This free math tutoring video shows my 6 and 8-year-old daughters figuring out the squares of numbers 10 through 20. We use a variety of strategies. This activity is helpful in building thinking skills and further developing number sense. They are beginning to see numbers as a picture in their minds that they will carry with them forever.
Square numbers are used frequently in higher math. If they come into contact with them enough now while they are young, they will have no trouble applying this knowledge later on in middle and high school.
Square numbers are fun and much more understandable when you use manipulatives like the Cuisenaire Rods to figure them out! Having a visual picture for things like this makes math so much clearer. My girls are learning that exponents are not something to be afraid of, but are something to enjoy!