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Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-4
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Featured UK Key Stage 2; US Grade 3 & 4
Featured UK Key Stages 3 & 4; US Grade 5-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
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The Fastest Cyclist
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
We are still waiting for some good student contributions on this problem but here are some thoughts to help you :
You could start with the three shape posibilities in this illustration :
First the triangle : suppose a length of say 20 cm was folded in the centre, for which angle would the cross-section area be greatest ? If the length had been 40 cm instead of 20 cm would that change your answer ?
Now the rectangle cross-section : maybe start with an overall length of 20 cm again and try different proportions of side length to base. What proportion created the largest area, was that a surprise or an expected result ?
Finally, for now, the arc : for a specified length, say 20 cm, you could curve it a lot or a little. If you curve it a lot you will have more of the full circle but it's a smaller circle. If you curve the material only a little you get less of a larger circle. A spreadsheet might help you find the best choice and ease the burden of calculation.
I hope you enjoy finding that result, if you didn't guess it. Now compare all three results : notice anything ? Can you account for that ?
Mathematical reasoning & proof
Manipulating algebraic expressions/formulae
Meet the team
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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