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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic

Topic A. Knowledge of Number and Place Value

Indicator 1. Apply knowledge of whole numbers and place value

Objective a. Extend concept of number

Clarification

There are two types of number knowledge: procedural knowledge and conceptual knowledge.

  1. Procedural knowledge includes:
    • reading and writing numerals
    • rote counting
    • orally counting on and counting back
    • accurately counting sets of objects
  2. Conceptual knowledge includes:
    • understanding quantity and cardinality, or "how muchness." A student with an understanding of cardinality knows that the last number counted in a sequence of items also indicates the total number of items in the set.
    • understandings about more or less (including: 1 more, 2 more;1 less, 2 less)
    • spatial (instant recognition of dot patterns or arrangements, such as the arrangement of dots on a dice or dominoes)
    • using five and ten as benchmarks
    • relative size
    • part-part-total (conceptual understanding of number that is crucial before students begin addition and subtraction)

Before procedural knowledge can be used meaningfully, students must have conceptual understandings of number concepts. It is important for children to experience numbers and counting in different contexts. Developing students' proficiency of cardinality must be an instructional focus in kindergarten when asking children to build and count quantities. As quantity size increases, students begin to use 5 as a benchmark number to compare other quantities.


 

Resource:
John A. Van deWalle. Mathematics for the Young Child: Concepts of Number. Reston, VA: National Council of Teachers of Mathematics, 1984.
/instruction/clarification/mathematics/gradeK/xml/6A1a.xml
Resources for Objective 6.A.1.a:
CLARIFICATIONS | Prerequisites | Lesson Seeds | Thinking Skills | Sample Assessments |