4, Teacher Edition, Independent Practice, Item 8, students use information in a tally chart to create a picture graph. They use information from the picture graph to solve, “How many more students voted for summer than for spring and winter combined?” (2.OA.1)
• Lesson 15-5, Visual Learning, Convince Me!, students use the bar graph, “Carnival Tickets Sold”  to solve, “How many tickets did Kim and Neil sell in all? How do you know?” (2.OA.1)
• Lesson 15-6, Independent Practice, Items 3 and 4, students are directed to observe data displayed in a bar graph, “Rick’s Vegetable Garden” and “Use the bar graph to write and solve word problems.” (2.OA.1)

Topic 15 addresses supporting standard 2.MD.9 (generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object) which connects to the major work in 2.MD.1 (measure the length of an object by selecting and using appropriate tools.)  

• Lesson 15-1, Independent Practice, students use a ruler to measure pictures of four objects in inches. They “record each length in the table. Show each length on the line plot.” (2.MD.1)
• Lesson 15-1, Problem Solving, Item 10, students solve “What are the lengths of the two pencils that have a total length of 16 inches? Explain.” (2.MD.1)
• Lesson 15-2, Visual Learning Bridge, Convince Me!, students use the line plot, “Student Heights”, and a table of data to solve, “In the example above, how many students measured their height?  Tell how you know.” (2.MD.1)

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet the expectations for the amount of content designated for one grade-level being viable for one school year in order to foster coherence between grades. 

The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. As designed, the instructional materials can be completed in 151 days.  Teacher’s Edition Program Overview p.22, “Each core lesson, including differentiation, takes 45-75 minutes.”

Included are 15 topics for the grade. Each Topic is broken down into lessons which include additional resources for differentiation, additional time, and additional practice activities. Each Topic also includes an assessment (Teacher’s Edition Program Overview, page 22). For example:

• There are 113 content focused lessons. 
• There are 8 days of 3-Act Math Activities
• There are 30 days of Topic Reviews and Assessments

Additional Resources that are optional and not counted in the program days include:

• Math Diagnosis and Intervention System
• 10 Step-Up to Grade 3 Lessons to use after the last topic
• Readiness Test; Review What You Know; Cumulative/Benchmark Assessment (4 in all); Progress Monitoring Assessment Forms A, B and C (3 in all)

The instructional materials reviewed for enVision Mathematics 2020 Common Core Grade 2 partially meet the expectations for being consistent with the progressions in the standards. Content from prior grades is identified and connected to grade-level work, and students are given extensive work with grade-level problems, however, there is some evidence of above grade level content.

The Teacher Edition contains a Topic Overview Coherence: Look Back and Look Ahead, and a Lesson Overview Coherence: Look Back and Look Ahead, which identify connections to content taught in previous grades, indicating the relevant topics and/or lessons. In addition, the sections include connections to content taught in future grades, topics, or lessons. For example, in Topic 5, the Math Background, Coherence: Look Back includes:

• Grade 1: “In Topic 5, students learned the meaning of the equal sign, decided whether equations were true or false, found the unknown in equations, and solved addition and subtraction problems by writing equations.” “Throughout Grade 1, students used bar diagrams and equations to solve problems involving addition and subtraction situations.”
• Earlier in Grade 2: “By the end of Topic 6, students developed fluency in adding and subtracting within 100. Students also solved one-step and two-step problems.”

In Topic 7, The Look Ahead includes:

• Later in Grade 2: “In Topic 14, students will write equations and add and subtract within 100 to solve word problems involving lengths.”
• Grade 3: “In Topic 11, students will solve two-step word problems involving all four operations. For each step, they will represent the situation using a bar diagram and they will use a letter variable to represent the unknown quantity.”

The instructional materials support the progressions of grade-level standards, as evidenced by the sequencing of the topics in the curriculum.  For example, in developing number concepts:

• Operations and Algebraic Thinking is addressed in Topic 1: Fluently Add and Subtract Within 20; Topic 2: Work with Equal Groups; and Topic 7: More Solving Problems Involving Addition and Subtraction
• Number and Operations in Base Ten is addressed in Topic 3: Add Within 100 Using Strategies;  Topic 4: Fluently Add Within 100; Topic 5: Subtract Within 100 Using Strategies; Topic 6: Fluently Subtract Within 100; Topic 9: Numbers to 1000; Topic 10: Add Within 1000 using Models and Strategies; Topic 11: Subtract Within 1000 Using Models and Strategies. 
• Measurement and Data is addressed in Topic 8: Work with Time and Money and in Topic 15: Graphs and Data
• Geometry is addressed in Topic 13: Shapes and Their Attributes

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. All Topics include a topic project, and every other topic incorporates a 3-Act Mathematical Modeling Task. During the Solve and Share, Visual Learning Bridge, and Convince Me!, students explore ways to solve problems using multiple representations and prompts to reason and explain their thinking. Guided Practice provides students the opportunity to solve problems and check for understanding before moving on to the Independent Practice. During Independent Practice, students work with problems in a variety of formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. For example:

• Lesson 12-8, Problem Solving, Problem 11, students solve, “A path has two parts. The total length of the path is 12 cm. If one part is 8 cm, how long is the other part? Explain.” (2.MD.5, 2.OA.1)
• Lesson 14-3, Solve and Share, students solve, “Alex has a piece of ribbon that is 45 feet long. He cuts the ribbon. Now he has 39 feet of ribbon. How many feet of ribbon did Alex cut?” (2.MD.5, 2.OA.1)
• Lesson 6-6, Independent Practice, Problem 4, students solve: “A.J. counts 44 acorns in his yard. He picks up 27 acorns. Then 16 more acorns fall from the tree. How many acorns are in the yard now? Show your work.”  (2.OA.1)
• Lesson 10-3 Solve and Share, students solve, “Use place-value blocks to find 243 + 354.  Tell which place value you added first and why. Then draw a picture to show your work.” (2.NBT.7)
• Lesson 8-3, Problem Solving, Problem  9, students solve “Mrs. Baker has two $10 bills and three $5 bills in her purse. Does she have enough money to buy a dress that costs $33. Explain.” (2.MD.8)

The Topics support the progression of Grade 2 standards by explicitly stating connections between prior grades and current grade level work. Each topic contains a Math Background: Coherence document with Look Back narratives that identify connections to what students learned in Grade 1 and previously in Grade 2:

• Topic 3, Coherence: Look Back, Grade 1: “In Topic 8, students used an understanding of tens and ones to compose and decompose two-digit numbers.” “In Topic 10, students learned various strategies, such as using an open number line for adding two-digit numbers. They were also introduced to regrouping when adding with place-value blocks.” “Throughout Grade 1, students used bar diagrams and equations to solve problems involving “add to,” “put together,” “take from,” “take apart,” and “compare” situations.” Earlier in Grade 2: “In Topic 1, students fluently added and subtracted within 20 and solved addition and subtraction word problems.”
• Lesson 7-2,  Coherence: Look Back: “In Lesson 7-1, students wrote equations to model and solve word problems using a symbol (?) to represent the unknown in each equation.”
• Topic 10, Add Within 1,000 Using Models and Strategies, Teacher Edition page 429F, The Look Back states, Grade 1: “In Topic 10, students learned to use various strategies, place value, and properties of operations to add within 100.” Earlier in Grade 2: “In Topic 4, students developed computational fluency in addition within 100 by using strategies that employ understanding of place value, properties of operations, the partial-sums strategy, and mental math.” “In Topic 9, students’ understanding of place value was extended to numbers up to 1,000.” 
• Lesson 12-6, Coherence: Look Back states, “In the previous lesson, students measured with centimeters.”

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• Topic 3, Lessons 3-3 and 3-4, Lesson Objectives, “Break apart numbers into tens and ones to find their sum,” and  “Break apart addends and combine them in different ways to make numbers that are easy to add mentally,” respectively.  These objectives are shaped by 2.NBT.B, Use place value understanding and properties of operations to add and subtract.
• Topic 8, Lessons 8-2, 8-3 and 8-8, Lesson Objectives, “Solve problems with coins,” “Solve problems with dollar bills and coins that model 100 cents,” and “Tell time and use reasoning to state if the event is happening in the a.m. or p.m.” respectively. These objectives are shaped by 2.MD.C, Work with time and money.
• Topic 1, Lessons 1-7 and 1-8, Lesson Objectives, “Make a 10 to subtract quickly and accurately,” and  “Add and subtract quickly and accurately using mental math strategies,” respectively. These objectives are shaped by 2.OA.B, Add and subtract within 20.
• Topic 15, Lessons 15-3 and 15-5, Lesson Objectives, “Draw bar graphs and use them to solve problems,” and “Draw conclusions from graphs,” respectively. These objectives are shaped by 2.MD.D, Represent and interpret data.

Materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where the connections are natural and important. For example:

• Topic 3, Lesson 3-3, Convince Me!, connects 2.NBT.A, Understand place value to 2.NBT.B, Use place value understanding and properties of operations to add and subtract. Students apply their understanding to, “Explain how you can break apart 28 to find 33 + 28.”
• Lesson 10-2, “Adding numbers within 1,000 on an open number line (2.NBT.B) connects to understanding 100s, 10s, and 1s in a three-digit number (2.NBT.A)” This is a connection between two major clusters: 2.NBT.A, Understand place value, and 2.NBT.B, Use place value understanding and properties of operations to add and subtract. In the Solve and Share, students “use the open number line to find 598 + 123. Explain your work.”
• Topic 12, Lesson 12-8, Independent Practice, Problems 5 - 8, connects 2.MD.A, Measure and estimate lengths in standard units to 2.OA.A, Represent and solve problems involving addition and subtraction. Students “Estimate the length of each path. Then use a centimeter ruler to measure each path. Compare your estimate and measurement. Which path is longer? How much longer?”

​The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

The structure of the lessons include several opportunities that address conceptual understanding. For example:

• Math Background: Rigor page contains information about where conceptual understanding is built within the topic
• The Lesson Overview includes a narrative on how conceptual understanding is included in the lesson.
• Solve & Share activity whose purpose is “to elicit productive struggle that builds understanding by connecting prior knowledge to new ideas.”
• Lessons are introduced via video, Visual Learning Animation Plus, at PearsonRealize.com building on conceptual understanding.
• Students have the opportunity to independently demonstrate conceptual understanding through Independent Practice and Problem Solving pages within lessons.

Materials include problems and questions developing conceptual understanding throughout the grade-level and provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. For example:

• In Lesson 1-6, Solve and Share, students answer the question, “How can you use an addition fact to solve 14 - 6?” and “use counters to show how.” (2.OA.2)
• In Lesson 5-4, Visual Learning Bridge, features a demonstration of how to break apart one of the addends (6 into 3+3) in order to make finding 33 - 6 easier. Convince Me!, students “look at the problem above. Why wasn’t the 6 broken apart into 1+5 to find 33 - 6?” (2.NBT.7, 2.NBT.9)
• In Lesson 9-8, Solve & Share, students solve, “Jay and Zach flipped three number cards. Then they each made a number. Jay made 501. Zach made 510. Who made the greater number? How do you know? Use place-value blocks to help you solve.”  (2.NBT.4)
• In Lesson 10-5, Guided Practice, “Add. Use partial sums. Show your work. Use place-value blocks if needed. Item 1, 425 + 148 = ___. “ There is a place value chart with room for partial sums with answers dotted for students to trace. (2.NBT.7)

​The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill and fluency throughout the grade-level. 

In the Teacher Edition, each Topic begins with Math Background: Rigor, where procedural skill and fluency for the topic is outlined for teachers. The structure of the lessons include several opportunities to develop procedural skill and fluency, including:

• Math Background: Rigor page contains information about where procedural skill and fluency is built within the topic
• The Lesson Overview includes a narrative on how procedural skills are addressed in the lesson, when applicable. 
• A Steps to Fluency Success chart details steps to move students to fluency and provides resources to use for practice, intervention, and enrichment. 

Later Topics include Additional Practice and Fluency worksheets, Math Diagnosis and Intervention Systems, and My Fluency Progress Forms. Additional practice is located online at PearsonRealize.com. 

Materials include items and questions intended to develop procedural skill and fluency throughout the grade-level and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. For example:

• In Lesson 1-2, Solve & Share, students “use counters. Show 6+6=12. Then show and explain how knowing that fact can help you find 6 + 7.”  (2.OA.2) 
• In Lesson 1-8, Guided Practice, Items 1-12,  “Add or subtract. Use any Strategy.” Item 1, “14 - 9 = ”.  (2.OA.2)
• In Lesson 3-5, Independent practice, Items 1-11, “Find each sum. Use any strategy. Show your work.” Item 1, “33 + 52 = __”, Item 2, “27 + 6 = __” (2.NBT.B.5)  
• In Lesson 6-5, Guided Practice, “Use any strategy to subtract. Show your work.  Draw blocks if needed. Explain why the strategy works.” Item 1, “67 - 39 = ” (2.NBT.5)
• In Lesson 12-9, Guided Practice, students look at a picture of a crayon lined up with a centimeter ruler that has space before the 0. Item 1. “Bev measures the crayon and says it is 5 centimeters long. Is her work precise? Explain.” The answer is “the work is not precise, because the crayon is not lined up with the 0 mark, it is lined up with the end of the ruler.” (2.MD.1)

The instructional materials for enVision Mathematics Common Core Grade 2 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

In the Teacher Edition, each Topic begins with Math Background: Rigor, where applications for the topic are outlined for teachers. Math Background: Rigor for Topic 7, Applications states, “Real-World Contexts In Lessons 7-1 to 7-5, students use addition and subtraction within 100 to solve one- and two-step real-world word problems.” Each Topic also includes a variety of application tasks, for example:

• Topic Opener, containing a contextual STEM problem designed to spark interest in the content of the topic,
• Topic Centers with application problems, 
• 3-Act Math activities where students engage in application problems, and
• Performance Tasks, where students apply mathematics of the topic in multi-step, real-world situations. 

The structure of the lessons includes several opportunities for students to engage in routine and non-routine application problems. Practice & Problem Solving sections provide students with a variety of problem types to apply what they have learned. The way in which application is incorporated into specific lessons is stated in the Rigor section of the Lesson Overview of those lessons. 

Examples of opportunities for students to engage in routine and non-routine application problems include:

• In Lesson 2-5, Solve and Share, students solve “There are 4 rows in a classroom. Two rows have 3 tables in each row. Two rows have 4 tables in each row.  How many tables are there in all? Draw a picture and write an equation to model and solve the problem.” (2.OA.4)
• In the Topic 5 Performance Task, Item 3, students solve, “Nina sees 34 red roses. She sees 9 fewer yellow roses than red roses. How many roses does she see in all?” (2.OA.1)
• In Lesson 7-4, Solve and Share, students solve, “3 bees land on some flowers. 10 more bees join them. Then 4 bees fly away. How many bees are left? Solve the problem any way you choose. Write equations to show how you solved each part of the problem.” (2.OA.1)
• In Lesson 14-5, Visual Learning Bridge, students solve, “Sara plays soccer. She is 56 feet away from the goal. Then she runs 24 feet straight toward the goal. How many feet from the goal is Sara now?” (2.MD.5)
• In Lesson 14-2, Solve and Share, students apply addition and measurement skills to determine which two pieces of yarn have a total length of 12 cm. “Julie and Steve each cut a piece of yarn. The total length of both pieces is 12 cm. Measure each piece of yarn. Circle Julie and Steve’s pieces. Then explain your thinking.” (2.MD.5)
• In Topic 7, Pick a Project - The Chrysler Building, students solve, “Find the total number of floors in the Chrysler Building. In 1930, there was a viewing deck. Do research to find what floor the deck was on. Then find the number of floors from the viewing deck to the top floor. Write two equations you could use to find the number.” (2.OA.1, 2.NBT.5)
• In Topic 14, Performance Task, Item 6, students see a picture of a car pulling a boat and the measurements of each component: car - 7 feet, space between car and boat - 2 feet, and boat - 21 feet. Students solve, “Jim’s family meets a man with a big boat. A parking spot at the dock is 32 feet long. Will the man’s car and boat fit in the parking spot?” (2.MD.5, 2.MD.6, 2.OA.1)

Examples of where instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts include:

• In Lesson 2-5, Independent Practice, Item 4, students solve, “Tina drew an array to show 9 shells. The same number of shells are in each row and each column. How many shells are in each row and each column? Explain how you know.” (2.OA.4)
• In Lesson 7-2, Solve and Share, students solve, “Aiden has 27 fewer crayons this week than last week. Last week he had 56 crayons. How many crayons does Aiden have this week?” (2.OA.1)
• In Lesson 7-5, Problem Solving, Item 7, students “write a two-step number story using the numbers 36, 65, and 16. Then solve the problem. Write equations to show each step.” (2.OA.1,  2.NBT.5)
• In Lesson 8-2, Independent Practice, Item 4, students solve, “Trina buys a ring. She pays for it with 9 dimes. She receives 8 pennies in change. How much did the ring cost?” (2.MD.8)

​The instructional materials for enVision Mathematics Common Core Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. 

Each Topic Overview contains Math Background: Rigor, where the components of Rigor are addressed. Every lesson within a topic contains opportunities for students to build conceptual understanding, procedural skill and fluency, and/or application. During Solve and Share and Guided Practice, students explore alternative solution pathways to master procedural fluency and develop conceptual understanding. During Independent Practice, students apply the content in real-world applications, use procedural skills and/or conceptual understanding to solve problems with multiple solutions, and explain/compare their solutions.

In some instances, the three aspects of Rigor are present independently throughout the instructional materials. For example:

• In Lesson 9-5, Solve and Share, students build conceptual understanding as they, “Use place-value blocks. Show two ways to make 213. Then draw each way. Tell how your ways are alike and different.” (2.NBT.3)
• In Lesson 14-4, students represent addition and subtraction with whole numbers on a number line. In Independent Practice, Items 3 and 4, students “use the number lines to add or subtract 80 - 35 and 19 + 63.”  (2.MD.6)
• In Lesson 4-4, Lesson Overview, “Using partial sums helps students develop fluency in adding within 100.” In Independent Practice, Item 4, students “Write the addition problem. Use partial sums. Add any way you choose”  as they solve 15 + 28. (2.NBT.5)
• In Lesson 10-5, Solve and Share, engages students with application: “On Monday, 248 people visit the museum. On Tuesday, 325 people visit the museum. How many people visit the museum on Monday and Tuesday? Solve any way you choose. Be prepared to explain your thinking.” (2.NBT.7)

Multiple aspects of Rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. For example:

• In Topic 3, Lesson 3-3, Lesson Overview, “Conceptual Understanding: Students deepen their conceptual understanding of addition when they break apart numbers to add. Procedural Skill: Students break apart the second addend into tens and ones to add to the first addend. This helps students develop fluency with addition within 100.” This is illustrated in Convince Me!, when students “explain how you can break apart 28 to find 33+28.” (1.NBT.7)
• In Lesson 2-5, Solve and Share, students apply their understanding of equal groups to solve the word problem, “There are 4 rows in a classroom. Two rows have 4 tables in each row. How many tables are there in all? Draw a picture and write an equation to model and solve the problem.” (2.OA.4)
• In Lesson 9-1, Lesson Overview, “Conceptual Understanding: Students understand that 100 can be thought of as a group of 10 tens. They learn that a number such as 300 can be expressed as 3 hundreds, 0 tens, and 0 ones. Procedural Skill: Students use drawings of place-value blocks to demonstrate understanding of composing and decomposing hundreds.” Students demonstrate both aspects of rigor in Problem Solving, Item 9, as they complete two sentences using the vocabulary words hundred, tens, and ones. “There are 100  ____ in 100. There are 10 ____ in one ____.” (2.NBT.1a, 2.NBT.1b)
• In Lesson 14-2, Lesson Overview, “Conceptual Understanding: Students further develop their understanding of measurement by solving word problems involving length. Procedural Skill: Students use equations and drawings, such as a number line, to solve problems about unknown measurements. Application: Students apply reasoning when determining whether to use addition or subtraction to solve problems about unknown measurements.” Students demonstrate all three aspects of rigor in the Independent Practice, Item 3, as they solve, “Filipe’s pencil box is 24 centimeters long. Joe’s pencil box is 3 centimeters shorter than Filipe’s. How long is Joe’s pencil box?”  (2.MD.5, 2.OA.1)
• In Lesson 15-3, Guided Practice, Item 2, students are given a Favorite Pet table and a bar graph to complete. The directions state, “Use the table to complete the bar graph and use the bar graph to solve the Item. How many students chose a bird or dog?” (2.MD.10)

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations that the Standards for Mathematical Practice (MPs) are identified and used to enrich mathematics content within and throughout the grade level, and are not treated separately.

The math practices are identified throughout the materials. For example: 

• Every Topic includes a Math Practices and ETP (Effective Teaching Practices) page with an explanation of how students engage with the MPs throughout the topic.
• Every lesson includes a Lesson Overview where an explanation of how students engage with the math practice during the lesson.  
• Special Item Solving lessons in each topic focus on specific math practices. 
• Specifically flagged comments and Items in all lessons focus on specific math practices. 
• Math Practice Animation videos for each MP provide a student-friendly explanation with demonstration Items. These can be found in the Digital Resources in Pearson Realize. 
• The Math Practices and Item Solving Handbook contains a detailed explanation for each MP, identifies “Thinking Habits” unique to each MP, connections to content and other MPs, and student behavior look-fors to monitor progress toward proficiency.

Examples of the MPs identified within individual lessons:

• MP1: Topic 7, Math Practices and ETP, “Students use information in a world Item to determine whether they should add or subtract to solve the Item. (e.g., p. 286, Visual Learning Bridge.)”
• MP2: Lesson 4-5, Lesson Overview, “Students reason about why breaking apart the second addend in a two-digit addition Item is a helpful mental math strategy for addition.”
• MP4:  Topic 7, Math Practices and ETP, “Students understand when and why to use subtraction to represent a real-world Item. (e.g., p. 284, Item 7.)”
• MP5: Topic 12, Math Practices and ETP, Teacher Edition, page 505H, “Students measure objects using units and different tools..  (e.g., p.511, Items 3-4.)”
• MP6: Lesson 2-1, Lesson Overview, “Students will communicate their understanding of odd and even numbers using clear definitions in their discussions and reasoning.”
• MP7: Lesson 13-4, Lesson Overview, states, “Students describe and draw cubes, looking for information about faces, edges, and vertices.” 
• MP8: Topic 7, Math Practices and ETP, states, “Students recognize that the same Item can be represented by different equations.  (e.g., p. 282, Convince Me!)”

Examples of where MPs are identified and used to enrich the content:

• In Lesson 10-1,Lesson Overview, students engage with MP1 as they “recognize that when adding 10 or 100 to a 3-digit number, only the tens or hundreds digit will increase by 1.” In Solve and Share, students use dollar bills, place value blocks, or mental math to solve, “Forest Park Nursery sells trees. Sal buys a maple tree for $125. A spruce tree costs $10 more than a maple tree. An elm tree costs $100 more than a maple tree. What is the cost of a spruce tree? An elm tree?” (2.NBT.8)
• In Lesson 10-6, Problem Solving, Item 7, students engage with MP2 as they solve each Item any way they choose and show their work. “There are 229 people at the football game. 108 more people arrive at the game. How many people are at the football game now?” (2.NBT.9)
• In Lesson 2-5, Lesson Overview, students engage in MP4 as they “draw and use arrays to write repeated addition equations to help them solve real-world Items.”  In Independent Practice, Item 2, “Mika has 4 rows of playing cards. If there are 4 playing cards in each row, how many cards does Mika have in all?” Students “draw a picture and write an equation to show each Item. Then solve.”  (2.OA.4)
• In Lesson 14-5, Lesson Overview, students engage in MP5 as they “consider the available tools when solving a  mathematical Item.” In Solve and Share, students are shown a picture of a straight line and a squiggly line and “Choose a tool to solve each part of the Item.  Be ready to explain which tools you used and why. Which line is longer? How much longer? Draw a line that is that length.” (2.MD.5)
• In Lesson 6-5, Lesson Overview, students engage in MP6 as they “attend to precision as they choose and use strategies to accurately subtract 2-digit numbers.” In Solve and Share, students “Find 82 - 56. Use any strategy you have learned or your own strategy. Show your work. Explain why your strategy works.” (2.NBT.5)
• In Lesson 9-10, Independent Practice, Item 4, “The blue team wants to sort their jersey numbers from greatest to least. After they sort the numbers, what number would come next? Look for a pattern in the sorted jersey numbers. What is the pattern rule?” (2.NBT.2)
• In Lesson 13-8, Lesson Overview, students engage with MP8, as they “use repeated reasoning to create designs in equal shares.” In Solve and Share, students “design two different flags. Draw 15 equal-size squares in each flag. Use rows and columns. Make three equal shares of different colors in each flag. Then write an equation for each flag to show the total number of squares.” (2.G.2)

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 partially meet expectations for carefully attending to the full meaning of each practice standard. 

The materials do not attend to the full meaning of MP5. The materials present few opportunities for students to choose tools strategically. In most instances, tools are chosen for students, or teachers are given guidance on what tools students should use. Examples of the materials not attending to the full meaning of MP5 include:

• Lesson 3-1, Guided Practice, Items 2-4, students “add using the hundred chart”, and “draw arrows on the chart if needed” to solve 28 + 21, 19 + 20, and 18 + 8. (2.NBT.5)
• Lesson 4-1, Lesson Overview, “Students use place-value blocks to represent and solve two-digit addition problems.” Solve and Share, “Leslie collects 36 rocks. Her brother collects 27 rocks. How many rocks do they collect in all? Use place-value blocks to help you solve. Show your place value blocks.” (2.NBT.5)
• Lesson 5-2, Independent Practice, Item 9, students “use an open number line to solve each problem.” “There are 47 raffle tickets to sell for the fair. Ms. Brown’s class sells 23 raffle tickets. How many raffle tickets are left to sell?” (2.NBT.5)
• Lesson 6-1, Independent Practice, Items 4-11, for each two-digit minus one-digit problem, like 29 - 1, students “subtract. Use place-value blocks. Draw blocks to show your work.” (2.NBT.5)
• Lesson 6-7, Convince Me!, “Why can you subtract 45 - 17 to solve 45 - ? = 17?” Teacher materials state Use Appropriate Tools Strategically: “Have students draw place-value blocks to show the relationship between 17 and 28 as parts of 45.” (2.OA.1)

Examples of the materials attending to the full meaning of the MPs include:

• MP.1: Lesson 8-4, Problem Solving, Item 9, “Isaac wants to buy a backpack for $20. He has two $5 bills and nine $1 bills. How much more money does he need to buy the backpack?” (2.MD.8, 2.OA.1)
• MP.2: Lesson 6-3, Convince Me! “The example above shows one way to find 64 - 36 using partial differences. Could you begin by subtracting ones instead of the tens? Explain.” (2.NBT.5)
• MP.4: Lesson 2-1, Problem Solving, Item 10, “Gemma fills 2 baskets with 9 berries each. She gives both baskets to Alan. Does Alan have an odd or even number of berries? Draw a picture to solve. Then write an equation.” (2.OA.3,  2.OA.2)
• MP.6: Lesson 12-4 Solve and Share, “Choose an object. Measure your object in feet. Then measure it in inches. Do you need more units of feet or inches to measure your object? Why?” (2.MD.2)
• MP.7: Lesson 9-10, Solve and Share, “Sort the numbers 500, 800, 600, 400, and 700 from least to greatest. Describe any number patterns that you see. Are there any other numbers that fit the pattern?” (2.NBT.2)
• MP.8: Lesson 10-7, Visual Learning Bridge, students are presented with two equations: 24 + 36 = ? and 324 + 136 = ? “How is adding 3-digit numbers like adding 2-digit numbers?” Students generalize, “What things repeat when you add two 2-digit numbers and when you add two 3-digit numbers?” (2.NBT.7)

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Specific features of the materials engage students in constructing viable arguments and/or analyzing the mathematical reasoning of others. Examples include:

• Convince Me! prompts provide the opportunity for students to share their thinking and to analyze the reasoning of others.
• In Three-Act Math, students critique other’s reasoning as solution methods for the task are shared with the class. 
• In Solve and Share, students share and justify solutions with the class, and they critique the reasoning of others as teachers select which solutions to share.
• In the Visual Learning Bridge, there are opportunities for students to construct viable arguments.
• “I Can” bubbles prompt students: 
• Construct Arguments: Lesson 3-7 Solve & Share, “I Can...use pictures, numbers, and words to explain why my thinking and work are correct.”  
• Critique Reasoning of Others: Lesson 5-8, Solve & Share, “I Can...critique the thinking of others by using what I know about addition and subtraction.” 
• Thinking Habits thought bubbles  prompt students:
• Construct Arguments: Lesson 3-7, Solve & Share, “How can I use math to explain why my work is correct? Am I using numbers and symbols correctly?  Is my explanation clear?”   
• Critique Reasoning of Others: Lesson 5-8, Solve and Share, “What questions can I ask to understand other people’s thinking?  Are there mistakes in other people’s thinking?”  
• Math Practices and Problem Solving Handbook.

The materials consistently provide opportunities for students to construct viable arguments. Examples include:

• Lesson 1-10, Independent Practice, Item 3, “The Lions scored 11 runs in a baseball game. The Tigers scored 7 runs. Did the Tigers score 3 fewer runs than the Lions? Explain.” (2.OA.1)
• Lesson 3-7, Guided Practice, Item 1, students “Solve. Use pictures, words, or numbers to make a math argument. Show your work.”  “There are 16 chickens in the yard. There are 19 chickens in the barn. There are 30 nesting boxes. Will all of the chickens have a nest? Explain.” (2.NBT.9)
• Lesson 8-2, Convince Me!, “Why is subtracting 75¢ - 68¢ like subtracting 75 - 68? Explain.” (2.MD.8, 2.NBT.2)

The materials consistently provide opportunities for students to analyze the reasoning of others. Examples include:

• Lesson 3-1, Convince Me!, “Max says that to find 54 + 18 on a hundred chart, you can start at 54, move down 2 rows, and move back 2 spaces. Do you agree? Explain.” (2.NBT.5)
• Lesson 4-6, Solve & Share, “12 + 34 + 28 = ? Tom says he can find the sum by adding 28 and 12 first. He says he can add 34 to that sum to find the total. Do you agree? Use pictures, words and numbers to make a math argument. Then solve the problem. Show your work.” (2.NBT.6)

The instructional materials reviewed for enVision Common Core Grade 2 meet the expectations of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. 

There are multiple locations in the materials where teachers are provided with prompts to elicit student thinking. For example:

• The Math Practices and Problem Solving Handbook provides guidance on implementing MP3 and questions that students might ask themselves as they reflect on MP3. The Problem Solving Lessons which focus on MP3 are identified, for example, in Lessons 1-10, 3-7, and 5-8.
• In the teacher’s notes for each lesson, MP3 is identified in red print as “Construct Arguments” or “Analyze Reasoning”. Questions to elicit student thinking are included below the prompts. 
• In the teacher notes for Solve & Share activities, questions to prompt students thinking are included in Share Solution Strategies and Key Ideas.
• The Convince Me! activity, when connected to MP3, provides prompts to assist students in constructing arguments and analyzing the reasoning of others.
• Three Act Math Tasks includes Construct Arguments which provides prompts for the teacher to help students construct arguments.

The materials provide guidance to support teachers in engaging students in constructing viable arguments. Examples include:

• Lesson 1-10, Problem Solving Performance Task, Item 7, the teacher narrative prompts “After students solve the problem, have them share their solution strategies. Elicit a variety of solution strategies. As they share their solutions and their strategies, look for opportunities to point out how their work has the qualities of a good math argument.” (2.OA.1)
• Lesson 4-2, Convince Me!, “Ken adds 43 + 27. His sum is 60. Is he correct? Explain.” The teacher is prompted to “remind students that as well as deciding if Ken is correct, they need to explain how they reached that decision. Some students may disagree on the answer or may agree on the answer but have different explanations. Discuss these differences, telling different ways to correctly make an argument.” (2.NBT.5)
• Lesson 10-5, Convince Me!, “Can the problem above (257 + 384) be solved by adding the ones first, then the tens, and then the hundreds? Explain.” The teacher is prompted to “have students explain why the order they add the partial sums will not change the sum.” (2.NBT.7)

The materials provide guidance to support teachers in engaging students in analyzing the reasoning of others. Examples include:

• Lesson 2-5, Problem Solving, Item 6, students are given the information that there are 3 rows of posters and 5 posters in each row. “Mr. Miller says that he will add 3 + 5 to find the total number of posters in the posters display. Do you agree with his plan? Explain.” The teacher is prompted to ask guiding questions if students have difficulty getting started. “How can you find the total number of posters in the poster display? What equation can you write to show the number of posters in the poster display?” (2.OA.4)
• Lesson 5-8, Convince Me!, “Have students share the questions they would ask Kelly to help her check her reasoning, so that students understand there is more than one way to help Kelly check her thinking.” (2.NBT.9)
• Lesson 9-5, Problem Solving,Item 8, students are presented with a problem: “Neha wants to make the same number in different ways. She says 300 + 130 + 9 equals the same number as 500 + 30 + 9. Do you agree with Neha? Explain.” In the lesson narrative, teachers are prompted to “Encourage students to compare the ways shown. What is the sum of the numbers in the first way? Compare the first and second ways. How are they different? What does that tell you about the sum of the  numbers in the second way?” (2.NBT.3)

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet the expectations of attending to the specialized language of mathematics.

The materials provide explicit instruction on the use of mathematical language including words, diagrams, symbols, and conventions. Each topic includes:

• My Word Cards are available online. In the Teacher Edition, page 1J Build Mathematical Literacy, explains how My Word Cards are used: “Students use the example on the front of the card to write the definition on the back.” 
• Vocabulary Activities at the beginning of Topics
• Vocabulary Review at the end of each Topic
• Glossary in the Student Edition
• Animated glossary is available online.
• Online vocabulary game in the Games Center

For each topic, the Topic Planner includes a list of the new vocabulary words for each lesson. The vocabulary words are also included in the Teacher Edition, Lesson Overview page for each lesson. For example in Topic 3:

• Lesson 3-1, identifies tens and ones
• Lesson 3-2: identifies open number line
• Lesson 3-3: identifies break apart

In the Vocabulary Review at the end of each Topic, teachers are provided several activities to help students review the vocabulary: For example, in Topic 12, Teacher Edition, page 546,

• “Have students define the terms in their own words”
• “Have students say math sentences or math questions that use the words.”
• Play a “What’s My Word?” guessing game in which you or a student thinks about one of the words and says a clue that others listen to before they guess the word.
• Play a “Right or Wrong?” game in which you or a student says a sentence that uses one of the words correctly or incorrectly. Then others say “right” or “wrong.”

The materials use precise and accurate terminology and definitions when describing mathematics, and they provide support for students to use them correctly. Examples include:

• Lesson 2-3, Visual Learning Bridge, states, “You can model repeated addition with an array. Arrays have equal rows. Each row has 3 strawberries. Arrays have equal columns. Each column has 2 strawberries. Write two equations that match the array. By Rows 3+3=6  By Columns 2+2+2=6”
• Topic 6, Vocabulary Review, Items 4 - 6, students are given three terms: equation, regroup, difference and three examples: a place-value model illustrating regrouping,  “the answer to 75 - 23”, and “72 + 25 = 97”. They are asked to “Draw a line from each term to its example.”
• Topic 12, Vocabulary Review, Item 8, Use Vocabulary in Writing, states “Use words to tell how to find the height of a table. Use terms from the Word List.” (centimeter, estimate, foot, height, inch, length, meter, nearest centimeter, nearest inch, yard)

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations that the underlying design of the materials distinguishes between problems and exercises for each lesson. It is clear when the students are solving problems to learn and when they are completing exercises to apply what they have learned.

Lessons include: Solve & Share, Look Back, Visual Learning Bridge, Convince Me!, Guided Practice, Independent Practice, Problem Solving, and Assessment Practice. Additional Practice is in a separate section of the instructional materials, distinguishing between problems students complete and exercises in the lessons. The Solve & Share section serves to either connect prior learning or engage students with a problem in which new math ideas are embedded. Students learn and practice new mathematics in Guided Practice. 

In the Independent Practice and Problem Solving sections, students have opportunities to build on their understanding of the new concept. Each activity lesson ends with an Assessment Practice in which students have opportunities to apply what they have learned from the activities in the lesson and can be used to help differentiate instruction.

Additional Practice problems are consistently found in the Additional Practice Workbook accompanying each lesson. These sets of problems include problems that support students in developing mastery of the current lesson and topic concepts.

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for not being haphazard; exercises are given in intentional sequences.

Overall, activities within lessons within topics are intentionally sequenced. Students have the opportunity to develop understanding leading to mastery of the content. The structure of the lesson provides students with the opportunity to activate prior learning and build procedural skill and fluency. Students also engage with multiple activities that are sequenced from concrete to abstract and increase in complexity.

Students are introduced to concepts and procedures through a problem-based situation in the Solve & Share, and then connect that problem to the content of the lesson during the Visual Learning Bridge. The Convince Me! portion of the lesson serves to solidify understanding of mathematical concepts through the MPs, followed by teachers and students working together through Guided Practice. Students engage in problems independently in the Independent Practice section. Lessons close with Problem Solving, where students apply learning from the lesson, and Assessment Practice, where students engage with two questions aligned to the daily lesson objective.

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for having variety in what students are asked to produce.

The instructional materials prompt students to produce written answers and solutions within Solve & Share, Guided Practice, Independent Practice, Problem Solving, and 3-Act Math. Students produce oral arguments and explanations through discussions that occur in whole group, small group, or partner settings. Students also produce written critiques of fictional students’ work including models, drawings, and calculations.

In the materials, students use a digital platform (Visual Learning Animation Plus) and paper-pencil activities to conduct and present their work. The materials prompt students to use appropriate mathematical language in their written and oral responses, and students frequently use various mathematical representations in their work even though the representation is often provided for students. For example:

• In Lesson 3-2, students use an open number line to find each sum.
• In Lesson 5-8, students use pictures, words, or equations to explain reasoning.
• In Topic 11, Reteaching, students use place-value blocks or mental math.
• In Lesson 14-4, students use a number line.
• In Lesson 15-2, students use a line plot.

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations that manipulatives are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

There are few hands-on manipulatives used in the materials. In general, the manipulatives are visual manipulatives printed in the materials or virtual manipulatives found in the online materials. Occasionally, students will be prompted to use tools such as counters, cubes, place value blocks, ten frames, ruler, protractor, or grid paper. When they are used, they are used appropriately. If manipulatives are used in lessons, students are usually directed as to when and which manipulatives to use.

The instructional materials for enVision Mathematics Common Core Grade 2 are not distracting or chaotic and support students in engaging thoughtfully with the subject. 

The page layout in the materials is user-friendly, and the pages are not overcrowded or hard to read. Graphics promote understanding of the mathematics being learned. The digital format is easy to navigate and is engaging for students. There is ample white space for students to write answers in the student book.

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet the expectation for supporting teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

Each lesson contains a narrative for the teacher including the Lesson Overview, suggested questions for discussion, and guiding questions designed to increase classroom discourse, support the teacher in knowing what to look for, and ensure understanding of the concepts. For example:

• In Lesson 3-2, Problem Solving, Item 9, teachers ask, “How can you label each jump of ten and each jump of one? Can you combine the tens jumps? Can you combine the ones jumps? Why must you label each jump?”
• In Lesson 5-5, Solve & Share, teachers ask, “How can you break apart 29 into tens and ones?
• In Lesson 11-1, Solve & Share, teachers ask, “What does $10 less mean? $100 less?”

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet the expectation for containing a teacher edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials also include teacher guidance on the use of embedded technology to support and enhance student learning.

• Each Topic has a Topic Planner that gives an overview of every lesson, the Objective of the lesson, Essential Understanding, Vocabulary, Materials needed, Technology and Activity Centers, along with the Standards. 
• The Topic Planner also includes Lesson Resources such as the Digital Student Edition, Additional Practice Workbook, print material available, and what can be found in the Digital Lesson Courseware and Lesson Support for teachers.
• Each lesson opens with a Lesson Overview including: an Objective, an Essential Understanding, Look Back, Look Ahead, Cross-Cluster Connections, aspect(s) of rigor addressed, support for English Language Learners, and any possible Daily Review pages with Today’s Challenge to be implemented. Within the lesson, technology resources or places to print PDF work pages are embedded. 
• Lessons include detailed guidance for teachers for the Warm-Up, Activities and the Lesson Synthesis.
• Each lesson activity contains an overview, guidance for teachers and student facing materials, anticipated misconceptions, extensions, differentiation support based on formative assessments called “Quick Checks,” and opportunities for further practice in the online materials. Included within the lessons are guiding questions and additional supports for students.
• The teacher materials that correspond to the student lessons provide annotations and suggestions on how to present the content within the lesson structure: Step 1 (Engage and Explore), Step 2 (Explain, Elaborate, and Evaluate) and Step 3 (Assess and Differentiate). A “Launch” section follows which explains how to set up the activity and what to tell students. During the Visual Learning Bridge in Step 2, supporting questions and narratives for students are provided.
• The materials are available in both print and digital forms. Additional online resources support the material. These opportunities are noted within the lessons. For example, each lesson has a Visual Learning Animation Plus video in Step 2, an Interactive Practice Buddy noted in Step 2 and Step 3, as well as Another Look Video found in Step 3.

​The instructional materials for enVision Mathematics Common Core Grade 2 partially meet the expectations that materials contain adult-level explanations so that teachers can improve their own knowledge. 

The Teacher Edition Program Overview includes resources to help teachers understand the mathematical content within a topic and a lesson. The Program Overview includes the overarching philosophy of the program, a user’s guide, and a content guide. Each Topic has a Professional Development Video presenting full adult-level explanations of the mathematics concepts in the lessons. The Professional Development Video includes clearly explained examples. A section titled, Math Background, is included for each Topic and Lesson identifying the connections between previous grade, grade-level, and future grade mathematics. However, these are not presented in ways supporting teachers to understand the underlying mathematical progressions.

The Assessment Source Book, Teacher Edition, and Mathematical Practices and Problem Solving Handbooks provide answers and sample answers to problems and exercises presented to students; however, there are no adult-level explanations to build understanding of the mathematics in the tasks.

The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

• Each topic opens with a Topic Overview including a Math Background for the Topic.
• The Coherence section has three parts: Look Back, Topic, and Look Ahead. Each section gives a clear, specific explanation of how the topic is connected across grades. 
• Each topic includes an Objective, Essential Understanding, (critical area for grade level), Look Back, This Lesson, Look Ahead, Cross-Cluster Connection, Conceptual Understanding, Procedural Skill, and Lesson Resources.
• The Teacher Edition Program Overview Materials contain an overview of mathematics for K-12.

​The instructional materials for enVision Mathematics Common Core Grade 2 cross-reference the standards addressed with an estimated instructional time for each unit and lesson.

The standards are cross-referenced in multiple places in the Teacher Edition, including in the Topic Planner at the beginning of each topic showing the lesson names, vocabulary, objectives, standards, mathematical practices, and essential understandings for the topic. The Topic Planner also includes a suggested pacing for each lesson. The Program Overview includes a Pacing Guide providing an overview of the number of days expected per Topic.

​The instructional materials for enVision Mathematics Common Core Grade 2 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement. 

The Teacher’s Resource Masters have Home School Connection Letters, in English and Spanish, for each Topic. The letters include information on the mathematical content, activities parents can use with their child, and a Focus on Mathematical Practices section encouraging parents to support their child with the mathematics presented in each Topic. For example, Topic 14:

• Sample Family Letter Introduction: “Dear Family, Your child is learning to add and subtract with measurements. He or she will also learn to solve problems by drawing pictures and writing equations to …”
• Sample Family Letter Activity: “Work with your child to make a list of 5 or 6 household items. Write the approximate length of each item in inches. Then make up addition and subtraction problems…”
• Sample Family Letter Focus on Mathematical Practices: “Observe Your Child: Have your child write an equation to represent each addition and subtraction measurement problem in the above activity. Ask him or her…”

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 contain explanations of the program's instructional approaches and identification of the research-based strategies.

The Teacher Edition Program Overview describes the organization of the curriculum and why the structure was chosen. The core instructional model for enVision Common Core is a two-step approach including Problem-Based Learning and Visual Learning. The two steps are described, with references in the teacher materials. 

​The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for providing strategies to gather information about students’ prior knowledge within and across grade levels.

The Assessment Sourcebook and the Teacher’s Program Overview provide information about the use of assessments to gather information about students’ prior knowledge. Every grade level includes a Grade-Level Readiness test. The Topic Readiness Assessment in each Topic helps teachers gather information about students’ prior knowledge within and across grade levels. Topic Readiness assessments can also be taken online, where they are auto-scored and interventions are auto-assigned. 

The Topic Opener assignment located at the beginning of each Topic helps students activate prior knowledge and prepare for the skills needed in the Topic. Each of these assignments has questioning strategies for the teacher. Each lesson also provides information for the teacher about prior, current grade level, and future math that is used.

The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions.

Each lesson identifies common errors and misconceptions for the teacher to address in the Guided Practice. The misconception/error is followed with prompts that the teacher can ask to help students understand their mistakes. For example:

• In Lesson 8-3, Error Intervention Item 1, “If students count on by the same amount each time, then remind them that the dollar bills, like coins, have different values. Refer them to the numbers on the bills and also to the second frame of the Visual Learning Bridge.”
• In Lesson 11-1, Error Intervention Item 2, “If students have difficulty subtracting 10, then have them display the number using place-value blocks and then take away 1 tens rod to show subtracting ten.”
• In Lesson 15-2, Error Intervention Item 1, “If students are having difficulty keeping track of the number of dots to draw on the line plot, then have them read the table one row at a time, counting the number of feathers that are 4 cm in length [3], crossing out those numbers in the table, and plotting that number of dots above 4. Have them do the same for each length, continuing with 5 cm.”

The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for providing 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, provide 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 where 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 them to engage with the content and receive timely feedback. Discussion prompts in the Teacher Guide provide opportunities for students to engage in timely discussion on the mathematics of the lesson.

Each Topic includes a “Review what you know/Concept and Skills Review” containing a vocabulary review and practice problems. This section also includes review and practice on concepts related to the new Topic. 

The Cumulative/Benchmark Assessments found at the end of Topics 4, 8, 12, and 15 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 2 meet the expectations for assessments clearly denoting which standards are being emphasized.

Assessments are located in a separate book, or the online portion of the program, and can be accessed at any time. For each topic, a Practice Assessment, an End-Unit Assessment, and a Performance task are included. Assessments in the Teacher Edition provide a scoring guide and standards alignment for each question.

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 partially meet expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. For example:

• There are “scoring guidelines” to assist the teacher in interpreting student performance; however, these are an answer key or sample student answers.
• A general rubric is provided to interpret student written responses, but it is not topic specific. 
• Topic Readiness and End of Topic Assessments have Item Analysis for Diagnosis and Intervention, which include standards being assessed and depth of knowledge levels.
• Assessments can be taken online where they are automatically scored, and students are assigned appropriate practice, enrichment, or remediation based on their results.
• Teachers interpret the results of print assessments and determine materials for follow up on their own.

​The instructional materials for enVision Mathematics Common Core Grade 2 do not include opportunities for students to monitor their own progress. There are no specific materials for students encouraging them to monitor their own progress.

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials include a detailed Scope and Sequence of the course, including pacing. The Topic Overview in the Teacher Edition includes Coherence which enhances scaffolding instruction by identifying prerequisite skills that students should have. Each lesson is designed with a Daily Review and a Solve & Share Activity reviewing prior knowledge and/or preparing all students for the following activities.

In lessons, the following explicit instructional supports are available for sequencing and scaffolding: the Lesson Overview, questions and extensions for the Solve & Share, Prevent Misconceptions in Visual Learning Bridge, Revisit the Essential Question in Convince Me!, Error Intervention during Guided Practice, and item-related support during Independent Practice and Problem Solving. This information assists the teacher in making the content accessible to all learners.

Lesson narratives often include guidance on where to focus questions in all lesson activities, sample student work, and guidance on what to look for. Optional activities are often included in Step 3 (Assess and Differentiate) and can be used for additional practice or support before moving on to the next activity or lesson.

The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

• The Additional Practice Materials include a lesson for each topic including specific questions for the leveled assignment for all learning ranges. These three levels of problems are I (Intervention), O (On-Level), and A (Advanced) and include verbal, visual, and symbolic representations.
• Response to Intervention strategies are included in each lesson. Teachers identify “Look Fors” and suggestions to address the needs of students who are struggling. Questions for the teacher to ask are also included.
• Each lesson has at least one Additional Example. These help students cement or extend their understanding of the concept being taught. It includes an extra problem for the teacher to use.
• Each lesson has Differentiated Interventions for a wide-range of learners, which include Reteach to Build Understanding (provides scaffolding to reteach) and Enrichment (extends concepts from the lesson).

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for embedding tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

The Solve & Share, Explore It, Visual Learning Bridge, Guided and Independent Practice, 3-Act Math Tasks, and Quick Check/Assessment Practice provide opportunities for students to apply mathematics from multiple entry points. Though there may be times when the material asks a student to use a specific strategy, there are still questions within the same lesson that allow for students to use a variety of strategies. 

The lesson and task narratives provided for teachers offer possible solution paths and presentation strategies from various levels. For example:

• In Lesson 7-2, Solve & Share, “Students solve a comparison word problem any way they choose.” During Small Group work, students can use “drawings, numbers, or symbols to represent the problem visually.” Students are encouraged to use different strategies to break apart the numbers.
• In Lesson 12-9, Solve & Share, “Students identify ways to measure with precision the length of a shape that is not straight.” Teachers “distribute inch rulers, measuring tape, string, and buttons or counters.”

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 meet expectations for suggesting support, accommodations, and modifications for English Language Learners (ELL) 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. An ELL Toolkit provides additional support for English Language Learners.

ELL suggestions are provided for every lesson, in the Lesson Overview, Solve & Share, and in the Visual Learning Bridge. Guidance includes ELL learners at the entering, developing, expanding, and bridging levels of language acquisition. Visual Learning support is embedded in every lesson to support ELL learners. This includes a Visual Learning Animation Plus online, Visual Learning Bridge for each lesson, and the Animated Glossary. These use motion and sound to reduce language barriers. Questions are read aloud, visual models are provided, and motion and sound definitions of mathematical terms are provided.

Additionally, a multilingual handbook is included with a mathematics glossary in multiple languages, and an English Language Learners Toolkit is a resource providing professional development and resources for supporting English Language Learners. 

An example of ELL supports within the instructional materials:

• In Lesson 3-3, Lesson Overview, English Language Learners, “Speaking: Read the problem with students. Pause after each sentence in the first paragraph and ask a question to help students retell the information. What does Josh have? [34 cans] What does Jill have? [27 cans] What do you need to do? [Find the total] 
• Emerging: You can choose any way to solve. What are some ways you could choose? [Sample answer: Use an open number line.] What can you draw? [A picture] What can you write? [An equation] Repeat students’ answers for the group and write them on the board. When students have solved the problem, ask each of them to say which way they used to solve it. Students may use one or two words, or short sentences. 
• Developing: What are some ways you can solve the problem? [Sample answer: I can add on an open number line.] Repeat students’ answers for the group and write them on the board. When students have solved the problem, ask each of them to say which way they used to solve it. Have other students tell if they used the same way or a different way. 
• Expanding: Have students work in pairs to reread the problem and discuss strategies. Then have them solve the problem, each using a different strategy. When they are finished, ask each pair to explain how they solve the problem in two different ways.”

Support for other special populations noted in the Teacher Edition Program Overview include:

• Resources are provided on for Ongoing Intervention (during a lesson), Strategic Information (at the end of the lesson), and Intensive Intervention (as needed 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 is provided through teachers notes to conduct a short lesson where vocabulary, concept development, and practice can be supported. 
• Online Auto Design Differentiation is included, and the supports within this part of the program include: Differentiation After a Lesson (based on an Online Quick Check where the Interactive Practice Buddy can be utilized), Differentiation after a Topic (based on the online topic assessments where Visual Learning Animations Plus are then assigned), and Differentiation after a Group of Topics (based on the online cumulative benchmark assessments where students can then receive remediation or enrichment). The teacher can track progress using Assignment Reports and analyze Usage Data.

The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth.

Each lesson offers differentiated instruction to extend the concepts in the lesson and provides opportunities to challenge advanced students:

• Extensions are found at the end of every Solve & Share;
• Higher Order Thinking items within the Independent Practice and Problem Solving section;
• Enrichment pages as a result of the Quick Checks in every lesson;
• Opportunities to engage in STEM activities during the activity centers;
• Noted advanced problems to complete during the Additional Practice portions of each lesson; and 
• Differentiation after a group of Topics based on the online cumulative benchmark assessments where students can then receive enrichment.

​The instructional materials for enVision Mathematics Common Core Grade 2 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics.

• The 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.
• The materials mostly contain pictures of objects or cartoonish drawings instead of photos or drawings of people.
• The materials reference roles instead of pronouns (e.g., the players, book fair, sailboats, collection of toy cars, piggy banks, carton of eggs).
• The materials include a set number of names used throughout the problems and examples (e.g., Carlos, Jada, Martha, Carl, Benito, Drake, Daniel, Yasmin, Jonathan). These names are presented repeatedly and in a way that does not stereotype characters by gender, race, or ethnicity.

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 provide opportunities for teachers to use a variety of grouping strategies. The materials include teacher-led instruction presenting options for whole-group, small-group, partner, and/or individual work. When suggestions are made for students to work in small groups, no specific roles are suggested for group members, but teachers are given suggestions and questions to move learning forward.

​The instructional materials for enVision Mathematics Common Core Grade 2 encourage teachers to draw upon home language and culture to facilitate learning.

The Teacher Edition Program Overview includes Supporting English Language Learners, which contains ELL Instruction and Visual Learning. The Teacher Edition Program Overview states, “Levels of English language proficiency are indicated, and they align with the following level identified in WIDA (World-Class Instructional Design and Assessment): Entering, Emerging, Developing, Expanding, and Bridging.” 

English Language Learners support for each lesson is provided for the teacher throughout lessons to provide scaffolding for reading, as well as differentiated support based on the students’ language proficiency level (emerging, developing, expanding, or bridging). The Home-School Connection letters for each topic are available in both English and Spanish. An English Language Learners Toolkit is available consisting of many Professional Development Articles and Graphic Organizers. A few of the examples of the Professional Development Articles that can help teachers support ELL learners include: English Language Learners in the Math Classroom, Strategies for Teaching English Language Learners, Welcoming Newcomers to the Mainstream Classroom, Multilingual Thinking Words, and Teaching Math to Culturally and Linguistically Diverse Students.

​The instructional materials reviewed for enVision Mathematics Common Core Grade 2 integrate technology including interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students in the Mathematical Practices.

Teachers and students have access to tools and virtual manipulatives within a given activity or task, when appropriate. Pearson Realize provides additional components online such as games, practice, instructional videos, links to other websites, differentiation, etc. For each Mathematical Practice, there is a detailed interactive video included in the online materials. However, in the teacher print materials, online resources are referenced generically without specific guidance. On the website, there is not an explicit link to activity directions for the online tools; they are not clearly labeled or connected to specific lessons.

​The instructional materials for enVision Mathematics Common Core Grade 2 include digital materials that are web-based and compatible with multiple internet browsers. 

Digital materials (either included as part of the core materials or as part of a digital curriculum) are web-­based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, Safari, etc.). In addition, materials are platform neutral (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow for the use of tablets and mobile devices including iPads, laptops, Chromebooks, MacBooks, and other devices that connect to the internet with an applicable browser.

​The instructional materials for enVision Mathematics Common Core for Grade 2 include opportunities to assess students' mathematical understandings and knowledge of procedural skills using technology.

• Online games enhance fluency and include games where students use procedural skills to solve problems.
• Virtual Nerd offers tutorials on procedural skills, but no assessment or opportunity to practice the procedures is included with the tutorials.
• The online Readiness Assessment tab for each topic includes a Remediation link including tutorials and opportunities for students to practice procedural skills using technology.

The instructional materials for enVision Mathematics Common Core Grade 2 include digital materials with opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. Teachers can select and assign individual practice items for student remediation based on the Topic Readiness assessment. Teachers can create and assign classes online for students. An online Accessible Student Edition can be assigned to students. Closed Captioning is included in STEM and 3-Act Math videos.

The instructional materials reviewed for enVision Mathematics Common Core Grade 2 can be easily customized for local use. Digital materials provide the same lessons to draw from on a topic as the print materials. Teachers can create and upload files, attach links, and attach documents from Google Drive and assign them to students. Teachers can also create assessments using a bank of items or using self-written questions that can also be assigned to students.

The instructional materials for Envision Mathematics Common Core Grade 2 include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.). There is a “Discuss” tab to assign discussion prompts to students in the “Classes” tab, and a file can also be attached.