> According to Chih-Han sah: > > > > > > Here is another explanation about the rule for division involving > > fractions: > > > > One way to explain "what is a number (positive ones)?" is to > > say that it is used to describe the "ratio" of "like quantities". > > > ><snip, snip> > > > Exercise: What is the average speed in mph of the ratio of a change > > of 88 ft in distance to a change of 1 second in time? > > > > > I would be delighted if my fifth graders were at the developmental level to really understand ratios, much less use them in the explanation of division. However, I did like the explanation and will save it for my math ed classes.
I do think Tad's explanation of division using unifix cubes is understood by fifth graders. I use unifix cubes all the time.
Fifth graders are still very concrete in their thinking. That's why a manipulative is essential to bridge that gap between the concrete and abstract. And, we who are operating at formal reasoning, must realize many of our students are not even developmentally near this level. --
Math History Lives!
Karen Dee Michalowicz VQUEST Math Lead Teacher/Trainer Upper School Mathematics Chair Virginia Quality Education The Langley School in Sciences and Technology 1411 Balls Hill Rd, McLean, VA 22012 USA 703-356-1920(w) E-Mail: firstname.lastname@example.org Fax: (703) 790-9712 --or-- KarenDM@aol.com