1st Grade - Gateway 2

The instructional materials reviewed for Zearn Grade 1 meet the expectation for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. There are demonstrations by the teacher and independent explorations for the students (with concrete materials). Conceptual understanding is targeted through concrete materials and multiple visual representations.

During Independent Digital Lessons, students engage with visual representations and virtual manipulatives. Multiple visual representations are presented with connections made between them. Students work flexibly with these visual models. For example, in Mission 4, Add and Subtract Bigger Numbers, focuses instruction on understanding place value (1.NBT.B) and using place value to add and subtract within 100 (1.NBT.4 and 1.NBT.6):

• In Lesson 2, students decompose two-digit whole numbers through place value to identify the tens and ones using unifix cubes, writing a number sentence, and using a place value chart to present multiple representations of the given numbers. One example question is: “17 will be in 2 parts. What parts will they be?”
• In Independent Digital Lesson 4, students use visual models to find two-digit numbers, decompose those numbers by examining pictures of unifix cubes and number bonds, and complete the corresponding addition sentences to represent the sum of the ones and tens for the given number.
• In Independent Digital Lesson 5, students use drawings and virtual manipulatives to identify 10 more, 10 less, 1 more, or 1 less than a given two-digit number.

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 including through place value, decomposing and recomposing of numbers with hands on and virtual manipulatives, and through place value charts. These representations are linked to addition and subtraction sentences within 100.

The instructional materials reviewed for Zearn Grade 1 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 2, Lesson 1 Teacher-Led Instruction Whole Group Fluency students play a game counting on with numbers one through ten and use card games to add within 10. During Independent Digital Lessons, Tower of Power students practice making ten when one addend is nine.
• In Mission 3, Teacher-Led Instruction, Whole Group Fluency Lesson 4, students play a game where pairs of students roll two dice and make a number sentence from the pair, for example 6+0=6 and 4+3=7. In the Independent Digital Lesson 4 students practice 15 questions adding within 20 during Blast (1.OA.6).
• In Mission 6, Teacher-Led Instruction, Whole Group Fluency Lesson 11, the teacher note states, “This activity reviews yesterday’s lesson, where students add and subtract tens within 100.” Using a can and ten dimes and ten pennies, students add and subtract as coins are added or removed from the can. The second activity contains a teacher note that states, “This fluency activity builds on yesterday’s Get to Ten(s) activity to prepare students for G1-M6-Lesson 13.” In this activity the teacher says a number, and students say an addition statement to get to the next multiple of 10.

Overall, Zearn includes time in every lesson during Independent Digital Lessons in Number Gyms, Sprints, and Blasts and in the Teacher-Led Instruction Whole Group Fluency Lessons for building 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 6, Teacher-Led Instruction, Whole Group Word Problems, Topic B Numbers to 100 includes teacher notes on what addition and subtraction situations are represented. The problems address representing and solving problems involving addition and subtraction (1.OA.1) and determining the unknown whole number in addition and subtraction equations (1.OA.8). For example:

• Teacher-Led Instruction Whole Group Word Problems, Lesson 3: “Tamra has 4 more goldfish than Peter. Peter has 10 goldfish. How many goldfish does Tamra have? The teacher note states that this problem is a “...compare with bigger unknown problem type…”
• Teacher-Led Instruction Whole Group Word Problems, Lesson 4: “Tamra has 14 goldfish. Darnel has 8 goldfish. How many fewer goldfish does Darnel have than Tamra? The teacher note states, “Today’s Application Problem presents a compare with difference unknown problem type.”
• Teacher-Led Instruction Whole Group Word Problems, Lesson 5: “Kiana has 6 fewer goldfish than Tamra. Tamra has 14 goldfish. How many goldfish does Kiana have?” The teacher note for this problem states, “Today’s Application Problem is the last in a series of three problems that use a related context. The three problems can be discussed together during the Student Debrief. As students share strategies and compare and contrast the problem stories, they gain a stronger sense of each particular problem type.”

The instructional materials reviewed for Grade 1 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 4, Independent Digital Lesson 5 Sprint, students use addition and subtraction to and from 10. Problems include finding the sum and difference as well as finding missing addends and minuends. For three minutes during Teacher-Led Instruction Whole Group Fluency Lesson 6, students practice “Quick Tens” to show and say numbers between 11 and 40 in varied ways. They then count dimes and pennies.
• Conceptual understanding is embedded into every lesson. In Mission 4, Teacher-Led Instruction Small Group Lesson 6, students compare the use of ten sticks and unit cubes to using dimes and pennies. For example, students look at one 10 stick and four unit cubes and find the equivalent expression using one dime and four pennies.
• Application problems are embedded into every lesson and often call for students to model their thinking and make connections to procedural skills. For example, in Mission 4 Teacher-Led Instruction Whole Group Word Problem Lesson 5, students are given the following application problem: “Lee has 4 pencils and buys 10 more. Kiana has 17 pencils and loses 10 of them. Who has more pencils now? Use drawings, words, and number sentences to explain your thinking.” In this task students apply their conceptual understanding to model and compare an addition and subtraction scenario, and they demonstrate procedural fluency in completing the addition and subtraction.

The instructional materials reviewed for Zearn Grade 1 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 4, Teacher-Led Instruction, Whole Group Word Problem, Lesson 7: "Benny has 4 dimes. Marcus has 4 pennies. Benny says, 'We have the same amount of money!' Is he correct? Use drawings or words to explain your thinking."
• Mission 6, Teacher-Led Instruction, Lesson 27 Sentence prompts: “How does your work help you solve the problem? A compliment I can give you is ___; A question I have for you is ___; One way you might improve your work is ___; Let’s look for similarities and differences in our drawings and strategies.”
• Mission 2, Mid-Module Assessment, Question 5: Students are given the information: "Eva has 6 marbles in her hand and 8 in her pocket" In part A students are presented with two representations of how two students modeled the marbles Eva has. They need to write a number sentence for each representation. In Part b they respond to a true false question that demonstrates the use of the commutative property of addition. The task continues with additional prompts. In each prompt students must show their thinking using and/or writing number sentences, representations, or explaining why.
• Mission 4, Mid-Module Assessment, Question 10: Students analyze the thinking of another response when someone says 30-20 is the same as 3 tens-2 tens; students decide if they are wrong or right and why.
• Mission 6, End-of-Module Assessment, Question 4: Students decide if someone is right or wrong and why.

Examples of opportunities to construct viable arguments:

• Mission 2, Teacher-Led Instruction, Lesson 1: "Talk to your partner. What are some ways we could add these blocks together?"
• Mission 4, Teacher-Led Instruction, Lesson 20: Two students show their process for solving word problems on chart paper while the rest of the class solves independently. Students assess the reasonableness of the solutions while talking to their peers.
• Mission 3, End-of-Module Assessment, Question 2 asks students to explain their choice of a measurement tool.
• Mission 6, End-of-Module Assessment: In Question 4, students explain their thinking in determining if two students are correct after each one represented the number 87 in a different way with tens and ones. In Question 6, students explain their thinking using a place value chart as they determine what number is 10 more than, 10 less than, 1 more than, and 1 less than 89.

The Zearn Grade 1 materials meet the expectations 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 3, Teacher-Led Instruction, Lesson 4 teachers demonstrate measuring a crayon with centimeter cubes. At different points in laying out the centimeter cubes, teachers are directed to lay them out incorrectly so that students can analyze the method used by the teacher and the final measurement that is obtained.
• In Mission 4, Teacher-Led Instruction, Lesson 18 teachers are given the following questions to ask students about two different methods used for adding 17 and 4: “Can both students’ work be correct, even though they broke apart different numbers?; What is a compliment you can give to each of these students?; and What are some ways they could improve their work?”

The instructional materials reviewed for Zearn Grade 1 meet the expectation 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 2 Teacher-Led Instruction Whole Group Word Problems, Lesson 9 states, “This problem uses three addends, revisiting the associative and commutative properties from earlier in this topic.”
• 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 4 Independent Digital, Lesson 10 Math Chat introduces students to the less than and greater than symbols, terminology associated with them, and examples that demonstrate how the symbols are used.
• Students are expected to use correct mathematics vocabulary as they Read, Draw, and Write for Whole Group Word Problems and complete Exit Tickets. For example, in Mission 6 Independent Instruction Exit Tickets Lesson 25, students have to be able to read, understand, and use a tape diagram and double tape diagram as they solve a problem about two students sliding down a slide.