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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Journal
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.
Maths you can see
Doubling a square’s side makes four times the area
Use a simple tile model to show why doubling a square’s side length multiplies its area by four, then separate length scale from area scale.
Everyday Mathematics
Why a repeating decimal can still be written as a fraction
A repeating decimal can represent an exact fraction. Use a short algebra example to distinguish an endless repeating pattern from a rounded display.
Understanding Mathematics
Why one is not a prime number
Explain why one is neither prime nor composite using positive divisors, factor lists and a simple prime-factorisation example.