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.

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

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

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

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

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

  • Teach gives information on practice, and differentiation. 

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

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

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

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

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

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

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

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

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

• Unit 1, Lesson 2, Describe and Compare Length and Height, Session 1, Explore, Discover It, Facilitate Whole Class Discussion, “To allow an opportunity to discuss their answers before sharing with the class, have partners turn and talk. ASK What attributes of the clay can you change? What attributes cannot change? How do you know? LISTEN FOR an explanation of which attributes can and cannot be changed for the clay and encourage children to demonstrate their thinking using the clay. ASK How can you use tall and short or long and short to describe the tower or snake? LISTEN FOR children to say they can use tall to describe the tower and long to describe the snake. They may say that short can describe the snake or the tower. ASK When describing an object, how are the height and length different? LISTEN FOR children to say that height is up-and-down, while length is side-to-side.”

• Unit 4, Lesson 13, Compose Shapes, Session 2, Develop, Apply It, Error Alert, “If children have trouble seeing how two or more shapes compose another shape, have them trace one pattern block at a time and then color the resulting composite shape one color.”

• Unit 7, Lesson 23, Compose and Decompose Teen Numbers With Drawings, Session 3, Develop, Discuss It, Select and Sequence Strategies, “One possible order for whole class discussion: Counting all; Recognizing a full 10-frame as 10 and counting on.”

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

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

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

• Lesson Progression links each lesson within the current unit to prior and future lessons so teachers know what students need to know to be successful with the current work as well as what the current work is preparing students for. This is important for a teacher’s complete understanding of how to scaffold and bridge the current content. For example, Unit 5, Lesson 16, Lesson Overview, Teacher Edition, Count Within 100 - Full Lesson, Learning Progression:

  • “Previously, earlier in Kindergarten, children learned number names and the count sequence to 80 (counting by 10s and by 1s) and they have begun extending that to 100. They have used one-to-one correspondence counting to determine quantities up to 20 and have used numbers to represent quantities.”

  • “In this lesson, children take the rote counting patterns they have practiced and develop a concrete understanding of the numbers they say when they count. They solidify their rote counting skills to 100 (by 10s and by 1s), including counting on from a number other than 1. Children gain a sense of the magnitude of greater numbers as they count groups of objects to 100 and use their familiarity with 10 as a benchmark number to understand that, just as 20 is 10 and 10 more, the other multiples of 10 each represent yet another 10.”

  • “Later, in Grade 1, children will build on the foundation provided by this lesson to read and write numbers to 120, compare numbers up to 100, and develop an understanding of place value, particularly tens and ones. They will use counting on as a strategy to add and subtract.”

• Understanding Content Across Grades provides explanations of instructional practices as well as information about necessary prior knowledge and concepts beyond the current course for teachers to improve their own knowledge of the subject. For example, Unit 7, Beginning of Unit, Understanding Content Across Grades related to Lesson 24, Teen Numbers and Shapes:

  • Current Lesson, “Insights on: Composing Three-Dimensional Shapes. At this point in the year, children have significant experience with two- and three-dimensional shapes. They can relate the abstract geometric shapes to shapes in their environment. Children should have multiple opportunities to identify, name, and sort individual shapes in their environment as well as discuss the attributes of various solids and flat figures. Children benefit from experiences combining simple shapes into more complex ones to represent objects they encounter in their daily lives. As children draw shapes to match ones they see, they are actively engaging with the defining attributes such as “straight sides that meet at corners” and the fact that different shapes have different numbers of sides. This is a good time to reinforce precise geometric vocabulary as children describe their creations to peers. For example, they may say, “I can make a rectangle out of 6 squares.”

  • Future Learning, “Insights on: Comparing and Decomposing Shapes. As children begin to experiment with part-whole relationships they will begin to recognize that smaller shapes can be combined to make larger shapes. Children will also begin to notice shapes within existing shapes. They should be given ample time to decompose larger shapes to determine what shapes are within them. Children should be given plenty of opportunities to manipulate and explore with both two-dimensional and three-dimensional shapes.”

• Each lesson includes a Reteach section with several pages called “Tools for Instruction” that provide explicit teacher guidance related to the current work and to prerequisite skills. These pages include adult explanations, step-by-step guidance for teaching, and check for understanding. For example, Unit 3, Lesson 7, Adding Numbers Within 5:

  • “Children are learning how to describe and represent addition using models and drawings that refer to real-world situations. This activity helps children see the real-world uses of addition. They classify objects in different ways to see what they can add. The activity also provides practice verbally describing addition situations using addition sentences with words such as and and is.”

  • “Step by Step: 1) Introduce the objects. Give the child five objects as follows: one red crayon, one blue crayon, one blue marker, one red connecting cube, and one red counter. If these are not available, use other objects that can be sorted in at least two different ways. (followed by 3 more prompts) 2) Model and draw addition sentences. (followed by 5 prompts)”

  • “Check for Understanding: Give the child one green connecting cube, one yellow counter, one yellow marker, one green marker, and one green crayon. Have the child sort the objects into two categories, model and draw an addition sentence to describe the situation, and say the addition sentence aloud. For the child who can benefit from additional support, use the table below to help pinpoint where extra help may be needed.’If you observe… the child may… Then try…’”

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

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

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

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

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

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

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

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

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

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

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

• The Unit and Lesson Support document provides descriptions of the purpose and unit themes in each unit. For example, Unit 3, Beginning of Unit, Unit Opener, the opening narrative provides the content of the unit, “Purpose This unit introduces children to adding and subtracting within 5. It also introduces them to two‐dimensional shapes. Children draw to show what they already know about these topics. They then reflect on what they learned about these topics at the end of the unit. Unit Themes The major themes of the unit are: Adding one group to another group makes more. When you take away objects from a group, you are subtracting. Two‐dimensional shapes have attributes that can be described. You can identify shapes as flat or solid. Flat shapes make the faces of solid shapes. You can use words to name a shape and describe its position.”

• In every teacher's Lesson Overview, the Learning Progression identifies how the standard is addressed in earlier grades, in the current lesson, next lesson, and in the next grade level. For example, Unit 3, Lesson 7, Overview, Learning Progression, “Earlier in Kindergarten, children practiced counting up to 10 objects in a set to find how many. They compared two sets of up to 5 objects to identify which set has more or less or if both sets have the same. Children also learned that when they count, each number is one more than the number before. In this lesson, children build on their understanding of one more to add within 5. They represent addition using their fingers and manipulatives to find the total. They tell story problems and model them using manipulatives and 5-frames. Children use numbers to write the starting number, the number added, and the total. In future Kindergarten lessons, children will apply their understanding of add-to situations to take away situations. They will use the symbols + and – to form addition and subtraction expressions, and they will extend their addition and subtraction skills to numbers within 10.”

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

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

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

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

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

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

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

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

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

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

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

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

The Lesson Overview for the teacher provides a Materials Required column for each lesson on the Pacing Guide; additional materials are listed in the Differentiation column. Any materials that need to be printed are also provided in the Overview, such as bear counters or spinners. For example:

• Unit 1, Lesson 3, Session 2, “Materials: Attribute buttons (16 per group) and presentation slides. Differentiation (only noted in the differentiation section): for each student: attribute buttons (1 pile per group) and Attributes workmat.”

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

• Manipulative List, Unit 7, Lesson 23, Number cards deck (set of numbers 11-19) (one deck per pair), connecting cubes (19 cubes per pair), and two-color counters (38 counters per pair). 

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

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

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

• Unit 5, Lesson 19, Lesson Quiz, Problem 1, “DOK 2, SMP 5, K.OA.A.3.”

Assess, End of Unit, Unit Assessments, Teacher Guide, Forms A and B are provided and include the content item with a solution. Form A includes Problem Notes, worked-out problems, DOK levels, content standards, Scoring Guide, Scoring Rubrics, and Responding to Student Needs. Form B appears to parallel all of the correlations provided for Form A, though it is not labeled. It is noted in the Scoring Guide, “For the problems in the Unit 1 Unit Assessments (Forms A and B), the table shows: depth of knowledge (DOK) level, points for scoring, standard addressed, and lesson assessed by each problem.” For example:

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

• Unit 4, End of Unit, Assess, Unit Assessment,  Form A, Problem Notes, Problem D, “DOK 1, K.CC.A.3.”

Digital Comprehension Checks “...can be given as an alternative to the print Unit Assessment. For this comprehension check, the table below provides the Depth of Knowledge (DOK), standard(s) assessed, and the corresponding lesson assessed by each problem.” For example:

Program Implementation, Comprehension Check Correlations, Unit 1 Comprehension Check Correlation Guide, Problem 6, “DOK 2, K.G.A.1, SMP 6.”

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

The assessment system provides opportunities to determine student’s learning that include teacher support for interpreting student performance in the Problem Notes and Recording Sheets provided. Examples include:

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

  • Unit 1, Lesson 2, Assess, Lesson Quiz, Problem B, “Children circle the top chenille stem. The bottom chenille stem is not correct. Children may have confused longer and shorter.”

  • Unit 2, End of Unit, Assess, Unit Assessment, Form A, Problem F, “Children circle the first and last shapes. The second share [is] not correct. Children may have confused rectangle and triangle. The third shape [is] not correct. Children may have misunderstood the prompt. The fourth shape [is] not correct. Children may have confused square and triangle.”

• Lesson Quizzes contain an Activity Based Assessment Recording Sheet to support the teacher in identifying students who have reached instructional outcomes. For example:

  • Unit 4, Lesson 12, Compare Numbers to 10, Assess, Activity-Based Assessment Recording Sheet, a grid is provided to write down names and track the following outcomes: “Correctly compares two groups, Correctly compares two numbers” and the following strategies, “Uses length or 1:1 matching, Uses number path, Uses the count sequence.”

The Lesson Quizzes and Unit Assessments provide guidance to teachers to follow-up with students. The follow up suggestions reference previous work rather than new material. For example:

• Unit 3, End of Unit, Assess, Unit Assessment, Form A, provides a section called Responding to Student Needs. This section directs teachers back to the relevant lessons for review and where teachers can access the Reteach and Extend options. “For students who answer problems incorrectly on the Unit Assessment, choose from the following resources on the Teacher Toolbox for additional support. Reteach Tools for Instruction, Adding Numbers Within 5 (Lesson 7), Describing and Comparing Shapes (Lesson 8), Subtracting Numbers Within 5 (Lesson 9), Adding and Subtracting Numbers Within 5 (Lesson 10) | For children who exceed proficiency on the Unit Assessment, choose from the following activities on the Teacher Toolbox. Extend Enrichment Activities, Make 5 (Lesson 7), Shape Pictures (Lesson 8), Draw Some - Take Some (Lesson 9), Ways to Make a Number (Lesson 10).”

• Unit 4, Lesson 14, Assess, Lesson Quiz provides three types of differentiation for possible follow up depending on student performance: Reteach, Reinforce, and Extend. Implementation Guide, Program Overview, Differentiation, “Reteach: Tools for Instruction provide targeted teacher-led activities to support prerequisite or on-level skills. Reinforce: Learning Activities provide leveled small group collaborative games to reinforce concepts and skills. Extend: Enrichment Activities provide additional challenges through group collaborative activities.”

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

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

• Fill-in-the-blank

• Multiple select

• Matching

• Graphing

• Constructed response (short and extended responses)

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

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

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

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

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

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

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

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

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

• i-Ready Homepage, Success Central, Plan & Teach, Differentiate, Accessibility and Accommodations, Create Accessible Experiences with Your Program, Start here, Accessibility and Accommodations Update, “To make i-Ready Classroom Mathematics accessible to the widest population of students, we offer a range of accessibility supports that may also meet the requirements of a number of student accommodations.” The table provided lists the Universal Supports, Designated Supports, and Accommodations that are both embedded and not embedded in the program. For example, embedded supports include audio support, closed captioning, calculator, zoom in/out, highlighting, and more. Available non-embedded supports include Native language translation of directions, noise buffer, alternate response options, scribe, and more.

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

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

• Each lesson has an Extend: Enrichment Activities column that provides an additional challenge task. For example, Unit 5, Lesson 16, Extend, Sets of Stickers, students are provided with a challenge situation. “Children count and group objects into groups of 11 to 20. Have children count a group of objects, making sure there are 11 to 20 objects. Then have them circle the group. Children repeat this process until all the objects have been grouped into groups of 11 to 20. If children are left with a number of objects that is less than eleven, have them explain how they will adjust the groups so that they are all numbers from 11 to 20.”

• In Explore and Develop sessions in each lesson, the materials contain Differentiation: Extend Deepen Understanding or Challenge for the lesson’s key concepts through the use of discourse with students. For example, Unit 2, Lesson 4: Count, Show, and Write Numbers to 5, Session 2, Develop, Centers, Differentiation, and Practice, Extend, “Use with children who are proficient with number recognition and placement of counters in the 5-frame. Materials: 5-frames, counters, Number and Dot Row Cards (1 to 5)  In pairs, have children take turns selecting a number card. Challenge the children to find all the ways they can arrange counters to show that number in the 5-frame. Have children check their responses by counting out loud as they place the counters in the 5-frame.”

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

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

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

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

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

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

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

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

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

• All classroom materials are available in Spanish.

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

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

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

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

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

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

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

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

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

• Program Implementation, Manipulative List, Manipulative Kit, includes Baby Bear Counters, Pattern Blocks, Linking Cubes, Number Cubes, GeoSolids, Two-Color Counters, Buttons, Color Tiles, Dice, Spinner, and 0-12 Number Cards.

• Program Implementation, Manipulative List by Lesson has specific manipulatives listed for each lesson. For example, Unit 3, Lesson 7: Connecting cubes, two-color counters, spinner. There is also a Manipulative Suggestions for At-Home Use document that provides ideas for using items commonly found at home or easily created that could be used in place of the actual manipulatives (e.g. Connecting Cubes could be replaced with Lego bricks). 

• Program Implementation, Activity Sheet Resources, K-5 Activity Sheet Resources includes a 178-page document full of visual models such as number lines, graphs, grid paper, graphic organizers, etc. 

Program Implementation, Try-Discuss-Connect Routine Resources, Understanding the Try-Discuss- Connect Instructional Routine, the foundational Try-Discuss-Connect routine is designed to “help children achieve greater mathematical agency by encouraging proficiency and rigor within a collaborative structure. Children develop greater understanding of mathematical representations and solution strategies using think time, partner talk, individual writing, and whole-class discourse. Language routines and teacher moves are built into the Try-Discuss-Connect framework to guide teachers and children in this discourse-based instruction.” For example:

• The Try It “begins with an emphasis on identifying important information that helps children make sense of a problem situation. The Try It section continues as children apply what they learned in the Make Sense of the Problem and begin responding to the problem.” Discuss It “begins when children work in pairs to share their thinking. With a partner, they reason quantitatively and abstractly about the problem situation. The Discuss It section continues as children share their thinking with the class.” During the Connect It section, “Teachers and children first connect and extend understanding they developed from solving the Try It problem and participation in Discuss It. The second part of Connect It, children apply their understanding from the discussion to new situations.”

• “Tip: After selected approaches are discussed, teachers encourage children to look at the strategies another way by having them identify similarities and differences among them. Children explain their thinking and teachers ask other children to critique their reasoning.”

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

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

• Try It, “Children analyze the problem in a very focused way to help them begin to develop concrete situations.”

• Discuss It, “Children begin to connect concrete approaches and representational or abstract approaches as they engage in partner discussions.”

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