TABLE 6-3 Linear Measurement (Space in One Dimension)

Steps/Ages (Levels of Thinking)

Goals

A. Perceive, Say, Describe/Discuss, and Construct Objects in 1-D Space

B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 1-D Space

C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 1-D Space

Step 1 (Ages 2 and 3)

Thinking visually/holistically

Informally recognize length as extent of 1-D space. Compare 2 objects directly, noting equality or inequality.

Informally combine objects in linear extent.

Step 2 (Age 4)

Thinking about parts

Compare the length of two objects by representing them with a third object.

  • Initial measurement by laying units end to end, often with units that are notably square or cubical (to facilitate physical concatenation).

Understand that lengths can be concatenated.

Relating parts and wholes

Seriate up to six objects by length (e.g., connecting cube towers).

 

Step 3 (Age 5)

Thinking about parts

Measure by repeated use of a unit, moving from units that are notably square or cubical to those that more closely embody one dimension (e.g., sticks or stirrers).

 

Relating parts and wholes

Seriate any number of objects by length, even if differences between consecutive lengths are not palpable perceptually.

  • Initial measurement with simple unit rulers, including sticks with unit lengths marked off and other unit rulers.

  • Explore the relationship between the size and number of units.

Interpret bar graphs to answer questions such as “more,” “less,” as well as simple trends, using length of the bars.

Add two lengths to obtain the length of a whole.

NOTE: Less time on 1-D than on 2-D; about 5 percent of the time on 1-D.



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