Odd Squares

Think of a whole number. Square it. Subtract the number you first thought of. Is the answer odd or even?

Try this with other numbers. What do you notice? Can you explain why? Can you find different ways to explain (and prove) the result that you noticed. You might use what you know about odd and even numbers or you might use a picture or algebra.

Now think of a number and square it. Does this picture make you think of another number pattern? Does it work for all squares?

Click here for the Notes for Teachers.

Thank you to NRICH for the idea for this question.