Using a digit grid when studying theme "Number systems"

Abstract

The information richness of the informatics course of the basic school makes you pay attention to the possibility for introducing the theme "Number systems" to students at the propaedeutic stage. The use in the fifth or sixth grades of the concept of a detailed form for recording a number to justify the studied algorithms, is impossible for obvious reasons. At this stage of training, you can arrange student actions using a digit grid, which allows you to include the concept of positionality in the orientation basis of actions with numbers in different number systems from the very beginning. The transition from work with a bit grid to the traditional design of algorithms is reasonable to be carried out in three stages. At the first stage, students are offered to operate with numbers in various number systems in a digit grid, replacing q units of the current digit with one unit of the next bit and vice versa. At the second stage, the correspondence between the actions performed at the first stage and the division (multiplication) operations is established, the digit grid is still used to mediate mental actions. At the third stage, the visual use of the bit scheme is refused, students move on to the traditional design of algorithms for actions with numbers in various number systems. For each of the stages, the article provides tasks and questions for organizing frontal solution.