An online game for students. Roll a six-sided dice, record the results and sum to 12.

On MathsLinks: https://mathslinks.net/links/sum-to-12

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An online game for students. Use 2 six-sided dice and the four operations to “make 100”.

Getting close to 100 is easy. What strategies can you use to get exactly 100?

On MathsLinks: https://mathslinks.net/links/make-100

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We discover how to quickly find a random option in an ordered set of options using a binary search game.

On MathsLinks: https://mathslinks.net/links/interactive-binary-search-game

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There was a secret message on the parachute of Perseverance, seen as it descended to Mars.

This “kid-friendly” file (PDF) explains how to decode the parachute.

via Tanya Fish on Twitter (@tanurai)

On MathsLinks: https://mathslinks.net/links/the-parachute-message

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A graphical method for finding Pythagorean triples (triads). Why does it work?

On MathsLinks: https://mathslinks.net/links/weird-shapes-giving-pythagorean-triples

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Some special right-angled triangles allow for a different application of Pythagoras' Theorem.

Can you prove why?

On MathsLinks: https://mathslinks.net/links/youave-been-doing-pythagoras-wrong-your-whole-life

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A video demonstrating the link between the formula for volume of a pyramid and cone and the volume of a prism or cylinder with the same cross section/base.

On MathsLinks: https://mathslinks.net/links/volume-of-pyramid-and-cone

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Input *f*(*x*) and *g*(*x*) then investigate the composite functions *f*(*g*(*x*)) and *g*(*f*(*x*)).

On MathsLinks: https://mathslinks.net/links/composition-of-function-fg-or-gf

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A silly look at Pythagoras.

On MathsLinks: https://mathslinks.net/links/horrible-histories-stupid-deaths-pythagoras

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A story based on Kruskal's Algorithm.

On MathsLinks: https://mathslinks.net/links/how-do-you-calculate-a-minimum-spanning-tree

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A good video to introduce the pigeonhole principle.

On MathsLinks: https://mathslinks.net/links/pigeonhole-principle-explained

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Aboriginal and Torres Strait Islander people use their understanding of the night sky for a range of reasons.

“Indigenous astronomy” is more than the star knowledge of Indigenous people: it is the First Astronomy – the science of the stars that existed before, and independently of, the development of Western science.

On MathsLinks: https://mathslinks.net/links/learning-the-star-knowledge-of-first-australians

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Expressing a vector in three dimensions.

On MathsLinks: https://mathslinks.net/links/expression-of-a-vector-in-3d

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An introduction to probability density functions.

See also part 1.

On MathsLinks: https://mathslinks.net/links/why-probability-of-0-does-not-mean-impossible-probabilities-of-probabilities-part-2

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Professor Ed Copeland shows a proof by Joseph Fourier that *e* is irrational.

On MathsLinks: https://mathslinks.net/links/a-proof-that-e-is-irrational-numberphile

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Given relevant dimensions (but not formulae) students find surface area and volume of famous buildings including Australia, France, Germany, USA, Brazil to name a few.

On MathsFaculty: https://mathslinks.net/faculty/surface-area-volume-of-famous-buildings-around-the-world

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A set of 40 investigations into different types of numbers - Narcissistic, Kaprekan, Keith, Betrothed, Bell, Proth and many more. Each investigation explains something about the number being investigated & then sets a challenge for the students. All answers are from 1 to 100. Solutions on last 2 pages.

On MathsFaculty: https://mathslinks.net/faculty/investigating-special-numbers

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I put this together for my strong Year 9 (13/14 yrs old) class. 4 terms of 8 weekly homework Challenges (includes answers for most) - use them any way you want for many other groups.

On MathsFaculty: https://mathslinks.net/faculty/a-year-of-weekly-homework-year-9

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This activity can be adjusted to any age, any topic & any ability level. Individual, pairs or teams. I've used with Yr 7 to Extension 2.

You will need to buy a lockable box & a 4 digit combination lock - I got mine at Bunnings.

- Print off one set of pages for each team/pair/person.
- Place a prize in a box locked with a combination padlock and set to the code given for the task (to the nearest whole number).
- Pupils try to complete the 12 questions and input these into the algebraic expression (project page 4 on the screen or print off for each group). (Some codes don't use all the letters). Final answer is to the nearest whole number.
- Pupils only get the prize if they crack the code. If a team try unsuccessfully you might want to tell them which questions they’ve got wrong.

On MathsFaculty: https://mathslinks.net/faculty/crack-the-code-or-lockbox

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An introduction to binomial distributions.

See also part 2.

On MathsLinks: https://mathslinks.net/links/binomial-distributions-probabilities-of-probabilities-part-1

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