## 'Interactive Number Patterns' printed from http://nrich.maths.org/

Interactive Number Patterns 1
• 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.

• Next include in the formula something added and watch how that changes the pattern.
• 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?

This spreadsheet file has a second sheet (see the tab called 'Patterns with differences' at the bottom of the work area). There are a lot of numbers to watch, so take your time.
• What are these numbers ? Perhaps begin by explaining the numbers in line Difference 1 and in line Difference 2. Use the buttons to change the formula so that you can check you were right.
• Do you see a connection between Difference 2 and the formula? Change the formula to check that you were right about the connection.

• Now see how the numbers in the bottom boxes work and the purple numbers between them. Take it row by row, changing the formula to be sure you understand where each value comes from.
• 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.