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DIVIDING AND SUBDIVIDING—CONSTRUCTING FRACTIONS

Grades: 3‒4

Students find different ways to split a unit segment into equal parts to locate fractions on a number line. For example, students construct 1/6 by splitting a unit segment into six equal parts. As an alternative method, they first split the unit segment in half and then split each half into thirds. The act of dividing and subdividing develops students’ understanding of fractions not just as locations on a number line, but as equal parts of a unit segment.

OBJECTIVES 
  • Students will use a number line model to explore fractions.
  • Students will develop strategies for dividing and subdividing a unit segment into equal parts to locate given fractions.
  • Students will recognize that a fraction like 1/12 may be obtained by splitting different fractions into different numbers of equal pieces, such as splitting halves into sixths, sixths into halves, thirds into fourths, or fourths into thirds.

COMMON CORE CONNECTIONS 
Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (5) Use appropriate tools strategically; (7) Look for and make use of structure.

Content Standards

3.NF1, 2, 3; 4.NF1, 2, 3

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This activity is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License: http://creativecommons.org/licenses/by-nc-sa/3.0/. If you adapt and/or share this activity, you must attribute it to "KCP Technologies, a McGraw-Hill Education Company." You may distribute it only non-commercially under the same or similar license.


This material is based upon work supported by the National Science Foundation under KCP Technologies Award ID 0918733, with grant period September 1, 2009 through August 31, 2013. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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