KCCB4 About the Math, Learning Targets, and Opportunities for Enrichment

Kindergarten Mathematics Counting and Cardinality

K.CC.B.4

Full Standard

Understand the relationship between numbers and quantities; connect counting to cardinality.

  1. 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.
  2. 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.
  3. Understand that each successive number name refers to a quantity that is one larger.

 

Measurement Topic

This standard is reported on the report card in these quarters as follows:

Kindergarten Students Learning Kindergarten Standards
Quarter 1 Quarter 2 Quarter 3 Quarter 4

Report Card Measurement Topic: Demonstrates understanding of counting principles.

 

 

 

About the Math

Skills and concepts below are learning goals for this standard.

  • Count objects in a group (each object is counted only once) regardless of arrangement and order.
  • Determine "how many" are in a group after counting all the objects.
  • Count on from a known number (without recounting the whole group) when one more object is added to the group.
  • Explain how things are counted. 
  • Explain that the next number is one more or one larger.

One of the first major concepts in a student’s mathematical development is cardinality. Cardinality is knowing that the number word said tells the quantity you have, and that the number you end on when counting represents the entire amount counted. The big idea is that number means amount and, no matter how you arrange and rearrange the items, the amount is the same. Until this concept is developed, counting is merely a routine procedure done when a number is needed. To determine if students have the cardinality rule, listen to their responses when you discuss counting tasks with them. For example, ask, “how many are here?”. The student counts correctly and says that there are seven. Then ask, “are there seven?”. Students may count or hesitate if they have not developed cardinality. Students with cardinality may emphasize the last count or explain that there are seven because they counted them. These students can now use counting to find a matching set.

Students develop the understanding of counting and cardinality from experience. Almost any activity or game that engages children in counting and comparing quantities, such as board games, will encourage the development of cardinality. Frequent opportunities to use and discuss counting as a means of solving problems relevant to kindergarteners is more beneficial than repeating the same routine day after day. For example, ask students questions that can be answered by counting up to 20 items before they change and as they change locations throughout the school building.

As students develop meaning for numerals, they also compare numerals to the quantities they represent. The models that can represent numbers, such as dot cards and dominoes, become tools for such comparisons. Students can concretely, pictorially or mentally look for similarities and differences in the representations of numbers. They begin to “see” the relationship of one more, one less, two more and two less, thus landing on the concept that successive numbers name quantities that are one larger. In order to encourage this idea, children need discussion and reflection of pairs of numbers from 1 to 10. Activities that utilize anchors of 5 and 10 are helpful in securing understanding of the relationships between numbers. This flexibility with numbers will build students’ ability to break numbers into parts.

Provide a variety of experiences in which students connect count words or number words to the numerals that represent the quantities. Students will arrive at an understanding of a number when they acquire cardinality and can connect a number with the numerals and the number word for the quantity they all represent.

 

Common Misconceptions

Some students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for counting and should be tagged with a different count word, the student uses the original count word. For example, a student counts four geometric figures: triangle, square, circle and rectangle with the count words: one, two, three, four. If these items are rearranged as rectangle, triangle, circle and square and counted, the student says these count words: four, one, three, two.

 

Progression of Standard within Kindergarten

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Count objects in a group (each object is counted only once) regardless of arrangement and order.
  • Determine "how many" are in a group after counting all the objects.
  • Count on from a known number (without recounting the whole group) when one more object is added to the group.
  • Explain how things are counted. 

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 1
  • Relate counting to adding and subtracting (1.OA.5

 

 

 

 

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