Kindergarten - Gateway 2

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 2, Lesson 4, Count, Show, and Write Numbers to 5, Session 2, students develop conceptual understanding of K.CC.5 (Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.) Try-Discuss- Connect, How can numbers be used to show how many?, Try It, “Read the problem aloud: There are 4 chickens. The cards show the numbers 0, 1, 2, 3, 4, and 5. How can you tell which number shows how many chickens?” Make Sense of the Problem, “Use Notice and Wonder to help children make sense of the problem. Ensure children understand that each card shows a different number.” Discuss It, Support Partner Discussion, “Have children respond to the Discuss It question with a partner: How can you tell which number is the 4?” Facilitate Whole Class Discussion, “Have two or three selected children share their strategies in the order you have chosen. ASK How did [child name] figure out which number is the 4? LISTEN FOR an explanation that the number of dots counted on the cards tells the number. Guide children to Compare and Connect the strategies.” Connect It, “Help children recognize that each card shows both a quantity of dots and the number that can be used to represent that quantity. ASK [point to the 2 card] How can I tell what number is on this card? LISTEN FOR children to count the 2 dots on the card. ASK [point to the 0 card] How many does this card show? LISTEN FOR children to identify that there are no dots on the 0 card, so it represents having no objects, or zero.”

• Unit 5, Lesson 18, Compose and Decompose 6 and 7, Session 1, students develop conceptual understanding of K.OA.3 (Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation. (e.g., 5=2+3 and 5=4+1)). Explore, Discover It, “What do you know about the numbers 6 and 7?” “This activity lets children think about where they encounter the numbers 6 and 7 in their daily lives. Have children do a scavenger hunt to find examples of the numbers 6 and 7. Encourage children to look for the numbers and for groups of 6 and 7 objects, such as 6 dry erase markers. When children have found two or three examples, have them meet at the rug for a discussion. Ask: Where did you discover 6 and 7 in the classroom? Show 6 counters in one 10-frame. Place 5 red counters in the top row and 1 yellow counter in the bottom row. Ask: How does 6 compare to 5? To 10? Show 7 counters in another 10-frame by placing 5 red counters in the top row and 2 yellow counters in the bottom row. Ask: How does 7 compare to 5? To 10?”

• Unit 7, Lesson 25, Compose and Decompose Teen Numbers with Symbols, Session 1, students develop conceptual understanding of K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18=10+8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.) Discover It, “How can you represent teen numbers in different ways? This activity allows children to explore three different ways to represent teen numbers. Project one of the Teen Number Model Cards sheets on the board. Draw children’s attention to the three different representations and ask: What do you notice? Describe what you see. When children have identified that all three representations show the same number, have them say the number. Write the number in the blank space. Put children into groups of 3 or 4. Give each child a Teen Number Model Cards sheet, making sure each child in a group has a sheet for a different number. Have children work together to decide what number they have on their sheet and write the number in the blank space.” Facilitate Whole Class Discussion, “To allow children an opportunity to discuss their answers before sharing with the class, have partners turn and talk. ASK What number is shown on your sheet? How do you know that each part of the sheet represents the same number? LISTEN FOR (for example) an explanation that the 10-frames show 10 ones and 2 more ones, the connecting cubes show 10 ones and 2 more ones, and the numbers and symbol show 10 ones and 2 more ones, so each representation shows the same number, 10 ones plus 2 ones is 12, so all the models show 12.”

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

• Unit 4, Lesson 15, Find Number Partners for 10, Session 1, students independently engage with K.OA.4 (For any number from 1 to 9, find the number that makes 10 when added to the given number…). Discover It, “Break the cube trains into same-color parts and give one part to each child. Instruct children to find a partner who has a train of a different color that makes 10 when it is joined with their train. Have partners prove that their trains make 10. Have children find another partner whose train makes 10 with theirs.” Session 4, Apply It, “Have children choose number partners for 10 (other than 5 and 5) and write the numbers in the equation. Then have children use the triangular models to show the number partners in as many different ways as possible. Instruct children to choose two different colors to show the number partners for 10.”

• Unit 5, Lesson 17, Count Within 100, Session 4, students independently engage with K.CC.2 (Count forward beginning from a given number within the known sequence (instead of having to begin at 1).) Apply It, “How can you count on from a number of objects? This activity allows children to practice counting on by 1s as they count objects. Have children draw between 1 and 20 beads at the top of the page. Then have them write the number of beads they drew. Have children circle any number of the other groups of beads. Tell children to start with the number of beads they drew and then count on the number of beads in the group or groups they circled. After children have finished counting, have them find a partner and share their work. Have partners check each other’s counting.”

• Unit 6, Lesson 20, Add Within 10, Session 4, students independently engage with K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings*, sounds, acting out situations, verbal explanations, expressions, or equations.) Apply It, “How can you show a number in different ways? This activity allows children to see connections between equations with the same total and different number partners. Tell children they will draw shapes and write equations to explore different ways to make a number. Have children write 7, 8, 9, or 10 in the box at the top of the page. Then have children show different ways to make their target number by drawing shapes on the socks and writing the corresponding equation.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 3, Lesson 10, Add and Subtract Within 5, students build procedural skills and fluency of K.OA.5 (Fluently add and subtract within 5) with teacher support. Session 2, Differentiation, Reteach, “Use with children who need support in connecting stories to expressions.” “Use addition and subtraction cards with expressions within 5. Choose two cards and place them face up for children to see. Ask children to read each card aloud and tell whether the symbol on the card shows addition or subtraction. Then have them identify the number you start with and how many are added (or subtracted). Tell a story based on one of the cards. Have children identify which card matches the story. Repeat with different cards.” Session 3, Differentiation, Reteach, “Use with children who need support in finding the values of expressions”, “Choose an addition or subtraction card and have children read it aloud, for example: 1 plus 3. Have children identify the first number and use counters to show that number. Have them identify the symbol and tell if they will add or subtract. Next, children identify the second number and add or take away that many counters. Finally, have children find the value of the expression by asking, What is 1 plus 3? [4] Repeat using other addition and subtraction cards.”

• Unit 3 Lesson 7, Add within 5, students build procedural skill and fluency with guided teacher support with K.OA.5 (Fluently add and subtract within 5). Session 3, Develop, Centers, Differentiation, and Practice, Differentiation, “Have each child place 1 yellow counter on their 5-frame. Ask: How many counters are on your 5-frame? [1] Tell children to add 1 red counter to their 5-frame. Ask: How many counters are on your 5-frame now? [2] Say: 1 yellow counter and 1 red counter is 2 counters in all. 1 and 1 is 2. Tell children to add 1 more red counter to their 5-frame. Ask them to say how many there are of each color counter and how many there are in all. Repeat up to 1 and 4 is 5. Ask children to repeat the exercise starting with 2, 3, and 4 yellow counters.”

• Unit 6, Lesson 21, Subtract Within 10, students build procedural skill and fluency with guided teacher support with K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings*, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.) and K.OA.5 (Fluently add and subtract within 5). Session 3, Develop, Apply It, Flip and Solve Activity, How can you model and solve subtraction problems? This activity guides children to practice subtracting within 10. Instruct children to place the set of cards facedown in a line. Have one child in each group turn over a card and place it in the first space on the game board. Then have them count out that many counters from the cup. Have the other partner roll the number cube and place it in the second space on the game board to make a subtraction problem. The second partner takes away that many counters from the first partner and returns them to the cup. The first partner records the equation on their workmat and reads or describes it to their partner. The second partner checks that the subtraction equation matches the subtraction they modeled with the counters. The first partner keeps the remaining counters, and places the card back in the line facedown. Partners switch and repeat the process until all equation frames on their workmat are filled. The partner with the most counters wins the game.”

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

• Unit 3, Lesson 10, Add and Subtract Within 5, students independently demonstrate procedural skills and fluency of K.OA.5 (Fluently add and subtract within 5). Session 3, Centers, Differentiation, and Practice, Extend, “Use with children who quickly add and subtract within 5. Use addition and subtraction cards with expressions within 5. Arrange children in pairs. Give each pair a pile of number cards, facedown. Place 10 of the addition and subtraction cards in a large grid, face up, on the table. Turn over the top card from the number card pile. Children pick up as many addition and subtraction cards as they can that make that number. Repeat, replenishing the faceup grid to have 10 expression cards as needed.” Session 4, Apply It, Tell a Story Activity, “Have children circle one addition problem on the page that they would like to tell a story about. Ask children to use the picture to think of a story to match the problem they circled. Have them solve the problem. Then have children circle one subtraction problem and repeat the process.” 

• Unit 5, Lesson 17, Count Within 100, students develop procedural skill and fluency as they count up to 100 objects. K.CC.1 (Count to 100 by ones and tens.) Session 2, Centers, Differentiation, and Practice, Student-led Practice, “Children strengthen their understanding of counting up to 100 objects by continuing the activity in a center.” Session 2, Apply It, Cover and Count Activity, “How can you count a large group of objects? This activity guides children to count a large group of objects. Tell children that they will count more large groups of objects. Tell one child in each pair to place the index card on their workmat so that some buttons are hidden. Explain that children should make sure no buttons are partially covered. Ask the other child to count the buttons they see. Then have their partner count to check. Have children switch roles and repeat. Encourage children to think of different ways to put their index card on their workmat, such as covering lots of buttons or only a few buttons, or covering whole columns or only parts of whole columns of buttons.” 

• Unit 6, Lesson 20, Add Within 10, Interactive Tutorials, Add Within 5, students develop procedural skills and fluency of  K.OA.5 (Fluently add and subtract within 5). This 17-minute tutorial begins with chickens sitting on a roost. “There are 3 chickens and 1 more chicken joins them. What is 3 and 1 more?” Choices provided are 5, 4, and 3. 

• Unit 6, Lesson 21, Subtract Within 10, Fluency and Skills Practice, Subtracting Within 10, students develop procedural skill and fluency as they subtract within 10. K.OA.5 (Fluently add and subtract within 5.)  Directions, “Have children write the number left to complete the equations. Then have them read each equation and explain how the subtraction and drawing are related.” Problem 1, “ 9-4=__.”  An image of nine triangles with four crossed out is on the student workmat.

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 math include:

• Unit 3, Lesson 7, Add Within 5, Session 3, Develop, the teacher supports students as they add and subtract to solve word problems within 10. K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.) Try-Discuss-Connect, “How can you add more and find the total?” Try It, “Read the problem aloud: There are 2 meatballs in the pan. Then more meatballs are added. How many meatballs are in the pan now? Children will draw 1, 2, or 3 more meatballs.” Make Sense of the Problem, “Use Say It Another Way to help children identify what they know and what they need to find out. Have children work independently to find their total.” Discuss It, Support Partner Discussion, “Have children respond to the Discuss It question with a partner: How did you find the total number of meatballs in your pan?” Facilitate Whole Class Discussion, “Have two or three selected children share their strategies in the order you have chosen. ASK How does [child name]’s strategy help them find how many meatballs in all? LISTEN FOR an understanding that all the strategies involve counting to find how many in all. Help children recognize that all their totals are more than the starting number, 2. Guide children to Compare and Connect the strategies.” Connect It, “ASK [Write 3, 4, and 5 on the board.] These are totals you recorded. How do the totals compare to the number of meatballs at the start, 2? LISTEN FOR children to recognize that their totals (3, 4, and 5) are all more than 2.”

• Unit 5, Lesson 18, Compose and Decompose 6 and 7, Session 2, Develop, students independently demonstrate decomposing numbers less than or equal to 10 to solve problems in a real-world context. K.OA.3 (Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation). Try-Discuss-Connect, “How can you show number partners for 6?” Try It,  “Read the problem aloud: The game mah-jongg has tiles with numbers and colorful designs. This tile breaks 6 apart into 2 and 4. How else could you break 6 into two parts? Use Connect to Culture to encourage children to make personal connections.” Make Sense of the Problem, “Use Say It Another Way to help children make sense of the problem. Have children work independently on the Try It.” 

• Unit 6, Lesson 22, Add and Subtract to Solve Word Problems, Session 2, Develop, students independently work on a routine problem and draw to represent addition and subtraction situations and solve story problems for numbers up to 10, K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10). Student Worktext, Problem 1 “There are 4 caterpillars. 4 more join them. How many caterpillars are there now?”

Examples of non-routine applications of math include:

• Unit 1, Math in Action, Imagine a Rainforest gives students the opportunity to independently demonstrate application of K.MD.3 (Classify objects into given categories…) through non-routine problems. Session 2, Develop, Apply It, “Tell children they will sort their cards into two or three groups and then tell the sorting rule(s) they used. Prompt children to start thinking about their plans by asking: How can you sort your cards? Which cards go in each group? Allow children adequate time to explore different ways of sorting their cards. After children have spent some time working independently, have them turn and talk with a partner about how they have sorted the cards so far. Encourage partners to give each other feedback.  Next, have children take a detective walk to examine problem solving in process. 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.”

• Unit 3, Lesson 8, Two-Dimensional Shapes gives students the opportunity to independently demonstrate application of K.G.1 (Describe objects in the environment using names of shapes, and describe relative positions of these objects…). Session 4, Refine, Apply It. “How can you put shapes together to draw an object? This activity allows children to draw variations of flat shapes and to describe the drawings using shape names and positional language. Have children think of an object that they can draw using only circles, squares, rectangles, and triangles, such as a truck, a rocket, or a robot. Instruct children to draw the object on the page using only circles, squares, rectangles, and triangles. Let children know that they can draw as many shapes as needed, in any size and turned any way. Have children describe their drawing to a partner by naming each shape in the drawing and using positional language. Have partners try to duplicate each other’s drawings based on their descriptions.”

• Unit 4, Math in Action, Plan a Playground gives students the opportunity to independently demonstrate application of K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g. claps, acting out situations, verbal explanations, expressions, or equations.) through non-routine problems. Session 2, Develop, Apply It, “Explain to children that they will use solid shapes or objects to build 10 pieces for their playground. Allow children to independently explore different ways of building combinations of 10 pieces. After some time for individual exploration, have children turn and talk with a partner about the type and number of pieces they built. Encourage partners to give each other feedback on their pieces and playgrounds.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 6, Three-Dimensional Shapes and Weight, Session 3, Develop, students demonstrate application of K.MD.A (Describe and compare measurable attributes). Centers, Differentiation, and Practice, Independent Practice, students are shown pairs of objects (ex. a pair of scissors and a button). “Have children circle the heavier object in each pair. Then have them cross out the lighter object in each pair.” Differentiation, “Choose two objects that are different in weight. Have children decide which object is heavier and which object is lighter by having them hold the objects. one in each hand. Have children say:___ is heavier than ___. Then have children say: ___ is lighter than ___.”

• Unit 4, Lesson 15, Find Number Partners for 10, Session 5, Refine, students develop procedural skill and fluency as they refine their understanding of the number partners to 10. K.OA.4 (For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.) Centers, Differentiation, and Practice, Student Worktext, “Have children draw to complete the 10-cube trains. Then have them write an equation for each 10-cube train.” Three cube trains are provided with space for the student to write the equation represented. 

• Unit 6, Lesson 20, Add Within 10, Session 3, Develop, students develop conceptual understanding of K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings*, sounds, acting out situations, verbal explanations, or equations.) and K.OA.5 (Fluently add and subtract within 5). Centers, Differentiation, and Practice, Student Worktext, “Have the children draw dots on each domino to show possible number partners for the total. Then have them write an equation that represents the dots on each domino.”

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 3, Sort and Count Objects, Session 4, Refine, students demonstrate conceptual understanding, procedural skill and fluency, and application of counting objects to tell “how many” with K.CC.5 (Count to answer “how many” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.) Apply It, Animal Sort Activity, “This activity allows children to practice sorting by having them sort animals. Tell children to choose one category they could make with some of the animals. Encourage them to choose a new type of sorting rule. For example, if they sorted by size in the previous activity, encourage them to sort by a different attribute. Have children circle all the animals that fit their category and then count the animals.”

• Unit 5, Lesson 19, Compose and Decompose 8 and 9, Session 2, Develop, Try-Discuss- Connect, students develop conceptual understanding through application of K.OA.3 (Decompose numbers less than or equal to 10 in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5=2+3 and 5=4+1)). Using their counters, connecting cubes, and 10-frame workmat in their math toolkit, students will solve the following problem. The materials state, “Make sense of the problem. There are 8 skaters. They all wear winter hats. Each hat is either red or blue. How many could be red? How many could be blue? Show how you know. Have children color some hats red and the rest of the hats blue. Then have them fill in the equation.” 

• Unit 6, Math in Action, Design a Dance, Session 1, students develop procedural skill and fluency, and conceptual understanding with K.OA.A (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from). Apply It, Plan Two Dance Groups Activity, “Explain to children that the workmat shows the stage. They will use the stage to show where the dancers start and how they are grouped. They will also complete the equation to show the groups.” “After children have spent some time working independently, have them turn and talk with a partner about where they will start each group and dancer on the stage. Next, have children 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. Many children will use counters on the workmat. Allow for other modes of expression, such as drawings, gestures, and spoken or written descriptions.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 1, Lesson 3, Sort and Count Objects, Session 4, Refine, Make Connections, students make sense of problems as they brainstorm different strategies to sort the objects. “How can you sort in different ways? This activity allows children to explore different ways to sort animals. Direct children's attention to the animals on their workmat. Have children brainstorm different ways they could sort the animals. Have children find one category they could make with some of the animals. Have them circle all the animals that fit their category, then count the animals in the category. Have them explain and compare their category with a partner’s to see if they sorted in a similar way.”

• Unit 4, Lesson 12, Compare Numbers to 10, students analyze and make sense of problems, and use a variety of strategies to show how many bears there are. Session 2, Try-Discuss- Connect, “Read the problem aloud: ‘Count the bears. How can you show how many bears there are?’ Use Connect to Culture to encourage children to make personal connections. Use Notice and Wonder to help children make sense of the problem.” Session 3, Try-Discuss- Connect, “Read the problem aloud: Find a cloud that has a number greater than the shaded number on the number path. Use Say It Another Way to help children make sense of the problem. Ensure children understand there is more than one correct answer.” 

• Unit 7, Math in Action, Build for Birds, Session 3, Collect, Organize, and Interpret Data, students make sense of problems as they sort and analyze data. “Read this new problem aloud: ‘The Nature Club is building a birdhouse for groups. We will choose the number of bird families for the birdhouse. How can we use data to help us?’ Use Say It Another Way to help children make sense of the problem. Discuss ideas for choosing the number of bird families with the class. Acknowledge all ideas and explain that their designs will help us choose the number of bird families. They will choose by answering: How many bird families can live in the birdhouse you designed? Have children circle [in their student pages] the number of bird families that can fit in their birdhouse. Have them write the number and then show the number using short lines, or tally marks. Explain that each tally mark stands for one bird family. Children trace over the first ten lines and then draw some more lines to show their teen number. Then have children respond to the discussion question with a partner: What is the same? What is different? Children may notice that they used different numbers.”

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 2, Lesson 6, Three-Dimensional Shapes and Weight, Session 2, Develop, Try-Discuss- Connect, Discuss It, students reason abstractly and quantitatively as they discuss strategies used to describe how they know shapes can roll or stack. Support Partner Discussion, “Have children respond to the Discuss It question with a partner: What other shapes can roll? What other shapes can stack? Instruct children to draw another shape that can roll under the ball and another shape that can stack under the box. Facilitate Whole Class Discussion Have two or three selected children share their strategies. ASK How do you know the shape you drew can roll? How do you know the shape you drew can stack? LISTEN FOR children to talk about testing shapes or to refer to experiences with objects that roll and stack. Encourage children to describe what makes them able to roll or stack. Guide children to Compare and Connect the strategies.

• Unit 3, Lesson 8, Two-Dimensional Shapes, Session 3, Try-Discuss-Connect, Try It, Problem 1, students reason abstractly and quantitatively as they design a shape that contains 4 squares and/or triangles. “The design should have four shapes. Draw two more shapes. Draw squares or triangles or both. How many squares are there? How many triangles? Have children add to the design and then count the squares and triangles and record their answers.” The shape shown is two squares. 

• Unit 7, Lesson 23, Compose and Decompose Teen Numbers with Tools and Drawings, Interactive Tutorials, Explore Teen Numbers, Practice 3, students reason abstractly and quantitatively as they make teen numbers when given a number between 11-19. The computer tutorial reads the instructions as such, “Move 16 goobers to the box. Tap the green buttons to add 10 at a time or one at a time. Tap the orange button to take away goobers.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 5, Compare Numbers to 5, 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, “Have children respond to the Discuss It question with a partner: How do you know which group has more dinosaurs? Facilitate Whole Class Discussion Have two or three selected children share their strategies in the order you have chosen. ASK How does [child name]’s strategy show which group has more? LISTEN FOR children to say the bottom group has more because they counted more dinosaurs in the bottom group than in the top group or that when they matched the objects, the bottom group has one left over. Children may question why the bottom group looks shorter but has more dinosaurs. Guide children to Compare and Connect the strategies.”

• Unit 3, Lesson 9, Subtract Within 5, 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, “Have children respond to the Discuss It question with a partner: How did you decide how many pumpkins you could pick? Facilitate Whole Class Discussion Have two or three selected children share their strategies in the order you have chosen. ASK What are all of the numbers of pumpkins that can be taken away from the patch? LISTEN FOR children to recognize that any number of pumpkins that is the same as or less than the starting number of pumpkins can be taken away. Guide children to Compare and Connect the strategies.”

• Unit 4, Lesson 12, Compare Numbers to 10, Session 3, Apply It, students justify their thinking as they share their understanding of comparing numbers with a partner. Facilitate Whole Class Discussion, “Guide children to share their understanding of comparing numbers. Have children turn and talk with a partner to share their ideas before discussion as a class. ASK How did you decide whether a number was greater than or less than the number on the card? LISTEN FOR children to explain that they used the number path or rote counting sequence. ASK Were there times when there was more than one number on your workmat that you could choose to cover? Why? Give an example. LISTEN FOR children to explain that more than one number can be less than or greater than a given number. For example, for a number greater than 8, you could choose to cover either a 9 or a 10.”

• Unit 5: Math In Action, Grow a Garden, Session 3, Share Information, students critique the reasoning of others in their class during the discussion of the notice and wonder activity they completed when compiling the class data display. Facilitate Whole Class Discussion. “Ask questions to help children make connections between their own work and the reasoning and that of others. Did anyone have a question like [child name]’s question? What was the same about how you answered? What was different? Did you agree with [child name]’s answer? Why or why not?”

• Unit 7, Math in Action, Build for Birds, Session 3, Share Information, students justify their thinking and critique the reasoning of others as they make connections between their own work and the reasoning of others. Facilitate Whole Class Discussion, “Ask additional questions to help children make connections between their own work and reasoning and that of others. Did anyone have a question like [child name]’s question? What was the same about how you answered? What was different?  Do you agree with [child name]’s answer? Why or why not?”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 2, Lesson 5, Compare Numbers to 5, Session 3, Connect It, with teacher support, students put the problem in their own words and identify important information. “Help children understand that they can use counting to tell the number that is one more. ASK [Draw to show 4 counters.] How can I show one more? LISTEN FOR children to say to draw one more counter. ASK Let’s count to 4 together: 1, 2, 3, 4. What number will we say next? [5] Draw one more counter. How did knowing the next number tell you what one more is? LISTEN FOR children to identify that when counting, the next number is one more.”

• Unit 4, Lesson 13, Compose Shapes, Session 2, Develop, Try It, students use the math they know to solve problems and everyday situations as they use different pattern blocks to compose a hexagon from smaller shapes. “Make sense of the problem: The mural designer is trying out different shapes for the center of the fish. What shapes could be put together to compose the hexagon? Have children draw lines on both blank fish to show different ways to compose the hexagon from other shapes.”

• Unit 5, Math in Action, Grow a Garden, Session 2, Apply It, students use the math they know to solve problems and everyday situations as they use counting cubes and drawings to design a garden. “Direct children’s attention to Our Garden Key and remind them to use plants from this list. Tell children to show one plant in each square of the garden. Prompt children to start thinking about their plan by asking: What groups of plants do you want in your garden? Where will you place your plants?  Allow individual think time and work time with the available tools. Then have children turn and talk with a partner about the groups of plants they want, where they want to place them, and the reasons for their choices. Have children complete their plan for the new garden. Allow for multiple modes of expression, including drawings, placement of concrete objects, and spoken or written descriptions.”

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 3, Lesson 9, Subtract Within 5, Session 5, Refine, with teacher support, students recognize both the insight and limitations to be gained from using different tools and strategies. Deepen Understanding, “When strategies have been shared, encourage children to talk about the different ways the problem was modeled. Understanding that there are multiple ways to model real-world problems, such as manipulatives, numbers, drawings, and even fingers, leads children to see that they can use mathematics to solve these problems. ASK What tools do you like to use to model subtraction problems? Why? LISTEN FOR children to discuss how they can use a variety of tools, including fingers, counters, 5-frames, drawings, and numbers to show what is happening in the problem. Prompt children to explain how using tools to model a story can help them better understand the problem and help them reach a solution. Have children explain which way works best for them and why.”

• Unit 4, Lesson 15, Find Number Partners for 10, Session 1, Explore, Investigate It, Problem 1, students recognize both the insight to be gained from different tools/strategies and their limitations. “Place a 10-train in one pan of the balance. Encourage children to make observations about what happens to the balance. ASK: What do you notice about the balance? What does it mean? LISTEN FOR children to notice that the pan with the 10-train moves down while the other pan moves up, which means that the sides do not have the same amount of cubes.Take one of the cube trains from the bag and place it in the empty pan. Have children describe how the balance changes.Take another cube train from the bag and put it in the pan. Have children say whether the sides of the balance have the same amount of cubes.If there is not the same amount of cubes on each side, take the second cube train out of the pan and replace it with a different cube train until the amount on each side is the same. Draw or display an equal sign (=) on the board. Explain to children that the equal sign is a sign that mathematicians use to show when two quantities or groups have the same amount of have an equal value. Write 10=10 on the board. Read it aloud as: ten equals ten. Say: This means both groups have the same amount. ASK  If there were 10 cubes on one side of the balance, what would you do to make the sides equal? LISTEN FOR children to say that they would put 10 cubes on the other side of the balance to make the sides equal.Show and count the two cube trains that equal 10. Have children say aloud: 10 equals ___ plus ___, and ___ plus ___ equals 10.Tell children they will write equations to show some of their solutions. Explain that an equation is a mathematical sentence that uses an equal sign (=) to show that two things are equal. Remind children that the plus sign means and or plus. Have children record two of their findings on the workmat by shading in the cube trains on each side of the balance.”

• Unit 5, Lesson 18, Compose and Decompose 6 and 7, Session 4, Refine, Independent Practice, Student Worktext, Practice, Problem 2, students recognize both the insight to be gained from different tools/strategies and their limitations when using a 10-frame and two-color counters to decompose the number 7. “Have children trace the numbers on the left and draw counters in the 10-frames to show a total of 6 or 7. On the right, have children write the number of red counters shown and the number of counters drawn to make the total.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten 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 5, Compare Numbers to 5, Session 3, Develop, Discuss It, students attend to precision as they share how they showed one more. Support Partner Discussion “Have children respond to the Discuss It question with a partner: How did you show one more?” Facilitate Whole Class Discussion, “Have two or three selected children share their strategies in the order you have chosen. ASK How does [child name]’s strategy show one more? LISTEN FOR an understanding that drawings or manipulatives can show the original quantity along with one more, allowing the ability to then count to find the new total. Guide children to Compare and Connect the strategies.”

• Unit 3, Lesson 8, Two-Dimensional Shapes, Session 4, Apply It, students attend to precision by using specific shapes to build other objects. “Have children think of an object that they can draw using only circles, squares, rectangles, and triangles, such as a truck, a rocket, or a robot. Instruct children to draw the object on the page using only circles, squares, rectangles, and triangles. Let children know that they can draw as many shapes as needed, in any size and turned any way.”

• Unit 5, Lesson 16, Count, Read, and Write Numbers 11 to 20, Session 5, Refine, Analyze It, students attend to precision as they independently count the number of beads on the workmat and defend who is correct. “Read the problem aloud: The cat and dog counted the beads. They both think they wrote the number that shows how many. Do you agree with the cat, the dog, or both? Why? Have the children circle who they agree with.” The teacher facilitates a whole class discussion, “Guide children to share how they made their choice. Have children turn and talk with a partner to share their ideas before discussing as a class. ASK Who do you agree with? Why? LISTEN FOR children to share their thinking. Children may say that they counted 17 counters. The cat shows 17 while the dog shows 16, so they agree with the cat and disagree with the dog.”

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, Describe and Compare Length and Height, Session 1, Explore, Discover It, students attend to the specialized language of mathematics as they describe the various attributes of different objects. “What things can you describe about an object? This activity lets children explore the various attributes of different objects. Allow children some time to play with the clay before rolling it into a ball for observation. Direct children’s attention to their ball of clay. Ask: What can you say about the ball of clay? Have children share what they notice, such as color, size, weight, material, smell, and texture. Say that the things they noticed about the ball of clay are called attributes of the ball of clay. Instruct children to change one attribute of their clay ball. Ask: Which attributes can you change? Have children share the attributes that can change, such as height, length, shape, and texture. Explain that they will change the height of their ball of clay to make a ‘tower.’ Ask: How can you make your tower tall? Then have children make their clay tall and compare their tower with another child’s tower. Ask: Whose tower is taller? Repeat by having children make a short tower. Explain that they will change their clay to make a ‘snake.’ Ask: How can you make your snake long? Then have children make their clay long and compare their snake with another child’s snake. Ask: Whose snake is longer? Repeat by having children make a short snake.”

• Unit 3, Lesson 9, Subtract Within 5, Session 2, Discuss It, students attend to the specialized language of mathematics as they explain their strategies for solving problems. “Have two or three selected children share their strategies in the order you have chosen. ASK How does [child name]’s model show what happens? LISTEN FOR children to explain how the child modeled that the squirrel had 5 acorns, then some were taken away.”

• Unit 7, Lesson 24, Build With Shapes, Session 3, Develop, Discuss It, students attend to the specialized language of mathematics with the support of their teacher by discussing how they would put different blocks together and using positional language. “Have children respond to the Discuss It question with a partner: How would you put the blocks together? What could you make? Have two or three selected children share their strategies in the order you have chosen. Have shapes available for children to show how they would put the shapes together. ASK How is what [child name] did with the shapes similar? How is it different? LISTEN FOR children to say that (for example) they put the shapes together in a different position or orientation. Guide children to Compare and Connect the strategies.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and partially meets expectations for 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, Math in Action, Imagine a Rainforest, Session 2, Revisit the Problem, students look for and make use of structure in repeated reasoning as they follow the sorting rules to sort cards into two and three groups. “How can you sort the rainforest cards into two or three groups? In this activity, children will use sorting rules of their choice to sort the cards. Make Sense of the Problem Read new details about the problem aloud: Our class needs many different bulletin boards. Each board will show a different rainforest group. You can help by sorting your cards into two or three groups in different ways. Use Three Reads to help children make sense of the problem. Remind children that there are many different sorting rules they can use to sort the cards. Thinking Point Read the following thinking point aloud, clarifying as needed: You can put only one card in each group. Have children indicate their level of agreement by showing thumbs up, down, or sideways. Then have children turn and talk with a partner about their reasoning before sharing with the class. Ask children whether they want to keep or change their answers and why. Confirm that one card or many cards can be placed in each group.”

• Unit 5, Math In Action, Grow a Garden, Session 2, Revisit the Problem, Facilitate Whole Class Discussion, students look for and make use of structure as they recognize that groups of 8 can be decomposed in more than one way. “Provide connecting cubes in groups of 8. Guide children to share what they know about ways to make 8. Allow children individual think time before answering. ASK How can the cubes help you make a new plan for the garden? How many different ways can you split 8 into 2 groups? LISTEN FOR the idea that groups of cubes can represent a group of plants of the same kind and that 8 can be split into 8 and 0, 7 and 1, 6 and 2, 5 and 3, or 4 and 4. ASK Do you think you will be able to use all of the plants on our key? LISTEN FOR the idea that there are not enough spaces on the grid to fit groups of 6 kids of plants.”

• Unit 7, Lesson 23, Compose and Decompose Teen Numbers with Tools and Drawings, Session 4, Refine, Make Connections, students look for and make use of structure as they put 10 ones together with some more ones to compose a teen number. “Have children count the red cubes and write the number of red cubes. Then have them read the number next to the second cube train and color the cube train and a group of ones to make the number.”

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 5, Compare Numbers to 5, Session 2, Develop, Apply It, Counter Compare Activity, students look for and express regularity in repeated reasoning as they use one-to-one matching to compare groups. “How can you use objects to compare numbers? This activity guides children to develop understanding of using one-to-one matching to compare groups. Tell children they will practice comparing numbers by using counters. They will show numbers with counters and decide which is more. Invite two volunteers to demonstrate the game. Place the stack of number cards face down next to a pile of 20 counters. Both players take a number card but do not show it to the other player yet. Each player uses counters to show their number. Players match counters to decide which group has more and which group has less. Players reveal their cards and check that the counters match the numbers. The player whose group shows less says the comparison aloud, for example: 1 is less than 3. The player whose group shows more says their comparison aloud: 3 is more than 1. The player whose group shows more keeps both cards. If the groups are the same, each player keeps a card. Place the counters back in the pile and repeat until all the cards are used. The player with more cards wins the game. After demonstrating the game, have children play in pairs.”

• Unit 3, Lesson 9, Subtract Within 5, Session 1, Explore, Investigate It, students look for and express regularity in repeated reasoning as they explore taking away objects from a group. “How does a group change when you take some away? This activity allows children to explore taking away objects from a group. Have children place 5 cubes and an empty cup on their desk. Choral count the cubes, and have children hold up fingers to show how many cubes they have. Say: I am going to ask a question. If your answer is yes, take away 1 cube and put it in your cup. Ask: Is your favorite color blue? Have children hold up fingers to show how many cubes they have left. Ask three more questions, having children hold up fingers after each question to show how many cubes they have left. Do you have a pet? Do you like bananas? Do you play a sport? For the fifth question, ask something everyone will say yes to, such as: Are you in kindergarten? While everyone holds up fingers to show how many cubes they have left, write those numbers on the board. ASK These are the numbers of cubes you have left. How do the numbers compare to the number of cubes at the start, 5? LISTEN FOR children to recognize that the numbers of cubes they have left are all less than 5. ASK Could anyone have more than 5 cubes left? Why or why not? LISTEN FOR children to explain that you cannot have more than 5 cubes if you do not add any. ASK Could anyone have 5 cubes left? Why or why not? LISTEN FOR children to say that to have 5 cubes left you have to answer no to every question and not take away any cubes. In this round everyone took away at least 1 cube. (Subtracting 0 will be discussed later in the lesson.)”

• Unit 7, Math In Action, Build for Birds, Session 2, Revisit the Problem, students look for and express regularity in repeated reasoning as they recognize that a teen number can be decomposed into a group of 10 ones and a group of more ones (1 to 9). “Facilitate Whole Class Discussion. Prompt children to share what they know about teen numbers. Allow individual think time before children answer. ASK How can you show that a number is a teen number? LISTEN FOR children to describe various strategies such as modeling the number with counters and showing that the counters fill all of one 10-frame and a part of another or by using an equation to write the number as 10 ones plus some more ones.”

Kindergarten Standards Correlations identify limited opportunities for intentional development of MP8. Correlation by Standard for Mathematical Practice indicates 8 Lessons that are correlated to MP8.