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Square Subtraction

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Choose any number. This is going to be your particular number for this proof.
Square your chosen number.
Subtract your starting number.
Is the number you're left with odd or even?
Create a model or a picture of your calculation, using your chosen number, and examine this model carefully.
Can you use this one model to prove that your result is always true and not just true for the particular number that you chose to start with?