2nd Grade - Gateway 1

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?”