Calendar Capers

Choose any three by three square of dates on a calendar page...

Card Trick 2

Can you explain how this card trick works?

Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Back to the Planet of Vuvv

Why do this problem?

This problem one which requires some knowledge of both place value and different bases. Working in another base can help with real understanding of our base-$10$ number system.

You could start this by either explaining or re-visiting counting in a base such as $6$. Base $7$ could be introduced using the days of a week as an example.

Key questions

If Zios count in $3$s, what will their first 2-digit number be in human numbers?
If Zepts count in $7$s, what will their first 2-digit number be in human numbers?
What is $122, 22, 101, 41$ in Zio counting?
What is $122, 22, 101, 41$ in Zept counting?
Would drawing a sketch help with sorting out the four compass points?

Possible extension

Learners could make a similar puzzle for themselves, or go on to this similar problem: Basically.

Possible support

Suggest trying Alien Counting instead which is a simpler problem of the same type.