K.CC.B.4

Understand the relationship between numbers and quantities; connect counting to cardinality.
 - 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. - 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. - Understand that each successive number name refers to a quantity that is one larger.

Summary:

Students should say number  names and manipulate objects in order to count the number of objects in a set. Students should be encouraged to count sets of different types of objects to see that even if their contents are different, sets can have the same size. Students need practice in counting objects in a set by connecting each object to a number name, and in connecting the number of objects in a set to a specific number.

For instance, the sets {Jill, Bill, Sue}, and {dog, cat, elephant} all have the same size (3). Through experiment, students can determine that the order they count in does not change the final outcome. For instance {dog, cat, elephant} has the same number of objects as {cat, dog, elephant}. Students can also determine that objects can be counted even if they are not arranged linearly; their arrangement does not affect the total number.

Students can be asked to count the number of objects in a set. For example, they can take a handful of counting objects (beads, coins, buttons, etc.) out of a container, pour them on a desk or table, and then count them one by one. Each number they count is greater than the number before, and the last number they use is the number of objects in the set. Students are expected to be able to count items from 0 to 20.

Understanding the Standard:

• Students need opportunities to connect number words (orally) and the quantities they represent.
• Students should have opportunities to arrange a set of objects in a variety of ways and discover that the arrangement of those objects does not change its quantity.
• Students need a variety of games and activities that will provide ample opportunities to match the size of a set of objects with its corresponding numeric symbol and its verbal form.
• The use of a variety of manipulatives and technologies is useful as well, especially for showing sets with more or less than an initial set.  For example, a teacher could use a Smartboard to display a set of 5 objects, and have students count and see that there are 5 objects. Then she could drag another object into the field of vision and see if students can figure out, without counting, that there are now 6 objects (the next number in the counting sequence).
• Students should be encouraged to draw their own examples of sets and determine the size of each set.

Questions to Focus Instruction:

• Are students able to point to objects as they count on to determine how many items are in a particular set?
• Can the student count objects in a manner that pairs each object with only one number in the number sequence? For instance, does the student double-count the same object or say the same number more than once?
• Can students match the numeric symbol and word form of a given amount of objects in a set?
• Can students accurately name the quantity of a set of objects regardless of their physical arrangement?
• Focus on the idea that each object can only be counted once.
• Can a student determine which of two consecutive numbers is less? For instance, "which is less: 5 or 6?"
• After counting a set of objects, are students able to represent that amount with a numeric symbol?
• If one object is added to a set, can students determone, wihout recounting all of the objects in the set, that the number of objects has changed to the next number in the count sequence?

Skills

Prior to: Students can count fluently to 100 and are able to recognize the numeric symbol for the numerals from 0 to 10.