Starting with the question:

What are the chances that there are two people in London with the same number of hairs on their head?

Includes The Pigeon Hole Principle.

On MathsLinks: https://mathslinks.net/links/a-hairy-problem-and-a-feathery-solution

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A proof without words of 1^{2} + 2^{2} + 3^{2} + … + n^{2} = ?

On MathsLinks: https://mathslinks.net/links/sum-of-squares-proof-without-words

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Investigate the area of a circle with this widget.

On MathsLinks: https://mathslinks.net/links/area-of-a-circle-revamped

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A visualisation of (*a* + *b*)^{2}.

On MathsLinks: https://mathslinks.net/links/a-b2-visualisation

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A 3D visualisation of *a*^{3} − *b*^{3} = (*a* − *b*)(*a*^{2} + *ab* + *b*^{2}).

On MathsLinks: https://mathslinks.net/links/a-b-visualisation

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Learn how the concept of infinity can be used to convert a round pizza into a rectangle, which explains the formula for the area of a circle, with this video excerpt from NOVA: *Zero to Infinity*. Use this resource to provide opportunities for students to reason abstractly and to construct an argument about the formula for the area of a circle.

On MathsLinks: https://mathslinks.net/links/the-area-of-a-circle-explained-with-pizza

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Marcus du Sautoy on Fibonacci Numbers, considering music and poetry.

On MathsLinks: https://mathslinks.net/links/the-truth-about-fibs

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Ben Sparks presents an integration problem. A good demonstration of ensuring students write +c.

On MathsLinks: https://mathslinks.net/links/an-integration-conundrum

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A simple online interactive that judges your ability to draw a circle.

On MathsLinks: https://mathslinks.net/links/can-you-draw-a-perfect-circle

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A growing collection of backward faded worked examples.

*'In backward faded worked examples, students are required to try to find a solution in the last step on problem 1, the last two steps on problem 2, and so on. In other words, students are required to continue the steps given to solve the problem.'*

On MathsLinks: https://mathslinks.net/links/backward-faded-maths

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This article presents 5 examples of positively skewed distributions in the real world.

On MathsLinks: https://mathslinks.net/links/5-examples-of-positively-skewed-distributions

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This article shares 5 examples of negatively skewed distributions in the real world.

On MathsLinks: https://mathslinks.net/links/5-examples-of-negatively-skewed-distributions

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What makes a proof stronger than a guess? What does evidence look like in the realm of mathematical abstraction? Hear the mathematician Melanie Matchett Wood explain how probability helps to guide number theorists toward certainty.

On MathsLinks: https://mathslinks.net/links/how-do-mathematicians-know-their-proofs-are-correct

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Using points around the unit circle to plot sine and cosine against each other.

On MathsLinks: https://mathslinks.net/links/plotting-sine-and-cosine-functions-by-segments-animated

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Matt shows that a single net can form two different shapes, and then investigates why.

On MathsLinks: https://mathslinks.net/links/can-the-same-net-fold-into-two-shapes

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Investigating 3D shapes and symmetry.

On MathsLinks: https://mathslinks.net/links/making-efficient-platonic-and-archimedean-shapes-in-a-kaleidoscope

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This mathematics segment deals with Perfect Numbers.

On MathsLinks: https://mathslinks.net/links/perfect-numbers

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The family tree of the male honey bee leads to Fibonacci!

On MathsLinks: https://mathslinks.net/links/bee-family-tree-fibonacci

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Deane and Rob play a number game in which each one tries to reach 100.

On MathsLinks: https://mathslinks.net/links/how-to-count-to-a-hundred

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From UNSW Mathematics and Statistics

There are many topics from school mathematics which we do not teach in first year classes, but which we assume that you know.

If you are not skilled in these topics you will experience a great deal of frustration and difficulty in progressing through first year. You will also lose a lot of marks - it is not unusual for half the marks lost in a first year class test or exam to be due to the student's lack of proficiency in school mathematics.

The worksheets on this page are designed to help students learn topics which they may not be coping with.

On MathsLinks: https://mathslinks.net/links/revision-worksheets-unsw-mathematics-and-statistics

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