Standards for Grades 3-5, page 152

Examining the effect of multiplying or dividing numbers can also lead to a deeper understanding of these operations. For example, dividing 28 by 14 and comparing the result to 28 by 7 can lead to the conjecture that the smaller the divisor, the larger the quotient. With models or calculators, students can explore dividing by numbers between 0 and 1, such as 1/2, and find that the quotient is larger than the original number. Explorations such as these help dispel common, but incorrect, generalizations such as, "division always makes things smaller."

visual fraction division