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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 b. Identify multiple representations for a number, such as: 12, 6 + 6, dozen

Clarification

Classroom Example 1

Providing students with opportunities to represent a number in a variety of ways strengthens their understandings about number concepts. These multiple representations also help students to think flexibly about a number and develop number sense. Examples of representations for 8 are:

  • 8 fingers (e.g., 4 and 4; 3 and 5)
  • 8 on a ten-frame
  • an arrangement of 8 dots
  • 8 tally marks
  • real-life examples (e.g., "There are 8 people in my family.").

When children represent 12 on a double ten-frame, connections to 5 and 10 are being made (important benchmark numbers). The double ten-frame visually shows students that 12 is 2 more than 10 and 3 less than 15. These ideas are important for children as they develop the foundation needed for thinking about the relationship between addition and subtraction.
 

Note: A ten-frame is a tool that develops understandings about the relationships to 5 and 10. It consists of two rows of five boxes. When representing numbers higher than 5 on a ten-frame, fill the top row first and then the bottom row. A double ten-frame is used to represent numbers up to 20.
 

Representation of 12 on a double ten-frame.
 

Resources:
Juanita V. Copley. The Young Child and Mathematics. Washington, DC: NAEYC, 2000.
Joseph N. Payne (ed). Mathematics for the Young Child. Reston, VA: National Council of Teachers of Mathematics, 1990.
National Council of Teachers of Mathematics. Curriculum and Evaluation Standards for School Mathematic. Reston, VA: NCTM, 1992.
National Council of Teachers of Mathematics. Illuminations. 2004. http://illuminations.nctm.org
/instruction/clarification/mathematics/grade1/xml/6A1b.xml
Resources for Objective 6.A.1.b:
CLARIFICATIONS | Prerequisites | Lesson Seeds | Thinking Skills | Sample Assessments |