Dynamic measurement model related to division
- Pellumb Kllogjeri
There is a model related to the concept of measurement division. This is the case of determining the number of groups in which a given number of objects is equally shared or spread. In other words, the task is to find the number of groups (which is unknown) when the total number of the objects is shared in equal quantities (which is known). The type of strategy used by the students is called the measurement strategy, because the students in each trial measure (count) the number of sets they have created. The measurement strategy relates to the common practice applied to find the number of containment of a given stick in a given straight part of a road, of a given segment in another bigger segment when the smaller segment is contained in it a whole number of times. The common practice is measuring the length of the straight part of the road, starting from one edge to the other, by the use of the stick as a unit. Assume our task is to find out how many times the segment (stick) OA is contained into the segment OP given that the length of segment OP is 14 units and the length of the stick is 2 units. The equivalent problem is: find out how many times number 2 is contained to number 14, or what is 14 : 2 ? To solve the problem we measure the length of OP, starting from point O, and using the stick OA. The model and the respective strategy of answering the above question is shown in the above applet. Watch it by putting in the slider: Animation On. Or, hit the slider and keep pressed the right arrow button on the key board, next try the left arrow button and observe the measurement process. Build your model for another case of division.
Try to find out how the measurement model related to division is constructed. Watch the procedure for measuring the length of segment OP using the stick OA by selecting in the slider Animatrion On. How many times is contained OA to OP? Watch and count as the stick is used by a hidden hand to measure the length of OP. Construct your measurement model for other cases of division such as 12 : 4, 15:3, 15 : 5, 18 : 6 etc..... If you are teacher use dynamic models in your class to perform demonstrations of the mathematical concepts and algorithms.