# K.1 - Counting

The student will

a)  tell how many are in a given set of 20 or fewer objects by counting orally; and

b)  read, write, and represent numbers from 0 through 20.

### BIG IDEAS

• So that I can tell how many pencils we need for school
• So that I can count to see how many friends are in our class
• So that I can count to see how many crayons are in a box
• So that I can  set the table for family or friends, pass out our snack, and count spaces in the games we play (like Chutes and Ladders)

### UNDERSTANDING THE STANDARD

 There are three developmental levels of counting:rote sequence;one-to-one correspondence; andthe cardinality of numbers. Counting involves two separate skills: verbalizing the list (rote sequence counting) of standard number words in order (“one, two, three...”) and connecting this sequence with the objects in the set being counted, using one-to-one correspondence. Association of number words with collections of objects is achieved by moving, touching, or pointing to objects as the number words are spoken. Objects may be presented in random order or arranged for easy counting.When counting objects, students should:Say the number names in standard order;Count one item for each number word (one-to-one correspondence);Understand that the number of objects is the same regardless of their arrangement or the order in which they were counted (conservation of number);Understand that the last number names the total amount of objects counted (cardinality); andUnderstand that each successive number name refers to a quantity that is one larger. Cardinality is knowing how many are in a set by recognizing that the last counting word tells the total number in a set.After having a student count a collection of objects, the teacher may be able to assess whether the student has cardinality of number by asking the question, “How many are there?”  Students who do not yet have cardinality of number are often unable to tell you how many objects there were without recounting them.Kinesthetic involvement (e.g., tracing the numerals, using tactile materials, such as sand, sandpaper, carpeting, or finger paint) facilitates the writing of numerals.If a set is empty, it has zero objects or elements.  Zero is both a number and a digit. It is used as a placeholder in our number system.Symbolic reversals in numeral writing are common for this age and should not be mistaken for lack of understanding.Describing a teen number as a ten and some more, will help students name how many are in a set of 13-19 objects.  This also lays a foundation for place value.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Count orally to tell how many are in a given set containing 20 or fewer concrete objects, using one-to-one correspondence, and identify the corresponding numeral. (a)
• Read, write, and represent numbers from 0-20 to include:
• Construct a set of objects that corresponds to a given numeral, including an empty set;
• Read and write the numerals from 0 through 20;
• Identify written numerals from 0 through 20 represented in random order;
• Identify the numeral that corresponds to the total number of objects in a given set of 20 or fewer concrete objects; and
• Write a numeral that corresponds to a set of 20 or fewer concrete objects. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018