The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Within the materials, Program Implementation, Program Overview, i-Ready has three different types of lessons to address the unique approaches of the standards and to support a balance of conceptual understanding, application, and procedural fluency. “Understand Lessons focus on developing conceptual understanding and help students connect new concepts to familiar ones as they learn new skills and strategies. Strategy Lessons focus on helping students persevere in solving problems, discuss solution strategies, and compare multiple representations through the Try- Discuss-Connect routine." The Math in Action Lessons "feature open-ended problems with many points of entry and more than one possible solution." Lessons are designed to support students to explore and develop conceptual understanding of grade-level mathematics. Additional Practice and Interactive Games are also provided so that students can continue to practice the skills taught during lessons if needed.

Students develop conceptual understanding with teacher guidance and support. For example:

• Unit 3, Lesson 12, Understand Three-Digit Numbers, Session 1, students develop conceptual understanding of 2.NBT.1a (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. a. 100 can be thought of as a bundle of ten tens — called a “hundred”). Explore, Model It, Problem 3, “Look at the blocks below. The blocks show ___ hundreds.” Teacher Edition, Differentiation, Reteach or Reinforce, Hands-On Activity, “If students are unsure about how many tens and ones are in 1 hundred use this activity to reinforce 1 hundred is the same as 10 tens and 100 ones. Instruct partners to show 3 groups of ten. Ask How many ones are in 3 groups of 10? [30] Have them show 6 groups of 10. Ask How many ones are in 6 groups of 10? [60] Have students justify their answers. Have students show a hundred flat. Ask: How many ones would you have if you could break apart the flat into ones units? [100] Have students use tens rods to show how many tens are in a hundred flat. Ask: How many tens would you have if you could break apart the flat into tens rods? [10]”

• Unit 3, Lessons 16 and 17, students develop conceptual understanding of 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method...). Lesson 16, Add Three-Digit Numbers, Session 1, Explore, students use base-ten blocks to add three-digit numbers. Teacher Edition, Differentiation, Reteach or Reinforce, Hands-On Activity, “If students are unsure about the concept of adding three-digit numbers, then use this activity to have them model similar problems. Write $164+312=$? on the board. Have students show 164 using base-ten blocks. Ask: How many hundreds do you need? [1] How many tens? [6] How many ones? [4] Repeat the process for 312 [3,1,2] Have students combine the hundreds, the tens, and the ones. Ask: How many hundreds do you have in all? [4] How many tens? [7] How many ones? [6] Ask: What is $164+312$? [476].” Session 3, Develop, Teacher Edition, p. 414 states, “There are 476 rocks and 148 minerals in a museum display. What is the total number of rocks and minerals in the display?” Pictures are shown of different strategies students can use to add. Facilitate Whole Class Discussion, “Call on students to share selected strategies. Remind students that a good explanation describes what you did and why. Guide students to Compare and Connect their representations. Allow time for students to think by themselves before discussing. Ask How does each model show adding tens?” Lesson 17, Subtract Three-Digit Numbers, Session 1, Explore, Teacher Edition, Differentiation, Reteach or Reinforce, Hands-On Activity, “If students are unsure about the concept of subtracting three-digit numbers, then use this activity to have them model similar problems. Write $576-254=$? on the board. Have students show 576 using base-ten blocks. Ask: How many hundreds do you need? [5] How many tens? [7] How many ones? [6] Say: To subtract 274, how many hundreds should you take away? [2] Have students remove 2 of the hundreds flats. Repeat the process for the tens and ones. Ask: How many hundreds do you have now? [3] How many tens do you have now? [2] How many ones do you have now? [2] Ask: What is $576-254$? [322].” Session 3, Develop, Regrouping Hundreds to Tens, Teacher’s Edition, p. 438, “A group picks corn and onions for a food bank. They pick 327 bags of corn and 276 bags of onions. How many more bags of corn than onions do they pick?” Pictures are shown of different strategies students can use to subtract. Facilitate Whole Class Discussion, states, “Call on students to share selected strategies. Ask students to refer to their model or diagram to justify their solutions. Guide students to Compare and Connect the representations. If discussion lags, ask students to turn and talk to about how a hundred is related to tens before continuing the discussion.”

• Unit 5, Lesson 31, Add Using Arrays, Sessions 1-3, students develop conceptual understanding of cluster 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends). Session 1, Explore, Connect It, students create arrays with manipulatives. Teacher Edition, Differentiation, Hands On Activity, Reteach or Reinforce, “If students are unsure about the concept of finding the total number of objects in an array, then use this activity to have them build arrays and count the number of objects in them.” A picture is shown for students of a 3 by 4 array of circles representing helmets from a previous problem. “Ask students to use their objects to replicate the array of 12 helmets shown on the Student Worktext page. Ask: How are all of the arrays alike? [They all have 3 rows with 4 objects in each row and 4 columns with 3 objects in each column.] Tell students to find the total number of objects in their array any way they choose. Ask: How did you find the total number of items in your array?” Session 2, Develop, students discuss strategies to find the total in an array. “Develop different ways to understand adding using an array. Lanelle puts some stickers into an array. Each row has 5 stickers. Each column has 4 stickers. How many stickers are there in all?” A picture is shown of a 4 by 5 array of star-shaped stickers. Teacher Edition, Facilitate Whole Class Discussion, “Call on students to share selected strategies. Review that one way to understand more about a problem is to explain how it is similar to and different from others they have solved. Guide students to Compare and Connect the representations.” Session 3, Refine, Adding Using Arrays, Apply It, Problem 1, “A roof has 3 columns of boards that get electricity from the sun. Each column has 5 boards. How many boards are in all 3 columns? Draw an array and write an equation as part of your answer.”

Students have opportunities to independently demonstrate conceptual understanding. For example:

• Unit 3, Lesson 16, Add Three-digit Numbers, Session 1, Explore, Additional Practice, Prepare for Adding Hundreds, Tens, and Ones, Problem 2, students independently engage with 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method…) as they use base-ten blocks to add three-digit numbers. “Salim has 263 silver paper clips and 124 gold paper clips. He will find $263+124$ to find out how many paper clips that he has in all. Explain how you would find $263+124$.” 

• Unit 4, Lesson 26, Add and Subtract on a Number Line, Sessions 1-3, students independently engage with 2.MD.6 (Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole- number sums and differences within 100 on a number line diagram.) as they utilize concrete and semi-concrete representations. Session 1, Additional Practice, Prepare for Adding and Subtracting on the Number Line, Problem 3, “Solve the problem. Show your work. Destiny starts to make a number line to show a length of 10. How can you complete the number line and show a length of 10?” A picture is shown of a number line with tics 0 through 5. Session 2, Develop, Apply It, Problem 5, “Zimo has a piece of string that is 41 centimeters long. He cuts off a piece that is 26 centimeters long. How much string is left? Show your work. Use the number line.” A picture is shown of a number line with tics 0 through 50. Session 3, Additional Practice, Practice Subtracting on the Number Line, Problem 3, “Use the number line to solve this problem. Show your work. Neena has 44 dollars. She spends 19 dollars on a T-shirt. How many dollars does Neena have now?” A picture is shown of a number line with tics 0 through 50. 

• Unit 5, Lesson 31, Add Using Arrays, Session 2, students independently engage with 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.) as they use arrays to solve word problems. Develop, Apply It, Problem 7, “Andre makes an array of toy cars. Write two equations you could use to find the total number of cars in Andre’s array. Show your work.  There are ___ cars in Andre’s array.” An array of 3 cars in 5 rows is shown. Additional Practice, Practice Using Arrays to Add, Problem 3, “Students line up in 3 rows for a relay race. There are 5 students in each row. How many students are in the race? Draw an array to show your answer. Show your work.” Problem 4, “Suppose another group of 5 students joins the race in problem 3. Does the array change? Does the equation change? Explain.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

Within the materials, Program Implementation, Program Overview, i-Ready has three different types of lessons to address the unique approaches of the standards and to support a balance of conceptual understanding, application, and procedural fluency. The materials include problems and questions, interactive practice, and math center activities that help students develop procedural skills and fluency, as well as opportunities to independently demonstrate procedural skills and fluency throughout the grade. Additional Practice and Interactive Games are also provided so that students can continue to practice the skills taught during lessons if needed.

Students develop procedural skills and fluency with teacher guidance and support. There are also interactive tutorials embedded in classroom resources to help develop procedural skills and fluency. For example:

• Unit 1, Lessons 1 and 2, students build procedural skills and fluency of 2.OA.2 (Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.). Lesson 1, Mental Math Strategies for Addition, Session 2, Develop, “Kadeem reads 9 books in June. Then he reads 3 more books in July. How many books does Kadeem read in both months?” The page then gives three different strategies to solve, “Picture It You can count on to add,” a picture is shown of 9 red counters and 3 blue counters. The equation to match the problem is written below the picture. Model It, “You can make a ten to add.” An equation is written to show how to decompose the three into $1+2$, and adding the 1 to the 9 to make a ten. Model It,“You can show making a ten to add on to an open number line.” An image shows an open number line with jumps of 9 and 3. Teacher Edition, Picture It and Model It, “If no student presented these models, have students analyze key features and then point out the ways each model represents: 9 at the start; 3 as the number being added to 9. Ask How are the 9 and the 3 shown on each model?” Hands-on Activity, “Connect the strategy of making a ten with an open number line. If students are unsure about how to use an open number line to show making a ten, then use the activity below to connect the number-line representation with the make-a-ten strategy. Write $8+4=$? on the board. How can you solve this problem by making a ten? Draw a blank open number line on the board. What number would you write first on the open number line? How would you show making a ten with a jump? How much more is left to add? Write other problems such as $7+5$ and $6+6$ on the board and have students show how to make a ten to find the sums on their blank open number lines.” Lesson 2, Mental Math Strategies for Subtraction, Session 2, Develop, “Sara has 11 balloons. She gives away 8 balloons. How many balloons does Sara have left? Model It You can count on to subtract. Picture this in your head. You can find $11-8=?$ by finding $8+?=11$. Start at 8 in the chart. Count on until you reach 11.” A number chart is shown 1 through 20. Model It, “You can make a ten to subtract. Picture this in your head.” A picture is shown of an open number line with the numbers 3, 10, and 11 labeled. Arrowed jumps are shown going from 11 to 10, and 10 to 3. “Subtract 1 to make a 10. $11-1=10$ Subtract 7 more to subtract 8 in all. $10-7=?$” 

• Unit 2, Lesson 6, Interactive Tutorials, contains three 17-minute tutorials to help students develop procedural skills and fluency with adding 2 two-digit numbers within 100 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.). Topics include adding within 100 on a number line and adding by breaking apart a two-digit number. 

• Unit 2, Lesson 8, Use Addition and Subtraction Strategies WIth Two-Digit Numbers, Sessions 1 and 3, students build procedural skills of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) Session 1, Explore, Try It, Teacher Edition, Start Connection to Prior Knowledge, Why? “Support students’ understanding of different ways to represent a two-digit number. Make Sense of the Problem Before students work on Use Notice and Wonder to help them make sense of the problem. Students may notice that only one number is given in the problem and there are many possible solutions, or they might wonder about how to determine the number of cars on each shelf. Discuss it, Support Partner Discussion After students work on Try It, have them respond to Discuss It with a partner. Listen for understanding of: two groups as partners of a larger group of 35; the number in each of the two parts is unknown; choosing the number for one part determines the number in the second part. Common Misconception Look for students who do not understand that when they choose a value for one of the parts, there is only one possible value for the second part and, therefore, choose addends that do not sum to 35. Select and Sequence Student Strategies One possible order for whole class discussion: connecting cubes or base-ten blocks to represent 35 broken apart in different ways; hundred chart to model counting on to 35 from numbers less than 35; open number lines to model counting on to 35 from different numbers less than 35; equations to solve $?+?=35$ or $35-?=?$” Connect It, Problem 2 Look Ahead, “You can use different strategies to solve addition and subtraction problems. Think about this problem. Ajay has 50 marbles. What are some different ways he can put them all into two bags? Complete the equations to show three different ways. $<strong>+</strong>$ $=50$; $50-$ $<strong>=</strong>$ ; $50=$ $<strong>+</strong>$.” Teacher Edition, Look Ahead, “Point out that some problems may have more than one unknown number and more than one solution. Students should be able to recognize that drawing pictures and writing equations are two ways to find unknown values that will solve the problem.” Session 3, Develop, “Bayo has recycled wire to make galimotos. He has 85 pieces of wire. Bayo uses some of the wire. There are 26 pieces of wire left. How many pieces of wire did Bayo use?” Model It, “You can regroup a ten first and then subtract. Find $85-$ ___ $=26$. $85-$ ___ $=26$ is the same as $85-26=$ ___. First make 10 ones with 1 ten in 85. Then subtract. 7 and 15 ones - 2 tens and 6 ones.” A picture is shown of base-ten blocks modeling the problem. The blocks are labeled as: “85 is 7 tens and 15 ones.” Model It, “You can use an open number line. Subtract 26 from 85 to find how many pieces of wire were used. Start at 85. Subtract 5 to the next ten. Next, subtract 1 more. Then subtract 20.” An open number line is shown with the jumps to solve the problem. Teacher Edition, Facilitate Whole Class Strategies, “Call on students to share selected strategies. After each strategy, allow individual think time for students to process the ideas. Guide students to Compare and Connect the representations. Review that one way to connect representations is to describe how they are alike and how they are different. Ask How do all of the models show the unknown number?”

The instructional materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. Examples include:

• Unit 1, Lessons 1 and 2, students independently demonstrate procedural skill and fluency of 2.OA.2 (Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers). Lesson 1, Mental Math Strategies for Addition, Session 2, Additional Practice, Practice Adding by Counting On or Making a Ten, Problem 4, “Make a ten to add. Fill in the squares on the open number line to find $8+5$.  $8+5=$ ___.” An open number line is pictured with 8 and 10 labeled, and a box to fill in for the sum. There are two boxes above the jumps pictured on the number line to fill in as well. Fluency Skills and Practice, Problem 1, “$8+2=$ ___.” Problem 2, “$8+3=$  ___.” Problem 7, “$9+1=$ ___.” Problem 8, “$9+6=$___.” Lesson 2, Mental Math Strategies for Subtraction, Session 3, Additional Practice, Practice Using Fact Families to Help Subtract, Problem 4, “Complete the number bond to find $16-7$.” A number bond is shown with 16 at the top, 7 in one box, and one box blank. Fluency Skills and Practice. Problem 6, “$11 - 7 = ?$” Problem 8, “___ $+$ ___ $=17$, $17=$ ___ $+$ ___, $17-$ ___ $=$ ___, $8=17-$ ___.” 

• Unit 1, Lessons 1 and 2, Learning Games, Hungry Fish and Match help students develop procedural skills and fluency with adding and subtracting within 20. (2.OA.2)

• Unit 1, Lesson 3, Center Activities; Flip, Spin, and Add, Keep on Subtraction, Apply It Problem helps students develop procedural skills and fluency with adding and subtracting within 20. (2.OA.2)

• Unit 2, Lesson 1, Subtract Two-Digit Numbers, Interactive Practice, students break apart two-digit numbers into tens and ones as place value strategy for adding.  2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.)

• Unit 2, Lessons 6-8, students demonstrate procedural skills and fluency of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) Lesson 6, Add Two-Digit Numbers, Session 3, Develop, Teacher’s Edition, Fluency Skills and Practice, students solve two-digit addition problems. “Within each problem, students may notice and make use of patterns in the addend being added to the first number.” Problem 4, “$26+4=$ ___, $26+24=$ ___, $26+27=$ ___.” Lesson 7, Subtract Two-Digit Numbers, Session 3, Develop, Teachers Edition, Fluency Skills and Practice, “In this activity students practice regrouping a ten when subtracting 2 two-digit numbers.” Problem 8, “$53-44=$ ___.” Lesson 8, Use Addition and Subtraction Strategies with Two-Digit Numbers, Session 2, Additional Practice, Practice Strategies to Find a Missing Addend, Problem 3, “Paloma raises money for new swings at a playground. She raises $26 from a book sale. Then Paloma raises more money from a car wash. She raises $51 in all. How much money did Paloma raise from the car wash? Show your work.” Session 3, Develop, Fluency and Skills Practice, Problem  2, “$74-36=$ ___.” Problem 6, “$84-53=$ ___.” Session 3, Develop, Apply It, Problem 6, “There are 65 cherries in a bowl. Rene eats 12 cherries. How many cherries are in the bowl now? Use two different strategies to solve this problem. Show your work.”

• Unit 2, Lesson 7, Center Activities, Solve a Subtraction Equation, students work with a partner to develop procedural skills and fluency with adding and subtracting within 100. (2.NBT.5)

• Unit 2, Lesson 7, Subtract Two-Digit Numbers, Interactive Practice, students decompose a ten as a strategy for subtracting two-digit numbers. (2.NBT.5)

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Within the materials, Program Implementation, Program Overview, i-Ready has three different types of lessons to address the unique approaches of the standards and to support a balance of conceptual understanding, application, and procedural fluency. “Understand Lessons focus on developing conceptual understanding and help students connect new concepts to familiar ones as they learn new skills and strategies. Strategy Lessons focus on helping students persevere in solving problems, discuss solution strategies, and compare multiple representations through the Try- Discuss-Connect routine." The Math in Action Lessons "feature open-ended problems with many points of entry and more than one possible solution." Lessons are designed to support students as they apply grade-level mathematics. Additional Practice and Interactive Games are also provided so that students can continue to practice the skills taught during lessons if needed.

There are multiple routine and non-routine application problems throughout the grade level, including opportunities for students to work with support of the teacher and independently. While single and multi-step application problems are included across various portions of lessons, independent application opportunities are most often found within Additional Practice, Refine, and Math in Action lessons.

Examples of routine applications of the mathematics include:

• Unit 1, Lesson 3, Solve One-Step Word Problems, Session 2, Apply It, Problem 6, students independently demonstrate the application of subtraction strategies to solve a routine problem, 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions…). “Ming goes to the store. He buys 12 carrots. 7 are purple. The rest are orange. How many orange carrots does Ming have? Write an equation to solve. Show your work.”

• Unit 2, Lesson 10, Solving Word Problems involving Money, Session 4, Develop, Apply It, Problem 8, students use addition and subtraction to solve one- and two-step word problems involving money, 2.MD.8 (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and ¢ symbols appropriately…). “Devyi and Alano help in their parents’ store. Together they earn $43 total. Devyi is paid with a $20 bill and a 5 bill. How much is Alano paid? Show your work.”

• Unit 4, Lesson 25, Add and Subtract Lengths, Session 2, Develop, Teacher’s Edition, p. 609, teachers support students to use addition and subtraction to solve real-world problems, 2.MD.5 (Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units…). “Kansas has 56 feet of rope to make a basket. She uses 8 feet of the rope to make the bottom of the basket. How long is the rope now?” Support Partner Discussion, “Encourage students to name the model or strategy they used as they discuss their solutions. Support as needed with questions such as: How did you represent what is unknown in the problem? How did you decide whether to add or subtract to solve the problem?”

Examples of non-routine applications of the mathematics include:

• Unit 1, Lesson 4, Draw and Use Bar Graphs and Picture Graphs, Session 4, Refine, Problem 6, students independently demonstrate creating a picture graph and using the data to write an addition equation, 2.MD.10 (Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph). “Dion records the weather for one week in the table at the right. Complete the picture graph below using the data from the table. Draw a ‘sun’ for sunny days and a ‘cloud’ for cloudy days.” Students use weather data to complete a picture graph. Problem 8, “Write an addition problem using the data about the weather. Then explain how to solve your problem.”

• Unit 2, Math in Action, Work with Two-Digit Numbers, Time, and Money, Session 2, teachers support students as they add and subtract to solve real-world problems involving money, 2.MD.8  (Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using and ¢ symbols appropriately). Butterfly Garden, “Alex is making a butterfly garden. She is trying to decide what flower seeds to buy. Here are her notes. Butterfly Garden Notes Buy 3 or 4 pounds of seeds. Spend up to $100 on seeds. Here are the seeds she can choose from. Butterfly Mix: $25 for 1 pound Wildflower Mix: $28 for 1 pound Early Bloom Mix: $24 for 1 pound Late Bloom Mix $22 for 1 pound What seeds should Alex buy? What is the total cost? If there is money left over, tell how much.” Teacher Edition, Facilitate Whole Class Discussion, “Read the problem aloud. Ask What are some clarifying questions you could ask about the details of the problem? Listen For Student responses may include questions about how many pounds of seeds to buy [3 or 4], the amount Alex can spend [up to $100], the seeds she can choose from and their costs, and the goal of the problem.”

• Unit 3, Lesson 18, Session 4, Refine, Apply It, Problem 1, students independently solve a non-routine problem by determining three different strategies to solve a money word problem. 2.NBT.7 (Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction….) “Dean has 250 coins. Some are pennies, and the rest are nickels. How many of each coin could Dean have? Complete three different equations to show the number of each coin Dean could have.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations in that 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 the grade.

Within the materials, Program Implementation, Program Overview, i-Ready has three different types of lessons to address the unique approaches of the standards and to support a balance of conceptual understanding, application, and procedural fluency. The materials include problems and questions, interactive practice, and math center activities that help students develop skills. 

All three aspects of rigor are present independently throughout the grade. Examples where instructional materials attend to conceptual understanding, procedural skill and fluency, or application include:

• Unit 2, Lesson 8, Use Addition and Subtraction Strategies with Two-Digit Numbers, Sessions 1-4, students build procedural skill and fluency with 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) Teacher’s Edition, Learning Progressions, In this lesson, “Students build fluency with addition and subtraction of two-digit numbers. They compose and decompose tens and apply inverse operations to find sums and differences.” Session 1, Additional Practice, Prepare for Using Addition and Subtraction Strategies, Problem 3, “Solve the problem. Show your work. Jasmine makes 42 dolls to sell. How many can she put on her top shelf and how many on her bottom shelf? Show three ways.” Session 2, Develop, Apply It, Problem 7, “Solve the problem by going to the next ten. $58+?=95$  Show your work.” Session 3, Develop, Additional Practice, Practice Using Subtraction Strategies with Two-Digit Numbers, Problem 2, “Which equations can you use to check if this subtraction equation is correct? Choose all that apply. $72-24=48$” Answer choices: “$72+24=96$, $48+48=96$, $48+24=72$, $72-48=24$, $24+48=72$.” Problem 3, “Show two different ways that you can use a number line to find $70-56$.” Session 4, Additional Practice, Practice Using Addition and Subtraction Strategies, Problem 3, “Choose Yes or No to tell if you can use the equation to solve the problem below. $?-23=61$.” Equations evaluated include: “$61-?=23$, $23+61=?$, $61-23=?$, $?-61=23$.”

• Unit 3, Lesson 16, Add Three-Digit Numbers, Session 1, Explore, Additional Practice, Problem 3, students build conceptual understanding with addition and subtraction within 1,000, 2.NBT.7 (Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction...). “Solve the problem. Show your work. Dakota is at a pow wow. There are 152 people dancing. There are 236 people watching the dance. How many people are dancing and watching?”  

• Unit 4, Lesson 25, Add and Subtract Lengths, Session 2, Develop, Apply It, Problem 6, students apply their knowledge of addition and subtraction within 100 to solve word problems, 2.MD.5 (Use addition and subtraction within 100 to solve word problems involving lengths that are given the same units…). “Use what you just learned to solve these problems. Adan throws a ball 59 feet. Amare throws a ball 15 feet less than Adan. How far does Amare throw the ball? Show your work.” 

Multiple aspects of rigor are engaged simultaneously throughout the materials in order to develop students’ mathematical understanding of grade-level topics. Examples include:

• Unit 1, Math In Action, Session 2, Persevere on Your Own, Nuts and Bolts, students develop procedural skill and fluency, conceptual understanding, and application as they solve real-world problems involving addition and subtraction. 2.OA.A, 2.OA.B, 2.OA.C. (Represent and solve problems involving addition and subtraction, Add and subtract within 20, Work with equal groups of objects to gain foundations for multiplication). “Beau has 18 bolts. He has 3 boxes to put them in. He wants to put at least 3 bolts in each box. How many bolts can Beau put in each box? Solve it: Show one way that Beau can put the bolts in the boxes. Draw a picture. Tell how many bolts Beau can put in each box. Explain why your answer works.”

• Unit 2, Lesson 6, Add Two-Digit Numbers, Session 3, Develop, More Ways to Show Addition, Apply It, Problem 6, students engage in the procedural skill and fluency and application to solve a word problem of 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.) “Matt’s dad makes 39 bales of hay. Then he makes 28 bales of hay. How many bales of hay does he make in all? Show your work.”

• Unit 4, Lesson 25, Add and Subtract Lengths, Session 4, Refine, Apply It, Problem 3, students develop procedural skills and fluency, conceptual understanding, and application as they use addition and subtraction to solve two-step word problems involving length. 2.MD.5 (Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units…). “Zahara uses 26 feet of string to mark the length of her garden. She uses 15 feet of string to mark the width of her garden. She has 47 feet of string left. How much string did she start with?” Answer choices: 36 feet, 41 feet, 58 feet, and 88 feet. “Abu chose B as the answer. How did Abu get his answer?”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Within Program Implementation, Standards for Mathematical Practice in Every Lesson, “The Standards for Mathematical Practice (SMPs) are embedded within the instructional design of i-Ready Classroom Mathematics.” Embedded SMPs Within Lessons, “In addition to SMPs 1, 2, 3, 4, 5, and 6, which are integrated into the instructional framework, the Teacher’s Guide includes additional opportunities for students to develop the habits of mind described by the Standards of Mathematical Practice. The table of contents indicates all of the embedded Standards for Mathematical Practice for each lesson (both integrated SMPs and the specific SMPs highlighted within the lesson). The Lesson Overview includes the Standards for Mathematical Practice addressed in each lesson. In the Student Worktext, the Learning Target also highlights the SMPs that are included in the lesson.” SMPS Integrated in Try-Discuss-Connect Instructional Framework, “i-Ready Classroom Mathematics” infuses SMPs 1, 2, 3, 4, 5, and 6 into every lesson through the Try-Discuss-Connect instructional framework (found in the Explore and Develop sessions of Strategy lessons , with a modified framework used in understand lessons).” Try It, “Try It begins with a language routine such as Three Reads, which guides students to make sense of the problem (SMP 1): For the first read, students begin to make sense of the problem (SMP 1) as the teacher reads the problem aloud. For the third read, students read the problem in unison or in pairs.  Students reason quantitatively and abstractly (SMP 2) by identifying the important information and quantities, understanding what the quantities mean in context, and discussing relationships among quantities.” Discuss It, “All students reason abstractly and quantitatively (SMP 2) as they find similarities, differences, and connections among the strategies they have discussed and relate them to the problem they are solving.” Connect It, “As students think through the questions and problems, they connect the quantitative, concrete/representational approaches to a more abstract understanding (SMP 2).”

MP1 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students make sense of problems and persevere in solving them as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 1, Math In Action, Solve Addition and Subtraction Problems, Study an Example Problem and Solution, Robot Motors, with teacher assistance, students analyze and make sense of what the word problem is asking. “Beau wants to build shelves to hold his 16 robot motors. Look at his plan. Shelf Plan, Build up to 6 shelves, Put at least 3 and no more than 6 robot motors on each shelf. How many shelves should Beau build? How many motors should he put on each shelf?” Teacher Edition, Study an Example Problem and Solution, “Present the Robot Motors problem and prompt students to recognize that in this problem, 16 is the number of robot motors, up to 6 shelves means 1, 2, 3, 4, 5, or 6 shelves, and at least 3 and no more than 6 means 3, 4, 5, or 6 motors on each shelf. Invite students to share their ideas about how they might solve this problem. Allow them to describe different approaches, for example draw a picture, use 16 counters, or try 2 shelves. Do not yet carry through with an actual solution.”

• Unit 2, Lesson 8, Use Addition and Subtraction Strategies with Two-Digit Numbers, Session 2, Develop, Connect It, Problem 5, students make sense of problems as they reflect on using open number lines and adding up to the next ten to find missing addends. “Look back at your Try It, strategies by classmates, and Model Its. Which models or strategies do you like best for finding a missing addend? Explain.”

• Unit 5, Lesson 32, Even and Odd Numbers, Session 1, Explore, Try It, students work to understand the information in the problem as they put objects into groups. “You know how to put objects into groups. Use what you know to try to solve the problem below. There are 8 wooden shoes on a shelf. How can the shoes be broken into equal groups?” Teacher Edition, Try It, Make Sense of the Problem, “See Connect to Culture to support student engagement. Before students work on Try It, use Notice and Wonder to help them make sense of the problem. After revealing the problem question, return to students’ ideas to see if they relate to the question.”

MP2 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students reason abstractly and quantitatively as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 1, Lesson 9, Solve Word Problems with Two-Digit Numbers, Session 3, Apply It, Problem 7, students reason abstractly to understand relationships between the problem scenario and the mathematical representation to solve word problems. “First explain how to model the problem below using words. Then explain how to model it using numbers. Takoda picks some apples. He uses 24 of the apples to make applesauce. He has 19 apples left. How many apples does Takoda pick?”

• Unit 3, Lesson 19, Add Several Two-Digit Numbers, Session 2, Develop, Try It, students reason quantitatively about how tens are related to hundreds. “Aki makes dream catchers with her parents. They use 16 blue beads and 41 brown beads. They also use 22 purple beads and 39 white beads. How many beads do Aki and her parents use in all?” Teacher Edition, Discuss It, Support Partner Discussion, “Encourage students to use the Discuss It questions and sentence starters on the Student Worktext page as they talk to each other. Support as needed with questions such as: Why did you group the addends the way you did? How is your strategy different from your partner’s?” Connect It, Problem 1, “Look at the first Model It. Fill in the blanks to find the total number of beads. $tens+ones=$ __.” Teacher Edition, Connect It, Monitor and Confirm Understanding, “Check for understanding that 10 tens and 18 ones are equal to 118, two-digit numbers can be added using the number of tens or the values of the tens, grouping addends that make a tens number or make 100 can simplify adding three or more two-digit numbers.” 

• Unit 4, Lesson 26, Add and Subtract on the Number Line, Session 1, Explore, Connect It, Problem 2, students reason abstractly about how numbers on a number line can be thought of as lengths on a number line to add. “You can show sums on a number line. Think about $15+18$.” A picture is shown of a number line with tics from 0-50, labeled by 5s. Problem 2a, “Show a length of 15 on the number line starting at 0.” Problem 2b, “Show a length of 18 more on the number line starting at 15.” Problem 2c, “What total length have you shown on the number line?” Teacher Edition, Look Ahead, “Point out that the addends of the addition problem can be thought of as lengths on a number line, with the first addend starting at 0 and ending at 15, and the second addend starting at 15 for a length of 18 that ends at 33. Students should be able to see that the end of the line segment representing the second addend is the sum of 15 and 18, or 33.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Within Program Implementation, Standards for Mathematical Practice in Every Lesson, “The Standards for Mathematical Practice (SMPs) are embedded within the instructional design of i-Ready Classroom Mathematics.” Embedded SMPs Within Lessons, “In addition to SMPs 1, 2, 3, 4, 5, and 6, which are integrated into the instructional framework, the Teacher’s Guide includes additional opportunities for students to develop the habits of mind described by the Standards of Mathematical Practice. The table of contents indicates all of the embedded Standards for Mathematical Practice for each lesson (both integrated SMPs and the specific SMPs highlighted within the lesson). The Lesson Overview includes the Standards for Mathematical Practice addressed in each lesson. In the Student Worktext, the Learning Target also highlights the SMPs that are included in the lesson.” SMPS Integrated in Try-Discuss-Connect Instructional Framework, “i-Ready Classroom Mathematics infuses SMPs 1, 2, 3, 4, 5, and 6 into every lesson through the Try-Discuss-Connect instructional framework (found in the Explore and Develop sessions of Strategy lessons , with a modified framework used in understand lessons).” Discuss It, “Discuss It begins as student pairs explain and justify their strategies and solutions to each other. Partners listen to and respectfully critique each other’s reasoning (SMP 3). As students/pairs share their different approaches, the teacher facilitates the discussion by prompting students to listen carefully and asking them to repeat or rephrase the explanations to emphasize key ideas (SMP 3).” 

Students construct viable arguments and critique the reasoning of others in connection to grade- level content as they work with support of the teacher and independently throughout the units. Examples include:

• Unit 2, Lesson 10, Solve Word Problems Involving Money, Session 4, Discuss It, students justify their thinking and critique the reasoning of their partner as they develop strategies for solving word problems about money. “Ask your partner: Do you agree with me? Why or why not? Tell your partner: A model I used was…It helped me…”

• Unit 3, Lesson 14, Compare Three-Digit Numbers, Session 3, Discuss It, students critique the reasoning of others as they develop strategies for comparing three-digit numbers by place value. “Ask your partner: Do you agree with me? Why or why not?” Teacher Edition, Support Partner Discussion, “Encourage students to use the terms digits, greater than, and less than as they talk to each other. Support as needed with questions such as: How are the two numbers the same? How are they different? How does comparing the digits in the ones place help you to find the greater number of votes?”

• Unit 3, Math in Action, Add, Subtract, and Compare Numbers, Session 1, Kabob Trays, Reflect, students critique the reasoning of others as they choose appropriate models and strategies to plan for and solve the problem. Use Mathematical Practices, “Talk about this question with a partner. Make an Argument, “How can you explain the reason for the trays that you chose?”

• Unit 4, Lesson 21, Measure in Feet and Meters, Session 1, Explore, Try It, students critique the reasoning of others as they explore the idea that different tools can be used to measure lengths and understand that it can be easier to use inch and centimeter rulers to measure small objects. “Davis’s school has a Top Spinning Day. Davis brings a trompo top. About how long is his trompo, measured in centimeters? How do you know?” Discuss It, “Ask your partner: Do you agree with me? Why or why not? Tell your partner: I disagree with this part because…”

• Unit 4, Lesson 22, Understand Measurement with Different Units, Session 1, Explore, Model It, Problem 5, Reflect, students justify their thinking for which measurement to use when they explore the idea of comparing measurements in inches and feet. “Why would you measure something in feet instead of inches? Why would you measure something in inches instead of feet?”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Within Program Implementation, Standards for Mathematical Practice in Every Lesson, “The Standards for Mathematical Practice (SMPs) are embedded within the instructional design of i-Ready Classroom Mathematics.” Embedded SMPs Within Lessons, “In addition to SMPs 1, 2, 3, 4, 5, and 6, which are integrated into the instructional framework, the Teacher’s Guide includes additional opportunities for students to develop the habits of mind described by the Standards of Mathematical Practice. The table of contents indicates all of the embedded Standards for Mathematical Practice for each lesson (both integrated SMPs and the specific SMPs highlighted within the lesson). The Lesson Overview includes the Standards for Mathematical Practice addressed in each lesson. In the Student Worktext, the Learning Target also highlights the SMPs that are included in the lesson.” SMPs Integrated in Try-Discuss-Connect Instructional Framework, “i-Ready Classroom Mathematics infuses SMPs 1, 2, 3, 4, 5, and 6 into every lesson through the Try-Discuss-Connect instructional framework (found in the Explore and Develop sessions of Strategy lessons, with a modified framework used in understand lessons).” Try It, “Try it continues as students work individually to model important quantities and relationships (SMP 4) and begin to solve the problem (SMP 1). They may model the situation concretely, visually, or using other representations, and they make strategic decisions about which tools or manipulatives may be appropriate (SMP 5).” Connect It, “For each problem students determine which strategies they feel are appropriate, and they model and solve (SMP 4) using pictures, diagrams, or mathematical representations. Students can also choose from a variety of mathematical tools and manipulatives (SMP 5) to support their reasoning.”

MP4 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students model with mathematics as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 1, Lesson 1, Mental Math Strategies for Addition, Session 1, Additional Practice, Prepare for Using Mental Math Strategies for Addition, Problem 2, students model with mathematics as they explain in their own words how to solve addition problems. “Explain one way to find $8+7$.”

• Unit 2, Lesson 9, Solve Word Problems with Two-Digit Numbers, Session 1, Connect It, Problem 2, students model situations with appropriate representations. Problem 2a, “Rosa has 38 pressed pennies. Lila gives her more pressed pennies. Now Rosa has 93 pressed pennies. How many pressed pennies does Lila give to Rosa?” Problem 2b, “You can use a model to help find how many pressed pennies Lila gives Rosa. Complete the model.” A number bond model is shown, with 1 box on top, connected to two boxes below. Teacher Edition, Look Ahead, “Point out that word problems may have an unknown number in any part of the problem situation and that they may be modeled in different ways. Students should be able to use the terms start, change, and total when talking about word problems and relate models to equations in order to solve them.”

• Unit 3, Lesson 15, Mental Addition and Subtraction, Session 3, Develop, Try It, students model with mathematics as they use the math they know to add and subtract 10 and 100. “An Amish furniture store has 432 mailboxes for sale. It has 100 more mailboxes delivered. How many mailboxes does the store have now?” Picture It, “You can draw a picture to show the number of mailboxes. 432 is 4 hundreds and 32 more. Adding 100 makes 5 hundreds and 32 more.” Space is allowed for students to draw base-ten block pictures to model the problem.

MP5 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students choose tools strategically as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 1, Lesson 3, Solve One-Step Word Problems, Session 2, Develop, page 58, students choose appropriate tools and strategies to solve word problems. “Marta and her mom use 15 tomatillos to make salsa verde. Marta peels 7 tomatillos. Her mom peels the rest. How many tomatillos does her mom peel? Picture It, You can draw a picture. Model It, You can use words and numbers in a bar model.” 

• Unit 3, Lesson 18, Use Addition and Subtraction Strategies with Three-Digit Numbers, Session 2, Additional Practice, Practice Addition Strategies with Three-Digit Numbers, Problem 5, students add three-digit numbers using a variety of tools and strategies. Students may choose to use connecting cubes, base-ten blocks, hundreds place-value mats, number charts, or open number lines to solve three-digit addition and subtraction problems. “What is the unknown number in this equation? Use two different strategies to solve. Show your work. $247+?=673$.”

• Unit 5, Math in Action, Use Shapes and Even and Odd Numbers, Session 1, Study an Example Problem and Solution, students recognize both the insight to be gained from different tools/strategies and their limitations. As teachers facilitate a whole class discussion, they ask questions such as: “Which piece of felt would you cut into halves? Thirds? Fourths? Why did you choose that piece?” and “How many ways could you cut the rectangular piece of felt into halves?” Teachers encourage students to think flexibly about how the felt can be cut horizontally, vertically, or diagonally to show understanding of equal parts.

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Within Program Implementation, Standards for Mathematical Practice in Every Lesson, “The Standards for Mathematical Practice (SMPs) are embedded within the instructional design of i-Ready Classroom Mathematics.” Embedded SMPs Within Lessons, “In addition to SMPs 1, 2, 3, 4, 5, and 6, which are integrated into the instructional framework, the Teacher’s Guide includes additional opportunities for students to develop the habits of mind described by the Standards of Mathematical Practice. The table of contents indicates all of the embedded Standards for Mathematical Practice for each lesson (both integrated SMPs and the specific SMPs highlighted within the lesson). The Lesson Overview includes the Standards for Mathematical Practice addressed in each lesson. In the Student Worktext, the Learning Target also highlights the SMPs that are included in the lesson.” SMPs Integrated in Try-Discuss-Connect Instructional Framework, “i-Ready Classroom Mathematics infuses SMPs 1, 2, 3, 4, 5, and 6 into every lesson through the Try-Discuss-Connect instructional framework (found in the Explore and Develop sessions of Strategy lessons , with a modified framework used in understand lessons).” Try It, “Multiple students share a word or phrase that describes the context of the problem as the teacher guides them to consider precision (SMP 6) of the mathematical language and communication.” Discuss It, “The teacher guides students to greater precision (SMP 6) in their mathematics, language, and vocabulary.”

Students attend to precision, in connection to grade-level content, as they work with teacher support and independently throughout the units. Examples include:

• Unit 2, Lesson 6, Add Two-Digit Number, Session 3, Additional Practice, Practice More Ways to Show Addition, Problem 6, students attend to precision as they create three different equations to solve addition problems. “The equation below shows a sum of 51. Write three different equations with a sum of 51. $22+29=51$.”

• Unit 4, Lesson 22, Understand Measurement with Different Units, Session 2, Develop, Model It: Measure in Inches and Centimeters, students attend to precision when measuring objects with different units. Problem 1, “Use a ruler. Measure the length of the caterpillar in inches and in centimeters. The caterpillar is ___ inches long. The caterpillar is about ___ centimeters long.” A picture is shown of a caterpillar.

• Unit 5, Lesson 29, Understand Partitioning Shapes into Halves, Thirds, and Fourths, Session 2, Develop, students attend to precision as they partition rectangles into equal parts. Problem 3, “Three equal parts.” Discuss It, ”How can you check that each third takes up the same amount of the rectangle?”

Students attend to the specialized language of mathematics, in connection to grade-level content, as they work with teacher support and independently throughout the units. Examples include:

• Unit 2, Lesson 10, Solve Word Problems Involving Money, Session 1, Explore, Connect It, Problem 2, students attend to the specialized language of mathematics as they learn the vocabulary and symbols for money. “Use ¢ to show cents and $ to show dollars. 5¢ is 5 cents. 5 is $5 dollars. Each type of coin and bill has a different value.” In addition, a table is provided that shows the name, value, and pictures of the front and back of a penny, nickel, dime, and quarter.

• Unit 3, Lesson 14, Compare Three-Digit Numbers, Session 1, Explore, Connect It, Problem 2, Look Ahead, students use mathematical vocabulary and symbols to compare numbers. “Start with the greatest place value to compare. A place-value chart can help you compare numbers. a. Compare the hundreds to complete this sentence. ___ hundred is greater than ___ hundreds. You can use =, < (less than symbol), and > (greater than symbol) to compare numbers. The symbol points toward the lesser number. It opens toward the greater number. b. Write 152 and 89 in the correct spaces below. ____<____ , _____>____.” 

• Unit 5, Lesson 28, Recognize and Draw Shapes, Session 1, Explore, Connect It, students use mathematical vocabulary to precisely describe shapes. Problem 2, “The number of sides, vertices (corners), and angles tells what group a shape belongs to.” Problem 2a, “Which arrow is pointing to: a side? a vertex? an angle?” Problem 2b, “The shape formed by two sides at an angle is a vertex. How many vertices does this shape have?” Problem 2c, “A quadrilateral is a shape with 4 sides, 4 vertices, and 4 angles. Name a quadrilateral shape:” Problem 3, “A pentagon has 5 sides, and 5 angles. Is the shape above a pentagon? Explain.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

Within Program Implementation, Standards for Mathematical Practice in Every Lesson, “The Standards for Mathematical Practice (SMPs) are embedded within the instructional design of i-Ready Classroom Mathematics.” Embedded SMPs Within Lessons, “In addition to SMPs 1, 2, 3, 4, 5, and 6, which are integrated into the instructional framework, the Teacher’s Guide includes additional opportunities for students to develop the habits of mind described by the Standards of Mathematical Practice. The table of contents indicates all of the embedded Standards for Mathematical Practice for each lesson (both integrated SMPs and the specific SMPs highlighted within the lesson). The Lesson Overview includes the Standards for Mathematical Practice addressed in each lesson. In the Student Worktext, the Learning Target also highlights the SMPs that are included in the lesson.” Structure and Reasoning, “As students make connections between multiple strategies, they make use of structure (SMP7) as they find patterns and use relationships to solve particular problems. Students may also use repeated reasoning (SMP 8) as they construct and explore strategies. SMPs 7 and 8 may be particularly emphasized in selected problems throughout the lesson. As students look for patterns and generalize about strategies, they always consider the reasonableness of their work.” 

MP7 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and make use of structure as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 2, Lesson 8, Use Addition and Subtraction Strategies with Two-Digit Numbers, Session 2, Develop, Model It, students analyze and look for more than one approach to solve a problem. “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 joined the line? Model It, You can use an open number line. Start at 39. Add tens until you reach 89. Next, add 1 to reach 90. Then add 3 more ones to reach 93. $50+1+3=?$ Model It, You can add up to the next ten. $39+1=40$; $40+50=90$; $90+3=93$; $1+50+3=?$”

• Unit 3, Lesson 18, Use Addition and Subtraction Strategies with Three-Digit Numbers,  Session 2, Model It, students analyze a problem and find more than one approach to solve. “There are 263 pipers and 137 drummers competing at a Highland festival. How many pipers and drummers are there in all? Model It, You can use a place-value chart. Write the numbers in the chart. Regroup ones and tens. Model It, You can use an open number line. Start at 263. Add the ones, tens, and hundreds in 137.” 

• Unit 5, Lesson 29, Partitioning Shapes into Halves, Thirds, and Fourths, Session 1, Discuss It, students look for and make use of structure when they explore partitioning squares into two, three, and four equal parts. "How do you divide shapes into 2, 3, and 4 equal parts?" Teacher Edition, Discuss It, Support Partner Discussion, "Encourage students to discuss whether the parts of each square represent the same amount. Review that one way to justify a response is to try and convince others by referring to a model. Look for understanding of: one fourth is 1 of 4 equal parts; four fourths are 4 of 4 equal parts or the whole shape."

MP8 is identified and connected to grade-level content, and there is intentional development of the MP to meet its full intent. Students look for and express regularity in repeated reasoning as they work with support of the teacher and independently throughout the modules. Examples include:

• Unit 2, Lesson 6, Add Two-Digit Numbers, Session 4, Develop, Teacher Edition, Model It, students evaluate the reasonableness of their answers and thinking. “If no student presented these models, have students analyze key features and then point out the ways each model represents: the number of flour tortillas, or a number close to this number, the number of corn tortillas, or a number close to this number, an estimate of the total number of tortillas. Ask Why is it important that the numbers you use to estimate are close to the number in the problem? Listen For The numbers for the estimate needed to be close to the numbers in the problem so that the estimate will be close to the actual sum.”

• Unit 3, Lesson 13, Read and Write Three-Digit Numbers, Session 3, Additional Practice, Practice Writing Three-Digit Numbers, students express regularity in repeated reasoning by writing numbers in different ways. “Use the chart below for problems 1-3.” A picture is shown of a place value chart with 3 in the Hundreds place, 2 in the Tens place, and 2 in the Ones place. Problem 1, “Write the number using only digits.” Problem 2, “Write the number in expanded form.” Problem 3, “Write the number using words.”

• Unit 4, Lesson 23, Estimate and Measure Length, Session 3, Refine, Problem 2, students evaluate the reasonableness of their answers and thinking. “Measure the actual length of your object in problem 1. What is the actual length of your object? How does the actual length compare with your estimate?”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. 

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• i-Ready Homepage, Success Central, Preparing for a Unit of Instruction, “Before delivering each unit of instruction, make sure to peruse the unit-level resources in your Teacher’s Guide. Learn about the unit goals by reading the Unit Opener, take note of the vocabulary and language supports, and study the mathematics in the unit by watching the Unit Flow and Progression Video or reading the Math Background pages.” 

  • Program Overview provides the teacher with information on program components and description about i-Ready classroom Mathematics implementation. 

  • Plan is broken down into Unit, Lesson, and Session. 

  • Teach gives information on practice, and differentiation. 

  • Assess includes support for the diagnostic, reports, and data. 

  • Leadership informs the teacher on getting started, building routines, fostering discussions, making connections, and top leader actions. 

• Program Implementation includes numerous supports such as digital math tools, videos, discourse cards, vocabulary, language routines, graphic organizers, games, correlations with standards and practices, etc.

• Each unit has a Beginning of Unit document that provides the teacher with extensive information on Unit Flow and Progression, Unit Resources, Unit Opener, Unit Prepare For, Unit Overview, Lesson Progression, Prerequisites Report Overview, Professional Development, Understanding Content Across Grades, Language Expectations, Math Background, Cumulative Practice, Yearly Pacing for Prerequisites, and Unit Lesson Support. Examples include:

  • Unit Opener, Self Check, “Take a few minutes to have each student independently read through the list of skills. Ask students to consider each skill and check the box if it is a skill they think they already have. Remind students that these skills are likely to all be new to them and that over time, they will be able to check off more and more skills.”

  • Prerequisites Report Overview, “Diagnostic data generates the Prerequisites report, which helps you identify students’ prerequisite learning needs and provides guidance on how to best integrate prerequisite instruction into your grade-level scope and sequence for the year.” These are specific to current students and classes providing valuable data about entry points for students. Note: Diagnostic assessments are an optional additional purchase.

  • Under the Prepare column, there is a Unit and Lesson Support document that provides multiple On-the-Spot Teaching Tips for each unit. These tips provide information on what to reinforce from prior learning promoting scaffolding to current content.

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Throughout each lesson planning information, there is narrative information to assist the teacher in presenting student materials throughout all phases of the unit and lessons. Examples include:

• Program Implementation, Teaching & Learning Resources, Discourse Cards, provides instruction on how to use the Math Discourse Cards. “These questions and sentence starters provide a way to engage all students in meaningful mathematical conversations. These cards will help students initiate, deepen, and extend conversations with partners, small groups, or the whole class. Each card has two questions or sentence starters on it-one on the front and one on the back. With each question, be sure to have students explain their reasoning for their response.”

• Unit 3, Lesson 15, Mental Addition and Subtraction, Explore, Session 1, Teacher Edition, Connect It, Problem 3, “What would be the next number in the skip-counting backward by hundreds pattern above? How do you know?” The Teacher Edition provides guidance for the teacher in the Exit Ticket, “Look for understanding of subtracting 1 from the hundred digit for each skip-counting backward by hundreds. Student responses should include references to the last written number in the pattern as 200, and connect it to the hundreds digit decreasing from 2 to 1. Common Misconception: If students do not identify 100 as the next number or are unclear in their explanations, then have them underline the hundreds digits in each of the numbers of the completed pattern, 700 through 200, to identify the pattern of the hundreds digit decreasing by 1 with each 100 that is skip-counted.”

• Unit 4, Lesson 23, Estimate and Measure Length, Develop, Session 2, Teacher Edition, Apply It, students answer questions about estimates and measurements of objects. The Teacher Edition provides guidance for the teacher, “For all problems, encourage students to record how they found their estimate or measurement for the length of each object.”

• Unit 5, Beginning of Unit, Prepare, Unit and Lesson Support, teachers are provided with guidance in using the manipulatives with students. This includes guidance in reviewing the  academic vocabulary associated with partitioning. “Students may benefit from a brief review of the terms halves, half, fourths, and fourth as they relate partitioning shapes into equal parts. Show examples of a shape partitioned into equal parts in more than one way to help students think more flexibly. Emphasize that the parts must be equal in size by showing an example of a shape divided into two parts that are not equal in size.”

• Unit 5, Lesson 29, Understand Partitioning Shapes into Halves, Thirds, and Fourths, Develop, Session 2, Teacher Edition, Develop, Model It, teachers are prompted to support partner discussion. “As students complete the problems, have them identify that they are being asked to model equal parts of a rectangle. Then have students turn and talk to answer the question: Is there more than one way to correctly divide each shape?” Common Misconception: “If students do not make equal parts, then ask students to restate what equal parts means and how they could check whether the parts are equal when they divide the shape.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for  containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. 

The Beginning of Unit section for every unit provides an abundance of information for teachers, including sections to support teachers with adult-level understanding of the content:

• Math Background includes Unit Themes, Prior Knowledge, and Future Learning. In the Math Background, as well as throughout the teacher materials, there are insights on the concepts taught, Common Misconceptions, and Error Alerts to watch for when students are incorrectly applying skills. 

• Lesson Progression links each lesson within the current unit to a prior and future lesson so teachers know what students need to know to be successful with the current work as well as what the current work is preparing students for. This is important for a teacher’s complete understanding of how to scaffold and bridge the current content. For example, Unit 2, Lesson 9, Lesson Overview, Teacher Edition, Solve Word Problems withTwo-Digit Numbers - Full Lesson, Learning Progression:

  • “In Grade 1 students solve simple one-step problems involving addition and subtraction within 20. They represent problems with objects, drawings, and equations that use a symbol to replace the unknown.”  

  • “In this Grade 2, students are expected to master solving one- and two-step problems with the unknown in all positions. They model problems using physical objects and diagrams and write equations using a symbol to represent the unknown. In this lesson students interpret and solve one- and two-step word problems involving two-digit numbers. They utilize concepts of fact families by representing a problem using more than one equation. They build fluency with representing and solving word problems using models such as number bonds, bar models, open number lines, and equations.”

  • “In Grade 3 students apply problem-solving strategies to problems involving multiplication and division.  At this level and beyond, students recognize mathematics as a tool for solving problems that arise within the context of a lesson and in daily life.”

• Understanding Content Across Grades provides explanations of instructional practices as well as information about necessary prior knowledge and concepts beyond the current course for teachers to improve their own knowledge of the subject. For example, Unit 4, Beginning of Unit, Understanding Content Across Grades related to Lesson 23, Estimate and Measure Length:

  • Prior Knowledge: “Insights on: Measuring Length. Children build on the idea of comparing the length of one object to another when they compare the length of an object to an iterated unit of measure. As children align physical units of measure such as connecting cubes or paper clips to an object, they will count the number of units to determine the object’s length…”

  • Current Lesson, “Insights on: Estimating Lengths. Students explore benchmark objects that can be used to approximate measurements; for example, a quarter is about 1 inch across and a crayon is about 1 centimeter across. They use these benchmarks to estimate lengths of an object. Be sure students get many opportunities to estimate lengths of things around them, as this helps develop excellent measurement sense.

  • Future Learning, “Insights on: Representing Fractions. Looking back, students have only used fraction names. In this grade, they will represent fractions symbolically with numerators and denominators. To support conceptual understanding, in third grade the denominators are limited to 2, 3, 4, 6, and 8. Students should have many opportunities to represent fractions with area models by partitioning shapes and with linear models such as number lines or fraction strips. In area models, parts do not have to be the same shape, but they must be the same area.”

• Each lesson includes a Reteach section with several pages called “Tools for Instruction” that provide explicit teacher guidance related to the current work and to prerequisite skills. These pages include adult explanations, step-by-step guidance for teaching, and check for understanding. For example, Unit 5, Lesson 31, Adding Using Arrays:

  • “Students have previously added using several strategies including making a ten, counting on, and number lines. Students have also learned to skip-count by different numbers. Now, students will use arrays to model repeated addition. Repeated addition can sometimes be difficult for students who struggle with skip-counting. Arrays can be used to provide a visual model to support this skill. This activity will provide a foundation for multiplication and division in future grades.”

  • “Step by Step: 1) Practice skip-counting. Have the students practice skip-counting by twos, threes, and fours up to 24 and by fives up to 25. If the student struggles, provide a hundreds chart and have the student shade in numbers to skip-count. 2) Count tiles in an array using skip-counting. (followed by four prompts) 3) Model an array using an addition equation. (followed by two prompts)”

  • “Check for Understanding: Have the student create an array with 8 rows of 3 tiles. Then have the student write an addition equation to find the total number of tiles. $(3+3+3+3+3+3+3+3=24)$ For the student who struggles, use the table below to help pinpoint where extra help may be needed: “If you observe… the student may… Then try…”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

In Program Implementation, correlation information is present for the mathematics standards addressed throughout the grade level using multiple perspectives. For example: 

• The Correlations document for Content Focus in the Common Core State Standards (CCSS) describes lesson correlation to the CCSSM through multiple lenses. The document identifies the major and supporting areas of focus within the CCSSM, and corresponding lessons that address those standards. Additionally, a table is provided that correlates each lesson with the standards addressed, designating standards as “Focus”, “Developing”, or “Applied” within each lesson. 

• The Correlations Document also identifies the Standards of Mathematical Practice that are included in each lesson; one table is organized by MP, another is organized by lesson. 

• The Unit Review Correlation identifies the associated standard and lesson to each problem within the Unit Review, along with their Depth of Knowledge level. 

• Digital Resource Correlations, Comprehension Check Correlations, and Cumulative Practice Correlations identify the lesson and a statement of the part of the standard it aligns to. 

• The WIDA PRIME V2 correlates the WIDA Standards Framework to examples in the material with descriptions of how they connect. 

• The English Language Arts Correlations provides a table that offers evidence of how the Common Core State Standards for English Language Arts are supported in every lesson and unit of the i-Ready Classroom Mathematics material.

In Beginning of Unit for each unit, there are numerous documents provided that contain explanations of the role of the specific grade-level mathematics in the context of the series. For example: 

• The Lesson Progression provides a flow chart delineating how each standard in the current lesson builds upon the previous grade levels and connects to future grade levels. This is developed in detail with examples in the Understanding Content Across Grades document. 

• There is a Unit Flow and Progression video for teachers that provides background about the content covered in the unit. 

• The Unit and Lesson Support document provides descriptions of the standards addressed in each unit with connections to prerequisites and teaching tips about prior knowledge. For example, Unit 4, Beginning of Unit, Unit and Lesson Support, the opening narrative provides the content of the unit, “In this unit, students build on what they know about measuring length to measure using standard units. They compare units of measurement such as inches, feet, yards, centimeters, and meters to develop an understanding of the relative size of those units. Students also explore benchmark objects that can be used to estimate the lengths of objects using standard units. They extend their knowledge of measurement as iterating units as they represent whole numbers as lengths on number lines and represent addition and subtraction problems on number lines. They also measure lengths and make line plots to display measurement data.” The document continues with Instructional Support identifying specific lessons from prior grades to develop understanding such as Unit 4, Lesson 20 - 24, “These lessons build on students’ understanding of comparing lengths of objects and using nonstandard units to measure length from Grade 1, Unit 5.”

• In every teacher's Lesson Overview, the Learning Progression identifies how the standard is addressed in earlier grades, in the current lesson, next lesson, and in the next grade level. For example, Unit 2, Lesson 7, Overview, Learning Progression, “In Grade 1, students subtract within 20, recognizing when decomposing a number leads to a ten and utilizing addition to solve subtraction problems. Students subtract multiples of ten within 100 and mentally find 10 more or less than a given number. In this lesson, students subtract a two-digit number from another two-digit number by counting back to a ten and by decomposing a ten. Students interpret picture models, number models, and open number lines to understand subtraction of two-digit numbers. They also estimate differences by using quick drawings or open number lines to identify easier numbers that are close to the original numbers. In Grade 3, students fluently add and subtract numbers within 1,000. They apply concepts of place value to division and recognize the role of subtraction in division with a remainder as well as in the division of multi-digit numbers.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

There are thorough explanations of the instructional approaches of the program. These are easily found under Program Implementation and in Classroom Central. For example:

• Program Implementation, “Try-Discuss-Connect Routine Resources”, is embedded throughout the program. “i-Ready Classroom Mathematics empowers all students to own their learning through a discourse-based instructional routine. Lessons are divided into Explore, Develop, and Refine sessions and are taught over the course of a week. In Explore and Develop sessions teachers facilitate mathematical discourse through a Try-Discuss-Connect instructional routine.” In i-Ready Classroom Central, videos model the six steps of the Try-Discuss-Connect routine as well as an Exit Ticket.

• Program Implementation, User Guide, Protocols for Engagement, describes multiple protocols and identifies the traits each protocol validates to help all students “feel accepted and included. Protocols provide structure for activities so that all students have a chance to think, talk, and participate equally in classroom activities. Each protocol incorporates modes of communication common to one or more cultures and leverages those behaviors for a particular instructional purpose.” For example, “Stand and Share: Students stand when they have something to share with the class. Validates: spontaneity, movement, subjectively, connectedness.” Protocols can be found in the Lesson Overview section of the Teacher Guide.

• i-Ready Homepage, Success Central, Building Community, Promote Collaborative Learning, has resources such as using Lesson 0 to introduce the Try-Discuss-Connect Routine and language routines, questions to support discourse, videos about sharing math ideas, ideas for promoting mathematical practices, and creating a positive mindset. 

• i-Ready Homepage, Success Central, has a link in the upper right under the search box called Explore all Resources that has all of the additional resources organized in a list of links by category that provide abundant information, including a section called Program Overview.

Materials include relevant research sources. In Program Implementation, Supporting Research, “i-Ready Classroom Mathematics is built on research from a variety of federal initiatives, national mathematics organizations, and experts in mathematics.” A table describes 16 concepts that are embedded in the program with examples of how and where each is used, an excerpt from the research that supports it, as well as an extensive reference list. Examples include: 

• “The Concrete-Representational-Abstract (CRA) Model is a three-part instructional model that enhances students’ mathematical learning.” This model is built into all i-Ready Classroom Mathematics lessons in the Try It, Discuss It, Connect It, and Hands-On Activities. “Using and connecting representations leads students to deeper understanding. Different representations, including concrete models, pictures, words, and numbers, should be introduced, discussed, and connected to support students in explaining their thinking and reasoning.” (Clements and Sarama, 2014)

• “Collaborative learning (partner or small group) encourages students to present and defend their ideas, make sense of and critique the ideas of others, and refine and amend their approaches.” Lessons provide multiple opportunities for collaborative learning during Discuss It and Pair/Share. “Research tells us that when students work collaboratively, which also gives them opportunities to see and understand mathematics connections, equitable outcomes result.” (Boaler, 2016)

• “An instructional framework supports students in achieving mathematical proficiency and rigor within a collaborative structure to develop greater understanding of how to reason mathematically.” The Try-Discuss-Connect instructional framework is foundational in this program. “Instructional routines are situated in the learning opportunity itself, providing students with a predictable frame for engaging with the content…” (Kelemanik, Lucenta, & Creighton, 2016)

• Program Implementation, User Guide, Routines that Empower Students identifies 9 research-based language routines. Each routine includes the purpose, the process, and which part of the Try-Discuss-Connect Routine it can be used with. For example, Say It Another Way is used with Try It, “Why: This routine helps students paraphrase a word problem or text so they know if they have understood it. It provides an opportunity to self-correct or to ask for clarification and ensures that the class hears the problem or story more than once and in more than one way.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

The Lesson Overview for the teacher provides a Materials required column for each lesson on the Pacing Guide; additional materials are listed in the Differentiation column. Any materials that need to be printed are also provided in the Overview, such as grid paper or double number lines. For example:

• Unit 1, Lesson 3, Session 3, “Materials tab: Math Toolkit bar models, counters, 10-frames, Presentation Slides. Differentiation Tab: for each student: 20 counters, 1 small paper plate, 1 large paper plate.”

Under Program Implementation, a Manipulatives List provides a document identifying manipulatives needed for each lesson K-8. For example: 

• Manipulative List, Unit 4, Lesson 24, identifies centimeter ruler - 1 per student, set of centimeter tiles - 1 per student, inch/centimeter ruler or yardstick and meter stick - 1 per student, and inch ruler - 1 per student. 

Program Implementation also includes digital math tools, discourse cards and cubes, activity sheets, data sets, and graphic organizers.

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

In the Teacher Toolbox, each lesson includes Assess which provides Lesson Quizzes & Unit Assessments. Lesson Quizzes, Teacher Guide lists information correlated to each problem: tested skills, content standards, mathematical practice standards, DOK levels, error alerts, problem notes, Short Response Scoring Rubric with points and corresponding expectations, and worked-out problems. For example:

• Unit 2, Lesson 10, Lesson Quiz, Problem 1, “DOK 2, 2.MD.C.8, SMP 7.”

Assess, End of Unit, Unit Assessments, Teacher Guide, Forms A and B are provided and include the content item with a solution. Form A includes Problem Notes, worked-out problems, DOK levels, content standards, Scoring Guide, Scoring Rubrics, and Responding to Student Needs. Form B appears to parallel all of the correlations provided for Form A, though it is not labeled. It is noted in the Scoring Guide, “For the problems in the Unit 4 Unit Assessments (Forms A and B), the table shows: depth of knowledge (DOK) level, points for scoring, standard addressed, and lesson assessed by each problem.” For example:

• Unit 4, End of Unit, Assess, Unit Assessment, Form A, Problem Notes, Problem 5, “DOK 1, 2.MD.A.1.”

• Unit 7, End of Unit, Assess, Unit Assessment, Form A, Problem Notes, Problem 12, “DOK 2, 2.G.A.2.”

Digital Comprehension Checks “...can be given as an alternative to the print Unit Assessment. For this comprehension check, the table below provides the Depth of Knowledge (DOK), standard assessed, and the corresponding lesson assessed by each problem.” While the Comprehension Checks identify the content standards, they do not identify the mathematical practices. For example:

• Unit 1, End of Unit, Assess, Comprehension Check Correlation Guide, Problem 6, “DOK 2, 2.MD.D.10.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

The assessment system provides opportunities to determine students’ learning that include teacher support for interpreting student performance in the Problem Notes and Rubrics provided, though the rubrics are generic rather than specific to the lesson. Examples include:

• Problem Notes for each problem in the Lesson Quizzes and Form A of the Unit Assessment provide guidance on steps to solve the problem and what students may have done incorrectly. For example:

  • Unit 1, Lesson 4, Assess, Lesson Quiz, Problem 1, “C; Students can solve the problem by comparing the number of dolls and chairs. A is incorrect because there are 3 more books than lamps. B is incorrect because there are 3 more books than chairs. D  is incorrect because there are more books than any other thing.”

  • Unit 2, End of Unit, Assess, Unit Assessment, Form A, Problem 5, “See possible solutions on student page. Students’ responses may include any combination of bills totaling $75.” 

• Lesson Quizzes contain a Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric and a Short Response Scoring Rubric. The Fill-in-the-Blank Scoring Rubric states: 2 points if, “Response contains the following: correct answer(s).” 1 point if, “Response contains the following: “One answer is correct.” 0 points if, “Response contains the following: Incorrect answers that do not demonstrate the correct mathematical procedures and/or thinking.” The Multiple Select/Choice Matrix Scoring Rubric states: “2 Points All answers are correct, 1 Point 1 incorrect answer, and 0 Points 2 or more incorrect answers.” The Short Response Scoring Rubric states: 2 points if the “Response contains the following: Correct computation,  solutions, and/or calculations; Well-organized work demonstrating thorough understanding of math concepts and/or procedures.” 1 point for “Response contains the following: mostly correct solution(s); Shows partial or good understanding of math concepts and/or procedures.” 0 points if the “Response contains the following: Incorrect solution(s);  No attempt at finding a solution; No effort to demonstrate an understanding of the math concepts and/or procedures.”

• Unit Assessments contain the Extended Response Scoring Rubric (if there is an extended response question included in the assessment), Short Response Scoring Rubric, and a rubric for Fill-in-the-Blank/Multiple Select/Choice Matrix. For example, the Extended Response Scoring Rubric, a response should earn 4 points if, “Response has the correct computation,  solutions, and/or calculations; Well-organized work demonstrating thorough understanding of math concepts.” This same expectation scores a 2 on the Short Response Scoring Rubric. The Fill-in-the-Blank/Multiple Select/Choice Matrix Scoring Rubric is the same as the Lesson Quizzes.

The Lesson Quizzes and Unit Assessments provide sufficient guidance to teachers to follow-up with students, although there is no follow-up guidance for the Comprehension Checks. The follow up suggestions reference previous work rather than new material. For example:

• Unit 1, End of Unit, Assess, Unit Assessment, Form A, provides a section called Responding to Student Needs. This section directs teachers back to the relevant lessons for review and where teachers can access the Review, Reinforce, and Extend options. “For students who answer problems incorrectly on the Unit Assessment, choose from the following resources on the Teacher Toolbox for additional support. Reteach Tools for Instruction, Addition/Subtraction Fact Families (Lesson 2), Draw and Use Bar Graphs and Picture Graphs (Lesson 4), Solve Two-Step Addition and Subtraction Word Problems (Lesson 5). For students who exceed proficiency on the Unit Assessment, choose from the following activities on the Teacher Toolbox. Extend Enrichment Activities Mystery Number (Lesson 2), Graph It (Lesson 2), Silver Coins (Lesson 5).”

• Unit 2, Lesson 11, Assess, Lesson Quiz provides three types of differentiation for possible follow up depending on student performance: Reteach, Reinforce, and Extend. Implementation Guide, Program Overview, Differentiation, “Reteach: Tools for Instruction are mini-lessons for reteaching lesson concepts. Reinforce: learning games offer fun, challenging, and personalized practice and help students develop a growth mindset. Extend: Enrichment Activities challenge students with higher-order thinking tasks.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

There are formative and summative assessments provided as PDFs as well as comparable assessments provided online. Lesson Quizzes and Unit Assessments provided include a variety of item types for students to demonstrate grade-level expectations. For example:

• Fill-in-the-blank

• Multiple select

• Matching

• Graphing

• Constructed response (short and extended responses)

• Technology-enhanced items (e.g., drag and drop, drop-down menus, matching) 

Throughout the lessons, there are opportunities to demonstrate critical thinking, develop arguments, or apply learning in a performance task, though these are not typically on the assessments.

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. i-Ready Success Central provides many suggestions and examples for how to accommodate and support special populations. Lessons have sections called Group & Differentiate to help special populations. Lesson quizzes have suggestions for reteaching. Examples of supports for special populations include:

• i-Ready Homepage, Success Central, Plan & Teach, Differentiate, provides information to support the teacher in planning for all special populations. Personalized Instruction provides resources for students who have taken the Diagnostic and will have access to online learning and instructional paths tailored to their individual needs to reinforce prerequisite skills and build grade-level skills. Support Small Group Instruction, “Every student can excel in mathematics with the right supports. Check out the resources below to help you plan for, organize, and facilitate small groups so you can meet the various needs of your students.” Support All Learners, “Every student can excel in mathematics with the right supports. Use the resources on this page to find ideas and strategies for adapting your instruction to meet the unique needs and learning styles of all students.” There are several links to documents to support teachers. For example:

  • Supporting Students' Needs – Reference Sheet, provides information regarding “Optional built-in supports embedded in i-Ready Classroom Mathematics that educators can choose from to best meet the needs of their students. These resources can be used to: Scaffold instruction by breaking learning experiences into smaller parts to help students reach higher levels of comprehension and skills acquisition with temporary supports along the way Differentiate instruction to meet individual students’ needs by modifying content, altering the delivery method, and/or providing alternate learning tasks.”

  • Tools for Accessible Instruction – Reference Sheet “Highlights i-Ready Classroom Mathematics supplemental tools and examples of student supports that can be used throughout a lesson and session. Examples of student supports may have some overlap with a student’s IEP/504 plan but should not supersede or contradict it, and they may be useful for students regardless of whether or not they have an IEP/504 plan in place.” For example, during Try It, a suggested support is, “Offer multiple means of representation, engagement, and action and expression such as: highlight important numbers, words, and phrases; Invite volunteers to act out the problem for the class; Offer options for how students express their ideas.” During Discuss It, “Use hand signals to agree, disagree, or share an idea.”

• In Refine, the last session of each lesson, the teacher’s edition provides suggestions to Group & Differentiate, “Identify groupings for differentiation based on the Start and problems 1-3. A recommended sequence of activities for each group is suggested below. Use the resources on the next page to differentiate and close the lesson.” Resources are suggested for groups Approaching Proficiency, Meeting Proficiency, and Extending Beyond Proficiency. 

• At the end of the Lesson Quiz in the Teacher’s edition, there is a section for differentiation that provides suggestions for Reteach (Tools for Instruction), Reinforce (Math Center Activity), and Extend (Enrichment Activity). Program Implementation, Program Overview, Differentiation, Reteach, “Tools for instruction are mini-lessons for reteaching lesson concepts.” Reinforce, “Learning Games offer fun, challenging, and personalized practice and help students develop a growth mindset.” Extend, “Enrichment Activities Challenge students with higher-order thinking tasks.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity. 

Materials do not require advanced students to do more assignments than their classmates. Instead, students have opportunities to think differently about learning with alternative questioning, or extension activities. Specific recommendations are routinely highlighted as Teacher Notes within parts of each lesson, as noted in the following examples:

• Each lesson has an Extend: Enrichment Activities column that provides an additional challenge task. For example, Unit 3, Lesson 12, Extend, Who Is Correct?, students are provided with a challenge situation. “Kim and Jim each make a statement about how many tens are in 352. Kim says 352 has 5 tens in it. Jim says 352 has 35 tens in it. 1. In what way is Kim correct? Use pictures to help explain. 2. In what way is Jim correct? Use pictures to help explain. How many tens are in 110? Make your own statement about how many tens are in 110. How can you use pictures to explain?”

• Refine sessions at the end of each lesson provide recommendations for students that demonstrate understanding “Extending Beyond Proficiency” to engage in problems for reinforcement and a challenge. The number of problems is the same as the work for students who are considered to be “Meeting Proficiency”. Additional Enrichment Activities can be found online in the Small Group Differentiation Extend section. In addition, Refine sessions include at least 1 problem identified as DOK 3 where students utilize strategic thinking. 

• In Explore and Develop sessions in each lesson, the materials contain Differentiation: Extend Deepen Understanding or Challenge for the lesson’s key concepts through the use of discourse with students. For example, Unit 5, Lesson 28, Session 2, Teacher Guide, Differentiation: Extend - Deepen Understanding, “Display a square and a rectangle. Ask A square can also be called a rectangle. Why?...Ask Why are squares and rectangles also called quadrilaterals?...Display a square, trapezoid, and rectangle. Ask What is one name that you can use for all of these shapes? Explain.”

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing strategies and support for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics. 

Guidance is consistently provided for teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. For example: 

• i-Ready Homepage, Success Central, Plan & Teach, Differentiate, Support All Learners, Supports for English Learners – Reference Sheet, explains where to find and how to use all of the supports built into the Teacher Guide for every lesson to “address the strengths and needs of ELs” such as, Build Your Vocabulary, Connect Language Development to Mathematics, Language Objectives, Connect to Community and Cultural Responsiveness, and Connect to Language Development.

• Program Implementation, Program Overview, Integrate Language and Mathematics, shows where teachers can access tips for targeted support using Language Routines in the Teacher Guide for every lesson.

• Program Implementation, Program Overview, Language Development and Discourse Support provides “support at the word/phrase, sentence, and discourse levels so that all students can engage in rigorous mathematics and communicate effectively.”

• Program Implementation, User Guide, Resources for Language Development describes nine features that are embedded in the teacher materials to “build academic language of all students, especially English learners. These supports help students learn how to communicate effectively across the language domains.”

• Program Implementation, User Guide, Routines that Empower Students, provides nine language routines. “While these routines support English learners, they are designed to be used by all students as they access mathematical concepts and their growing mathematical understanding.” Three routines, in particular, are differentiated for English Learners: Act it Out, Co-Constructed Word Banks, and Stronger and Clearer Each Time. 

• Program Implementation, User Guide, Support for Academic Discourse describes “a variety of ways to support students in communicating with academic and math-specific vocabulary and language.”

• Program Implementation, Discourse Cards, provide sentence starters and questions to help students engage in conversations with their partners, small groups or the whole class such as “Did anyone get a different answer?; What would you add to what was said?”

• All classroom materials are available in Spanish.

• Program Implementation, Multilingual Glossary is available in Arabic, Chinese, Haitian Creole, Portuguese, Russian, Tagalog, Urdu, and Vietnamese. There is a Bilingual glossary in the student textbook that includes mathematics vocabulary in English and Spanish.

• Beginning of Unit, Connect Language Development to Mathematics, Language Expectations for Differentiation is a chart that “shows examples of what English Learners at different levels of English language proficiency can do in connection with one of the Common Core State Standards (CCSS) addressed in this unit. As you plan for this unit, use these examples of language expectations to help you differentiate instruction to meet the needs of English Learners.”

• Beginning of Unit, Build Academic Vocabulary includes a chart of academic words for the units paired with their Spanish cognates. There are three routines provided in Professional Development to support vocabulary development: Math Vocabulary, Academic Vocabulary, and Cognate Support. 

• Each lesson in Lesson Overview, Teacher Guide’s Full Lesson, includes Language Objectives, Connect to Culture, and Connect to Language. 

• Session 1 of every lesson uses graphic organizers to help students access prior knowledge and vocabulary they will develop in the lesson. Support for Academic language is used during the “Try-Discuss-Connect Language” routines in each lesson. 

• All sessions throughout the lesson embed support including references back to previously listed items.

The materials reviewed for i-Ready Classroom Mathematics Grade 2 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Students have access to both virtual and physical manipulatives throughout the program. For example:

• Program Implementation, Digital Tools, are available for students. These tools include Counters and Connecting Cubes, Base-Ten Blocks, Number Line, Multiplication Models, Perimeter and Area, and Fraction Models. Also in Program Implementation, support videos are available for each of the digital tools, explaining how they may be used and their functions. 

• Program Implementation, Manipulative List, Manipulative Kit, includes Base-Ten Flats, Base-Ten Rods, Base-Ten Units, Blank Cubes, Linking Cubes, Two-Color Counters, Tape Measure, Ruler. 

• Program Implementation, Manipulative List by Lesson has specific manipulatives listed for each lesson. For example, Unit 2, Lesson 8: Set of base-ten blocks; connecting cubes. There is also a Manipulative Suggestions for At-Home Use document that provides ideas for using items commonly found at home or easily created that could be used in place of the actual manipulative (e.g. Linking Cubes could be replaced with Lego bricks). 

• Program Implementation, Activity Sheet Resources, K-5 Activity Sheet Resources includes a 172-page document full of visual models such as number lines, graphs, grid paper, graphic organizers, etc. 

Program Implementation, Try-Discuss-Connect Routine Resources, Understanding the Try-Discuss-Connect Instructional Routine, the foundational Try-Discuss-Connect routine is designed to “encourage proficiency and rigor within a collaborative structure.” A primary purpose is to “expose students to a number of representations and approaches” to help them make connections, develop mathematical language and thinking, and improve written and oral communication skills. This routine helps students transition from manipulatives to written methods. For example: 

• In the Try It activity, “students have access to a variety of tools and manipulatives to use to represent the problem situation.” During the Discuss It activity, “Students present and explain their solution methods and listen to and critique the reasoning of others, models and representations.” During the Connect It activity, “Students write their answers to Connect It questions independently (or in pairs to support language production, as needed) to solidify understanding and make further connections.” 

• “Tip: If students are struggling with writing responses…. have multiple students share answers orally while writing key words or phrases on the board. Have students use these key words and phrases to write their own response to the question in their worktexts.”

• “Tip: Encourage students to represent and solve problems in more than one way to build flexibility in their thinking.”

The Try-Discuss-Connect routine also integrates the Concrete-Representational-Abstract (CRA) model, for example:

• Try It, “Students may use concrete, representational, or abstract strategies to solve the problem, based on their understanding of the problem or mathematical concept.”

• Discuss It, “Students who use more concrete approaches begin to make connections to representational or abstract approaches as they engage in partner discussions.”

• Connect It, “Through the Connect It questions, students connect concrete and representational approaches to more abstract understanding as they formalize their connections.”