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Start with a formula that has only multiples of n, nothing added or subtracted, for example : $2n$, $3n$, $4n$ or $5n$
Look at the sequence of blue numbers and notice the pattern - explain why it happens.
When you can explain what happens, switch to a formula where something is subtracted.
Interactive Number Patterns 2
The hidden blue comes from substitution, but predicting the hidden red needs you to solve an equation. Perhaps you can solve it using algebra or maybe you could guess and test, improving your guess until you hit the right value. Could there be more than one value that works as a solution to your equation?Do you see a connection between Difference 2 and the formula? Change the formula to check that you were right about the connection.
Finally, use those numbers in the bottom half of the screen to help you explain why the connection you discovered in Difference 2 actually works.