2nd Grade - Gateway 2

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. 

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop conceptual understanding. For example:

• In Lesson 17, Session 1, Explore, Try It, students build on what was learned in Lesson 16 with addition to solve subtraction strategies. The beginning of each session focuses on the use of visual/concrete models. Apply It focuses on the use of expanded form to teach the standard algorithm. Regrouping starts at Session 2 with tens and ones, Session 3 regroups hundreds to tens, Sessions 4 and 5 allow for regrouping anywhere in the problems.
• In Lesson 18, Session 1, Explore, students use whatever strategies they are comfortable with to solve three-digit number problems. Students review using open number lines and place value charts. Apply It states, “For all problems, encourage students to use a drawing, a model, or equations to support their thinking.” For Sessions 2-4, students are given choices to use the strategies they want. In Session 5, students have to solve two open number line problems in the Apply It problems.
• In Lesson 19, Session 2, Develop, Model It states, “Break each number into tens and ones. Then add pairs of numbers.” The problem shows the addends 16, 41, 22, and 39 written into a place value chart. Students are developing conceptual understanding of 2.NBT.6.

Examples of students independently demonstrating conceptual understanding include:

• In Lesson 5, Student Worktext, Session 2, Develop, Problem 5, Reflect states, “Look back at your Try it, strategies by classmates, and Picture it and Model it. Which models or strategies do you like best or solving two-step problems? Explain.” (2.NBT.9)
• In Lesson 16, Session 2, Develop, Apply It states, “For all problems, encourage students to break apart the addends into hundreds, tens and ones to find the solution.” (2.NBT.7) 
• In Lesson 31, Student Worktext, Session 2, Develop, Try It states, “Mike puts some stickers into an array. Each row has 5 stickers. Each column has 4 stickers. How many stickers are there in all?” (2.OA.4)  Understanding arrays builds conceptual understanding for multiplication in later grades. 
• In Interactive Practice, Understand Three Digit Numbers, students use virtual base ten blocks, place value charts, and expanded form to understand three-digit numbers. (2.NBT.1)
• In Interactive Practice, Understanding Partitioning Shapes, students reason about how shapes are partitioned and whether more pieces is the same as a greater amount of the whole. (2.G.3)

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. The materials include problems and questions, interactive games, and math center activities that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. 

In i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources students develop procedural skill and fluency throughout the grade level. For example:

• In Lesson 1, Session 1, Explore states, “complete each equation to show how to make a ten to add 8+5.” Students then show “8+2=10, 10 +3=13, so, 8+5=13” by filling in the blanks with missing numbers.  Students build procedural skill by learning to make a 10 to add numbers with sums greater than 10.
• In Lesson 6, Session 1, Explore, Connect It, students use two different procedures with base-ten blocks for adding 27+15. In the first procedure, students “Go to the next ten” by showing “27+3=30, 30+10=40, 40+2=42.” In the second procedure, students “Add tens, then ones.” Students show that 20+10=30, 7+5=12, and 30+12=42.
• In Lesson 20, Session 2, Develop, Apply It states, “Tony says the crayon is 8 centimeters long. Explain what Tony did wrong. Then find the correct length of the crayon.” A picture of a crayon being measured by a ruler is shown, the crayon is being measured starting at the one inch mark. Students are developing the procedural skill of measuring from the 0 inch mark. 

2.OA.2 (Fluently add and subtract within 20 using mental strategies. By the end of 2nd grade know from memory all sums of two one digit numbers) requires students to develop grade level fluency. This standard is addressed in several lessons, including:

• In Lesson 2, Session 4, Refine, Develop Fluency states, “Why: Support students’ facility with fact families. How: Have students write the four equations to represent the fact family below.” 
• In Unit 1, Math in Action, Student Worktext states, “Beau wants to build a shelf to store his 16 robot motors. Look at his plan. Shelf Plan: Use up to 6 shelves. Put at least 3 and no more than 6 robot motors on each shelf. How many shelves should Beau make? How many motors should he put on each shelf?”

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. Within each lesson, there are Fluency and Skills Practice pages that children complete on their own.  Some examples of when students get opportunities to demonstrate procedural skill and fluency in Classroom Resources include:

• In Lesson 2 Fluency and Skills Practice, eight problems show a subtraction equation and the related addition equation (ex. 12-3=?, 3+?=12) and Problem 9 states, “In problem 6, how did you use your first answer to find your second answer?”
• In Lesson 6 Fluency and Skills Practice, seven pairs of problems are presented where one shows the numbers decomposed as tens and ones and the other problem that shows two addends. For example, Problem 1 shows 30+7+50+3 and Problem 2 shows 37+53, and Problem 15 states, “How does the information in number 9 help you solve number 10?” (2.NBT.5)
• Learning Games which provide independent practice include: 
• In Match, students match the card that has two numbers or a number and dots that are being added/subtracted to the other card that shows the correct answer.
• In Hungry Fish, students combine the numbers in the bubble together until they equal the amount shown on the fish. Levels Addition 11-15, 16-20, 21-30, 31-100, 10s and 100s and Subtraction 11-15, 16-20, 21-30, 31-100, 10s, and 100s are appropriate for Grade 2.
• In the Math Center Activities, there are games provided to work on adding within 20. 
• The Lesson 1 game, Make a Ten, focuses on solving missing addend equations so that the student can solve, his/her partner checks, and then he/she moves the marker on the game board. 
• In Lesson 2 game, Use Mental Math to Subtract, students pick a card, put connecting cubes together, break off some and hide them, and then the partner has to guess how many are hidden. 
• In the Math Center Activities, there are games provided to work on adding with 100, including:
• In the Lesson 2 game Doubles and Near Doubles, students use dice to roll and double numbers covering a game board based as students play. 
• In the Lesson 6 game 100 or Not, students use number cards to make two-digit numbers to add. If their solution is within 100, students get a counter. 
• In the Lesson 8 game First to 5 (or 10), students play using an operation pile and number card pile. Students draw an operation (+ or -) and then two number cards.  

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 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 some opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level.

Opportunities for students to independently demonstrate the use of mathematics flexibly are present in a variety of contexts. The instructional materials demonstrate multiple opportunities for students to engage in routine application of mathematics of the grade level in the i-Ready, Assess & Teach, Classroom Resources, including:

• In Lesson 3, Session 1, Explore states, “Fola has 8 berries. Her dad gives her some more berries. Now, Fola has 13 berries. How many berries did Fola’s dad give her?” (2.OA.1)
• In Lesson 3, Student Worktext, Session 3, Develop, Problem 7 states, “Explain how you would solve this problem. Ken has 10 toy cars. He has 4 more toy cars than Sarah. How many toy cars does Sarah have?” (2.OA.1) 
• In Lesson 6, Session 3, Develop states, “Directions- Read and try to solve the problems below. There are 48 students on Bus A and 43 students on Bus B. How many students are on both buses?” 
• In Lesson 7 Subtract Two-Digit Numbers, Session 2, Develop states, “Directions- Read and try to solve the problem below. There are 54 children at camp. 27 are girls. How many boys are at camp?” 
• In Lesson 8, Session 3, Develop states, “Directions- Use what you learned to solve these problems. Problem- There are 65 cherries in a bowl. Dan eats 12 cherries with his lunch. How many cherries are in the bowl now?” 
• In Lesson 25, Student Worktext, Session 3, Develop, Problem 6 states, “Luisa has a piece of yarn that is 38 inches long. Daryl has a piece of yarn that is 4 inches shorter than Luisa’s. They need 75 inches of yarn for their craft project. Do they have enough yarn? Explain your answer.” 
• In Lesson 25, Session 3, Develop states, “Ed has two dog leashes. The purple leash is 84 inches long. The red leash is 75 inches long. How much shorter is the red leash than the purple leash?” 

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

For example, in Classroom Resources:

• In Unit 1, Math in Action states, “Solve each problem on a separate sheet of paper. Example Problem- Beau has 17 jars. He needs at least 8, but no more than 12 jars for a Science project. He will put the rest of the jars on a shelf. How many jars could Beau use for the science project? How many will be left to put on the shelf?” (The problem shows a picture of 18 jars.) 
• In Lesson 3, Session 5, Refine, Apply It, Problem 5 states, “Write a problem that can be solved using the bar model at the right. (6, ?, 8) Then show how to solve your problem.” This non-routine problem gives a sample student solution of “I have 8 stuffed toys. 6 are bears. The rest are dogs. How many stuffed dogs do I have? I can write and solve an equation 8 - 6 = 2; I have 2 stuffed dogs.”
• In Unit 2, Math in Action, Session 1 states, “Zoo Tours: A total of 58 people sign up for a tour of the zoo today. Alex has to make groups for the tour. Look at the notes. Zoo Tour Notes - tour groups must have at least 12 people, Tour groups can have no more than 20 people, There can be up to 4 groups in one day.” 
• The Unit 2 Performance Task provides an opportunity for students to solve a non-routine application problem. Students are tasked with finding out how many of each type of cupcake Nicole bakes. The materials state: “Nicole bakes chocolate and vanilla cupcakes for a party. Some of the cupcakes have frosting. The rest have no frosting. Use the clues to find out how many of each cupcake Nicole bakes.” Students are then given clues to figure out the problem.

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately.  

All three aspects of rigor are present independently throughout the program materials. The instructional materials attend to conceptual understanding, procedural skill and fluency, and application independently throughout the grade level.

Students engage in instruction and activities to develop conceptual understanding of grade level mathematics:

• In Lesson 3, Session 1, Explore, Connect to Prior Knowledge, students practice conceptual understanding of part-part-whole. The directions state, “Why: Support students' understanding of part-part-whole relationships to prepare for solving addition and subtraction word problems. How: Have students use counters to show 14 as the sum of any two of its addends.”

Students engage in instruction to develop procedural skills and fluency appropriate for Grade 2:

• In Lesson 31, Session 2, Develop, Picture It & Model It, students are given an array of stickers. Students show that they can add 4 together 5 times or add 5 together 4 times. Students continue to practice drawing arrays and finding two ways to write repeated addition problems for each problem in the rest of this Session.

Students use mathematical understanding and skill to solve application problems:

• In Lesson 18, Session 1, Explore states, “You know how to add and subtract three-digit numbers. Use what you know to try to solve the problem below. Ms. Mendez’s class has 243 storybooks. Then the class gets some new storybooks. Now the class has 372 storybooks. How many new storybooks does Ms. Mendez’s class get?” Students apply the skills they have learned about adding and subtracting to a problem with three-digits. 

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

Examples where two or more of the aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials include:

• In Lesson 3, Session 3, Explore, students develop conceptual understanding of solving one-step word problems by using a ten-frame to solve the problem. As students develop conceptual understanding of building tens to help in adding, they also gain fluency in grade level appropriate addition. Students also apply their understanding and procedural skill to solve mathematics applications to real-world word problems. 
• In Lesson 4, Student Worktext, Session 2, Develop, students use their conceptual understanding of reading bar graphs and creating equations to solve the problem. For example, “Martin asks the students in his class: What is your favorite sport? He makes a picture graph and a bar graph to show his results. How many students does Martin ask?” Students are applying their understanding of bar graphs and equations to application problems.
• In Lesson 27, Session 3, Develop, Additional Practice, Problem 5, students measure lengths of ribbon to organize and label the measurements in a line plot. This is an example of both real world application and procedural skills together within one problem. 

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations for carefully attending to the full meaning of each practice standard. 

The instructional materials attend to the full meaning of each mathematical practice in i-Ready, Assess & Teach, Ready Classroom Mathematics, Classroom Resources. 

Ready Classroom Mathematics materials fully meet the intent of the following math practices:  

Math Practice 1: Make sense of problems and persevere in solving them.

• In Math In Action, Unit One, the Purpose section states, “Students examine a problem that involves using addition and subtraction to find a number of shelves and the number of items per shelf. They discuss the problem to understand what it is asking and brainstorm different approaches. Then they refer to a problem-solving checklist to analyze a sample solution and identify what makes it a good solution.”
• In Math in Action, Unit Four, the Purpose section states, “Students examine a problem that involves measuring and understanding units of measurement to create a design for decorating a pencil box with buttons. They discuss the problem to understand what it is asking and brainstorm different approaches. Then they refer to a problem-solving checklist to analyze a sample solution and identify what makes it a good solution.” 

Math Practice 2 Reason abstractly and quantitatively. 

• In Lesson 4, Session 2, Develop, Deepen Understanding, the directions state, “MP2 Reason abstractly and quantitatively. When discussing the Favorite Sports bar graph, prompt students to consider other questions that can be answered from the graph. Generalize: Do you think this always true? How do the bars for Baseball and Football support your answer? Ask for volunteers to explain their reasoning. Listen for understanding that greater numbers correspond to taller bars and lesser numbers correspond to shorter bars.”
• In Lesson 6, Session 1, Explore states, “In this session, students draw on their knowledge of place value and adding one-digit numbers to add two-digit numbers. They examine a model of two-digit numbers and explore strategies to add those numbers. They look ahead to adding two-digit numbers using base-ten blocks, going to the next ten, and adding tens and then ones.” Try it, Make Sense of the Problem states, “Present the problem and guide students as needed to understand that 27 is the number of cans at the start and 15 is the change in the number of cans. Students may want to use base-ten blocks (tens and ones), connecting cubes, number bonds, bar models or open number lines.”  Discuss it, Support Partner Discussion states, “Encourage students to name or model the strategy they used to solve the problem. Look for, and prompt as necessary, understanding of: Two groups being joined to form a larger group regrouping 10 ones as 1 ten and making a ten to add.”
• In Lesson 13, Session 2, Develop states, “In this session, students solve a problem that requires them to find the total value of 2 hundreds, 1 ten, and 3 ones. Students model the quantities either on paper or with manipulatives. The purpose of this problem is to have students develop strategies for connecting digits to the values that they represent so that they can find the value of three digit numbers.” The Student WorkText page states, “Read and try to solve the problem below. Amir plays a board game that uses play money. He wins 1 tens bill, 2 hundreds bills and 3 ones bills. What is the total value of the bills Amir wins? The materials state, “Students use base-ten blocks, play money bills, hundreds place value charts, 200 charts and/or and open number line. After students try it, they discuss their answers, strategies and have partner discussion.”

Math Practice 4: Model with mathematics.

• In Lesson 8, Session 2, Develop states, “At the fair 39 students wait in line for a ride. Then some more students join the line. Now there are 93 students in line. How many more students join the line?” Students use two representations, a number line and adding up to the next 10. Deepen Understanding states, “When discussing the two subtraction equations used to represent the word problem, prompt students to consider how the equations are connected.” 
• In Unit 4: Math in Action: Use Measurement, Deepen Understanding, Using Diagrams and Equations states, “Bella saves buttons to decorate things she makes. Bella wants to glue some buttons on the top of a pencil box. Each button is the same distance across. How can Bella decorate the pencil box? Draw a picture/ Tell how many buttons she needs.” Students look at multiple solutions and solve the problem another way. The materials state, “As you discuss the sample solution, prompt students to look for connections between the addition equations and the diagram. Have them describe what part of the diagram each number represents. Ask, How do the equations represent the buttons and the spaces? Listen for 7 and 9 represent the lengths of the sides of the pencil box top. The addends represent the buttons and the 1-centimeter spaces between them. Ask, What would happen to the design if you decided to use more space between the buttons? Less space? Explain. Listen for More space leads to fewer buttons, and less spaces leaves room for more buttons on each side. There could be no space left between buttons or different amounts of space between them.”

Math Practice 5: Use appropriate tools strategically.

• In Lesson 9, Student Worktext, Session 3, Develop, Try It, in the math toolkit students are given a choice of using base-ten blocks, number bonds, bar models, hundreds charts, or open number lines to solve, “Some books are on a shelf. Students take 24 books from the shelf. Then there are 38 books on the shelf. How many books are on the shelf to begin with?”
• In Lesson 32, Student Worktext, Session 2, Develop, Try It, in the math toolkit students are given a choice of using counters, hundreds charts, number lines, or sticky notes to solve, “Ms. Ruiz brings 15 footballs and 14 soccer balls to gym class. Which number is odd?”

Math Practice 6: Attend to Precision

• In Lesson 4, Session 2, Develop, Deepen Understanding section provides guidance to ensure students can attend to precision. This section states, “When discussing organizing Lynn’s data set, emphasize the need for precision in recording data when graphing. Ask, Why do you think it is important to organize the data before making a picture graph or bar graph? Listen for, Sorting and counting the data makes it easier to count the totals in the groups. The numbers in each group need to be correct to be sure the graph will be correct.”
• In Lesson 26, Session 3, Develop, Try It, students attend to precision as they use a number line to solve, “Lucas is 49 inches tall. His little sister is 27 inches tall. Use the number line to find how much taller Lucas is than his sister.”

Math Practice 7: Look for and make use of structure.

• In Lesson 15, Session 2, Develop, Deepen Understanding, the directions state, “MP7 Look for structure. When discussing the number line model, prompt students to consider how the number line is labeled to model skip counting by tens.” 
• In Lesson 16, Session 2, Develop, Deepen Understanding, the directions state, “MP7 Look for structure. Generalize: How could you use an open number line to add any three-digit numbers? Listen for understanding that when adding any 2 three-digit numbers, the problem can be solved on an open number line by starting at one addend and then making jumps to show adding the hundreds, tens and ones of the other addend.” 

Math Practice 8: Look for and express regularity in repeated reasoning.

• In Lesson 1, Session 3, Develop, Deepen Understanding, the directions state, “MP8 Use repeated reasoning. Generalize: Can you use doubles plus one to find the sum of any two numbers that are 1 apart? Explain. Have students share their reasoning. Listen for understanding that when addends are 1 apart, doubling the lesser of the two addends then adding one more can simplify finding the sum of the addends.” 
• In Lesson 2, Session 3 Develop, Deepen Understanding, the directions state, “MP8 Use repeated reasoning. When discussing the number bond model, prompt students to look for patterns between fact families that have the same whole.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the instructional materials prompt 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 to analyze the arguments of others. In the Program Implementation tab, Implementation Support, Try-Discuss-Connect Routine Resources, teachers find different ways to encourage Math Practice 3 in their math classrooms. Try It provides Three Reads routine, Co-Craft Questions and Problems, and Turn and Talk routine. Discuss It provides the Turn and Talk, Collect and Display, Say It Another Way, and Compare and Connect routines. Connect It provides Collect and Display, Turn and Talk, and Say It Another Way routines. Second grade curriculum includes Math In Action sections that allow children to read other students' solutions of math problems and analyze them themselves. They reflect on what was done well and what could be done differently.

These routines provide students with opportunities to construct viable arguments. Examples include:

• In Lesson 2, Student Worktext, Session 1, Explore states, “Chen has 14 stamps. He uses 6 of them to mail letters. How many stamps does Chen have left?” During the whole class discussion, students have modeled this problem with counters. Students answer follow up questions: “How do [student’s name] and [student’s name] models show the starting amount and the amount subtracted? How do they show the number of stamps Chen has left?”
• In Lesson 13, Student Worktext, Session 2 Develop, Item 4 states, “Reflect: Look back at your Try It, strategies by classmates, and Picture It and Model It. Which models or strategies do you like best for solving two-step problems? Explain.” Students then write their critiques and explanations in their worktext.

• In Lesson 28, Session 2, Develop, Reflect, Item 3 states, “Look back at your Try It, strategies by classmates, and Model Its. Which models or strategies do you like best for naming and drawing shapes you see? Explain.” Students then write their critiques and explanations in their worktext The directions for Reflect in the teacher section states, “If time allows, have students share their preferences with a partner.”

Ready Classroom Mathematics materials give students opportunities to analyze the mathematical arguments of others. Examples include:

• In Lesson 5, Student Worktext, Session 4, Refine, Item 3 states, “Bev gets 6 dollars from her mom and 4 dollars from her dad. She wants to buy a game that costs 18 dollars. How many more dollars does Bev need? (A-2 B-8 C-10 D14) Allie chose C as the correct answer. How did Allie get her answer?”
• In Lesson 10, Student Worktext, Session 1, Explore, students solve, “Lee, Seth, and Jack each have 5 coins. Lee’s coins are worth 1 cent each: 1¢ 1¢ 1¢ 1¢ 1¢. Seth’s coins are worth 5 cents each: 5¢ 5¢ 5¢ 5¢ 5¢. Jack’s coins are worth 10 cents each: 10¢ 10¢ 10¢ 10¢ 10¢. Which child has the most money?” “Discuss it Support Partner Discussion To reinforce the values of different coins, encourage students to say the value of each coin as they talk to each other.”
• In Lesson 6, Reinforce, Math Center Activities, On Level Activity states, “100 or Not! What You Need 10 Counters, Digit Cards 0-9 (2 sets). FInd 24+36. What You Do:  1. Take turns. Shuffle the Digit Cards and place them face down in a pile. 2. Take 2 cards and make a two-digit number. Take 2 more cards and make a different two-digit number. 3. Add the 2 two-digit numbers. 4. Your partner checks your answer. 5. If the sum is less than 100, take a counter. If the sum is 100 or greater, then do not take a counter. 6. Return cards to the bottom of the pile. Repeat. 7. The first partner to get 5 counters wins.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

In i-Ready, Teach and Assess, Ready Classroom Mathematics, Program Implementation, Teaching and Learning Resources, there are Discourse Cards. The cards encourage students to answer questions such as “Do you agree with the strategy, answer, or explanation? Do you disagree with the strategy, answer, or explanation? What do you think about what another student said?” In the Program Implementation tab, Implementation Support, the Student Handbook lists the eight Mathematical Practices in student-friendly language. Listed for MP3 are discussion strategies that teachers can use. The materials state, “Show and explain. Share your math ideas to help others understand you.” Discuss It states, “Ask your partner: Do you agree with me? Why or why not? Tell your partner: The strategy I used to find the answer was ...”

Ready Classroom Mathematics instructional materials support teachers to engage students in constructing viable arguments. Examples include:

• In Lesson 3, Session 3, Develop, the teacher is provided with the following questions to support engaging students in constructing viable arguments, “How does the number of soccer balls in the small bag compare to the number of soccer balls in the large bag?”
• In Lesson 32, Session 2, Develop, Discuss It, Support Partner Discussion states in Common Misconception, teachers are directed to “Look for students who group the 15 footballs in 3 equal groups or 5 equal groups to justify the 15 is even, instead of making two equal groups.”
• In Unit 2, Math In Action states, “Review Yoop’s solution to the Zoo Tours problem on the previous page. Ask: How can you summarize the steps in Yoop’s solution? Listen for: Put 12 people each in 4 groups, find the total number of people in the 4 groups, subtract the total from the people who signed up for the tour, and then split up and put these 10 leftover people into the 4 groups. Ask: What are some different steps you could use to solve the problem? Listen for: Use the greatest number of people they can put into a group and then add to find how many groups are needed.” 

Ready Classroom Mathematics instructional materials support teachers to engage students in analyzing the arguments of others. Examples include:

• In Lesson 9, Session 1, Explore, Support Whole Class Discussion states, “Prompt students to note the relationship between the numbers in each model and the numbers in the problem. Ask How do [student name]’s and [student names]’s solutions show the start? THe change? The total? Listen for 7 is the total. 49 is the number from which you jump to 75 on the number line. The change is unknown and can be found by subtracting 49 from 75.”
• In Lesson 1, Session 2, Develop, Discuss It, Support Partner Discussion states, “Encourage students to talk about the model or strategy they chose and to use the terms start and change as they discuss their solutions.” Guided questions are listed: “How is your strategy the same as your partner’s? How is it different? What do you like about your partner’s strategy? What do you disagree with?”
• In Unit 2 Math in Action, Session 2, Solve It states, “Have students work in pairs to discuss their preliminary solutions. Then they are confident that their plan will work, have students independently write their solution on a blank sheet of paper.” Reflect states, “Have students work with a partner to share their thinking and discuss the Reflect questions.”

The instructional materials reviewed for Ready Classroom Mathematics Grade 2 meet expectations that materials explicitly attend to the specialized language of mathematics. The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. 

In the Program Implementation tab, an Academic Vocabulary Glossary is provided. This is set up with the vocabulary explicit to each unit.  In the Classroom Resources tab, there is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit. There is also a “Connect Language Development to Mathematics” that helps to develop language routines with students..

The Ready Classroom Mathematics materials provide explicit instruction on the use of mathematical language. In the Classroom Resource tab, evidence includes:

• In Unit 1 “Beginning of Unit Tab” tab, there is a Build Your Vocabulary page and a Connect Language Development to Mathematics page. The Build Your Vocabulary page is a student work page designed to introduce the vocabulary for the unit. The Connect Language Development to Mathematics page provides information on how to use the student vocabulary page. This page has a vocabulary routine that extends to other units. The routine calls for the following to be done with each vocabulary word: Assess prior knowledge, Say (pronounce) the word, Define the word, and Use the word. This routine is defined only in the Connect Language Development in Unit 1 but is referenced in later units.
• On the Build Your Vocabulary page students are given two different sets of words, “My Math Words” and “My Academic Words.” The guidance provided to the teacher under the Connect Language Development to Mathematics page states, “My Math Words in all units, My Math Words provides access to prior knowledge and understanding of critical math words and phrases through teacher-guided activities. My Academic Words in Units 4-6, My Academic Words provides an early entry point to those all-purpose academic words students will engage with throughout their study of mathematics. Use the Academic Vocabulary Routine to provide explicit instruction and active engagement.” The Academic Vocabulary Routine directions are then provided and broken up into four parts. The four parts listed are, “Assess Prior Knowledge, Pronounce the Words, Define the Words, Use the Words.” 
• In Lesson 2, Session 3 Develop, Develop Language states, “Why: Develop the multiple meanings of the word left, focusing on the meaning relevant to the problem. How: Using examples of the word in context, explain that the word left has three meanings: 
• She left the cafeteria (past tense of “to leave”) 
• There are no crayons left in the box (What remains) 
• She turned left at the corner (direction; opposite of right) 

Ask students to identify the meaning of the word left as it is used in the problem.”  

• In Lesson 3, Session 3, Develop, the materials provide explicit instruction on the use of mathematical language. Teachers clarify the meaning and usage of the word fewer. The materials state, “Have students talk with partners to compare the number of different items or persons in the classroom using the word fewer. There are fewer erasers than pencils on the desk. There are fewer girls than boys sitting down. Explain that the word fewer is used when comparing things that can be counted, while the word less is used for things that cannot be counted. Examples: less milk, fewer cups.”
• In Lesson 13, Session 2, Develop, Develop Language states, “Why: Support students’ understanding of the term expanded form. How: Explain to students that when something expands, it gets longer. The expanded form of a number is a longer way of writing it, by separating out the units, tens, and hundreds. For example, the longer or expanded form of 284 is 200+80+4. By using expanded form, you can clearly see that there are 2 hundreds, 8 tens, and 4 ones.”

Ready Classroom Mathematics materials support students to learn and use precise and accurate terminology. IIn the Classroom Resource tab, evidence includes:

• There is a “Build Your Vocabulary” Sheet that goes along with each unit to help develop the vocabulary within the unit. This page can be found in the Beginning of the Unit link for each unit.
• Lesson Vocabulary is listed on every Lesson Overview page for each section. For example, Lesson 6, Lesson Overview, the following Lesson Vocabulary is listed: 
• Regroup: to put together or break apart ones, tens, or hundreds. For example, 10 ones can be regrouped as 1 ten, or 1 hundred can be regrouped as 10 ones. 
• In Lesson 30, Session 1, Additional Practice has a Support Vocabulary Development section which the teacher uses to build the understanding of partitioning rectangles (e.g., “What is it?” “What I know about it.” 3 area models to partition).

In the Program Implementation tab there is:

• An Academic Vocabulary Glossary with the vocabulary explicit to each unit. 
• A Teacher’s Guide Table of Contents provides the overall view of each unit. In each unit there is a Build Your Vocabulary section with the vocabulary addressed in the unit. 

In the Program Implementation materials and throughout lessons in Ready Classroom Mathematics, students are provided with graphic organizers that assist with mathematical language to ensure students are using precise vocabulary. There are five different graphic organizers provided throughout the lessons which allow students to organize learning concepts and vocabulary through definitions, illustrations, examples, etc.