## DIVIDING AND SUBDIVIDING—CONSTRUCTING FRACTIONS

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