Prime or Square

We are currently working on a new mental routines product for Year 6, matched to the content descriptors in the Australian Curriculum: Mathematics. The very first Year 6 content descriptor (ACMNA 122) is:

Identify and describe properties of prime, composite, square and triangular numbers.

As we were writing the mental routine for this content descriptor, we had an idea for the following game.


  • a pack of cards, picture cards removed,
  • a calculator (optional),
  • a list of square and prime numbers (optional),
  • a timer (optional).


Each player is dealt 3 cards.

Players manipulate their cards to create number sentences with the intent of creating square or prime answers. Each square or prime answer scores 1 point.

Failure to create a square or a prime results in a zero score for that round.

The player with the highest score at the end of 5 rounds is the winner.


  • Use only 2 cards not 3 each hand.
  • Use cards Ace to 5 only to reduce the range of multiplication and division facts and answers required.
  • Include triangular numbers if appropriate.
  • Allow use of calculators for working out answers or for checking answers.
  • Provide a list of square numbers and prime numbers for those who need them.
  • Introduce a time limit for finding answers for those who need more challenge.
  • Increase the number of cards to 4 or 5 and score an extra point every time a division is involved. It’s a fact; most students and adults will avoid division if they can.
  • Encourage some students to apply rules for divisibility and the Sieve of Eratosthenes to find the prime numbers.

Okay, back to work – writing Mental Routines for Year 6 … which is coming soon!