Unit 15 · Irrational Numbers
Irrational Numbers
Mathematics · Grade 7
What You Will Be Able To Do
🚫Say what makes a number irrational, and what does NOT
√Decide instantly whether any square root is rational or not
🧠Follow the 2500-year-old proof that √2 is irrational
📏Trap an irrational number between decimals, as closely as you like
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Every fraction terminates or recurs. So a number whose digits run on for ever with no repeating block cannot be a fraction, no matter how hard anyone looks.
Presenter notes: Open by drawing a square of side one on the board and drawing its diagonal. Ask how long that diagonal is. Somebody will say about 1.4, so ask for the exact value and let the class try. They cannot find one, and today they will learn that nobody can, because no fraction and no finite decimal describes that length. The line is right there in front of them, which is what makes this unsettling and worth an hour.