Square subtraction

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

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Square subtraction

For this activity, you just need to follow three simple steps:

  1. Choose any number.
  2. Square your chosen number.
  3. Subtract your starting number.

Once you've done that, answer the question: 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 model to prove that your result is always true, not just true for the particular number that you started with?