2nd Grade - Gateway 1

​The materials reviewed for enVision Mathematics Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Above-grade-level assessment items are present but could be modified or omitted without significantly impacting the underlying structure of the instructional materials.

The series is divided into topics that include a Topic Assessment, available for online and/or paper and pencil delivery, and a Topic Performance Task. Additional assessments include a Grade 2 Readiness Test; Basic-Facts Timed Tests; four Cumulative/Benchmark Assessments addressing Topics 1–4, 1–8, 1–12, and 1–15; and Progress Monitoring Assessments A–C. Assessments can be found in the digital teacher interface and the Assessment Sourcebook online or in print. The materials also include an ExamView Test Generator that allows teachers to build customized tests. 

Examples of items that assess grade-level content include:

• Topic 5, Assessment, Problem 8, “Part A Write the equation that the number line shows. Part B Then, explain what the jumps are showing. -=__.” Students engage with a number line that ranges from 30 to 64 that shows various jumps. (2.NBT.5 and 2.NBT.9)

• Topic 11, Performance Task, Problem 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? Part A What is the hidden question in the problem? Part B Solve the problem. Show your work. Explain which strategy you used. __ stamps of places.” (2.NBT.7)

• Topic 13, Online Assessment, Problem 3, “Mark was able to find three ways to divide a square into fourths.Which was NOT one of his ways?” Students choose from amongst four squares: one is partitioned into three rectangles, one is partitioned into four rectangles, one is partitioned into four squares, and one is partitioned into four triangles. (2.G.3)

• Topic 14, Assessment, Problem 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? A) 88 cm B) 36 cm C) 33 cm D) 24 cm.” (2.MD.5)

Examples of above grade-level assessment items that could be modified or omitted include, but are not limited to:

• Topic 2, Performance Task, Problem 3, “Scott hangs animal drawings at the art show. He hangs 3 rows of animal drawings, with 6 drawings in each row. Part A Draw an array to show how Scott hangs the drawings. Part B Write an equation to match your array. How many animal drawings does Scott hang?” This question requires students to produce an array with more than 5 rows and/or columns. (3.OA.3)

• Topic 13, Assessment, Problem 4, “Draw a polygon with 5 angles. Make one angle a right angle. Then name the polygon. Name: ____” This question requires students to apply knowledge of angle measurements. (4.G.2)

The materials reviewed for enVision Mathematics Grade 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The 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. During Independent Practice, students work with problems in various formats to integrate and extend concepts and skills. The Problem Solving section includes additional practice problems for each of the lessons. Examples of extensive work with grade-level problems to meet the full intent of grade-level standards include:

• In Topic 2, Lessons 2-3, 2-4, and 2-5, students engage in extensive work with grade-level problems to meet the full intent of 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). In Lesson 2-3, Independent Practice, Problem 4, students write two equations—repeated addition using rows and repeated addition using columns—to match each rectangular array and to determine the sum. Problem 4, shows a 3 ✕ 4 rectangular array of green apples, students show repeated addition of 4 to represent the 3 rows and repeated addition of 3 to represent the 4 columns; the total is 12. In Lesson 2-4, Independent Practice, Problem 5, students draw an array and use repeated addition to solve a problem. Directions,“ Draw an array to show each problem. Use repeated addition to solve. 5. Malcolm puts his marbles in two columns. He puts 2 marbles in each column. How many marbles does Malcolm have in all? ___+___=___ marbles” In Lesson 2-5, Guided Practice, Problem 1, students draw a picture and write an equation to show a problem before solving it. “Ray has 2 rows of books. He has 5 books in each row. How many books does Ray have in all?” Shown are two rows of 5 traceable circles each and the equation with traceable 5 + 5 = ____ books.

• In Topic 8, Lessons 8-1, 8-2, and 8-4, students engage in extensive work with grade-level problems to meet the full intent of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately). In Lesson 8-1, Independent Practice, Problem 6, students identify a missing coin given the total value of all the coins pictured. “Stacey had 92¢ this morning. Write the name of the coin she lost.” Pictured are a half dollar, a quarter, a dime, and two pennies. In Lesson 8-2, Independent Practice, Problem 4, students solve a word problem involving money by working backwards. Directions, “Solve each problem. Show your work. Trina buys a ring. She pays for it with 9 dimes. She receives 8 pennies in change. How much does the ring cost?” In Lesson 8-4, Convince Me!, students solve a word problem involving dollar bills. “Tammy has a $100 bill. She buys the game and the toy dog. To find how much money she has left, she adds the price of the game and the toy dog, then subtracts the total from $100. Tina solves the problem by subtracting $100 − $25 and then subtracting $21 from that difference. Do you think she got the same answer as Tammy? Explain. Pictured are images of a game with a $25 price tag and a toy dog with a $21 price tag.

• In Topic 9, Lessons 9-2, 9-3, and 9-5, students engage in extensive work with grade-level problems to meet the full intent of 2.NBT.3 (Read and write numbers to 1000 using base-ten numerals, number names, and expanded form). In Lesson 9-2, Independent Practice, Problem 4, students use base-ten blocks to write three-digit numerals. Direction,  “Write the numbers shown. Use models and your workmat if needed.” Pictured are 4 hundred flats and 3 tens rods. Provided is a three-column place-value chart. In Lesson 9-3, Independent Practice, Problem 8, students use words and their understanding of place value in base-ten to write a three-digit number: “Higher Order Thinking Write the number that has the following values. The tens digit has a value of 70. The ones digit has a value of 5 ones. The hundreds digit has a value of 8 hundreds.” In Lesson 9-5, Reteach to Build Understanding, Problem 1, students respond to prompts involving base-ten blocks: complete a place-value chart, break apart one of the hundreds into tens, and write the number in expanded form.

• In Topic 13, Lessons 13-2-13-4, students engage in extensive work with grade-level problems to meet the full intent of 2.G.1 (Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes). In Lesson 13-2, Independent Practice, Problem 6, students look at polygons, write the number of angles, and write the name of the shape. Directions, “Write the number of angles and then name the shape. ___ angles Shape: ___” Pictured is a hexagon. In Lesson 13-3, Interactive Practice Buddy, Problem 5, students consider a word problem and choose between a triangle, a pentagon, and a hexagon.  “Jerry drew three shapes. The first shape is a triangle. Each of the next shapes has one more vertex than the shape before it. What is the third shape? You can draw shapes to help.” The answer options are the following: Triangle, Pentagon, and Hexagon. In Lesson 13-4, Solve & Share, students use tools to describe how two shapes are the same and are different. “Describe the two shapes in 4 or more ways. Tell how they are different and how they are the same. Use a tool to include measurements in your description.” Pictured are two cubes: one in 3D and the other in the front face only.

The materials reviewed for enVision Mathematics Grade 2 meet expectations for that, when implemented as designed the majority of the materials address the major clusters of each grade.The materials devote at least 65% of instructional time to the major clusters of the grade.

• 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 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 materials focus on the work of the grade.

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

Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher’s Edition, Lesson Overview, Coherence, Cross-Cluster Connections on a document titled “Lessons and Standards” found within the Course Guide tab for each unit. Connections are also listed in a document titled “Scope and Sequence.” Examples of connections include:

• Topic 2, Lesson 2-4 connects the supporting work of 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.) connects to the major work of 2.OA.2 (Fluently add and subtract within 20 using mental strategies.).  In Problem Solving, Problem 7, students draw arrays to show problems and use repeated addition to solve. “Draw an array to show each problem. Use repeated addition to solve. 7. Reasoning Jenny has 5 rows on each page in her photo album. She puts 2 pictures in each row. How many pictures does she have on each page?” The materials provide the skeleton of the addition equation “ ___ + ___ + ___ + ___ + ___ = ____ pictures” and a box in which to draw the arrays. 

• Topic 8, Lesson 8-1 connects the supporting work of 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.) to the major work of 2.NBT.2 (Count within 1000; skip-count by 5s, 10s, and 100s.). In Interactive Additional Practice, Problems 1 and 2, students write the value of each coin and count to find the total value. “1. Sarah has these coins. How many cents does Sarah have?” Pictured are five dimes.  “2. Marc has these coins. How many cents does Marc have?” Pictured are one half-dollar, two dimes, and two pennies.  Problem 5, Assessment Practice, students solve a word problem involving quarters. “Jamal has these coins. He needs 85¢ to buy a toy car. How many more cents does Jamal need? Draw the coin or coins he needs.” Pictured are three quarters.

• Topic 13, Lesson 13-2 connects the supporting work of 2.G.A (Reason with shapes and their attributes) to the major work of 2.MD.A (Measure and estimate lengths in standard units). In Solve & Share, students engage with three quadrilaterals that differ by their angles and side lengths. “Look at the three plane shapes below. How are they alike? How are they different? Measure the length of the sides to help describe them. Name each shape.”

The materials reviewed for enVision Mathematics Grade 2 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. These connections are listed for teachers in the Topic Overview, Scope and Sequence, and Teacher Guides within each topic. Examples include:

• In Topic 1, Lesson 1-6, Independent Practice, Problems 5–11, students think about how subtraction is related to addition as they work through problems. The directions state, “Subtract. Complete the addition fact that can help you. 5. 8 - 1 = ___,   1 + ___ = 8“. This connects the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract) to the major work of 2.OA.B (Add and subtract within 20).

• In Topic 3, Lesson 3-3, Convince Me!, students apply their understanding of place value to add two-digit numbers. “Explain how you can break apart 28 to find 33 + 28.” This connects the major work of 2.NBT.A (Understand place value) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract).

• In Topic 5, Lesson 5-8, Interactive Additional Practice, Problem 1, students use pictures, words, or equations to agree or disagree with the claim, “Circle your answer. Use pictures, words, or equations to explain. There were 64 runners in a race last year. This year there were 25 fewer runners. Latoya says 39 runners were in the race this year. She says 64 - 30 is easy to subtract. So she added 25 + 5 = 30. Then she found 63 - 30 = 34, and added 5 to 34 to get 39.” Students are provided two answer choices “Agree” or “Do Not Agree.” This connects the major work of 2.OA.A (Represent and solve problems involving addition and subtraction) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). 

• In Topic 14, Lesson 14-1, Guided Practice, Problem 2, students decide if they add or subtract and write an equation to answer the question, “Decide if you need to add or subtract. Then write an equation to help solve each problem. What is the distance around the puzzle?” The materials show a photo of a horse and the dimensions of its width (15 in.) and height (12 in.). In Reteach to Build Understanding, Problem 3, students measure and add two lengths. “Use a ruler to draw two lines with different lengths. What is the total length of the two lines? Show your work.” This connects the major work of 2.MD.A (Measure and estimate lengths in standard units) to the major work of  2.MD.B (Relate addition and subtraction to length). 

The materials reviewed for enVision Mathematics Grade 2 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades. 

Prior and Future connections are identified within the Teacher Edition Math Background: Focus, Math Background: Coherence, and Lesson Overview. Examples of connections to future grades include:

• Topic 2, Lessons 2-3 and 2-4 connect 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) with the work of future grades. “In Lesson 2-3, students learn the relationship between arrays and repeated addition. In Lesson 2-4, they extend this understanding to solve problems by creating arrays and writing repeated-addition equations.” In Grade 3, Topic 1, students will “use repeated addition and arrays to understand the relationship between multiplication and addition.”

• Topic 9, Lessons 9-1 – 9-3 connect 2.NBT.1 (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones) with the work of future grades. In Topic 9, students “learn that 3-digit numbers represent amounts of hundreds, tens, and ones.” In Lessons 9-1 through 9-3, “students learn that the position of a digit in a number determines its value.” In Grade 3, Topic 8, students will “use place-value understanding within 1,000 to round whole numbers to the nearest 10 or 100.”

• Topic 13, Lesson 13-5 connects 2.G.2 (Partition a rectangle into rows and columns of same-size squares and count to find the total number of them) to the work of future grades. In Lesson 13-5, “Students partition rectangles into rows and columns of equal-sized squares. They also use repeated addition to write equations that represent the partitioned rectangles.” In Grade 3, Topic 6, “students will be introduced to the concept of area. They will cover a region with unit squares and count them to determine area.”

Examples of connections to prior knowledge include:

• Topic 3 connects 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction) to the work of previous grades. In Grade 1, Topic 8, “students used an understanding of tens and ones to compose and decompose 2-digit numbers.” In this topic, students add “within 100 using strategies that employ a hundred chart, an open number line, breaking numbers apart, and compensation.” 

• Topic 7 connects 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions) to the work of previous grades. In Grade 1, “students used bar diagrams and equations to solve problems involving addition and subtraction situations.” In Lessons 7-1 - 7-3, students write “equations to represent one-step addition and subtraction problems, using a ? for the unknown.” In Lessons 7-4 and 7-5, students use representations from previous lessons “in each step of two-step problems.”

• Topic 15, Lessons 15-1 and 15-2 connect 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. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units) to the work of previous grades. In Grade 1, Topics 6, students “learned to collect, organize, represent, and interpret up to 3 categories of data using tally charts and picture graphs.” In Lessons 15-1 and 15-2, students “measure everyday objects to the nearest inch. … Students use line plots to display measurement data, including data they collected themselves.”