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' Tis Whole
problem

'tis Whole

14 to 18

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

Fitted
problem
Favourite

Fitted

7 to 11

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Shear Magic
problem
Favourite

Shear Magic

11 to 14

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Subtraction Surprise
problem
Favourite

Subtraction Surprise

7 to 14

Try out these calculations. Are you surprised by the results?

Spherical triangles on very big spheres
problem

Spherical Triangles on Very Big Spheres

16 to 18
Shows that Pythagoras for Spherical Triangles reduces to Pythagoras's Theorem in the plane when the triangles are small relative to the radius of the sphere.
Whole Number Dynamics II
article

Whole Number Dynamics II

14 to 18

This article extends the discussions in "Whole number dynamics I". Continuing the proof that, for all starting points, the Happy Number sequence goes into a loop or homes in on a fixed point.

Gosh Cosh
problem

Gosh Cosh

16 to 18

Explore the hyperbolic functions sinh and cosh using what you know about the exponential function.

Geometric Parabola
problem

Geometric Parabola

14 to 16

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.

Logic
article

Logic

7 to 14

What does logic mean to us and is that different to mathematical logic? We will explore these questions in this article.

Poly Fibs
problem

Poly Fibs

16 to 18

A sequence of polynomials starts 0, 1 and each poly is given by combining the two polys in the sequence just before it. Investigate and prove results about the roots of the polys.

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