1st Grade - Gateway 2

The instructional materials for Eureka Grade 1 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade-level.

• In Module 2, Lesson 26, students develop conceptual understanding of place value. Students practice bundling groups of 10 with various models (a Rekenrek bracelet, a 5-group card of ten, a ten-frame) in a whole group setting and understand that some ones are left over which clarifies the meaning of the ones unit. Students practice this concept by using visual models in the Problem Set. Problem Set Question 1 states, “Circle ten. Write the number. How many tens and ones?” (1.NBT.2).

• In Module 6, Lesson 1, students develop conceptual understanding of solving addition and subtraction word problems. Teachers guide students through drawing the double tape diagrams to solve a word problem in the Concept Development section of the lesson. The teacher is prompted to ask the following questions, “Tamra collected 9 seashells on the beach. Julio collected 11 seashells. How many more seashells did Julio collect? How many fewer seashells did Tamra collect? How many seashells did Tamra and Julio collect? (This component provides a contrast between the comparison problem type and a put together problem type.)” (1.OA, 1.NBT)

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade.

• In Module 2, Lesson 23, students independently demonstrate conceptual understanding of solving word problems involving addition and subtraction. Students draw a model and write a number sentence when solving a word problem. Problem Set Question 1 states, “Read the word problem. Draw and label. Write a number sentence and a statement that matches the story. Janet read 8 books during the week. She read some more books on the weekend. She read 12 books total. How many books did Janet read on the weekend?” (1.OA.1)
• In Module 4, Lesson 3, students independently demonstrate conceptual understanding of place value. Students interpret two-digit numbers as either tens and some ones or as all ones. Problem Set Question 1 states, “Count as many tens as you can. Complete each statement. Say the numbers and the sentences. ___ ten ___ ones is the same as ___ ones.” (1.NBT.B)

The instructional materials for Eureka Grade 1 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade-level.

• In Module 1, Lesson 7, students develop procedural skill and fluency of adding within 10 by using pictures and number bonds. Problem Set Question 1 states, “Circle 7. How many more does 7 need to make 9?”
• In Module 2, Lesson 22, students develop procedural skill and fluency of subtracting by using pictures and creating number sentences that match a given story. Problem Set Question 4 states, “Read the word problem. Draw and label. Write a number sentence and a statement that matches the story. 4. Oziah read some non-fiction books. Then, he read 7 fiction books. If he read 16 books altogether, how many non-fiction books did Oziah read? Meet with a partner, and share your drawings and sentences. Talk with your partner about how your drawing matches the story.”

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level.

• In Module 2, Lesson 1, students independently demonstrate procedural skill and fluency of adding within 10 by participating in the activity “Take Out”. This activity supports fluency by decomposing numbers within 10 as students need to get 1 out of the second addend when adding to 9. The teacher is prompted to ask the following questions, “T: Take out 1 on my signal. For example, if I say “5,” you say “1 and 4.” T: 3 S: 1 and 2 T: 10 S: 1 and 9. Continue with all numbers within 10.”

• In Module 4, Lesson 20, students independently demonstrate procedural skill and fluency of adding within 10 by using number bonds for addition and subtraction. The Fluency Practice note states, “This fluency activity builds students’ ability to add and subtract within 10 or 20, while reinforcing the relationship between addition and subtraction. The first two to three minutes should be spent reviewing the core fluency within 10. In the last one to two minutes, allow students who are very strong with sums and differences to 10 to work with a partner and choose totals between 10 and 20. Write a number bond for a number between 0 and 10, with a missing part or whole. Students write an addition and a subtraction sentence with a box for the missing number in each equation. They then solve for the missing number.”

Students build fluency for adding and subtracting to 10 in 5-10 minute fluency practice activities before lessons. These fluency practices are provided in all of the 6 modules. For example:

• In Module 1, Lesson 5, students create number bonds with partners to practice addition fact fluency to 10.
• In Module 2, Lesson 24, students practice fluency of subtraction within 10 by filling in the missing number of a problem. Sprint Question 29 states, “9 - ___ = 10 - 5”

The instructional materials for Eureka Grade 1 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade-level.

• In Module 2, Lesson 16, students engage in grade level mathematics when using the take from ten strategy or the count on strategy to solve word problems. The Application Problem states, “There were 16 coats on the rack. Nine students took their coats to go outside. How many coats were still on the rack? Extension: If 4 more students take their coats to go outside, how many coats will still be hanging?” (1.OA.6)
• In Module 6, Lesson 21, students engage in grade level mathematics by using tape diagrams to solve word problems. The Application Problem states, “Willie saw 11 monkeys at the zoo. He saw 4 fewer monkeys than tigers. How many tigers did he see at the zoo? (1.OA.6)

The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts.

• In Module 2, Lesson 2, students independently demonstrate the use of mathematics when solving word problems involving three addends. The Application Problem states, “Lisa was reading a book. She read 6 pages the first night, 5 pages the next night, and 4 pages the following night. How many pages did she read?” (1.OA.2)
• In Module 2, Lesson 21, students independently demonstrate the use of mathematics when analyzing peer solutions to subtraction problems as well as creating a correct model to represent the solution. Problem Set Question 1 states, “There were 16 dogs playing at the park. Seven of the dogs went home. How many of the dogs are still at the park? Circle all the student work that correctly matches the story. Fix the work that was incorrect by making a new drawing in the space below with the matching number sentence.” (1.OA.6)
• In Module 6, Lesson 2, students independently demonstrate the use of mathematics by drawing a double tape diagram and writing a number sentence that matches the given story when solving comparison word problems. Problem Set Question 2 states, “Emi planted 12 flowers. Rose planted 3 fewer flowers than Emi. How many flowers did Rose plant?” (1.OA.1)

The instructional materials for Eureka Grade 1 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.

The lessons include components such as: Fluency Practice, Concept Development, and Application Problems. Conceptual understanding is addressed in “Concept Development”. During this time, the teacher guides students through a new concept or an extension of the previous day’s learning. Students engage in practicing procedures and fact fluency while modeling and solving these concepts. Fluency is also addressed as an independent component within most lessons. Lessons may contain an “Application Problem” which connects previous learning to what students are learning for the day. The program balances all three aspects of rigor in every lesson.

All three aspects of rigor are present independently throughout the program materials.

• In Module 1, Lesson 14, students develop conceptual understanding when pictures and 5-group cards are used to practice the addition strategy “Count on”. Problem Set Question 4 states, “ Use your 5-group cards to count on to add. Try to use as few dot cards as you can. a. 6 + 1 = ___” (1.OA.6)
• In Module 3, Lesson 5, students practice subtraction fluency within 20 when writing the missing number in a subtraction equation. Sprint Question 17 states, “18 - 9 = ___” (1.OA.6)
• In Module 5, Lesson 6, students engage in the application of mathematics by solving a word problem involving subtraction. The Application Problem states, “Emi lined up 4 yellow cubes in a row. Fran lined up 7 blue cubes in a row. Who has fewer cubes? How many fewer cubes does she have?” (1.OA.1)

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials.

• In Module 2, Lesson 29, students engage in the application of mathematics and practice fluency of subtraction within 20 when solving subtraction word problems. Problem Set Question 3 states, “Solve the problems. Write your answers to show how many tens and ones. Show your solution in two steps: Step 1: Write one number sentence to subtract from ten. Step 2: Write one number sentence to add the remaining parts. Tatyana counted 14 frogs. She counted 8 swimming in the pond and the rest sitting on lily pads. How many frogs did she count sitting on lily pads?” (1.OA.6)
• In Module 4, Lesson 14, students develop conceptual understanding of place value and practice fluency of addition within 20 by using models to complete addition equations. Problem Set Question 10 states, “Make a number bond to solve. Show your thinking with number sentences or the arrow way. Complete the place value chart. 17 + 2 = ___” (1.OA.6)

The instructional materials reviewed for Eureka Grade 1 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Student materials consistently prompt students to construct viable arguments and analyze the arguments of others.

• In Module 3, Lesson 4, the materials prompt students to analyze a measurement solution and explain why the solution was incorrect. Homework Question 11 states, “Explain what is wrong with the measurements for the pictures you did NOT circle.”
• In Module 4, Lesson 18, the materials prompt students to analyze two students solutions to an addition problem and justify why both students are correct or not. Homework Question 1 states, “Two student both solved the addition problem below using different methods. 18 + 9. Are they both correct? Why or why not?”
• In Module 6, Lesson 11, the materials prompt students to solve an addition problem and to explain their thinking to a partner. Problem Set Question 6a states, “Solve and explain your thinking to a partner. 2 + 50 = ___”
• In Module 6, Lesson 18, the materials prompt students to analyze two different solutions to an addition problem and to correct the mistake. The Exit Ticket states, “Circle the work that is correct. In the extra space, correct the mistake in the other solution using the same solution strategy the student tried to use.”

The instructional materials reviewed for Eureka Grade 1 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Teacher materials assist teachers in engaging students in both constructing viable arguments and analyzing the arguments of others, frequently throughout the program. The teacher materials consistently provide teachers with question prompts for student discussion and possible student responses to support that discussion.

• In Module 3, Lesson 4, the teachers are prompted to engage students in constructing an argument by asking students to discuss with a partner which errors the teacher made in their measurement and how they know he/she is incorrect. “T/S: 5 centimeter cubes! 6 centimeter cubes,....,11 centimeter cubes! T: Great. The end of this eleventh centimeter cube lines up with the end of the crayon. So, the crayon is as long as 11 centimeter cubes. Do you agree? Turn and talk with your partner.”
• In Module 4, Lesson 18, the teachers are prompted to engage students in constructing an argument and analyzing the arguments of others by having students observe two ways of solving the addition problem 17 + 4. “Let’s compare Student C’s work and Student D’s work. Did they solve the problem in the same way? What similarities and differences do you notice? Turn and talk to your partner.”
• In Module 6, Lesson 11, the teachers are prompted to engage students in constructing an argument and analyzing the arguments of others by having students choose a method to show that they know the answer to 40 + 30 = 70. Rather than solving the problem they are given the answer and must prove it is correct. “Explain how you know that 40 + 30 = 70. You can draw or write on the chart paper to explain your thinking.”
• In Module 6, Lesson 27, the teachers are prompted to engage students in constructing an argument and analyzing the arguments of others by having students solve varied word problems independently and discuss their methods for solving with a partner. The whole class then participates in a discussion and asks each other questions about their solutions. “Note: In today’s lesson, students work on their Problem Set and solve the varied problem types they encountered throughout the year. Selected pairs of students then discuss their methods for solving the problems and explain their work. After they share, the whole class participates in a discussion as students make comments and suggestions and ask each other questions. How does your work or tape diagram help you solve the problem? A compliment I could give you is…? A question I have for you is…? One way you might improve your work would be…? Let’s look for similarities and differences in our drawings and strategies.”

The instructional materials reviewed for Eureka Grade 1 meet expectations for explicitly attending to the specialized language of mathematics.

In each module, the instructional materials provide new or recently introduced mathematical terms that will be used throughout the module. A compiled list of the terms along with their definitions is found in the Terminology tab at the beginning of each module. Each mathematical term that is introduced has an explanation and some terms are supported with an example.

The mathematical terms that are the focus of the module are highlighted for students throughout the lessons and are reiterated at the end of most lessons. The terminology that is used in the modules is consistent with the terms in the standards.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols.

• In Module 1, Lesson 4, the Notes on Multiple Means of Representation states, “Look for ways to connect real life experiences in math. Use apples during this lesson as a connection to science curriculum. Cut the apples to explore the parts of the apple connecting to total and part vocabulary.”
• In Module 2, Lesson 5, the Notes on Multiple Means of Engagement states, “It is important to partner important vocabulary with captions or pictorial representations for all students. It is especially beneficial to English language learners and students with hearing impairments. Have students model or demonstrate their understanding of more difficult vocabulary such as efficient.”
• In Module 4, Lesson 17, the Notes on Multiple Means of Representation states, “Highlight the critical vocabulary such as quick ten drawings, number bonds, tens, ones, and addends, and use pictorial representations to support student understanding. Have students use these terms as they share their thinking. This supports vocabulary development.”

The materials use precise and accurate terminology and definitions when describing mathematics, and support students in using them.

• In Module 1, Lesson 2, the mathematical term “count on” is in bold writing within a question listed in the Student Debrief section. These questions guide teachers in leading a class discussion. “Talk to your partner about how you found the total in Problem 6. Did you count all of the dots, or did you count on from a part you saw?”
• In Module 2, Lesson 27, the materials use precise terminology of tens and ones while using the terms when showing an example of subtraction. The Concept Development states, “T: How can we take from the ten here? T: (Draw a matching illustration on the board, showing 10 and 3 separated. Touch the 10.) And, how many are left? T: (Write 10 - 4 = 6 on the board.) How many do we have altogether? (Touch the 6 and the remaining 3.) T: 9 tens or 9 ones? T: How many Tens are left?”

• In Module 5, Lesson 4, the materials use accurate terminology when students learn to create composite shapes. Problem Set Question 1 states, “Use pattern blocks to create the following shapes. Trace or draw to record your work. Use 3 triangles to make 1 trapezoid.”