Kindergarten - Gateway 1

The materials reviewed for Imagine Learning Illustrative Mathematics Kindergarten meet expectations for assessing grade-level content and if applicable, content from earlier grades. The materials for Kindergarten are divided into eight units, and each unit contains an End-of-Unit Assessment. Unique to Kindergarten, Unit 1 End-of-Unit Assessment includes an Interview Assessment. All other units include an End-of-Unit Written Assessment. Additionally, the Unit 8 Assessment is an End-of-Course Assessment, and it includes problems from the entire grade level. Examples of End-of-Unit Assessments include: 

• Unit 1, Math in Our World, End-of-Unit Interview Assessment, Problem 1, “Can you please count as high as you can?” When the student stops, ask, “Do you know what number comes after ____ (the number the student stopped at)?” (K.CC.1)

• 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 4, Understanding Addition and Subtraction, End-of-Unit Assessment, Problem 5, ‘Write the value of each expression. 1. 2 + 3 =___, 2. 8 - 1 =___, 3. 3 + 0 =___.” (K.OA.1)

• Unit 5, Composing and Decomposing Numbers to 10, End-of-Unit Assessment, Problem 2, “Write the number that makes 10 with each number. a. 5, b. 9, c. 4.” (K.OA.4)

• Unit 8, Putting It all Together, End-of-Course Assessment, Problem 6 says, “Write numbers to make each equation true.1. 10+6=__, 2. 3+10=__, 3.$$___+___=13$$,  4.$$___+___=17$$.” (K.NBT.1)

The materials reviewed for Imagine Learning Illustrative Mathematics Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide extensive work with and opportunities for students to engage in the full intent of Kindergarten standards by including in every lesson a Warm Up, one to three instructional activities, and Lesson Synthesis. Within Kindergarten, students engage with all CCSS standards.

Examples of extensive work include:

• Unit 2, Numbers 1-10, Lessons 3,15,16 engage students in extensive work with 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)). In Lesson 3, Groups that Look Very Different, Activity 3: Introduce Number Race, Numbers 1–10, students recognize and write numbers as they roll a connecting cube on a number mat and trace the number that it lands on. Directions include, “We are going to learn a new center called Number Race. Let's play a round together.” “I am going to roll the cube onto the number mat. Which number did the cube land on?” 30 seconds: quiet think time. Share responses. “Now I find that number on the recording sheet and trace the number at the bottom.'' Demonstrate tracing the number the cube landed on. “Take turns with your partner. During each turn, roll the cube and trace the number on the recording sheet. Play until you’ve traced all of one number. That number is the winner.”” In Lesson 15, Draw Groups of Things, Cool-down: Unit 2, Section C Checkpoint, students practice counting and writing the numerals 1 through 10. “Count out 1–10 objects or draw 1-10 images to match a given number. Write numbers 1–10.” In Lesson 16, Write Numbers to Represent Quantities, Cool-down: Unit 2, Section C Checkpoint, students write numbers 1 through 10. “Write numbers 1–10.” 

• Unit 4, Understanding Addition and Subtraction, Lessons 4, 6, and 15 engage students in extensive work with K.OA.1 (Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations). In Lesson 4, Add Objects, Activity 1: Add Counters, students add and subtract with objects. “Count out 2 counters. Add 2 more. There are ____ counters.” In Lesson 6, Tell and Act Out Stories, Activity 2: Act Out A Story, students use addition to act out stories. “ ‘Now we are going to hear and act out some stories about students playing at recess. Close your eyes and picture what is happening in the story.’ Display and read the story about students jumping rope. Problem 1: There are 4 students jumping rope at recess. 2 more students came out to play with them.” In Lesson 15, Expressions and Drawings, Activity 3: Introduce Shake and Spill, students represent addition with objects. drawings, and expressions. “Give each group of students two-color counters and red and yellow crayons. Give each student a recording sheet. ‘We are going to learn a new way to play Shake and Spill. One partner will choose some counters, shake them and spill them. Then draw a picture to show the red and yellow counters. Work together to figure out how to fill in an expression to show how many red and yellow counters. Take turns shaking and spilling the counters.’”

• Unit 8, Putting It All Together, Lessons 1 and 3 engage students in extensive work with K.CC.2 (Count forward beginning from a given number within the known sequence (instead of having to begin at 1). In Lesson 1, Sort, Count, and Compare Groups of Objects, Warm-up, students chorally count forward starting at a known number. “Count by 1, starting at 57”. In Lesson 3, Count to Add and Subtract, Warm-up, students practice counting forward and backward. “Let’s count to 20.” Record as students count. “This time, instead of starting a 1 and counting forward, we are going to start at 10 and count backward until we get to 1. Let’s start at 10 and count backward to 1.”

Examples of 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: Connect the Dots, “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: Create Shapes with Clay, students build and compare flat and solid shapes using clay, “Give each student a piece of clay. ‘Use your clay to make a shape that you know. 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. Display a cone. “Make this shape with your clay. 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: Count On “‘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: Count On, 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 5, Composing and Decomposing Numbers to 10, Lessons 12 and 13 engage students with the full intent of 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). In Lesson 12, How Many Are Missing?, Activity 2: How Many to Fill the 10-frame?, students are asked to find how many counters are needed to fill a 10-frame. “Figure out how many counters are needed to fill each 10-frame. Write a number to show how many counters are needed to fill it. Circle the equation that shows the number of counters in the 10-frame and the number of counters needed to fill the 10-frame.”  In Lesson 13, Make 10, Activity 1: Introduce Math Fingers, Make 10, students are asked to show a number on their fingers and determine how many fingers are needed to make 10. Students fill in an equation to represent each composition and decomposition of 10. “I rolled 7, so I am going to hold up 7 fingers. Now my partner needs to figure out how many more fingers I need to put up to show 10 fingers. How many more fingers do I need to hold up to make 10? Now we need to fill in an equation to show how many fingers are up and how many more fingers are needed to make 10. How should I fill in an equation? Take turns with your partner rolling to find a number and showing that number with your fingers. Your partner figures out how many more fingers are needed to make 10. You both fill in an equation to show how many fingers are up and how many more fingers are needed to make 10.”

The materials reviewed for Imagine Learning Illustrative Mathematics Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major clusters of the 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 the major work of the grade (including assessments and supporting work connected to major work) is 6 of 8, approximately 75%.

• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to major work) is 123 out of 145, approximately 85%. The total number of lessons include 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 major work) is 131 days out of 153 days, approximately 86%.

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

The materials reviewed for Imagine Learning 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 with supporting standards/clusters 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 on the Course Guide tab for each Unit. Teacher Notes also provide the explicit standards listed within the lessons. Examples of connections include:

• Unit 3, Flat Shapes All Around Us, Lesson 10, Put Together Pattern Blocks, Activity 1, Introduce Pattern Blocks, Count Out and Build, connects the supporting work of K.G.6 (Compose simple shapes to form larger shapes) 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). Students count shapes and then build patterns with their shapes. Student-facing Task Statement, students are shown how many triangles, hexagons, rhombuses, and squares they will need to count. “We are going to learn a new way to do the Pattern Blocks center. It is called Count Out and Build. You are going to count out the pattern blocks and use them to make your own pattern for a quilt. The numbers tell me how many of each pattern block I need to count out. How many orange triangle pattern blocks do I need? Count out the pattern blocks. Then put your pattern blocks together to make a pattern for a quilt. Tell your partner about what you are making.”

• Unit 7, Solid Shapes All Around Us, Lesson 4, Pattern Block Puzzles and Equations, Activity 2, connects the supporting work of K.G.6 (Compose simple shapes to form larger shapes) 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). Students use pattern blocks to build shapes that represent given equations. During the launch, the teacher says, “‘Put together pattern blocks to make a shape that matches each equation. Trace or draw each shape that you make.’” Student Task Statements include: 4=1+3, 10+0=10, 5+4=9, 8=2+6, 3+3=6, 7=2+5.

• Unit 8, Putting It All Together, Lesson 1, Sort, Count, and Compare Groups of Objects, Activity 1, Sort, Count, and Compare, 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, then represent and compare the number of objects in each category. Teacher Guide, “Give each student a bag of beads. “Sort your beads into two groups.” “How many beads are in each group? Show your thinking using drawings, numbers, or words.” “Compare the number of beads in each group. Which has more beads? Which has fewer beads? Circle the group that has fewer beads.” “Tell your partner which group has fewer beads using this sentence: “There are fewer ___ than ___.” Student Task Statements, “How many beads are in each group? Show your thinking using drawings, numbers, or words. Circle the group that has fewer beads.”

The materials reviewed for Imagine Learning 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. Examples of connections between major work to major work and/or supporting work to supporting work throughout the materials, when appropriate, include:

• Unit 2, Numbers 1-10, Lesson 3, Groups That Look Very Different, 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). In the Lesson Synthesis, students say the number names and count each group of objects in order to compare them. The question is posed, “Are there fewer yellow counters or red counters? How do you know? (image of 10 red counters and 3 yellow counters).” 

• Unit 4, Understanding Addition and Subtraction, Lesson 2, Count 2 Groups of Images, Activity 2: How Many Apples?, 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). In the Teacher Guide Launch, students count 2 groups of images to find the total. “As you continue working to find out how many apples there are altogether, tell your partner how many red apples there are, how many green apples there are, and how many apples there are altogether.”

• Unit 7, Solid Shapes All Around Us, Lesson 11, Compare and Sort Solid Shapes, 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). In Activity 2, Sort Solid Shapes, students sort shapes. In the Teacher Guide Launch, teachers “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.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.”

• Unit 8, Putting It All Together, Lesson 6, Create Number Books (Part 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). In Warm-up, Notice and Wonder, All Hands On, students count objects around them. In the Teacher Guide Launch, “Display the image. What do you notice? What do you wonder?” An image shows six hands in a circle.

The materials reviewed for Imagine Learning 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. 

The Section Dependency Chart explores the Unit sections relating to future grades. The Section Dependency Chart states, “arrow indicates the prior section that contains content most directly designed to support or build toward the content in the current section.” 

Examples of connections to future grades include:

• Unit 3, Flat Shapes All Around Us, Lesson 6, Rectangles and Squares, About this Lesson, 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) and 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.) to work in grade 1. “In kindergarten, it is not important that students articulate the difference between squares and rectangles, only that they can identify examples of each shape. Refer to squares as ‘a special type of rectangle with four sides that are the same length,’ but do not hold students responsible for the definition. In grade 1, students will distinguish between defining and non-defining attributes of shapes, which will allow them to discuss how squares and rectangles are the same and different.”

• Unit 5, Composing and Decomposing Numbers to 10, Section C: Make and Break Apart 10, Section Learning Goals, connects 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), 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)., and 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) to work in grade 1. “Throughout the section, students continue to build their familiarity with equations. They connect compositions and decompositions of 10 represented on their fingers and on 10-frames to addition equations and write missing numbers in such equations. Students are not expected to write equations independently in kindergarten. And although students may start to learn combinations that make 10 from memory, fluency with sums of 10 is not required until grade 1.”

• Unit 8, Putting It All Together, Lesson 3, Activity 1, Ride the Bus, connects K.CC.2 (Count forward beginning from a given number within the known sequence instead of having to begin at 1), K.CC.4 (Understand that each successive number name refers to a quantity that is one larger), and 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) to work in grade 1. About this lesson, “Students may still choose to use objects or drawings to represent and solve story problems, which is great. In grade 1, students will build on this work as they relate counting to addition and subtraction” when they use estimation skills. (1.OA.5)

Examples of connections to prior knowledge include:

• Unit 4, Understanding Addition and Subtraction, Full Unit Narrative, “Previously, students built their counting skills and represented quantities in a group with their fingers, objects, drawings, and numbers.” Lesson 1, About this lesson, “In a previous unit, students counted groups of up to 10 objects, recognized and wrote numbers 1–10, and connected numbers to quantities. In this lesson, students are introduced to addition as they count to find the total of 2 groups. Many students may approach these activities the same way that they answered “how many” questions in previous units—by putting the 2 groups of objects together and then counting all of the objects. The syntheses focus on different strategies for finding the total number of objects given 2 groups of objects.”

• Unit 6, Numbers 0–20, Full Unit Narrative, “Previously, students have counted, composed, and decomposed numbers up to 10, using tools such as counters, connecting cubes, 5-frames, 10-frames, drawings, and their fingers. They wrote expressions to record compositions and decompositions.” Lesson 8, About this lesson, “In previous lessons, students saw numbers 11–19 as ten ones and some more ones as they counted, composed, and represented these numbers. The purpose of this lesson is for students to use the understanding that a full 10-frame contains 10 ones to compose numbers 11–19.”

• Unit 7, Solid Shapes All Around Us, Full Unit Narrative, “In an earlier unit, students investigated two-dimensional shapes. They named shapes (circle, triangle, rectangle, and square) and described the ways the shapes are different. Students used pattern blocks to build larger shapes and used positional words (above, below, next to, beside) along the way.” In Lesson 2, About this lesson, “In previous lessons, students put together and counted pattern blocks to fill in puzzles. Students have noticed that different combinations of pattern blocks can be used to create the same shape. Students use methods developed in previous units to compare the number of pattern blocks.”