Factors and multiples, tables and long division โ€“ students who are relieved at mastering these in numbers are confounded when the same topics rear their head in algebra. Here is a nice collection of problems that allow students to play with algebraic expressions and study them through the lens of divisibility.

Just imagine, in a routine mathematics class a teacher enters the class room with a colorful board game. Instead of instructing students to take out their math textbooks/note books and setting work for them, he just opens the game board and allows students to play the game. The eyes of the students sparkle and they enjoy playing. Even the back benchers (who generally do not get involved in class room work) come forward to play and give a neck to neck fight to the scholars in the class.

Consider this puzzle. Three brothers โ€“ Youngest, Middle and Oldest โ€“ each receive some money in the form of some inheritance. Youngest keeps half the amount he receives and divides the balance equally among Middle and Oldest. After Middle receives his share, he too keeps half the amount and distributes the balance equally among Youngest and Oldest. Oldest in turn keeps half of the amount he now has (after receiving the shares from his brothers) and divides the remaining equally among Youngest and Middle.

This article deals with a simple test for divisibility by 7 for natural numbers having a minimum of four digits. Here, a case of a six-digit number is proved initially and similar proofs follow for other higher-digit numbers.

Invite your middle school students to this set of problems.

CoMaC shares a problem on the sum of digits adapted from one that appeared in an online column on the Math Forum site.

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