Contents
B. Prior Knowledge and Skills Used
D. Content Standards Addressed
E. Standards for Mathematical Practice Featured
G. Connections to the Three Curriculum Threads
A. Key Concepts Developed
Students should understand these concepts by the end of the unit.
 Key Concept 1: Numbers exist in a sequence that does not change, and can be counted.
 Key Concept 2: Each item in a collection must be counted once and only once.
 Key Concept 3: The last number name used names the quantity of objects in the set.
Key Concept 1: Numbers exist in a sequence that does not change, and can be counted.

The Math: In every lesson in this unit, students work on rote counting. Students count to 20 by ones by the end of this unit (K.CC.A.1). In addition to these lessons, students should have many opportunities to practice saying the number names in sequence and incorporate counting in daily activities in the classroom.

Lesson Contexts: Most contexts used in this unit involve realworld problems of interest to kindergarteners. For example, students begin with a familiar context of counting fingers on a hand in a hideandseek game context, then apply that work to counting the correct number of pretzels to match the number of pretzels the students ordered in a later lesson. These contexts support onetoone correspondence and cardinality.

Representations: Cubes, ten frames, disc counters, and teddy bear counters are used to represent the mathematical thinking because they offer discrete representations for the objects students need to count.
Key Concept 2: Each item in a collection must be counted once and only once.

The Math: All of the lessons following Lesson 3 in this unit provide students the chance to count objects, saying the number names in order and pairing each object with one and only one number name (K.CC.B.4a). Students implement correct counting procedures by pointing to, touching or moving one object at a time (onetoone correspondence). They also use one counting word for each and every object (synchrony/onetoone tagging), while keeping track of objects that have and have not been counted. These two concepts are foundational to counting.

Lesson Contexts: The context counting a set of cubes provided to the student establishes the need to count a collection and that each object in the collection can be counted only once. Students will also play games to interest them in the work of counting and understanding the relationship between numbers and quantities.

Representations: Students will use teddy bear counters, ten frames, cubes, disc counters, and their own fingers to represent the objects they need to count. These representations support the idea of onetoone correspondence, as students can keep track of what has and has not been counted while moving or touching the objects.
Key Concept 3: The last number name used names the quantity of objects in the set.

The Math: Students answer the question “How many are there?” by counting objects in a set and understanding that the last number stated when counting a set (…8, 9, 10) represents the total amount of objects (K.CC.B.4b): “There are 10 bears in this set.” (cardinality). An important goal for students is to count with meaning, so it is important to have students answer the question, “How many do you have?” after they count. Frequently, students who have not developed cardinality will count the amount again, not realizing that the 10 they stated means 10 objects in all.

Lesson Contexts: Students encounter the need to count and name the quantity in the set in the context of pets that the students in the class own. In subsequent lessons, student will practice the skills in the context of games and will apply their knowledge in the context of inventorying the class set of teddy bear counters.
 Representations: The concept is developed through work with cubes, disc counters, teddy bear counters, and ten frames.
Students are introduced to rote counting to ten in Lesson 1, which focuses on building conceptual understanding. They may approach this counting problem by using their fingers to represent the counting situation, or simply counting in sequence without their fingers. The finger representation shown in the solution example video connects the discrete model to the rote counting sequence.
Lesson 2 also focuses on conceptual understanding, requiring students to think about counting a collection of blocks to understand pairing each object with one and only one number name and each number name with one and only one object With this experience, students see that each object is counted one time by saying one number name. Students may go beyond counting to five if the teacher provides a collection of more than five objects to the student.
The focus in Lesson 3 is on understanding that the last number name said tells the number of objects counted. Kindergarteners believe what they think they see and may believe that a pile of cubes that they counted may be more if spread apart in a line. Students need many different experiences with counting objects, before they can reach this developmental milestone of number conservation. This lesson begins the process of building that understanding through counting pets that the students in the class own.
In Lesson 4, students practice counting to 5 to develop fluency with that skill. The lesson video shows how to play the game Build a Tower in which students flip a number card to determine how many cubes to connect, building a tower containing that number of cubes. Students then have an opportunity to practice this skill while playing the game. This work is extended to counting to ten with the same game in Lesson 7.
In Lesson 5, students have an opportunity to apply their knowledge and understanding of counting objects within 5 to a realworld situation. Students are asked to help a teacher distribute the correct number of pretzels to each students according to the number they ordered.
Lesson 6 provides students with the opportunity to build counting fluency as they practice counting to ten. Balloons are used in the instruction video in Lesson 6 to provide a familiar context with which to practice counting. Lesson 8 continues this work as students play the game, Fill the Board. In this game, students flip over a tenframe card to indicate how many counters to place on the board. Play continues as students work toward the goal of filling the entire board with counters. This work develops students' understanding that objects must be counted once and only once and the last number said when counting a collection tells the quantity of items in the collection. In Lesson 9, students continue to work with counting to 10, applying that knowledge to a realworld situation of inventorying the teddy bear counters in the classroom. Lesson 10 continues to develop procedural skills with counting quantities of up to 20 objects.
B. Prior Knowledge and Skills Used
Students will begin Kindergarten with various understandings and skills regarding counting. While there is no expectation of prior knowledge for this unit, some students will arrive to Kindergarten with counting and cardinality skills, therefore, counting to 20 should not be a limit.
C. Units on the Horizon
Rote counting to 50 and representing up to 20 objects (Grade K, Unit 7)

By Unit 7 students are expected to fluently rote count to 20 and represent the number of objects in writing. Building a solid understanding of onetoone correspondence by counting to tell the number of objects and developing a system for ensuring they have counted each object will help students in keeping track of the objects that have already been counted. Work in this unit will support this fluency as students extend their work with the counting sequence by counting forward beginning from a given number.
Counting to 100 by tens and ones (Grade K, Unit 13)

Prior experience with rote counting to 50 and representing the number of objects (to 20) in writing are extended as students work with counting up to 100.

Student are introduced to the pattern of counting by tens in this unit. This will be foundational in their understanding early place value concepts and prepare them to understand teen numbers as being composed of ten ones and some more ones (K.NBT.A.1).

Work from Kindergarten, and this unit in particular, will support them in understanding that a twodigit number such as 53 is made up of 53 ones or 5 tens and 3 ones. This notion relies heavily on the idea that a ten is both ten ones and a ten.
D. Content Standards Addressed
K.CC.A: Know number names and the count sequence.
K.CC.A.1: Count to 100 by ones and by tens.
K.CC.B: Count to tell the number of objects.
K.CC.B.4: Understand the relationship between numbers and quantities; connect counting to cardinality.
 K.CC.B.4a: 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.
 K.CC.B.4b: 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.
E. Standards for Mathematical Practice Featured
S.MP.2. Reason abstractly and quantitatively. Students work to make the connection between the number names and quantities.
S.MP.6. Attend to precision. Students work on counting precisely, so as to not miss an object or count any object more than once.
F. Common Misconceptions
 Students may think the last number they say when counting represents the last object counted, when that number actually represents the total number of objects in the set.
 Students may think that the order of objects counted might affect the amount.
 Student may think different arrangements of the same quantity are different.
 Students might skip or double count when counting instead of counting objects once and only once.
G. Connections to the Three Curriculum Threads
Operations, Number, and Equivalence are the threads that tie the curriculum together within and across grades. Read below to learn how the threads are incorporated into this unit. Learn more about the Three Curriculum Threads at this link.
Operations: Students build understandings that will support K.OA.5 (adding within 5.)
Number: Students understand that each number they say as they count names the amount in the collection, not only the object they last counted.
Equivalence: Students will begin to understand that any number is equal to one more than the number before it.