Everyday Mathematics
Why a triangle’s angles add to 180 degrees on a flat surface
Use a paper triangle to explore the 180-degree angle sum, then connect the observation to a parallel-line argument that explains why it works.
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Learning Mathematics
A straight-line graph is not always a proportional relationship
A proportional relationship has a constant ratio and a graph through the origin. Compare two simple pricing examples to see why a straight line is not enough.
Learning Mathematics
A shape can have rotational symmetry without mirror symmetry
Use paper shapes to distinguish turning symmetry from mirror symmetry and explain why one test does not replace the other.
Mathematics Explained
Why Pythagoras’ theorem needs a right angle
Use the right angle to identify the hypotenuse before applying Pythagoras’ theorem, with a worked example and a check for common mistakes.
Learning Mathematics
Why pi stays the same when a circle gets bigger
Compare circular lids to see why circumference divided by diameter approaches the same number. A practical activity separates pi from measurement error.
Learning Mathematics
Why zero divided by five works, while five divided by zero does not
Use multiplication and equal groups to explain why zero divided by five is zero, while division by zero has no defined answer in ordinary arithmetic.