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Guide and features
Guide and features
Science, Technology, Engineering and Mathematics
Featured Early Years Foundation Stage; US Kindergarten
Featured UK Key Stage 1&2; US Grades 1-5
Featured UK Key Stage 3-5; US Grades 6-12
Featured UK Key Stage 1, US Grade 1 & 2
Featured UK Key Stage 2; US Grade 3-5
Featured UK Key Stages 3 & 4; US Grade 6-10
Featured UK Key Stage 4 & 5; US Grade 11 & 12
Curve Fitter 2
Why do this problem?
draws learners into ideas concerning curve fitting and the way in which curve fitting problems can be greatly simplified by using 'sensible' coordinate systems and the way in which length-preserving transformations can be used to create these.
An important part of this problem is students coming to the realization that the problem is greatly simplified by choosing the right sorts of coordinates. Students might benefit from doing this question individually and it might make a good starter activity to return to once students have had a chance too think about it.
How can the transformations be used to create a 'simple' cubic equation?
The extension referred to in the equation is very interesting. You might like to inform students that there is in fact an algebraic solution to any cubic equation, which they might use in this problem.
One way into this problem might be to draw a few simple cubic equations, find their turning points and then work out the squared distance between them. Alternatively, first try the easier problem
which will start to get students to think about cubic equations and turning points.
Maths Supporting SET
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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NRICH is part of the family of activities in the
Millennium Mathematics Project