Kindergarten - Gateway 1

The materials reviewed for i-Ready Classroom Mathematics Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

The i-Ready Classroom Mathematics assessments are found in the Teacher Toolbox and include Unit Assessments. The Kindergarten materials contain seven units, with each unit providing numerous opportunities for both formative and summative assessments. Summative assessment items include:

• Unit 2, Assess, Unit Assessment, Form A, Item B, “For the next problem, have children circle the heavier object on the pan balance.” A picture of a pan balance is shown with a block on one side and a paperclip on the other. The pan balance is tilted towards the block. (K.MD.2)

• Unit 2, Unit Assessment, Form A, Item E, “For the last problem, have children circle the sphere.” Choices include images of 3-D shapes. (K.G.2)

• Unit 4, Unit Assessment, Form B, Item G, “For the first problem, ask children to color the connecting cubes in two different colors to match the number given and then write the missing number partner for 10.” A picture is shown of ten uncolored linked cubes and the expression ___+9. (K.OA.4)

• Unit 5, Assess, Unit Assessment, Form B, Item D, “Have children count the number of bear counters at the top of the page. Then have them circle the group of counters that show the same number.” A picture is shown of 24 bear counters and three columns below of circle counters with 24 in the first column, 34 in the second column, and 23 in the third column. (K.CC.1)

• Unit 7, Unit Assessment, Form A, Item C, “For the next problem, have children write an equation to show 10 ones plus some more ones.” A picture is shown of two ten-frames with 10 counters on the first ten-frame and 4 counters on the second ten-frame. A blank line, a circle, a blank line, a circle, and another blank line are provided for students to write the equation. (K.NBT.1)

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

According to the Program Overview, Program Organization document, “The lessons in i-Ready Classroom Mathematics span multiple days and integrate several standards to help students make connections and develop a deep understanding.” There are three types of lessons: 1. Strategy Lessons, which comprise the majority of lessons in the program and “help students make important connections and deepen their understanding while acquiring and developing mathematical skills and strategies,” 2. Understand Lessons, which “begin with the word ‘Understand’ focus primarily on conceptual understanding and occur at key points in the instructional sequence,” and 3. Math in Action Lessons, which occur at the end of each unit and “review and apply unit content and teach students how to develop complete responses to a performance task.” 

The i-Ready Classroom Mathematics materials provide a consistent structure within each lesson, which is a session or “day” and each “plays a different role in supporting student understanding. Each session takes 45-60 minutes to complete and includes time for a number sense routine, instruction, practice, and differentiation.” Day 1 consists of an Explore session which “connects prior knowledge and introduces new content.” Days 2-4 consist of Develop sessions which “build multi-dimensional understanding using rich tasks, problem solving, discourse, and multiple representations.” Day 5 consists of a Refine session which “strengthen skills and understanding with in-class practice time” and “reteach, reinforce, and extend learning.” The materials present all students with opportunities to meet the full intent and engage in extensive work with each grade-level standard. Examples include:

• Unit 1, Lesson 2, Describe and Compare Length and Height, Sessions 1-3, engage students with the full intent and extensive work with K.MD.2 (Directly compare two objects with a measurable attribute in common, to see which object has “more of”/”less of” the attribute, and describe the difference). Session 1, Explore, students “Explore comparing the length or height of two objects.” Number Sense, “Show the slide. ASK What do you notice? What do you wonder? Allow children to explore the illustration before they share with a partner and then with the class. Accept all responses.” An image shows trains, lemurs, suitcases, and benches. Investigate It, “This activity allows students to explore the attributes of length and height by comparing common classroom items to determine which is longer/shorter or taller/shorter. Tell children that they are going to look for objects around the classroom. Hold up a pencil horizontally and point out the pencil’s length. Say: I wonder if there is an object that is longer than this pencil.” In a follow-up activity, students are asked to find objects that are longer than their shoe and objects that are shorter than their shoe. The teacher then facilitates a whole group discussion. Session 2, Develop, students “Develop understanding of how to compare the lengths of two objects” and “Recognize which object is longer and which object is shorter when comparing the lengths of two objects.” Try-Discuss-Connect, “Circle something in the picture. Then find something that is longer or shorter than it.” An image shows a bridge with a train, a bus, a car, a boat, and a fish. The teacher leads a whole class discussion. Session 3, Develop, students “Develop understanding of how to compare the heights of two objects” and “Recognize which object is taller and which object is shorter when comparing the heights of two objects.” Try-Discuss-Connect, “Circle something in the picture. Then find something that is taller or shorter than it. How can you tell?” An image shows buildings, trees, and street lamps. The teacher facilitates a whole group discussion. Apply It, “How can you compare the heights of towers? This activity guides children to practice comparing the heights of cube towers to find which are taller and which are shorter.” Students are instructed to build two cube towers, each using a single color. Students walk around the room with their cube towers to music. When the music stops, students are to find the person closest to them and discuss how their towers compare to their partner’s towers. (“Example: My red tower is taller than your green tower.”) 

• Unit 2, Lesson 4, Unit 4, Lesson 11, and Unit 5, Lesson 16, engage students with the full intent and extensive work with K.CC.3 (Write numbers 0 to 20. Represent a number of objects with a written numeral 0-20 …). Unit 2, Lesson 4, Count, Show, and Write Numbers to 5, Session 2, students “Develop an understanding of written numbers.” and “Recognize connections between written numbers and quantities.” 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?” 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.” Session 4, Refine, Apply It, Toy Boxes Activity, “How can numbers be used to show how many? This activity allows children to connect numbers with the quantity they represent. Explain that children will draw 0, 1, 2, 3, 4, or 5 toys in each box. Once they have drawn toys in a toy box, they will count the toys they drew and write the numbers to show how many. Ask children to repeat or rephrase the instructions before they begin working.” Unit 4, Lesson 11, Count, Show, and Write Numbers 6 to 10, Session 3, Develop, students “Develop skills in writing numbers 6 to 10.” and “recognize attributes of written numbers.” Apply It, Write to the Top, “This activity gives students practice forming the numbers 6 to 10. Show children the number card 6. Read the line of the poem about 6 as you demonstrate tracing the number 6 with your finger. Have children trace the number on their card with their fingers as you say the line again. Repeat for 7, 8, 9, and 10. The poem is as follows: A curve and loop do the trick, that is how you make a 6. Make a line across the top, finish 7 with a drop. Make an S and do not wait. Go back up and make an 8. Draw a circle, then a line. That’s the way to make a 9. To make a 10, draw a 1. Write a 0, and you are done. After children practice tracing the numbers with their fingers, choose a volunteer to help demonstrate the activity. Pick a 10-frame card and have the volunteer count the dots on the card out loud and find the column on their workmat with the matching 10-frame. Once the volunteer says the number, have all children trace the number at the bottom of that column. Working from bottom to top, have partners take turns picking cards, tracing numbers, and writing the corresponding numbers on their workmat until all columns are filled.” Unit 5, Lesson 16, Count Read, and Write, Numbers 11 to 20, Session 4, Refine students “Refine writing numbers 11 to 20” and “Refine counting quantities 11 to 20.” Make Connections, “How can you count and show quantities from 11 to 20? Children write a number 11 to 20 and then count out that many objects. Have children write a teen number on the line. Direct children’s attention to the stars on the page. Tell children to pick a crayon and color a number of stars to match the number they wrote on the paper.” 

• Unit 3, Lesson 7 and Lesson 9, and Unit 6, Lesson 22, engage students with the full intent and extensive work of K.OA.2 (Solve addition and subtraction word problems, and add and subtract within 10…). Unit 3, Lesson 7, Add Within 5, Session 2, Develop, students “Develop modeling addition problems.” and “Recognize that there are different ways to model addition problems.” Try-Discuss-Connect, “How can you model a real-world addition story problem?” Try It, “Read the problem aloud: 3 plates are on the table. 2 more plates are added. How many plates are on the table now? How can you model the problem?” Make Sense of the Problem, “Use Three Reads to help children make sense of the problem. Ensure children understand that they need to model the problem to find how many plates in all. Have children work independently on the Try It.” In Lesson 9, Subtract Within 5, Session 2, Develop, students “Develop an understanding of subtraction.” and “Recognize that there are different ways to model real-world subtraction story problems.” Try-Discuss-Connect, “How can you model a real-world subtraction story problem?” Try It, “Read the problem aloud: A squirrel has 5 acorns. The next day, the squirrel has less than 5 acorns. How can you show what you think happened?” Make Sense of the Word Problem, “Use Three Reads to help children make sense of the problem. Ensure children understand they should take away from the starting number of acorns. Have children work independently on the Try It and write how many acorns are left.” In Session 3, Develop, students “Develop an understanding that taking away results in a number that is less.” and “Recognize that you can take away all, some, or none from a group of objects.” Try-Discuss-Connect, “How do you know how many you can take away?” Try It, “Read the problem aloud: There are 4 pumpkins in the patch. How many pumpkins do you want to pick? How many will be left?” Make Sense of the Problem, “Use Say It Another Way to help children make sense of the problem. Ensure students understand they should cross out pumpkins and write a subtraction sentence.” In Unit 6, Lesson 22, Add and Subtract to Solve Word Problems, Session 2, Develop, students “Develop solving addition and subtraction story problems by drawing.” and “Recognize that objects in a problem can be represented in a drawing by simple shapes.” Try-Discuss-Connect, “How can you use a picture to show and solve story problems?” Try It, “Read the problems aloud one at a time: There are 4 caterpillars. 4 more join them. How many caterpillars are there now? There are 8 butterflies. Then 1 flies away. How many butterflies are there now?” Make Sense of the Problem, “Use Three Reads to help children make sense of each problem before trying it. Ensure children understand they should draw and write an equation.” Session 5, Refine, students “Refine representing addition and subtraction story problems with drawings and equations.” Analyze It, “What have you learned in this lesson? Ask children to name some things they learned or activities they did in this lesson. Read the problem aloud: There are 7 butterflies in the garden. Then 2 fly away. How many butterflies are in the garden now? The cat and dog both think they have modeled the problem. Do you agree with the cat, the dog, or both? Why? Have children circle who they agree with.” Facilitate Whole Class Discussion, “ASK Who do you agree with? Why? LISTEN FOR children to share their strategies. Children should recognize that the action in the story describes the subtraction, but the dog’s drawing shows addition.”

• Unit 7, Lesson 24, Build with Shapes, Sessions 1-4, engage students with the full intent and extensive work with K.G.5 (Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes). Session 2, Develop, students “Develop combining two-dimensional shapes to make recognizable images.” and “Recognize images of objects made up of two-dimensional shapes.” Try-Discuss-Connect, “An artist puts shapes together to make animals. What is one way the artist can put shapes together to make an animal? Have children choose an animal and put shapes together to make the animal.” The student page has seven varying shapes of varying sizes at the top of the page for reference and work space underneath. Session 3, Develop, students “Develop modeling real-world objects with three-dimensional shapes.” and “Recognize three-dimensional shapes in real-world objects.” Apply it, “Use common objects to build a table. ASK What could this be? What is another way you could make a table?” Session 4, Refine, students “Refine using two-dimensional shapes to make pictures.” and “Refine using three-dimensional shapes to build objects.” Apply It, “Have children look at the shapes on the workmat. Instruct children to combine three or more shapes to make a picture or build a model of an object. Tell them they may use items that match the shapes on the page, such as pattern blocks, attribute blocks, tangram shapes, or common objects such as building blocks, books, erasers, boxes, cans, and cardboard tubes. Have children circle the shapes they used and draw a representation of their object on the workmat when they have finished building it.” The student workmat has thirteen two-dimensional or three-dimensional shapes. 

• Unit 7, Lessons 23 and 25, engage students with the full intent and extensive work of K.NBT.1 (Compose and decompose numbers from 11 to 19 into ten ones and some further ones…). Lesson 23, Compose and Decompose Numbers with Tools and Drawings, Session 1, Explore students “Explore making and breaking apart teen numbers.” and “Explore the idea that teen numbers can always be composed of ten ones and some more ones.” Number Sense, Notice and Wonder, “Show the slide. Ask: What do you notice? What do you wonder? Allow children time to explore the illustration before they share with a partner and then with the class. Accept all responses.” The slide is an image of a garden with flowers, chili peppers, and melons. In Session 2, Develop, students “Develop using objects to compose teen numbers.” and “Recognize that every teen number is composed of 10 ones and some more ones.” Try, Discuss, Connect, “How can you use counters to show a teen number?” Try It, “Read the problem aloud: Count the beans and write the number. Then use the ten-frame to show how many.” In Session 3, Develop,  students “Develop using drawings to decompose teen numbers.” and “Recognize that every teen number can be decomposed into 10 ones and some more ones.” Apply It, Circle and Count Activity, “How can you use a drawing to decompose a teen number? This activity guides students to draw to break apart teen numbers. Have one pair demonstrate the activity. Ask Partner A to pick a card, keep hidden, and draw that many dots on their whiteboard. Then have Partner A give the whiteboard to Partner B. Tell Partner B to circle dots to make them easier to count and then label each group they circled with the number of dots in the group. Note that children may break apart numbers however they like. For example, they may decompose 13 into 10 and 3, 7 and 6, or 5 and 5 and 3. Partner B says the number of dots. Partner A shows the card and confirms they are correct. Have all children complete the activity by taking turns picking cards and drawing dots. When children have completed the activity, have them record one round by drawing and writing on their workmat.” Lesson 25, Compose and Decompose Numbers with Symbols, Session 2, Develop, students “Develop an understanding of decomposing teen numbers into ten ones and some more ones” and “Recognize teen numbers as 10 ones and 1 to 9 more ones.” Try-Discuss-Connect, “How can a model help you decompose a teen number?” Try It, “Read the problem aloud: A family counted 12 snail shells in the tide pool. Write an equation to show what the family found.” In Session 3, Develop, students “Develop adding 10 ones and some more ones to compose teen numbers.” and “Recognize that the number added to 10 helps you know the resulting teen numbers.” Apply It, Make Teen Numbers Activity, “How can you compose teen numbers? This activity guides children to compose teen numbers by adding a group of 10 ones and a group of ones using 10-frame representations. Arrange children in pairs. Have children write a teen number on the top blank in each space of their workmat. Then have them mix up the cards and place them in a pile, facedown. Each player chooses a different color crayon to use. Player 1 turns over a card, adds that number to 10, and says the addition aloud. For example: I have 3, 10 plus 3 is 13. Children can use counters and the 10-Frames Workmat to model the addition. If their partner confirms that the total is correct, Player 1 finds that number on the workmat, names the number, and uses their crayon to circle the number and complete the equation. It then becomes the next player’s turn. If a player picks a number that is already taken or is not found on the workmat, then it becomes the next player’s turn. After all the numbers on the workmat have been circled, the game ends. The player with more numbers circled wins.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the grade. 

• The approximate number of Units devoted to major work of the grade, including supporting work connected to major work is 6 of 7 units, approximately 86%.

• The number of Lessons (Strategy and Math in Action) devoted to major work of the grade, including supporting work connected to major work is 24 of 32, approximately 75%.

• The number of instructional days (including Strategy and Math in Action Lessons, and Unit assessments) devoted to major work of the grade, including supporting work connected to major work is 119 of 153, approximately 78%.

An instructional day analysis is most representative of the instructional materials because this comprises the total number of Strategy Lessons, Math in Action Lessons, and Unit Assessments. As a result, approximately 78% of the instructional materials focus on the major work of the grade.

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

The materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. Within Program Implementation, Correlations, Content Focus in the Common Core State Standards (CCSS), teachers are encouraged to "Use the tables to help inform i-Ready Classroom Mathematics instructional pacing so that students spend the majority of their time on the work of the major clusters, with time spent on supporting and additional clusters used to enhance that work." Examples of connections include:

• Unit 1, Lesson 3, Sort and Count Objects, Session 4, Refine, connects the supporting work of K.MD.3 (Classify objects into given categories, count the number of objects in each category and sort the categories by count.) to the major work 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.) as students count the number of objects in a category and tell “how many.” Apply It, Animal Sort Activity, “Tell children to choose one category they can 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 3, Math In Action: Make a Mobile, connects the supporting work of K.G.2 (Correctly name shapes regardless of their orientations or overall size.) to the major work 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.) as “children apply several skills to solve real-world problems related to mobiles. Problems involve designing a mobile using any flat shapes, designing a second mobile using only two kinds of flat shapes…”.  In Session 2, Apply It, Design a Mobile with Two Shapes Activity, “Tell children to choose two kinds of flat shapes for their mobile. Have them complete the mobile with a total of five shapes. Then have them record the addition to show the shapes on their mobile.”

• Unit 5, Math In Action: Grow a Garden, connects the supporting work of K.MD.3 (Classify objects into given categories, count the numbers of objects in each category and sort the categories by count) to the major work of K.CC.4 (Understand the relationship between numbers and quantities; connect counting to cardinality. (a) When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (b) Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.) as students create their own class garden activity, design a different garden with groups activity, and finally collect, organize and interpret the data. In Session 3, Collect, Organize, and Interpret Data, p. 425 in the Student Book, “Have children make a shopping list for their garden with groups of 8. Have them draw a symbol for each kind of plant they used and then record how many of each they need.” Also in Session 3, Collect, Organize, and Interpret Data, Facilitate Whole Class Discussion, the teacher uses a chart paper to help “Build a class data display to decide what plants to place in the class garden.” Teacher states, “Draw symbols from the key on chart paper. Survey the class. Point to each kind of plant and say its name. Have each child place a sticky note above their symbol for each plant that they have on their shopping list. Point to the group of sticky notes above each symbol. Help children understand that the group of sticky notes shows how many people have that plant on their list and want that plant in the class garden.”

• Unit 7, Math In Action: Build for Birds, connects the supporting work of K.G.6 (Compose simple shapes to form larger shapes.) to the major work of K.CC.3 (Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects.)) as “children apply several skills to solve real-world problems related to gardening. Problems involve composing flat shapes to make pictures of birdhouses, choosing the number of holes for a birdhouse…” Session 1, Apply It, Design Birdhouses Activity, “Provide each child with a large sheet of paper for making their pictures. Children may choose to draw, cut, and paste, and/or position objects such as pattern blocks, depending on their preferences and materials available.” Session 1, Apply It, Design Birdhouses Activity, Student Book, “Have children put flat shapes together to design different birdhouses. Then have children color each kind of shape they used and write the number of each kind.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials are designed so major standards/clusters are connected to the major standards/ clusters of the grade as well as supporting standards/clusters being connected to supporting standards/clusters. Within Program Implementation, Correlations, Content Focus in the Common Core State Standards (CCSS), teachers are encouraged to "Use the tables to help inform i-Ready Classroom Mathematics instructional pacing so that students spend the majority of their time on the work of the major clusters, with time spent on supporting and additional clusters used to enhance that work.” Examples of connections include:

• Unit 2, Lesson 4, Count, Show, and Write Numbers to 5 connects the major work of K.CC.A (Know number names and the count sequence.) to the major work of K.CC.B (Count to tell the number of objects.), as students recognize connections between written numbers. Session 2, Develop, Centers, Differentiation, and Practice, Independent Practice, “Have children count each group of animals. Then have them color the number card that shows how many animals they counted.” Session 3, Develop, Centers, Differentiation, and Practice, Independent Practice, “Ask children to count the counters in each group. Then have them trace and write the number of counters in each group.” Session 4, Refine, Centers, Differentiation, and Practice, Independent Practice, “For each problem, ask children to trace the number. Then have them draw that many counters.”

• Unit 2, Lesson 5, Compare Numbers to 5 connects the major work of K.CC.B (Count to tell the number of objects.) to the major work of K.CC.C (Compare numbers.), as children compare groups of objects and numbers up to 5 and recognize that each counting number is one more than the last. Session 3, Develop, Apply It, Hide One More Activity, “Place a bowl upside down and have the first child hide their counter under the bowl. Ask: How many counters are under the bowl? Have the next child put their counter under the bowl. Say: We hid one more. How many counters are under the bowl now? Reveal the counters. Say: Let’s count them to check: 1, 2. Correct! When you count, the number after 1 is 2. Repeat by having the remaining children take turns to hide one more counter until all 5 counters are under the bowl. The class tells how many counters are now under the bowl and counts them aloud to check.” 

• Unit 3, Lesson 8, Two-Dimensional Shapes connects the supporting work of K.G.A (Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).) to the supporting work K.G.B (Analyze, compare, create, and compose shapes.), as students draw shapes and describe their attributes and positions. Session 1, Explore, Discover It, “Have children trace the faces of some solid shapes onto quarter sheets of paper. Emphasize the flatness of the shapes. Instruct children to show and describe their shapes to each other.” Investigate It, “As children describe each group, have them count how many sides and corners each shape in the group has, and introduce the name of the shape in that group. By the time all groups of shapes have been described, children should know the terms square, triangle, rectangle, circle, and hexagon.” Session 2, Explore, Centers, Differentiation, and Practice, Independent Practice, “Have children draw lines to match shapes with the same name.” An image with four shapes and four real-world shapes, a clock, a road sign, a map, etc., is shown. “Have children draw the shape of each object.” An image of four real-world shapes such as a tv remote and a coin is shown. Session 3, Develop, Centers, Differentiation, and Practice, Independent Practice, “Have children draw a design with the given number of shapes.” An image of three connected triangles and a square is shown, with a space for students to count the triangles and squares. 

• Unit 6, Lesson 21, Subtract Within 10 connects the major work K.CC.B (Count to tell the number of objects.) to the major work of K.OA.A (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.), as students model a subtraction story and count the objects to tell how many. Session 1, Explore, Discover It, “This activity allows children to draw upon their knowledge of subtraction story problems within 5 to tell and solve subtraction story problems within 10 using a variety of tools. Write 7-2 on the board and explain that the numbers and symbols can be used to tell a story. Share a take-away subtraction story problem: 7 children ride bikes to the park. Then 2 children ride bikes home. How many bikes are still at the park? Ask: Where are the numbers and symbols represented in the story? Ask a volunteer to model the problem using a tool of their choice and share how many bikes are left. [5] Give each child a card. Provide each group with various manipulatives. Have children take turns using their card to tell a story problem. Remind children they may use the picture on the Number Sense page as inspiration. Have each child in the group model and solve the problems using different tools.”

• Unit 7, Lesson 24, Build With Shapes connects the supporting work of K.G.A (Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).) to the supporting work K.G.B (Analyze, compare, create, and compose shapes.), as students identify shapes, compare, analyze, and compose shapes. Session 2, Develop, Apply It, Tangram Puzzle Activity, “How can you make pictures using two- dimensional shapes. Introduce the tangram shapes by having children look at the shapes and name the shapes they know. Ask: Are any tangram shapes exactly the same? Are any of the shapes different even though they share the same name? Explain that tangram shapes represent two-dimensional shapes. Have each child take two tangram shapes and put them together to make a new shape. Encourage children to make one shape they recognize and one shape they do not recognize. Let children know that the shapes need to be touching but the sides do not have to line up exactly for this activity.”

The materials reviewed for i-Ready Classroom Mathematics Grade Kindergarten meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Each Unit contains a Beginning of Unit section that provides several resources including a Lesson Progression and Math Background document. The Lesson Progression document identifies “Which lessons are students building upon?” and “Which lessons are students preparing for?” This Lesson Progression document identifies the connections to future and prior work. Additionally, the Math Background identifies “Information to unpack the learning progressions and make connections between key concepts.”

Each Lesson contains a Learning Progression that also identifies connections to future and prior work and a Prior Knowledge section that identifies prior skills. Examples of connections made to future grades include:

• Unit 3: Addition and Subtraction Within 5 and Shapes, Lesson 10, Add and Subtract Within 5, Learning Progression, “In This Lesson, Children solve addition and subtraction problems, determining the operation to use and showing their thinking with concrete objects, visual models, and/or words. Children are introduced to the plus (+) and minus (–) signs and match given expressions with their models.” “Later, in future Kindergarten lessons, children extend their understanding to addition and subtraction within 10 and use equations to record the results.”

• Unit 4: Numbers to 10 and Shapes, Lesson 13, Compose Shapes, Learning Progression, “Previously, Children have explored three-dimensional (solid) and two-dimensional (flat) shapes in their environment. They learned to name common solid shapes (cone, cylinder, sphere, cube) and flat shapes (triangle, square, rectangle, circle, hexagon). They have begun to distinguish between defining attributes, such as the number of faces and whether a shape has curved or straight sides, and non-defining attributes, such as size and orientation.” “Later in Grade 1, children will compose two-dimensional shapes by combining smaller shapes, and they will partition shapes into two or four equal parts, using the words half, fourth, and quarter to describe one of the equal parts.”

• Unit 6: Addition and Subtraction Within 10, Lesson 22, Add and Subtract to Solve Word Problems, Learning Progression, “In This Lesson, Children continue to practice solving addition and subtraction story problems to 10. Building off their exposure to addition and subtraction problems, children now decide whether to add or subtract to solve a problem. They draw pictures and write equations to represent the problems.” “Later, In Grade 1, children will develop a variety of strategies to add and subtract within 20 and build an understanding of the relationship between addition and subtraction. They will use these strategies to solve story problems to 20 with unknowns in all positions, including comparison situations.”

Examples of connections made to prior grades include:

• Unit 1: Position, Length, Height, and Sorting, Lesson 1: Describe Position, Prior Knowledge, “Describe objects using informal terms.” Learning Progressions, “Children may enter kindergarten with some informal experience with describing positions of objects and listening to descriptions of where objects are. They may have used or heard some positional words.”

• Unit 2: Beginning of Unit, Math Background, Prior Knowledge, “Children will build on a wide range of skills. They may: be able to rote count to 10 or beyond, be able to count 5 or more objects with understanding of quantity.” 

• Unit 3: Addition and Subtraction Within 5 and Shapes, Beginning of Unit, Math Background, Prior Knowledge, “Children will build on solid counting skills. They should: have repeated practice with counting quantities, understand that the next number in the counting sequence represents one more, be able to count and compare quantities up to 5, have had informal exposure to shapes and their names, be able to identify basic shapes in standard configurations.”