Does an equation exist to describe a square? What about any polygon?

Yesterday I saw some awesome Mr Men Math posters created by @solvemymaths (www.solvemymaths.com) and have already stuck some of them up in the corridor at school. Mr Astroid particularly caught my eye as one of the interesting Mr Men shapes.

mr astroid 3 You can see, and understand intuitively, that the equation is a variation on a circle. In fact, the shape of the astroid looks quite close to a square. This got me thinking…does a function exist to describe any given polygon? So here goes…

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Moving towards more Meaningful Mathematics Assessment in the 21st Century

I’ve always believed that there’s nothing wrong with a sit down test if the test items assess the core philosophy and values of the subject. Hence, I’ve tried to make an assessment for my Year 7 students (grade 6) which I believe is more meaningful in the 21st century. It’s so easy now to do a quick search on Google to find the formula for anything. Indeed, during a planets investigation today with Grade 9, we simplified the problem of planetary orbits to consider them as circles instead of ellipses – pretty standard. However, one of the students put his hand up a minute later to ask why we weren’t just using one of the many formulae he had found through a Google search for the perimeter of an ellipse. This is great but it means that we need to teach students how to derive formulae and analyse formulae instead of simply using them without thinking. I guess this is similar to when students just pick information from a website without critiquing it – so frustrating and meaningless.

Anyhow, here’s the assessment. Any feedback to improve would be appreciated.

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Allowing Students to Discover the “Mystery” of Square Roots (Surds)

Here’s my attempt at investigating operations with square roots (surds) when you’re not prescribed by a GCSE/IGCSE syllabus. This is only a general outline of the lessons we’ve had so far but it’d be great to hear how other people go about teaching surds.

To start off, we hadn’t spent much time discussing irrational numbers but I thought the question below would push us into a discussion/debate about them and then things would start flowing:

(An irrational number) x (An irrational number) = (A rational number). Discuss

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Percentage Increase and Decrease Applet: Any improvements?

Here’s a Geogebra app I made to help students who were struggling with percentage increase and decrease. Can anyone think of any improvements? Click the picture to go to the link.

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Estimation Calculator (Multiplication) on Geogebra

Click the picture to go to the Applet.

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Why I like Mathematics and why Students should Discover and Create their Own

An old video – and in some points cringe-worthy now I look back – but I do sometimes like to look back at it. [By the way, I don’t have a clue where I plucked out the 90% statistic towards the end – extra planning was needed here I think!]

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Introduction to Fractal Geometry 2: Julia Sets and the Mandelbrot Set

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The Mandelbrot Set – created with Geogebra

It’s possible, or more like probable, that the most mysterious shape ever to arise from the study of Mathematics is that of the Mandelbrot Set. It’s amazing how such an intriguing shape could arise from purely mathematical pursuits. The shape of the Mandelbrot set (often likened to a Beetle), is highly complex yet it is derived from such a simple equation.

Before I get into the post, it’s important to give huge credit to Professor Lee Stemkoski who works at Adelphi University. He figured out a simple and effective way to paint the Mandelbrot set in Geogebra using a lovely little trick – have ten points trace the fractal instead of one! The pictures in this post are a result of some small tweaks to his method.

Any discussion of the Mandelbrot set should start with Julia Sets…

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