Explorations and Games
A pencil writing out a list of four digit numbers. In the list are 2222, 2332, and 322.

Learning Goals:

  • Make predictions related to patterns
  • Develop and apply reasoning skills to make and test math predictions
  • Communicate mathematical thinking orally and visually

The Exploration:

A palindrome is a word that is the same when it is read forwards and backwards, like racecar. Numbers can also be palindromic, if they are the same when read forwards and backwards, like 4554.

Try creating some other 4-digit palindromic numbers.

How many different 4-digit palindromic numbers can you make, if you only use the digits 1, 2, and 3? How will you know when you’ve found them all?

Questions and Prompts to Support your Child:

  • How did you organize your listing of these palindromic numbers? Will this organization help you prove that you’ve found all possibilities?
  • What are some of the largest of these palindromic numbers that you found? Which ones are the smallest?

Extensions & Adaptations:

  • How would your list of palindromic numbers change if you also included the digit 0? How would this change how you organized your list?
  • What if you made a list of all possible 5-digit palindromic numbers using the digits 1, 2, and 3 instead? How would this change how you organized your list?

Adapted from: Puzzle of the Week