1st Grade - Gateway 2

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 1, Lesson 1, Number Partners for 10, Session 1, students develop conceptual understanding of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.) Investigate It, “How can you find and show missing number partners for 10? This activity allows children to make sense of the relationship between number partners for 10 to find the missing number. Read the problem aloud: A page has 10 stickers. Some are (image of a green triangle pattern block). Some are (image of an orange square pattern block). Find how many (image of a green triangle pattern block) and how many (image of an orange square pattern block) there could be. Have children mix up the cards and place them in a pile, facedown. Instruct children to spin the spinner to choose the first shape. Then have them choose a number card. Instruct children to put that many of the first shape in the 10-frame. ASK How do you know how many more are needed to fill the page? LISTEN FOR children to describe their strategies. They may mention filling the 10-frame, counting up to 10 and keeping track on their fingers, or recognizing number partners for 10. Have partners take turns spinning the spinner to determine the first shape and choosing a number card to identify how many shapes to put in the 10-frame. Have partners work together to find how many of the other shape are needed to make 10 and then record the number partners on their workmat.”

• Unit 3, Lesson 12, Solve Compare Problems, Session 2, students develop conceptual understanding of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.) Apply It, “How can you use models to find unknown differences? This activity lets children use a model as a tool for solving difference-unknown compare problems. Have partners decide who will represent frogs and who will represent lily pads. Have children place their mixed pile of number cards facedown. Have each child take a number card and count out that many counters. Have partners work together to arrange their counters and find the difference. Have children describe aloud how many more and how many fewer of each item there are. For example, the child representing frogs says, There are 3 more frogs than lily pads. The child representing lily pads says, There are 3 fewer lily pads than frogs. Have one child spin the spinner to decide whether the child with more or fewer keeps the cards from that turn. Have children record two turns on their workmat. Children continue until all the cards have been used. The child with more cards wins.” Facilitate Whole Class Discussion, Guide children to share their understanding of using a model to find how many more or fewer objects are in one group than another and how the model shows the difference. ASK How did you organize the counters to find how many more or fewer there are? LISTEN FOR children to describe the importance of lining the counters up to compare correctly, and understanding that the space above or below the unmatched counters represents the difference. ASK How does using a model help you find the difference? LISTEN FOR children to explain that making a model helps them see how many more (or fewer) counters are in one group than the other and lets them count to find the number.”

• Unit 5, Lesson 19, Addition with Two-Digit Numbers, Session 2, students develop conceptual understanding of 1.NBT.4 (Add within 100, including a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten). Develop, Model It, Student Workbook, Problem 1, “There are 23 sheep in a barn. A dog herds 4 more sheep into the barn. How many sheep are in the barn now? Use a 100 chart or base-blocks to help you solve the problem.  20+7=___  23+4=___ There are ___ sheep.” 

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

• Unit 3, Lesson 12, Solve Compare Problems, Session 4, students students independently engage with 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.) Centers, Apply It Problems, Problem 1, “Owen has 8 stickers. Amber has 17 stickers. How many fewer stickers does Owen have than Amber? (image of blank bar model) Owen has __ fewer stickers than Amber.” “These problems are an opportunity for guided or center-based practice. As children work, remind them to use strategies such as using counters or using a bar model. Make tools from the Math Toolkit available.”

• Unit 4, Lesson 15, Tens and Ones, Session 2, students independently engage with 1.NBT.2a and c (Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones — called a “ten.” c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).) Try-Discuss-Connect, “How can you organize objects to find out how many there are?” Try It, “Read the problem aloud: Pala starts counting the acorns on the ground. Show how you can finish counting.” Make Sense of the Problem, “Use Notice and Wonder to help children make sense of the problem. Have children work independently on Try It.” Discuss It, “Support Partner Discussion After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions such as: How did you keep track of the acorns you had counted?”

• Unit 4, Lesson 17, Compare Numbers, students independently engage with 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <). Session 3, Develop, Apply it, Flip and Compare, “This activity guides children to compare numbers by using the tens and ones digits. Tell children they will be doing an activity to compare numbers. Arrange children in pairs and distribute the base-ten blocks, cards, and place-value workmats. Tell children that on each turn, both children will flip two cards over from the deck, lay them in the place-value chart to describe a two-digit number, and build their number with blocks. Partners work together to compare the numbers. Each child records the comparison, using their number as the first number in the comparison. For example, one partner records 65>37. The other records 3<65. Have children check each other's work. Repeat to record eight comparisons. As children play, encourage them to use the words tens, ones, greater than, and less than to describe their comparisons.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 skill and fluency, as well as opportunities to independently demonstrate procedural skill 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 skill 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, Lesson 3, Use Counting Strategies to Add and Subtract, students build procedural skills and fluency with teacher support and guidance of 1.OA.5 (Relate counting to addition and subtraction) and 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationships between addition and subtraction; and creating equivalent but easier or known sums). Session 2, Develop, Model It, “If no child presented the model shown on the Student Worktext page, connect the number paths to the children’s models by having children identify how they represent the problem. Invite a volunteer to show placing a finger on the first number of each problem and sliding their finger forward along the number path as they count on the second number. The number their finger ends on is the total. If children need support, have them lift their finger and touch each number. Moving from one number to the next instead of making one large jump reinforces counting.”

• Unit 2, Lesson 10, Doubles and Near Doubles, students develop procedural skill and fluency of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as…). Interactive Tutorials, Doubles, The tutorial begins with six gardens containing several seeds. Gardens with doubles,  1+1, 2+2, and 3+3 are labeled. “Help us match the rest of the addition problems to the pictures.” Choices are 2+3, 3+4, and 1+2.

• Unit 5, Lesson 19, Addition With Two-digit Number, students develop procedural skill and fluency as they reinforce addition with multiples of 10, 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.) and 1.NBT.5 (Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.) Centers Library, Skills Review, Roll, Solve, and Cover, Card 10 Directions, “1. Player 1 rolls a number cube and finds one of the corresponding problems on their workmat. 2. Player 1 solves the problem and says the total. Both players cover the total on their workmats. 3. Players take turns rolling a number cube and then solving an addition problem. 4. Play continues, until one player fills a row across/down on their workmat, based on teacher directions. 5. Remove the counters, select a new workmat, and repeat.”

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

• Unit 1, Lesson 4, Use Addition to Subtract, students individually demonstrate procedural skill and fluency of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as…). Interactive Tutorials, Count On to Subtract, The 17-minute tutorial begins with a carnival game. Beans are on the stage and a bean launcher is used by students to hit the total. “On this side, we have 7 beans. Use the bean launcher to launch beans until we have 11 beans.”

• Unit 2, Lesson 10, Doubles and Near Doubles, Sessions 4 and 5, students individually demonstrate procedural skill and fluency of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as…). Session 4, Centers, Differentiation, and Practice, Apply It Problems, Problem 2, “There is 1 bluebird. There are 2 robins. How many birds are there?” Independent Practice, Problem 2, “Sam has 5 stickers. She gets 5 more stickers. How many stickers does Sam have now?” Session 5, Refine, Centers, Differentiation and Practice, Independent Practice, Problem 4, “7 geese are in the park. 8 geese join them. How many geese are there now? Circle. 14 geese 15 geese, 17 geese.” Practice, “Match. Put each shoe on its hopscotch square.” There are 6 shoes with 6 different addition problems. The numbers 11-19 are arranged in the traditional hopscotch pattern.

• Unit 3, Lesson 11, Solve World Problems to 20, students demonstrate procedural skill and fluency with 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as…) Session 5, Refine, Centers, Differentiation, and Practice, Apply IT Problems, Problem 1, “Linda has 8 crayons. She finds some more. Now she has 12 crayons. How many crayons did she find?”

• Unit 4, Lesson 17, Tens and Ones, Card 22, Build to Compare, students demonstrate procedural skill and fluency as they compare or measure length, 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.) Directions, “1. Taking turns, each partner turns over a number card and builds a cube train with that number of cubes. 2. Partners then compare their cube trains as instructed on their workmat. 3. When directed, partners record their comparisons. 4. If using Option C, partners use tools to measure the length of their cube trains. Then they record the measurement and tool on the workmat. 5. Play continues until time is called.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of 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 the 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 math include:

• Unit 1, Lesson 1, Number Partners to 10, Session 3, Develop, students independently demonstrate applying properties of operations as strategies to add and subtract to solve problems in a real-world context. 1.OA.3 (Apply properties of operations as strategies to add and subtract.) Try-Discuss-Connect, “What connections do you see between number bonds and equations?” Try It, “ Read the problem aloud: Maria has 10 teddy bears. 3 have bow ties. The rest have hats. How many teddy bears have hats? How do you know?” Make Sense of the Problem, “Use Say It Another Way to help children make sense of the problem. Have children work independently on Try It.” Discuss It, Support Partner Discussion, “After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions, such as: How does your model show number partners for 10? Encourage children to use the term number partners as they discuss their solutions.”

• Unit 4, Lesson 17, Compare Numbers, Session 2, Develop, students independently demonstrate comparing two-digit numbers to solve problems in a real-world context. 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.) Try-Discuss-Connect, “How can we use base-ten blocks to compare numbers?” Try It, “Read the problem aloud: There are 38 baby puffins. There are 51 adult puffins. Are there more adult or baby puffins? Show how you know. Use Connect to Culture to support engagement.” Make Sense of the Problem, “Use Say It Another Way to help children make sense of the problem. Ensure children understand that there are different ways to model and solve the problem. Have children work independently on Try It.”

• Unit 5, Lesson 20, Add Two-Digit and One-Digit Numbers, Session 3, Develop, students independently demonstrate adding within 100 to solve problems in a real-world context. 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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 and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.) Try-Discuss-Connect, “How can thinking about tens and ones help you add two-digit numbers?” Try It, “Read the problem aloud: There are 37 large blocks and 8 small blocks in a bin. How many blocks are in the bin? Show two different ways to solve the problem.” Make Sense of the Problem, “Use Three Reads to help children make sense of the problem. Have children work independently on Try It.”

Examples of non-routine applications of math include:

• Unit 1, Lesson 2, Add and Subtract Within 10, Season 3, Develop students work independently and with teacher support to demonstrate the application of 1.OA.A (Represent and solve problems involving addition and subtraction.) Try-Discuss-Connect, “How can story problems connect to numbers and symbols?” Try It, “Read the problems aloud one at a time: Think of a story to match the additional problem. Draw to show your story and solve the problem. Then think of a story to match the subtraction problem. Draw to show your story and solve the problem.” Facilitate Whole Class Discussion, “Have two or three selected children share their strategies in the order you have chosen” Select and Sequence Strategies, “One possible order for whole class discussion: Drawing to represent the action, then using the drawing to solve. Finding the solution, then drawing to check the solution.”

• Unit 3, Lesson 13, Collect and Compare Data, Session 2, Develop, Apply It, Student Worktext, students independently work on (solve) a non-routine problem of collecting, organizing, and representing data with a graph, and make comparison and equality statements about data sets using addition and subtraction, 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another). “Collect and Graph. Write a survey question. Write or draw 3 answer choices. Survey the class. Make a picture graph for your data.”

• Unit 6, Lesson 25, Compare and Order Lengths, Session 3, Develop, students independently solve a non-routine problem by indirectly comparing two lengths, 1.MD.1 (Order three objects by length; compare the lengths of two objects indirectly by using a third object). Apply It, Student Worktext, “No Moving! Choose two objects. Do not move them. Use your string to compare the lengths of the objects. Draw to record. Circle the longer object.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 1, Lesson 2, Add and Subtract Within 10, students demonstrate application of 1.OA.1 (Use addition and subtraction within 20 to solve word problems…). Session 4, Centers, Differentiation, and Practice, Independent Practice, “Toya sees 3 trucks. Then she sees 4 more. How many trucks does she see in all?” Students are presented with 5 different word problems as well as space for students to create a ten-frame for each problem. 

• Unit 2, Lesson 10, Doubles and Near Doubles, students develop procedural skill and fluency of 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums). Session 1, Investigate It, “Have children search through the dominoes at their station to find dominoes that show doubles. When they find doubles, have children record them by drawing dots to show those dominoes, writing doubles facts to represent them, and finding totals. After each group has found two doubles, have groups move to a new station. Repeat until children have visited each station.” Session 2, Centers, Differentiation, and Practice,  Differentiation, Reteach, “Use with children who need additional support with the idea of using doubles to find totals. Have pairs of children sit facing each other with their connecting cubes in front of them. Stand up the file folder in between them. Have each child build two trains of the same length using connecting cubes. When finished, have children hold up both of their trains so their partner can see them. Take down the file folder. Have partners work together to name the doubles facts and totals each of them have built. Have each child add 1 cube to one of their trains. Have partners say their new facts and find their new totals. Repeat by having children make two different cube trains to start a new round.”

• Unit 4, Lesson 17, Compare Numbers, students develop conceptual understanding of 1.NBT.3 (Compare two two-digit numbers based on meanings of the tens and ones digits…). Session 1, Explore, Investigate It, “Hold up a tens rod and a ones unit. Tell children they will use base-ten blocks to show quantities. ASK How can you describe how the ones unit compares to the tens rod? LISTEN FOR descriptions that a tens rod looks like 10 ones units connected together. ASK How can we show a tens rod as ones? LISTEN FOR understanding that you cannot break the rod apart, but you can trade it for 10 ones. Demonstrate trading a tens rod for 10 ones units. Emphasize the need to put the original block(s) aside when making the trade.” Session 2, Develop,  Connect It, “Help children make sense of the base-ten block models in Model It by comparing the models to their own. After individual think time, have children share and discuss their ideas. Children may also use pictures, numbers, or words to record ideas.”

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, Lesson 4, Use Addition to Subtract, Session 3, Develop, students develop procedural skill and fluency, conceptual understanding, and application as they solve word problems by using models and equations with 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.) Connect It, “Help children make sense of the equation model by comparing it to their own. After individual think time, have children share and discuss their ideas. Children may also use pictures, numbers, or words to record ideas. ASK How did you show 8 and 5? How does Model It show 8 and 5? LISTEN FOR descriptions of how the total number of stickers, 8, is shown as the whole and the number of big stickers, 5, is shown as one of the parts in both children’s models and Model It. ASK How can an addition fact help you subtract? LISTEN FOR an understanding that the result of a subtraction problem is the same as one of the numbers that are added in an addition problem.”

• Unit 2, Lesson 6, Teen Numbers, Session 3, students develop procedural skill and fluency with application of 1.NBT.2 (Understand that the two digits of a two-digit number represent amounts of tens and ones…). Try-Discuss-Connect, “Read the problem aloud: You have 17 markers. You put 10 markers in a box. How many markers are left? Have children work independently on Try It. After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions, such as: How did you organize the number of markers in the box? How did you show the number of markers outside of the box?” Facilitate Whole Class Discussion, “Have selected children share their strategies in the order you have decided on. One possible order for whole class discussion: Using objects. Drawing. Using numbers and symbols.” 

• Unit 3, Lesson 11, Solve Word Problems to 20, Session 2, Develop, students demonstrate conceptual understanding, procedural skill and fluency, and application of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem), 1.OA.4 (Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8), and 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making 10; decomposing a number leading to a ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums). Apply It, Spin and Find a Missing Number, “This activity gives children opportunities to make sense of and solve add-to word problems with a missing number. Tell children they will solve word problems on their own. Have each child take a turn spinning their shared spinner. Then have them independently pick a word problem on their workmat and fill in the box in the word problem with the number on the spinner. Give children number paths, number bonds, and counters to support their work. Have children tell their partners two ways they could use a number bond or a number path to solve the problem. Using a sheet of paper, have children write and solve one equation. Have children continue spinning and solving word problems, generating new numbers that will make new subtraction or addition equations for each scenario.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 the support of the teacher and independently throughout the modules. Examples include:

• Unit 2, Lesson 6, Teen Numbers, Session 2, Develop, Try-Discuss-Connect, Try It, students make sense of problems as they use the Act It Out strategy to solve word problems. “Read the problem aloud: A bin of 10 glue sticks is full. Another bin of glue sticks is not full. How many could be in both bins? Give two different answers. Use Connect to Culture to support engagement. Make Sense of the Problem Use Act It Out to help children make sense of the problem. Ensure that children understand the second bin is not full, meaning it cannot have 10 glue sticks. It could have any number of glue sticks from 1 to 9. Have children work independently on Try It.”

• Unit 4, Lesson 15, Tens and Ones, Session 3, Develop, Model It, students make sense of problems as they look at connections between different models. “If no child presented the model shown on the Student Worktext page (Image of 37 unit cubes shown as tens and ones and quick drawing shown as tens and ones), connect the written description, cubes, and quick drawing to the children’s models by having children identify how they represent the problem. ASK How did you write 37 as tens and ones? LISTEN FOR understanding that 37 has the same value as 3 tens 7 ones and 30+7. ASK How are the cubes and quick drawing the same? How do they each show 37? LISTEN FOR children to explain that both models show tens and ones and that they both show 3 tens 7 ones, which is 37.”

• Unit 6, Lesson 22, Shapes, Session 3, Develop, Try-Discuss-Connect, Try It, students make sense of problems as they use the Notice and Wonder routine to solve word problems. “Read the problem aloud: Ria built a castle using solid shapes. Find which solid shapes Ria used to build the castle. How can you describe the shapes? Make Sense of the Problem Use Notice and Wonder to help children make sense of the problem. Have children work independently on Try It.”

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 the support of the teacher and independently throughout the modules. Examples include:

• Unit 1, Lesson 5, Solve Word Problems to 10, Session 1, Explore, Investigate It, students reason abstractly and quantitatively as they use number bonds to write fact families. “How can you use number bonds to help write a fact family? This activity lets children use cubes and number bonds to help them write fact families. Tell children they will model related equations to show fact families. Have one child break apart their cube train into two smaller trains. Have children complete the number bond to match their unbroken and broken trains and place the trains next to the matching numbers. Tell one child to cover a train with their paper. Then have pairs write the equations that model the hidden train. For example, if a child shows a 3, 4, 7 number bond and covers the 7-cube train, they write 3+4=7 and 4+3=7. Have them repeat, covering each train. ASK How do you identify the numbers that are part of a fact family? LISTEN FOR children to explain that in a fact family, the two lesser numbers are equal to the whole and the whole minus one part is equal to the other part. Have pairs put their trains back together and the other partner breaks a train apart in a different way. Have them repeat the activity and discuss.”

• Unit 3, Lesson 13, Collect and Compare Data, Session 1, Explore, Discover It, students reason abstractly and quantitatively as they sort objects into categories to solve problems. “Show children 20 buttons that are arranged randomly. Ask: What questions can you ask about the buttons? What attributes might you look for?As children share their questions about the buttons, write them on the board. The questions may be about size, shape, color, or number of holes. Have children choose one of the questions and use the collection of buttons to answer it. Have volunteers report their results to the class, showing how they answered a question from the chart.”

• Unit 5, Lesson 20, Add Two-Digit and One-Digit Numbers, Session 3, Develop, Connect It, students reason abstractly and quantitatively as they combine ones first and then combine tens when adding a two-digit number to a one-digit number, and connect to the base-ten blocks and the action shown on a 100 chart. Facilitate Whole Class Discussion, “Help children make sense of how first combining all the ones and then adding tens and ones can help them add one-digit and two-digit numbers by comparing their models to the base-ten blocks and action shown on the 100 chart in Model It. After individual think time, have children share and discuss their ideas. Children may also use pictures, numbers, or words to record ideas. ASK How is this way of adding different from making a ten? How is it the same? LISTEN FOR understanding that instead of adding ones to the two-digit number to make it a tens number, you take ones away from the two-digit number to make it a tens number. In both cases, you break apart one of the addends and you find the total by adding a tens number with another number. ASK Why is changing the equation to add to a tens number a helpful strategy? LISTEN FOR descriptions of how children can quickly add to tens numbers or add tens to any number. Children's descriptions may include using a 100 chart as support.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 8, Make a Ten to Add, Session 1, Explore, Build Concepts, students justify their thinking as they share what it means to make a ten using words, numbers, and pictures. “What does it mean when you say make a ten? This graphic organizer guides children to construct their ideas about the meaning of the concept make a ten. 1. Ask children what the word make means. Encourage them to share how they use this word in their daily lives. Have children use words, numbers, and pictures to show what they already know about how they can make a ten. Have children share their examples with a partner and look for similarities in their thinking. For many children this will include different representations of partners for 10. 2. Check understanding by having children restate the problem in their own words. Have them work with a partner to answer problem 2. For additional support, provide counters and ask them to model each set of addends. Encourage children to use the phrase make a ten to explain their choices. Read the problem aloud: Find all the addends with a total of 10. Circle.”

• Unit 3, Lesson 12, Solve Compare Problems, Session 2, Develop, Discuss It, students justify their thinking and critique the reasoning of others as they share their own thinking and discuss another student’s strategy. Support Partner Discussion, “After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions such as: What does more mean? How can finding the difference help you solve the problem? Common Misconception If children associate more with addition and fewer with subtraction, then have them use counters to model and solve compare problems. Have them connect their model to each part of the problem and describe what is known and what is unknown. Reinforce that compare problems may be solved with addition or subtraction, so it is important to understand the math action.” Facilitate Whole Class Discussion “Have selected children share their strategies in the order you have decided on. ASK How does [child name]’s model show how to solve the problem? LISTEN FOR a variety of methods. For example, some children may use matching. Others may count on from 5 to 9. ASK We compared apples to pears by saying "How many more?" How can we compare pears to apples? LISTEN FOR children to use the words less or fewer. GUIDE CHILDREN to Compare and Connect the strategies.”

• Unit 4, Lesson 16, Numbers to 120, Session 2, Develop, Model It, students justify their thinking and critique the reasoning of others as they connect the 100 chart to the models. “If no child presented the model shown on the Student Worktext page, connect the 100 chart to the children’s models by having children identify how it represents the problem. ASK What part of the problem does the circled number represent? What does the highlighted number represent? LISTEN FOR children to say that the circled 88 represents the 88 seeds the small roadrunner eats. The highlighted 98 is 10 more than 88, so it represents the seeds the large roadrunner eats. ASK What do you notice about where 88 and 98 are on the chart? LISTEN FOR children to note that 98 is directly below 88 on the chart.”

• Unit 5, Lesson 20, Add Two-Digit and One-Digit Numbers, Session 3, Develop, Discuss It, students justify their thinking and critique the reasoning of others as they share their own thinking and discuss another student’s strategy. Support Partner Discussion, “After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions, such as: What are some different ways you could break apart these numbers? Facilitate Whole Class Discussion Have selected children share their strategies in the order you have decided on. ASK How does [child name]'s strategy show finding 37+8? LISTEN FOR an explanation of how the strategy was used to find the total of 37 and 8 by breaking apart either 8 or 37. ASK How could you predict if you will make a new ten when you add a two-digit number and a one-digit number? LISTEN FOR an explanation of how children identify if the ones will total 10 or more. For example, some children may think of number partners for 10. Guide children to Compare and Connect the strategies.”

• Unit 6, Lesson 26, Measure Length, Session 5, Analyze It, students justify their thinking and critique the reasoning of others as they read two different approaches to the same problem. “Read the problem aloud: Boom and Buzz both measured the length of the marker. Do you agree with Boom, Buzz, or both? Why? Tell children to use what they know to decide who they agree with and to circle that character. Have them use numbers, words, or drawings to show their thinking.” Facilitate Whole Class Discussion, “Guide children to share how they made their choice. Have them turn and talk to share ideas before discussing as a class. ASK Do you agree with Boom, Buzz, or both? Why? LISTEN FOR descriptions of how Boom correctly used same-size squares to measure the marker. Buzz used paper clips of different sizes to measure the marker.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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, Number Partners to 10, Session 2, Develop, Connect It, with teacher support, students describe what they do with the model(s) and how it relates to the problem situation as they use pictures, numbers, and words to break apart 10 into two groups. Facilitate Whole Class Discussion, “Help children make sense of how the bond with counters is used in Model It to break apart 10 into two groups by comparing it to their own model or strategy. After individual think time, have children share and discuss their ideas. Children may also use pictures, numbers, or words to record ideas. ASK How did you represent number partners for 10? How does Model It represent number partners for 10? LISTEN FOR descriptions of how children represented number partners for 10. Children explain that in Model It 10 counters moved from the large box to the two small boxes and the small boxes show number partners for 10. ASK How can using a bond with counters help you find number partners for 10? LISTEN FOR children to say that they can put 10 counters in the large box and then move some to one small box and the rest to the other small box to represent number partners for 10.”

• Unit 2, Lesson 8, Make a Ten to Add, Session 2, Develop, Connect It, students model with mathematics as they examine how a 10-frame model shows the solution to a word problem. “Facilitate Whole Class Discussion Help children make sense of how to represent the problem and make a ten to add by examining the 10-frame model in Model It and comparing it to their own. After individual think time, have children share and discuss their ideas. Children may also use pictures, numbers, or words to record ideas. ASK How did you show 8 and 5? How does Model It show 8 and 5? LISTEN FOR descriptions of how children showed 8 and 5 accompanied by explanations that 8 is shown with red counters in the 10-frame and 5 is shown with 2 yellow counters in the 10-frame and 3 below it. ASK How can a 10-frame help you show making a ten to add? LISTEN FOR children to note that when a 10-frame is full, they know they have made a ten. Then they can use counters outside of the 10-frame to show and add the number that is left over, and find the total.”

• Unit 5, Lesson 18, Add and Subtract Tens, Session 4, Refine, Make Connections, Problem 1, students put the problem in their own words and identify important information in the problem as they apply and explain their strategies for adding and subtracting tens from two-digit numbers. “Read the Example problem aloud and have children compare the two problems modeled on the 100s chart. Review that you can understand a problem better when you can say how that problem is like another problem you have solved.” Problem: “Add and subtract 30. 45+30= ___, 80-30= ___”, Make Connections, “57+30= ___.”

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 2, Lesson 9, Use a Ten to Subtract, Session 3, Develop, Connect It, students choose tools strategically with teacher support as they use 10 as a benchmark number to subtract using a number path and a number bond. “Facilitate Whole Class Discussion Help children make sense of using 10 as a benchmark number to subtract by comparing the number path and number bond in Model It to their own work. After individual think time, have children share and discuss their ideas. Children may also use pictures, numbers, or words to record ideas. ASK How did you show 13 and 4? How does Model It show 13 and 4? LISTEN FOR descriptions of how children showed a total of 13 and modeled subtracting 4. Listen also for explanations of how Model It shows 13 with shading on a number path and uses moves to show subtracting 4, one move that goes back 3 to get to 10 and another move that goes back 1 to finish subtracting. ASK How can using a number path help you subtract? LISTEN FOR children to note that a number path can show how to subtract in parts. The first move shows subtracting one part to get to 10. The next move shows subtracting the rest.”

• Unit 4, Lesson 16, Numbers to 120, Session 3, Develop, Apply It, More or Less, students choose appropriate strategies that help develop their mathematical knowledge as they use a hundreds chart to find 10 more or 10 less than any number with 120. “This activity guides children to see connections between using cubes and using a 100 chart to find 10 more and 10 less. Choose a volunteer to help demonstrate the activity. Have the child place their counter on any number on the 100 chart and then build the number with the 10-cube trains and loose cubes. Then have them write the number in the middle space of one of the pieces of the 100 chart on their More or Less Workmat. Next, have the child spin the spinner to decide whether to find the number that is 1 more, 1 less, 10 more, or 10 less. Then have them build the number with the blues and move their c counter to show the new number. If the spin would force the counter off the board, they skip a turn. Finally, have the child write the new number in the space on the 100 chart piece that represents 1 more, 1 less, 10 more, or 10 less. Have children take turns spinning the spinner, building new numbers, moving their counter, and recording their turn on their More or Less Workmat. After recording six turns, have children swap their More or Less Workmat with a partner. Ask children to complete all of the remaining spaces in their partner’s 100 chart pieces. Have pairs work together to check the numbers in their pieces of the 100 chart.”

• Unit 6, Math In Action, Craft a Kite, Session 1, Apply It, students choose appropriate tools and/or strategies that will help develop their mathematical knowledge as they choose between pattern blocks and geoboards to create kite shapes. “Have children choose a kite sail shape and plan their design, using one copy of the kite sail and/or tools such as pattern blocks or geoboards. Then have them draw and color the shapes on the second copy. As children begin working, circulate and ask questions to deepen thinking. How did you choose your sail shape?  What tools could help you plan and draw shapes on your kite sail? After children have completed their individual kite designs, have them work with one or three partners to build a big kite by gluing or taping their individual kites together. As children work in their groups, circulate and ask questions to deepen thinking. What do you notice about the small kites in your group? What do you notice about your big kite? Allow for multi-modal responses as needed, including drawings, words, numbers, speech, and/or gestures.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 support of the teacher and independently throughout the units. Examples include:

• Unit 2, Lesson 6, Teen Numbers, Session 1, Explore, Investigate It, students attend to precision as they investigate how organizing objects can help them count them. “How can organizing objects into groups help you count? This activity lets children investigate how organizing loose objects into groups can help when counting. Have each small group find a table. Confirm children notice the objects are not organized. Ask them to think how organizing into groups might make them easier to count. Have children count the objects. Encourage them to organize in ways that make sense to them. Once children agree on the total, have them break apart the groups and move to the next table to repeat. Encourage them to try different ways to organize and count. For example, if they count by 2s, have them try 5s or other ways. Have them draw how they organized and write how many. Encourage them to circle each of their groups. Have children reflect on which ways were most helpful.”

• Unit 3, Lesson 14, True and False Equations, Session 2, Apply It, students practice attending to precision by modeling two equations to determine if they are equivalent or not. Students are given a set of equation cards. “Model the quantity on each card. Copy the cards on the blanks [in the student book] Trace the = if the equation is true. Cross out the = if the equation is false.”

• Unit 4, Lesson 16, Numbers to 120, Session 4, Refine, Make Connections, students attend to precision, in connection to grade-level content, as they work with the support of the teacher when explaining their strategies for finding 10 more or 10 less than a number. “Facilitate Whole Class Discussion. Read the Example problem aloud and have children describe the cube model. Remind children that using math words and describing words when they can explain can help others understand their ideas better. ASK How do the cubes show 54? LISTEN FOR children to say that 54 is shown with 5 tens and 4 ones. ASK How do the cubes show 10 less? LISTEN FOR children today that one of the tens is crossed out, which shows subtracting 1 group of 10. ASK How can you use the cubes to solve the problem? LISTEN FOR children to say that they can count the remaining cubes to find 10 less than 54. Have children fill in the chart and then solve the problem. ASK How does the missing number in the 100 chart help you solve the problem? LISTEN FOR children to explain that in a 100 chart, 10 less than a number is directly above the number. The missing number, 44, is 10 less than 54.”

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

• Unit 1, Lesson 2, Add and Subtract Within 10, Session 2, Develop, Discuss It, students attend to the specialized language of mathematics as they are encouraged to use the word add when discussing their solutions. “Support Partner Discussion After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions, such as: How can acting out a problem help you? Encourage children to use the word add as they discuss their solutions. Facilitate Whole Class Discussion Have selected children share their strategies in the order you have decided on. ASK How does [child name]'s model show starting with 5 and adding 4 more? LISTEN FOR an explanation of how the child first showed 5 and then 4 more. Guide children to Compare and Connect the strategies.”

• Unit 2, Lesson 10, Doubles and Near Doubles, Session 3, Develop, Discuss It, students attend to the specialized language of mathematics as they explain how they added using the language counting all, counting on, making a ten, or using known facts. “Support Partner Discussion After children have worked independently on Try It, have them respond to Discuss It with a partner. If children need support in getting started, prompt them to ask each other questions such as: How can you use what you know to help you add? Facilitate Whole Class Discussion Have selected children share their strategies in the order you have decided on. ASK How does [child name]'s strategy show finding the total number of marbles? LISTEN FOR explanations of how different strategies can be used to find 7+6. Encourage children to describe the meanings of the objects, drawings, or equations they used, focusing on how their models support strategies such as counting all, counting on, making a ten, or using known facts. Guide children to Compare and Connect the strategies.”

• Unit 6, Lesson 26, Measure Length, Session 5, Deepen Understanding, students attend to the specialized language of mathematics by explaining why one method is better for measuring than the other. “When strategies have been shared, discuss how Boom described the length of the marker. Understanding that a length measurement involves a number and a unit shows that children can attend to precision in the language they use. ASK How did Boom describe how long the marker is? LISTEN FOR understanding that Boom said how many units were used to measure the marker and what the units were. ASK Why is it important to include the name of the unit when you say a measurement? LISTEN FOR understanding that if you do not include the name of the unit you use, then other people will not know how long the object is. Prompt children to explain how to describe the lengths of objects they have measured.”

The materials reviewed for i-Ready Classroom Mathematics Grade 1 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 1, Lesson 5, Solve Word Problems to 10, Session 1, Explore, Discover It, students look for and make use of structure as they notice connections among equations. “What does it mean for equations to be in a family? This activity lets children notice connections among equations as they find equations that go together. Give each child a card from the Equation Cards. Have children move around the room and try to find three other equations that go with the equation on their card. Children should explore and determine the groups of equations on their own without explicit instruction on which equations make a family. If children form groups with only addition or only subtraction equations, encourage them to notice connections among the other equations.”

• Unit 3, Lesson 14, True and False Equations, Session 1, Explore, Build Concepts, students look for and make use of structure as they find addends that equal 11. “What does it mean for quantities to be equal? This graphic organizer guides children to construct their ideas about the meaning of the concept equal. 1. Ask children what the word equal means. Encourage them to share how they use this word in their daily lives. Have children use words, numbers, and pictures to show what they already know about quantities being equal. Have children share their examples with a partner and look for similarities in their thinking. For many children this will include different representations of equal quantities. 2. Read the Problem Aloud: Find the addends that are equal to 11. Circle. Check understanding by having children restate the problem in their own words. Have children work with a partner to answer problem 2. For support, provide counters or connecting cubes and ask them to model each addition problem and the number 11. Encourage children to use the word equal to explain their choices.”

• Unit 5, Math In Action, Donate Pet Toys, Session 1, Apply It, Donate Pet Toys Activity, students look for and make use of structure as they add two-digit numbers. “A pet store gives pet toys to an animal shelter. What toys would you choose for the pets? Between 50 and 100 pets live at the animal shelter at a time. You can choose up to 36 of each toy. Write how many of each toy you want. Find the total number of toys.”

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 8, Make a Ten to Add, Session 1, Explore, Discover It, students look for and express regularity in repeated reasoning as they investigate patterns in a 10-frame. “This activity lets children investigate patterns by filling a 10-frame to make a ten when one of the addends is given. Invite children on an imaginary bus ride. Explain that the chairs represent seats on a bus. Ask: How many people can ride this bus? [10] Have 9 children sit on the chairs to represent 9 riders. Have 4 more children line up to represent more riders who want to get on the bus. Ask children to explain whether 4 more riders will be able to get on the bus and find a seat. Repeat with 7 and 8 children sitting on the chairs. Each time have 4 additional riders who want to get on the bus. Ask children to explain whether the additional riders will be able to find a seat.”

• Unit 4, Lesson 16, Numbers to 120, Session 2, Develop, Apply It, students look for and express regularity in repeated reasoning as they see patterns in using a 100 chart to find 10 more and 10 less. “Facilitate Whole Class Discussion. Guide children to share their understanding of finding 10 more and 10 less than a number on a 100 chart. ASK How did you use a 100 chart to find 10 more or 10 less than a number? LISTEN FOR children to explain their strategies. Some children may have counted on 10 to find 10 more and counted back to find 10 less. Other children may have realized that on a 100 chart, you can look directly below a number to find 10 more and directly above the number to find 10 less. ASK Look at the numbers you circled and the numbers you colored on the 100 chart. What patterns do you see? LISTEN FOR children to say that when comparing the numbers they circled to the numbers they colored, the first digit changes and the second digit is always the same. Children may note that the first digit increases by 1 as you go down the chart.”

• Unit 6, Math in Action, Craft a Kite, Session 1, Apply It, Craft a Kite, students look for and express regularity in repeated reasoning as they make noticings about their small kite and big kite. “Have children choose a kite sail shape and plan their design, using one copy of the kite sail and/or tools such as pattern blocks or geoboards. Then have them draw and color the shapes on the second copy. As children begin working, circulate and ask questions to deepen thinking. How did you choose your sail shape? What tools could help you plan and draw shapes on your kite sail? Reflect and Revise After children have spent some time working independently, have them take a detective walk to examine problem solving in progress. After children finish their detective walk, have them continue to work on the problem. Remind them to revise, adjust, or add to their work, using what they learned. After children have completed their individual kite designs, have them work with one or three partners to build a big kite by gluing or taping their individual kites together. As children work in their groups, circulate and ask questions to deepen thinking. What do you notice about the small kites in your group? What do you notice about your big kite? Allow for multi-modal responses as needed, including drawings, words, numbers, speech, and/or gestures. Facilitate Whole Class Discussion Have children turn and talk with their partner(s) to share their strategies for making their individual kites and putting their small kites together into a big kite. Then ask several children to share their kites and strategies with the class. ASK How did you put together your small kites to make the big kite? How is your strategy for your small kite the same as the strategy for your big kite? How is it different? LISTEN FOR children to describe their process, such as using blank copies of the sail shapes and moving the kites around until the group agreed on the best design.”