## DIVIDING AND SUBDIVIDING—REPEATED HALVING

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. 