Unit 12 · Squares and Square Roots
Squares and Square Roots
Mathematics · Grade 7
What You Will Be Able To Do
🔲Square any number, and take the root of any perfect square
🔍Tell at a glance that some numbers cannot be perfect squares
🧮Find a root of a large number by prime factorisation, not by guessing
📏Trap a root that is not whole between two whole numbers
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Take 4 counters and you can arrange them in a 2 by 2 square. Take 10 and you cannot make a square at all, however you push them about.
Presenter notes: Start with counters rather than notation. Hand each pair about twenty pebbles or bottle tops and ask them to arrange exactly ten into a square. They will push them around for a while and fail, and somebody will say it cannot be done. Then ask for nine, and it works immediately. That contrast is the definition of a square number, discovered rather than announced, and the word square now means something they have handled.