2nd Grade - Gateway 1

​The instructional materials reviewed for enVision Florida Mathematics Grade 2 meet expectations that they assess grade-level content.

The series is divided into topics, and each topic has a topic assessment that can be given both online and/or paper and pencil and a topic performance assessment. Additional assessments include a Grade 2 Readiness Test and four Cumulative/Benchmark Assessments addressing Topics 1-4, 1-8, 1-12, 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 2, Topic Assessment, Problem 3, students solve, “David plants peas in the school garden. He plans 4 rows of peas with 3 plants in each row. Part A: Draw an array to show how David planted the peas. Part B: Write an equation to match the array. How many pea plants does David plant?” (2.OA.3.4)
• Topic 5, Topic Assessment, Problem 1, students solve, “Maya’s class visits a garden. Maya counts the flowers she sees. How many more roses does Maya see than lilies. Use the open number line to solve.” (2.OA.1.1 and 2.NBT.2.5)
• Topic 6, Topic Assessment, Problem 13, students answer, “Choose all of the problems that you will solve by regrouping if you subtract using place-value blocks. Draw blocks if needed.” (2.NBT.2.7)
• Topic 8, Topic Assessment, Problem 8, students solve, “Alicia eats dinner at the time shown on the clock. What time does Alicia eat dinner?” (2.MD.3.7)
• Topic 8, Topic Assessment, Problem 1, students solve, “Malak has these coins. How much money does he have? If he spends a dime and a nickel, how much money will he have? Count to find the total.” (2.MD.3.8)
• Topic 13, Topic Assessment, Problem 3, students solve, “Which squares are shown in thirds? Choose all that apply.” (2.G.1.3)
• Topic 15, Topic Assessment, Problems 1-3, students solve, “1. Use the table to complete the bar graph, 2. Use the Favorite Lunch table to complete the picture graph, 3. Use the graphs you made to answer these questions.” (2.MD.4.10)

​The instructional materials reviewed for enVision Florida Mathematics 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 7 out of 14, which is 50%.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 104 out of 113, which is approximately 93%.
• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 122 out of 151, which is approximately 80%.

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 93% of the instructional materials focus on major work of the grade.

​The instructional materials reviewed for enVision Florida Mathematics 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’s Edition. For example:

• Topic 2, Lesson 2-5 addresses supporting cluster 2.OA.3 in the following:
• Independent Practice Problem 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 an array and write an equation to show the problem, then solve. This connects to cluster 2.OA.1 (Represent and solve problems involving addition and subtraction).
• In the Problem Solving Performance Task: Window Displays students solve, “Mr. Miller’s Hobby Shop has 3 window displays. One is for posters, one is for paint cans, and one is for crayon boxes. The displays are described at the right. Which display has the least number of items? Question 5: What are you asked to find? Question 6: Mr. Miller says he will add 3+5 to find the total number of posters in the posters display. Do you agree with his plan? Explain. Question 7: Draw an array to help you find which display has the least number of items. Give your answer and show your work.” This connects 2.OA.3 (Work with equal groups of objects to gain foundations for multiplication) to 2.OA.2 (Add and subtract within 20).
• In Topic 8, Lesson 8-5, Visual Learning Animation Guided Practice, students solve, “Tony wants to buy a pencil. He has half-dollars, quarters, and nickels. Find all the ways he can make 55 cents.” Supporting work 2.MD.3.8.d (Work with time and money) is identified and connected to major work 2.OA.1 (Represent and solve problems involving addition and subtraction).
• In Topic 15, Lesson 15-6, Solve and Share, students “Make a picture graph to show how many connecting cubes, counters, and ones cubes you have. Then write and solve a problem about your data.” Students use addition/subtraction to solve their problem. This is an example of a connection between supporting cluster 2.MD.4 (Represent and interpret data) and major work of cluster 2.OA.1 (Represent and solve problems involving addition and subtraction).

​The instructional materials reviewed for enVision Florida Mathematics 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.

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

​The instructional materials reviewed for enVision Florida Mathematics Grade 2 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.

Overall, the materials develop according to the grade-by-grade progressions in the standards. Typically, material related to prior and future grades is clearly identified and related to grade-level work. In the Teacher Edition Program Overview, all grade-level standards are present as noted in the Correlation to Florida Grade 2 Standards.

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. Though explicit connections are made to prior and future mathematical content, no standards are listed in either Look Back or Look Ahead. For example, in Topic 10, Add Within 1,000 Using Models and Strategies, Overview, Coherence:

• The Look Back states, “Grade 1, Addition Within 100 - In Topic 10, students learned to use various strategies, place value, and properties of operations to add within 100.”
• The Look Back also states, “Earlier in Grade 2, Fluently Add Within 100 - 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.”
• The Look Ahead states, “Later in Grade 2, Subtract Within 1,000 - In Topic 11, students will adapt the strategies from this topic to subtract within 1,000.”

The instructional materials support the progressions of the standards. The Topics for Grade 2 address the following domains:

• Operations & Algebraic Thinking begins in Topic 1: Fluently add and subtract within 20; Topic 2: Work with equal groups; Topic 3: Add within 100 using strategies; and Topic 4: Fluently add within 100 (Lessons focus on strategies).
• Number & Operations in Base Ten begins in Topic 3: Add within 100 using strategies; Topic 4: Fluently add within 100 (Lessons focus on strategies); Topic 5: Subtract within 100 using strategies; Topic 6: Fluently Subtract within 100; and Topic 7: More solving problems involving addition and subtraction. Numbers to 1000 is addressed in Topic 9, Add within 1000 using models and strategies and Topic 10;  and Subtract within 1000 using models and strategies is addressed in Topic 11.
• Measurement & Data begins in Topic 8: Work with Time and Money. Measuring length is addressed in Topic 12, More Addition, Subtraction, and Length is addressed in Topic 14, and Graphs and Data are addressed in Topic 15.
• Geometry is addressed in Topic 13: Shapes and their attributes and Topic 15: Equal Shares of Circles and Rectangles.

The instructional materials attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. For example:

• In Lesson 1-6, Problems 1-6, students solve, “Use fact patterns to complete the equation (all within 20).” (2.OA.2.2)
• In Lesson 5-3, Solve and Share, students solve, “There are 50 children at the park. 28 are boys and the rest are girls. How many girls are at the park? Use the open number line to solve. Show your work.” (2.NBT.2.5)
• In Lesson 5-4, Solve and Share, students “Use any strategy to find 42-7. Use pictures, words, or numbers to explain.” (2.NBT.2.5)
• In Lesson 6-6, sample question, “Trevor made 20 apple muffins for the bake sale. Ryan made 15 banana muffins. They sold 23 muffins in all. How many muffins are left to sell? Solve any way you choose. Show your work.” (2.OA.1.1)
• Topic 7, Interactive Math Story, “Frida flies 10 kites on Friday, she loses 5 kites to angry flies. Then she buys 7 more kites from a man in a bumble-bee sweater.  How many kites does Frida have now?” (2.OA.1.1)
• In Lesson 11-3, Solve & Share, students “Use place-value blocks to find 482-127. Tell which place value you subtracted first and why. Then draw a picture to show your work.” (2.NBT.2.7)

Each topic also includes: digital practice, extra worksheets, reteach to build understanding, build mathematical literacy, enrichment activities, envision STEM activities, leveled reading, and problem solving.

​The instructional materials reviewed for enVision Florida Mathematics 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:

• In Lessons 3-1 and 3-2, the objectives are, “Add within 100 using place-value strategies and a hundred chart” and “Use an open number line to add tens and ones within 100,” respectively, and shaped by 2.NBT.2, Use place value understanding and properties of operations to add and subtract.
• In Lessons 8-1 and 8-2, the objective is, “Solve problems with coins,” and shaped by 2.MD.3, Work with time and money.
• In Lessons 13-3 and 13-4, the objectives are, “Draw polygon shapes” and “Draw cubes and describe how they look,” respectively, and shaped by 2.G.1, Reason with shapes and their attributes.

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

• In Lesson 3-3, Visual Learning Animation Plus: Convince Me!, students solve, “Explain how you can break apart 28 to find 33+28.” This problem connects 2.NBT.2, Use place value understanding and properties of operations to add and subtract, to 2.NBT.1, Understand place value.
• In Lesson 3-6, Solve and Share, students analyze the strategies Griffin and Kiera used to solve 36 + 15, which connects 2.OA.1, Represent and solve problems using addition and subtraction, to 2.NBT.2, Use place value understanding and properties of operations to add and subtract.
• In Lesson 14-3, Independent Practice Problem 3, students solve, “Brent’s rope is 49 inches long. He cuts off some of the rope and now it is 37 inches long. How much rope did Brent cut off?” The directions state, “Write an equation using a ? for the unknown number. Solve with a picture or another way.” This problem connects 2.OA.1, Represent and solve problems involving addition and subtraction, to 2.MD.2, Relate addition and subtraction to length.