Testing numbers for divisibility by small numbers like 9 and 11 are part of standard math curricula in many countries. These tests are often taught as rules to be blindly followed and even teachers have no idea why they work. This document is a series of activities through which students are convinced about the validity of the tests and also gain an understanding of why they work. The approach does not use formal proofs but uses a pre-algebraic technique which convinces most students about the validity of the tests.
The document also contains cards to be printed.
The preview document only deals with tests for 2, 4 and 8, while the full document also deals with 3, 5, 7, 9 and 11 (including why there are no simple tests for divisibility by 7).