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DIVIDING AND SUBDIVIDING—REPEATED HALVING

Grades: 3‒4

Students repeatedly divide and subdivide a unit segment on a number line into halves, fourths, eighths, sixteenths, and thirty-seconds. Through these processes, students locate fractions on the 0-1 interval with denominators of 2, 4, 8, 16, and 32. The act of repeated splitting develops students’ understanding of such fractions not just as locations on a number line, but as the result of repeated halving of a unit segment.

OBJECTIVES 
  • Students will use a number line model to explore fractions.
  • Students will use halving strategies to divide and subdivide a unit segment into smaller parts.
  • Students will locate and identify fractions along a unit segment by repeatedly dividing and subdividing segments into halves.

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.

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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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