Kindergarten - Gateway 1

The materials reviewed for Kendall Hunt's Illustrative Mathematics Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades. The curriculum is divided into eight units and each unit contains an End-of-Unit Assessment. While Unit 1 includes an End-of-Unit Assessment as an Interview, all other units include a written assessment for individual student completion. Additionally, the Unit 8 Assessment is an End-of-Course Assessment and it includes problems from across the grade. Examples from End-of-Unit Assessments include: 

• Unit 2, Numbers 1-10, End-of-Unit Assessment, Problem 4, “a. Circle the number that is more. 4, 6. b. Circle the number that is less. 8, 5.” (K.CC.7)

• Unit 5, Composing and Decomposing Numbers to 10, End-of-Unit Assessment, Problem 3, “Mai has a train of 7 connecting cubes. She snaps the train into two pieces. Show 1 way to snap the cubes. Show a different way to snap the cubes.” A picture of seven snap cubes is shown. (K.OA.3)

• Unit 6, Numbers 0 - 20, End-of-Unit Assessment, Problem 1, ”Draw 17 dots. Use the 10-frame if it helps you.” An image of a ten frame is provided. (K.NBT.1)

• Unit 7, Solid Shapes All Around Us, End-of-Unit Assessment, Problem 3, “Consider the ball and box your teacher has displayed. How are the shapes the same? How are they different? Show your thinking with drawings or words.” (K.G.4) 

• Unit 8, Putting it All Together, End-of-Course Assessment, Problem 4, “a. How many dots are there?  b. How many triangles are there?  c. How many counters are there?” There is a picture of 11 dots, 14 triangles arranged in a circle, and 17 counters on ten frames. (K.CC.5)

The materials reviewed for Kendall Hunt's Illustrative Mathematics Kindergarten meet expectations for the materials giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials provide extensive work in Kindergarten as students engage with all CCSSM standards within a consistent daily lesson structure, including a Warm Up, one to three Instructional Activities, a Lesson Synthesis, and 15-25 minutes for Centers. Examples of extensive work include:

• Unit 1, Math in Our World, Lesson 12; Unit 3, Flat Shapes all Around Us, Lesson 4; Unit 4, Understanding Addition and Subtraction, Lesson 12; Unit 5, Composing and Decomposing Numbers to 10 Lesson 9; Unit 6, Numbers 0-20, Lesson 11; and Unit 7, Solid Shapes all Around Us, Lesson 9 engage students in extensive work with K.CC.1 (Count to 100 by ones and by tens). Unit 1, Lesson 12, How Many Are There (Part 1), Activity 2, students work on the verbal count sequence to 10, “‘Let’s count to 10 all together.’ Count to 10 all together. ‘Let’s count to 10 and clap our hands when we say each number.’ Count to 10 and clap all together. ‘Let’s count to 10 and touch the table when we say each number.’ Count to 10 and touch the table all together. ‘Let’s count to 10 and put up 1 finger when we say each number.’ Count to 10 and put up each finger all together.” Throughout Kindergarten, students work up to counting to 100. Unit 3, Lesson 4, Describe, Compare and Sort Shapes, Warm Up: Choral Count, students continue the counting up to 30, “Count to 30 together. Record as students count. Count to 30 1–2 times. Point to the numbers as students count.” Unit 4, Lesson 12, Compare Addition and Subtraction Story Problems, students and the teacher count to 40 together. Warm Up: Choral Count, “Count to 40 together. Record as students count. Count to 40 1–2 times. Point to the numbers as students count.” As students progress to Unit 5, they count up to 70, count to 90 in Unit 6, and count to 100 in Unit 7. Unit 5, Lesson 9, All of the Story Problems, Warm Up: Choral Count, “Let’s count to 70. Count to 70 1–2 times as a class.” Unit 6, Lesson 11, Count Images (Part 1), Warm Up: Choral Count, “Let’s count to 90. Count to 90 1–2 times as a class.” Unit 7, Lesson 9, Compare Capacity, Warm Up: Choral Count, “Display numbers from 1 to 100. ‘Let’s count to 100.’ Point to the numbers as students count to 100.”

• Unit 2, Numbers 1-10, Lessons 5, 8, and 10 engage students in extensive work with K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. Include groups with up to ten objects). Lesson 5, Make Groups of More, Fewer, or the Same, Warm-up: How Many Do You See?, students recognize quantities represented on fingers, without having to count, “How many do you see? How do you see them?” Lesson 8, Compare Matching Images, Activity 1, students compare groups of images that are lined up and decide which group has more or fewer items. Directions state, “Groups of 2, Display the image from the student book. ‘What do you notice? What do you wonder? (There are people and apples. There are 6 people. How many apples are there? Are there enough apples for each person to get one?) Have you ever helped to set the table for a meal or pass out a snack? What did you do?’” Lesson 10, Find More or Fewer, Cool-down: Unit 2, Section B Checkpoint, students use the structure of 5 (in 5-frames or fingers) to count on from 5 to tell how many, “Use ‘more,’ ‘fewer,’ and ‘the same number’ to describe comparisons.”

• Unit 5, Composing and Decomposing Numbers to 10, Lessons 7 and 8, and Unit 8, Putting It All Together, Lesson 3 engage students in the extensive work with 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). Unit 5, Lesson 7, Solve Both Addends Unknown Story Problems, Activity 1, students notice multiple ways to solve a Put Together/Take Apart, Both Addends Unknown story problem. Student Facing, “Jada made 6 paletas with her brother. They made two flavors, lime and coconut. How many of the paletas were lime? Then how many of the paletas were coconut?” Unit 5, Lesson 8, More Than One Way, Activity 2, students solve a Put Together/Take Apart, Both Addends Unknown story problem about dates stuffed with cheese or almonds in more than one way. Student Facing, “Andre and his older brother have 8 dates.They stuff some of the dates with cheese. They stuff the rest of the dates with almonds. How many of the dates did they stuff with cheese? Then how many of the dates did they stuff with almonds?” In Unit 8, Lesson 3, Count to Add and Subtract, Activity 2, students complete and solve numberless Add To, Result Unknown and Take From, Result Unknown story problems. Student Facing, “1. ___ students were singing. Then 1 more student came to sing with them. How many students are singing now? Show your thinking using objects, drawings, numbers, or words. 2. ___ students were singing. Then 1 student stopped singing and went home. How many students are singing now? Show your thinking using objects, drawings, numbers, or words.”

The materials provide opportunities for all students to engage with the full intent of Kindergarten standards through a consistent lesson structure. According to the IM Teacher Guide, A Typical IM Lesson, “Every warm-up is an instructional routine. The warm-up invites all students to engage in the mathematics of the lesson. After the warm-up, lessons consist of a sequence of one to three instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class. After the activities for the day, students should take time to synthesize what they have learned. This portion of class should take 5-10 minutes.” In Kindergarten, most lessons do not include cool-downs like those common in other grades, “During these lessons, checkpoints are used to formatively assess understanding. Since activities are shorter, each lesson includes 15-25 minutes of time for centers.” Examples of meeting the full intent include:

• Unit 3, Flat Shapes All Around Us, Lesson 8, and Unit 7, Solid Shapes All Around Us, Lesson 7 engage students with the full intent of K.G.5 (Model shapes in the world by building shapes from components [e.g., sticks and clay balls] and drawing shapes). In Unit 3, Lesson 8, Draw Shapes, Activity 1, students draw lines to connect dots and practice drawing shapes, “‘These dots will help us draw shapes. I need to connect the red dots using straight lines.’ Demonstrate drawing a straight line between 2 of the red dots. ‘Where should I draw the next line?’ Repeat until the rectangle is drawn. ‘What shape did I draw?’ (A rectangle.) ‘Draw straight lines to connect the dots. When you’re finished, color in the shape and tell your partner about the shape you drew.’” In Unit 7, Lesson 7, Flat and Solid Shapes, Activity 1, students build and compare flat and solid shapes using clay. Directions state, “Give each student a piece of clay. ‘Use your clay to make a shape that you know.’ 1 minute: independent work time. ‘Share your shape with your partner. How are they the same? How are they different?’ (The shapes are different. I made a circle and my partner made a triangle.) Display a cylinder. ‘Make this shape with your clay.’ Display a cone. ‘Make this shape with your clay. Describe the shape that you made to your partner. What does it look like?’ (It looks like an ice cream cone. It’s tall. It has a point on the bottom).”

• Unit 4, Understanding Addition and Subtraction, Lesson 14, and Unit 5, Composing and Decomposing Numbers to 10, Lesson 4 engage students with the full intent of K.CC.2 (Count forward beginning from a given number within the known sequence). In Unit 4, Lesson 14, Expressions and Story Problems, Warm-up: Choral Count, students count on from a given number, “‘Let’s count to 10.’ Count to 10. ‘Now start at the number 3 and count to 10.’ Count on from 3 to 10. Repeat 3–4 times starting with other numbers within 10.” In Unit 5, Lesson 4, Find All the Ways, Warm-up: Choral Count, students count on when given a number, “‘Let’s count to 60.’ Count to 60. ‘Now, start at the number 9 and count to 20.’ Count on from 9 to 20. Repeat 3–4 times starting with other numbers within 10.”

• Unit 3, Flat Shapes All Around Us, Lessons 6 and 7, and Unit 7, Solid Shapes All Around Us, Lessons 8 and 9 engage students with the full intent of 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. For example, directly compare the heights of two children and describe one child as taller/shorter). In Unit 3, Lesson 6, Rectangles and Squares, Activity 2, students use the language longer and shorter to compare the lengths of rectangles, “Circle the rectangle that is longer. Tell your partner how you know which rectangle is longer. Circle the rectangle that is shorter. Tell your partner how you know which rectangle is shorter.” In Unit 3, Lesson 7, Build With Straws, Activity 1, students compare two objects to determine which object is longer or shorter, “Give each group of students a bag of straws. ‘Today we will use these straws to build shapes. First let’s compare the lengths of the straws and figure out which is longer. Work with your partner to compare the length of the straws to the line on your paper. If the straw is shorter than the line, put it on the left side of the page. If the straw is longer than the line, put it on the right side of the page. Tell your partner about each straw using ‘longer than’ and ‘shorter than’.’” In Unit 7, Lesson 8, Compare Weight, Activity 1, students work in pairs to describe and compare the weight of objects, “Display bags 1 and 2. ‘Here are 2 bags, but we can’t see what is inside. Which bag is heavier? How could we figure out which bag is heavier?’ (We could pick them up and feel which one is heavier.) Pass the bags around so that each student can hold both bags to compare the weights.” In Unit 7, Lesson 9, Compare Capacity, Activity 1, students think about and compare the capacity of containers, “Display 2 cups and give each student a sticky note. ‘Which of these cups do you think would hold more lemonade? Put your sticky note by the cup that you think would hold more lemonade.’ 3 minutes: Independent work time. ‘People had different answers about which cup would hold more lemonade. What can we do to figure out which cup can hold more lemonade?’ Demonstrate filling one of the cups with water and then slowly pour that water into the other cup. ‘I filled up the red cup and poured the same water into the blue cup, but the blue cup overflowed. Which cup do you think can hold more lemonade? The red cup can hold more lemonade than the blue cup.’”

The materials reviewed for Kendall Hunt's Illustrative Mathematics Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade: 

• The approximate number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 8, approximately 75%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 123 out of 145, approximately 85%. The total number of lessons devoted to major work of the grade includes 115 lessons plus 8 assessments for a total of 123 lessons.

• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 131 out of 153, approximately 86%.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work, supporting work connected to major work, and the assessments embedded within each unit. As a result, approximately 85% of the instructional materials focus on major work of the grade.

The materials reviewed for Kendall Hunt's Illustrative Mathematics Kindergarten meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed so supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers on a document titled “Pacing Guide and Dependency Diagram” found within the Course Guide tab for each unit. Examples of connections include:

• Unit 1, Math in Our World, Lesson 4, Activity 1 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.3 (Understand the relationship between numbers and quantities; connect counting to cardinality). Students are introduced to geoblocks and explore, sort, and count the geoblocks. The activity states, “10 minutes: partner work time, ‘Share with your partner one thing you did or made with the blocks.’ 2 minutes: partner discussion. Sample responses: Students use geoblocks to build towers, buildings, and other things. Students sort the geoblocks by shape. Students use comparison language like more, bigger, or smaller when discussing their creations. Students use shape names to describe the blocks.”

• Unit 3, Flat Shapes All Around Us, Lesson 5, Activity 1 connects the supporting work of K.G.5 (Model shapes in the world by building shapes from components) 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) and 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). Students identify examples of circles and triangles. The activity states, “‘Choose 1 triangle that you colored in. Tell your partner 1 thing that you know about that shape.’ 30 seconds: quiet think time. 30 seconds: partner discussion. ‘Write a number to show how many triangles you colored. Write a number to show how many circles you colored.’ 1 minute: independent work time. ‘Did you color more triangles or more circles? How do you know?’”

• Unit 8, Putting It All Together, Lesson 1, Activity 1 connects 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.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) and 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]). Students sort objects into categories and represent and compare the number of objects in each category. The Launch states, “Give each student a bag of beads. ‘Sort your beads into two groups.’ 1 minute: independent work time.” The activity states, “How many beads are in each group? Show your thinking using drawings, numbers, or words. 3 minutes: independent work time. ‘Compare the number of beads in each group. Which has more beads? Which has fewer beads? Circle the group that has fewer beads.’ 1 minute: independent work time. ‘Tell your partner which group has fewer beads using this sentence: There are fewer ___ than ___.’” Student Facing states, “How many beads are in each group? Show your thinking using drawings, numbers, or words. Circle the group that has fewer beads.”

The materials for Kendall Hunt's Illustrative Mathematics 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. 

Materials are coherent and consistent with the Standards. These connections can be listed for teachers in one or more of the four phases of a typical lesson: warm-up, instructional activities, lesson synthesis, or cool-down. Examples of connections include:

• Unit 4, Understanding Addition and Subtraction, Lesson 4, Warm Up connects the major work of 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). Students count two groups of numbers to find a total. The activity states, “‘How many students would rather be a bird? How do you know?’ Share responses. Demonstrate or invite students to demonstrate counting. ‘How many students would rather be a fish? How do you know?’ Share responses. Demonstrate or invite students to demonstrate counting.”

• Unit 6, Numbers 0–20, Lesson 5, Activity 1 connects the major work of K.CC.B (Count to tell the number of objects) to the major work of K.NBT.A (Work with numbers 11-19 to gain foundations for place value). Students count to answer “how many” questions about images displayed on fingers. The Launch states, “Groups of 2. Display the student page. ‘Let’s practice reading numbers.’ Point to and read each written number. Invite students to chorally repeat each written number 1–2 times. ‘Now, figure out how many fingers there are. Draw a line from the fingers to the number that shows how many there are.’” Student Facing shows questions 1-5 with a pair of hands with fingers corresponding to numbers 13 to 19. 

• Unit 7, Solid Shapes All Around Us, Lesson 11, Activity 2 connects the supporting work of K.G.B (Analyze, compare, create, and compose shapes) to the supporting work of K.MD.B (Classify objects and count the number of objects In each category). Students determine defining characteristics for sorting solid shapes into groups. The Launch states, “Give each group of students a collection of at least 6-8 solid shapes. ‘Work with your partner to sort the shapes into two groups. Write a number to show how many shapes are in each group.’” The activity states, “‘Think of a name for each group of shapes that describes why you put those shapes together. You can write the name above each group. Pair up with another group. Explain to them which shapes you put together and why. Sort your shapes in a different way.’ Monitor for students who sort the shapes based on attributes, as described in the activity narrative.”

• Unit 8, Putting It All Together, Lesson 2, Activity 1 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). Students count collections of up to 20 objects and represent their count with drawings and numbers. The Launch states, “Give each student a collection of objects and access to 10-frames.” Student Facing states, “How many objects are in your collection? Show your thinking using drawings, numbers, or words ___.”

The materials reviewed for Kendall Hunt's Illustrative Mathematics 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. 

Prior and Future connections are identified within materials in the Course Guide, Section Dependency Diagrams which state, “an arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.” Connections are further described within the Unit Learning Goals embedded in the Scope and Sequence, within the Preparation tab for specific lessons, and within the notes for specific parts of lessons. 

Examples of connections to future grades include:

• Unit 3, Flat Shapes All Around Us, Lesson 3, Preparation connects K.G.4 (Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts and other attributes) to work defining attributes of shapes in Grade 1. Lesson Narrative states, “Students look at pictures of objects in the environment as well as common flat shapes. They describe and compare shapes. This lesson is an opportunity to see what attributes of shapes students notice and attend to. Students notice and describe both defining (number of sides and corners, flat or straight sides) and non-defining (size, color, orientation) attributes of shapes. This allows teachers to see the vocabulary students use to describe shapes (MP6). In grade 1 students will distinguish between these defining and non-defining attributes of shapes.”

• Unit 6, Numbers 0-20, Lesson 7, Preparation connects 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) to work with relating counting to addition and subtraction in 1.OA.5. Lesson Narrative states, “Students write a number to represent a quantity greater than 10 for the first time. Students use full 10-frames and some more to identify and create numbers 11–19. Students may count all of the dots or counters to determine the teen number, or they may count on from 10. Counting on to determine the total is not an expectation in kindergarten.”

• Course Guide, Scope and sequence, Unit 7, Solid Shapes All Around Us, Unit Learning Goals connect K.G.5 (Model shapes in the world by building shapes from components and drawing shapes) and K.G.6 (Compose simple shapes to form larger shapes) to the work of creating composite shapes in Grade 1. Lesson Narrative states, “Students use their own language to describe attributes of solid shapes as they identify, sort, compare, and build them, while also learning the names for cubes, cones, spheres, and cylinders. The work here prepares students to identify defining attributes of shapes and to use flat and solid shapes to create composite shapes in grade 1.”

Examples of connections to prior knowledge include:

• Course Guide, Scope and Sequence, Unit 1, Math in Our World, Unit Learning Goals connect K.CC.A (Know number names and the count sequence), K.CC.B (Count to tell the number of objects), and K.G.A (Identify and describe shapes) to previous work with counting. Lesson Narrative states, “Students enter kindergarten with a range of counting experiences, concepts, and skills. This unit is designed to be accessible to all learners regardless of their prior experience. To that end, no counting is required for students to engage in the activities in the first three sections, though students may choose to count. Students also have opportunities to work with math tools and topics related to geometry, measurement, and data through a variety of centers.”

• Unit 2, Numbers 1–10, Lesson 4, Preparation connects K.CC.6 (Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group) to previous work comparing quantities in Kindergarten. Lesson Narrative states, “In a previous lesson, students identified groups that had more or fewer objects than a given group. The number of objects in the groups made it easy to compare the groups visually. For example, students could tell by looking that a group of two cubes was fewer than a group of nine cubes. In this lesson, students compare groups of objects that are closer in quantity. Students also practice using the words fewer, more, and the same in sentences that compare quantities (MP6). For example, students hear and repeat statements such as, “There are fewer red counters than yellow counters.”

• Unit 5, Composing and Decomposing Numbers to 10, Lesson 2, Preparation connects K.OA.3 (Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from) to work composing shapes in Kindergarten Unit 3. Lesson Narrative states, “In a previous unit, students made designs with pattern blocks and counted how many of each pattern block they used. In this lesson, students make and share a design with the same total number of pattern blocks but different numbers of individual pattern blocks.”