K.CC.4

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. c. Understand that each successive number name refers to a quantity that is one larger. || ===**Anchor Standard/Mathematical Practice(s)**=== K.MP.2. Reason abstractly and quantitatively. K.MP.7. Look for and make use of structure. K.MP.8. Look for and express regularity in repeated reasoning. || **Remembering** **:** can the student recall or remember the information? define, list, recall **Understanding:** can the student explain ideas or concepts? sort, classify, describe, discuss, explain, identify, locate, recognize, select **Applying** : can the student use the information in a new way? demonstrate, illustrate, sketch, write. **Analyzing** : can the student distinguish between the different parts? compare, distinguish, examine, **Evaluating** : can the student justify a stand or decision? appraise, argue, defend, judge, select, support, value, evaluate **Creating** : can the student create new product or point of view? create, design, write. ||
 * ===**Common Core Standard**===
 * ===**Information Technology Standard**===
 * K.TT.1.1 Use a variety of technology tools to gather data and information (e.g., Web-based resources, e-books, online communication tools, etc.). || ===**Revised Bloom's Level of thinking**===

**Learning Target/Task Analysis**

 * I can...**


 * a.** count every object.
 * b.** understand the last number I say tells the number of objects I counted.
 * c.** add one more to a group and tell how many there are.

**Essential Vocabulary**

 * **count, more, add, objects**

**Sample Assessments**

 * **With partners, students count sets of objects to match given numbers (e.g., place beans in egg cartons or muffin tins labels with numbers in sequence.)**
 * **Students answer questioning prompts to establish the understanding of numbers in sets.**

**Differentiation**

 * **Students use number dot cards to play a memory match game**
 * **Students use dominoes to count the dots and match with number cards.**
 * **Give students index cards with a number 0-20 in the corner of the index card. Students must illustrate**

**Intervention:**

 * **Have students point to and move each object as they count aloud.**
 * **Decrease the amount of objects to be counted (e.g., work with numbers 0-5 then progress foward to bigger numbers).**

**Enrichment:**

 * **Give students index cards with a number 0-20 in the corner of the index card. Students must illustrate by drawing objects for that corresponding number.**

**Instructional Resources**

 * Unifix cubes
 * Counting books
 * Dot set cards
 * manipulatives
 * __Anno's Counting__ book by Mitsumasa Anno
 * __Count!__ by Denise Fleming
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**Notes and Additional Information**
Students count a set of objects and see sets and numerals in relationship to one another. These connections are higher-level skills that require students to analyze, reason about, and explain relationships between numbers and sets of objects. The expectation is that students are comfortable with these skills with the numbers 1-20 by the end of Kindergarten.

a. Students implement correct counting procedures by pointing to one object at a time (one-to-one correspondence), using one counting word for every object (synchrony/ one-to-one tagging), while keeping track of objects that have and have not been counted. This is the foundation of counting.

b. 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: “There are 10 bears in this pile.” (cardinality). Since an important goal for children is to count with meaning, it is important to have children answer the question, “How many do you have?” after they count. Often times, children who have not developed cardinality will count the amount again, not realizing that the 10 they stated means 10 objects in all. Young children believe what they see. Therefore, they may believe that a pile of cubes that they counted may be more if spread apart in a line. As children move towards the developmental milestone of conservation of number, they develop the understanding that the number of objects does not change when the objects are moved, rearranged, or hidden. Children need many different experiences with counting objects, as well as maturation, before they can reach this developmental milestone.

c. Another important milestone in counting is inclusion (aka hierarchal inclusion). Inclusion is based on the understanding that numbers build by exactly one each time and that they nest within each other by this amount. For example, a set of three objects is nested within a set of 4 objects; within this same set of 4 objects is also a set of two objects and a set of one. Using this understanding, if a student has four objects and wants to have 5 objects, the student is able to add one more- knowing that four is within, or a sub-part of, 5 (rather than removing all 4 objects and starting over to make a new set of 5). This concept is critical for the later development of part/whole relationships. Students are asked to understand this concept with and without (0-20) objects. For example, after counting a set of 8 objects, students answer the question, “How many would there be if we added one more object?”; and answer a similar question when not using objects, by asking hypothetically, “What if we have 5 cubes and added one more. How many cubes would there be then?”