This month’s puzzle is designed to foster math-ematical thinking
as students apply problem-solving skills. In this activity, students are
presented with the following paradoxical scenario: Two students each pick
four whole numbers less than 10 and multiply them to €nd the product. Although
the chosen numbers are not all identical, the products are the same. The
challenge in this Puzzle Corner activity is to €nd out how this is possible
and to come up with several sets of numbers that work.
This activity is written
using precise mathematical vocabulary. Students need to know that whole numbers
are the natural numbers (1, 2, 3, 4, …) with the addition of zero (0,
1, 2, 3, …). They also need to know that a product is the answer obtained
when multiplying.
In addition to thinking mathematically and knowing the
correct vocabulary, students will need to employ some problem-solving strategies
in order to solve this paradox. One of the most-used strategies is guess
and check, and this is an appropriate one to start with. Some students may
get lucky and accidentally €nd a solution, but others will have to employ
some other strategies in order to be successful. A few of the strategies
that can be used are organizing the data, logical thinking, and using mathematical
reasoning. Each of these strategies can help students €nd a solution to this
paradox.
As with all Puzzle Corner activities, you should try come up with
your own solution(s) before assigning it to your students. This will give
you an idea of what students will be facing when tackling this problem. In
addition, be sure to remind students to work on this problem independently
and tell those who €nd solutions to keep these solutions to themselves until
the sharing session later in the week. This way they won’t spoil the
joy of discovery for their classmates.
Worksheet
