jaunt (noun) a short excursion or journey for pleasure

mental-jaunt (noun) a short mental excursion or mental journey for pleasure, nothing too heavy!

Mental-jaunts are trails that will evoke certain ways of thinking that are very helpful both in understanding more complex mathematical concepts as well as life in general.

One person’s thinking along one possible trail is supplied to assist you in taking your students on the trail.

To students (of all ages):

**jaunt (noun)** a short excursion or journey for pleasure

**mental-jaunt (noun)** a short mental excursion or mental journey for pleasure, nothing too heavy!

Halving, in mathematics, means to divide by 2. Halving is not “harfing”.

Let’s define “Harfing” as taking an integer with an even number of digits and separating them (centrally) into two digits (which are called the ‘harfs’)

e.g. the result of harfing 73 is 7 and 3 and the result of harfing 4580 is 45 and 80.

Can you find an integer for which squaring the sum of its harfs gives the integer?

If you find one can you find more?

If you do, what questions are you now wondering about?

Most importantly, will you share the mental-jaunt you went on – explaining what you were thinking at the very start and how you reached your destination.

Below you can download elements of one person’s thinking, punctuated with reasoning why this activity is a positive one for students to explore.