Random Spectacular! - July 2012, Stage 4&5

This month we've chosen some old favourites as well as some new ideas. They're just right to round off the school year, and can be used in the classroom or at home during the holidays.

Problems

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Witch's Hat

Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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Making Moiré Patterns

Age 11 to 18 Challenge Level:

Moiré patterns are intriguing interference patterns. Create your own beautiful examples using LOGO!

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Kite in a Square

Age 14 to 16 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square?

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Simply Graphs

Age 16 to 18 Challenge Level:

Look for the common features in these graphs. Which graphs belong together?

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Hyperbolic Thinking

Age 16 to 18 Challenge Level:

Explore the properties of these two fascinating functions using trigonometry as a guide.

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Fundamental Particles Collection

Age 16 to 18 Challenge Level:

A collection of problems related to the mathematics of fundamental physics.

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Interpolating Polynomials

Age 16 to 18 Challenge Level:

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.