2nd Grade - Gateway 2

The instructional materials reviewed for Zearn Grade 2 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The use of visual representations builds conceptual understanding of place value (2.NBT.A) and addition and subtraction (2.NBT.B). During Independent Digital Lessons and Teacher-Led Instruction students engage with visual representations and virtual manipulatives.

• In Mission 3, Counting and Place Value, Independent Digital Lesson 14 students use place value disks to model numbers through 1,000 and then connect these models to reading and writing numbers to 1,000.
• In Mission 5, students add and subtract large numbers. Place value is the underlying concept referenced for each iteration from lesson to lesson as larger multi-digit numbers are introduced. Students use a traditional algorithm, but there is a constant tie to place value. In Lesson 1 students begin adding within 1,000 using a place value chart. Students represent each addend by place value, one over the other, to simulate the standard algorithm. During Independent Digital Lesson 6 students are using the associative property and tape diagrams to subtract numbers such as 330-290. In Independent Digital Lesson 9 students use virtual place value disks to add numbers such as 672+249. The use of multiple representations of place value builds student understanding of grouping and regrouping as they conduct addition and subtraction within 1,000.

Overall, Lessons within Missions, whether Teacher-Led Instruction or Independent Digital Lessons, present opportunities for students to develop conceptual understanding of the mathematics. Students engage in multiple addition and subtraction problems as described in Table 1 of the CCSSM. Students encounter multiple representations of whole numbers through place value, decomposing and recomposing of numbers with hands-on and virtual manipulatives, place value charts, and number bonds, and these representations are linked to addition and subtraction sentences within 1,000.

The instructional materials reviewed for Grade 2 meet the expectation for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Missions address procedural skill and fluency in both the Independent Digital Lessons, with Fluency activities titled Number Gym, Sprint, and Blast, and in Small Group Instruction, with Fluency activities for most lessons.

• In Mission 1, Teacher-Led Instruction, Whole Group Fluency, Lesson 1 students play Ten-Frame Flash, Happy Counting using a rekenrek, and finger play. Students also alternate between counting and using the “Say Ten” way where students compose numbers with tens; for example 12 is ten 2.
• In Mission 1, Independent Digital Lesson 1 Sprint students practice making 10 and adding to 10 (2.OA.2).
• In Mission 7, Length, Money, and Data, students participate in Fluency Games during Teacher-Led Instruction. For example, during Lesson 21 students play Roll and Follow the Rule Game where the students are given a base number between 0 and 100 (2.NBT.5). In Lesson 22 students play a mental math game called Compensation where the students add numbers such 420+190 by taking from one number to round the other number to the next hundred (2.NBT.B).

Overall, Zearn includes time in every lesson during Independent Digital Lessons through Number Gyms, Sprints, and Blasts, and in Teacher-Led Instruction Whole Group Fluency Lessons to build fluency. These lessons are designed to complement one another, reinforcing student development of procedural skills and fluency.

The materials meet the expectation for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade.

Missions address application in most Teacher-Led Instruction Lessons through Whole Group Word Problems that model the situations from Table 1 of CCSSM “Common Addition and Subtraction Situations.”

Mission 8, Teacher-Led Instruction, Whole Group Word Problems, Topic B Composite Shapes and Fraction Concepts includes teacher notes on what addition and subtraction situations are represented. The problems address representing and solving problems involving addition and subtraction (2.OA.1). For example:

• Teacher-Led Instruction, Whole Group Word Problems, Lesson 6: “Frank has 19 fewer cubes than Josie. Frank has 56 cubes. They want to use all of their cubes to build a tower. How many cubes will they use?” The teacher note states, “This is a two-step problem with a compare with bigger unknown type problem as one step. Encourage students to draw a tape diagram to help visualize the comparison.”
• Teacher-Led Instruction, Whole Group Word Problems, Lesson 7: “Mrs. Librarian’s students are picking up tangram pieces. They collect 13 parallelograms, 24 large triangles, 24 small triangles, and 13 medium triangles. The rest are squares. If they collect 97 pieces in all, how many squares are there?” The teacher note states, “This is a two-step put together with addend unknown problem type. The numbers in this problem invite students to call upon a variety of strategies to solve.”
• Teacher-Led Instruction, Whole Group Word Problems, Lesson 8: “The students were making larger shapes out of triangles and squares. They put away all 72 triangles. There were still 48 squares on the carpet. How many shapes were on the carpet when they started?” The teacher note states, “This is a take from with a start unknown type of problem. Encourage students to visualize the relationships within the problem.”

The instructional materials reviewed for Grade 2 meet the expectation for balancing the three aspects of rigor. Overall, the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within Teacher-Led Instruction and Independent Digital Lessons.

In each Mission students develop procedural skills and fluency and conceptual understandings, and apply these to solve real-world problems.

• Fluency is embedded into every lesson. In Mission 3, Teacher-Led Instruction Whole Group Fluency, Lesson 6, students practice addition using a meter strip with two-digit numbers, and using tens to add nines. For example 9 + 5 = 10 + 4.
• Conceptual understanding is embedded into every lesson. In Mission 3, Teacher-Led Instruction, Lesson 6, students use place value to understand expanded form in unit order. Students connect expanded form into statements, such as “2 hundreds 4 tens 3 ones.” They count up: “1 hundred 2 hundred 2 hundred ten 2 hundred twenty…” They then reread the number using addition symbols: “100 + 100 + 10 + 10 + 10 + 10 + 1 + 1+ 1.” During the Independent Digital Lesson students write the number from a set of expanded numbers often presented using the commutative property: “10 + 400 + 2 = ______ and decompose numbers into expanded form 385 = _____ + _____ + _____.”
• Application problems are embedded into every lesson and often call for students to model their thinking and make connections to procedural skills. In Mission 3, Teacher-Led Instruction Whole Group Word Problem, Lesson 6, students read the problem with the teacher: “Timmy the monkey picked 46 bananas from the tree. When he was done, there were 50 bananas left. How many bananas were on the tree at first?” Students work with the teacher and a partner to answer questions: “Visualize the problem and talk with your partners. What can you draw with what you see? What is the question asking you? How many bananas were on the tree at first? How many different ways can you find the answer? Etc.” In this task, students use procedural fluency to add and subtract within 100, and they apply their conceptual understanding of addition and subtraction situations to explore different solution strategies.

The instructional materials reviewed for Zearn Grade 2 meet the expectations for prompting students to construct viable arguments and analyze the arguments of others. The students’ materials in the Teacher-Led Lessons, Whole Group Word Problems, Optional Problem Sets, and Assessments provide opportunities throughout the year for students to both construct viable arguments and analyze the arguments of others. The students’ materials sometimes prompt students to construct viable arguments and include some opportunities for students to analyze the arguments of others.

Students are asked daily to explain their thinking while completing application problems. MP.3 is identified through Whole Group Word Problems, Whole Group Fluency, and Assessment. Examples of opportunities to analyze the arguments of others:

• Mission 1, Teacher-Led Instruction, Optional Problem Set, Lesson 3, Question 5: Students prove a student’s claim about having more money than another student right or wrong, using pictures, numbers, or words.
• Mission 3, Teacher-Led Instruction, Lesson 7: As students work with a partner to compare 12 ones to 12 tens and 15 ones to 15 tens, each is able to analyze the representations created by the other and the verbal explanations that accompany the representations.
• Mission 5, End-of-Module Assessment, Question 5: Students analyze what Martha did wrong when subtracting 378 from 456 and explain the error to her. Students also offer Martha “an alternative strategy for 456 - 378, to help Martha avoid making this mistake again.”
• Mission 7, Teacher-Led Instruction, Optional Problem Set, Lesson 14, Question 2: Students compare two different measurements obtained by two students, and after determining which measurement is correct, students explain their reasoning behind the measurement they chose.

Examples of opportunities to construct viable arguments:

• Mission 1, Teacher-Led Instruction, Lesson 6: “Explain to your partner how 10-9 helps us to solve 30-9.”
• Mission 2, Independent Digital Lessons, Lesson 6, Math Chat: Students briefly explain how they solved the problem where centimeters are the units being used to measure objects.
• Mission 3, Independent Digital Lessons, Lesson 19, Learning Lab: Students explain how they used virtual base-10 blocks to see patterns in counting by tens and ones in numbers greater than 100.
• Mission 4, Teacher-Led Instruction, Lesson 2: “'If I asked you to add 3 tens to 26, how could you do that?'...show on whiteboard a strategy for 18+20...54-20...56-30.”
• Mission 6, Independent Digital Lessons, Lesson 18, Math Chat 18: Students briefly explain how they used different representations of numbers to determine whether a number was even or odd.
• Mission 7, Independent Digital Lessons, Lesson 4, Learning Lab: Students explain how they used different models to solve the problem by comparing visual models.

The Zearn Grade 2 materials meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards. Overall, there is guidance for teachers on how to lead student discussions in which students construct their own viable arguments and analyze the arguments of others.

The Teacher-Led Instruction Lessons provide opportunities for teachers to discuss the mathematics with their students and for students to discuss the mathematics with each other as directed by the teacher, for example:

• In Mission 2, Teacher-Led Instruction, Lesson 7 teachers are given the following prompts and questions to assist students as they consider how measuring the same object can lead to different outcomes: “Why do you think the measurements are different? Turn and talk.; Do you know why your measurements were different?; Why does the size of the paperclip matter?; and What does that tell you about measurement and unit size?”
• In Mission 5, Teacher-Led Instruction, Lesson 20, Problem 2 teachers are given the following prompts to assist students as they subtract 297 from 546: “Instruct them to find a partner who used a different solution strategy.; Turn and talk to your partner: How efficient were the strategies you used and why?; and How were the strategies you discussed similar, and how were they different? Turn and talk to your partner.”
• In Mission 8, Teacher-Led Instruction, Lesson 7, Part 2 teachers are given a series of questions to assist students in constructing a viable argument as they determine how many pattern blocks of different types can be used to cover a regular hexagon, and what fraction of the hexagon each type of block represents.

The instructional materials reviewed for Zearn Grade 2 meet the expectations for explicitly attending to the specialized language of mathematics. Overall, the materials for both students and teachers have multiple ways for students to engage with the vocabulary of mathematics that is present throughout.

The instructional materials provide instruction on how to communicate mathematical thinking using words, diagrams, and symbols. Students have opportunities to explain their thinking while using mathematical terminology, graphics, and symbols to justify their answers in Teacher-Led Instruction and Independent Digital Lessons.

• Vocabulary is used directly in the Teacher-Led Instruction, Small Group Lessons and then reinforced in the Whole Group Word Problems. Teachers, when applicable, model the vocabulary. For example, Mission 7, Teacher-Led Instruction, Whole Group Word Problems, Lesson 2 states, “This comparative problem type invites the use of a tape diagram. It leads into today’s lesson, in which students will use data involving animals to solve simple compare word problems. It also prepares students to notice the relationship between the tape diagram and the bars on a bar graph in Lesson 3.”
• Vocabulary is sometimes explicitly taught during the Guided Practice part of the Independent Digital Lessons. Vocabulary words are in bold and explained and are followed up by models or examples. For example, Mission 6, Independent Digital Lesson 5 Learning Lab introduces students to the term array and shows many examples of how they can be created and arranged.
• Students are expected to use correct mathematics vocabulary as they Read, Draw, and Write for Word Problems and complete Exit Tickets.