Dear all,
The October NRICH website is now live at http://nrich.maths.org . The
fresh problems and articles this month are all on the theme of Geometry
and Algebra, and you will find activities to challenge and excite you
and your pupils, no matter how long they have been studying mathematics.
To start off, you could investigate Tubular Path
<http://nrich.maths.org/public/viewer.php?obj_id=5040&part=index> . Can
the children in your class direct the blue point through the tube by
moving the yellow one? It looks easier than perhaps it is! Once they've
cracked that, have a look at A Maze of Directions
<http://nrich.maths.org/public/viewer.php?obj_id=5039&part=index> .
Again, they need to work out how the trace of the yellow spot is related
to that of the blue spot. Can students use what they find out to move
the yellow spot from one star to the other? There are also two problems
centring on tessellation this month which are well worth tackling:
Tessellating Capitals
<http://nrich.maths.org/public/viewer.php?obj_id=4976&part=index> and
Escher Tessellations
<http://nrich.maths.org/public/viewer.php?obj_id=4975&part=index> .
At a slightly higher level, three inter-related problems will pose some
challenges which relate to transformations. Decoding Transformations
<http://nrich.maths.org/public/viewer.php?obj_id=5331&part=index>
invites your class to describe transformations represented by different
letters and then asks them to simplify a series of transformations. This
idea of simplification is taken up in the follow-up problems Combining
Transformations
<http://nrich.maths.org/public/viewer.php?obj_id=5332&part=index> and
Simplifying Transformations
<http://nrich.maths.org/public/viewer.php?obj_id=5333&part=index> .
Another series of three problems features at Stage 4 this month,
beginning with Points in Pairs
<http://nrich.maths.org/public/viewer.php?obj_id=5472&part=index> . Can
students use the relationship between the two points and the radius of
the circle to calculate the distance shown? Both The Line and Its
Strange Pair
<http://nrich.maths.org/public/viewer.php?obj_id=5473&part=index>
<http://nrich.maths.org/public/viewer.php?obj_id=5473&part=index> and
Mapping the Wandering Circle
<http://nrich.maths.org/public/viewer.php?obj_id=5474&part=index> delve
more deeply into this same relationship, taking the ideas from static to
dynamic.
Geometry and algebra are intertwined in all three problems at the
highest level. Pick's Theorem is the theme for both Pick's Quadratics
<http://nrich.maths.org/public/viewer.php?obj_id=5440&part=index> and
Proof of Pick's Theorem
<http://nrich.maths.org/public/viewer.php?obj_id=5441&part=index> . The
former asks pupils to verify the generalised form of the Theorem for a
particular rectangle and the latter leads up to a proof that Pick's
Theorem holds for any planar polygon.
If this isn't enough, there are also two articles to whet your pupils'
appetites. Grouping Transformations
<http://nrich.maths.org/public/viewer.php?obj_id=5336&part=index> links
to the Stage 3 problems and takes the mathematics in them a little
further. Alternatively, something completely different: Have you ever
wondered how many ways there are to shuffle a pack of cards? Why not
take a sensible guess? Now read Card Shuffle
<http://nrich.maths.org/public/viewer.php?obj_id=5402&part=index> and
you might well be surprised.
Finally, don't forget that we would still welcome your contributions
towards our 10th anniversary website in January. If you have a
favourite NRICH problem or game that you use again and again with
students, then please let us know what it is and your reasons for
choosing it. We hope to feature a selection of these in the January
site. In addition, we would welcome your suggestions for new problems
which we could add to the month for others to try.
With best wishes from The NRICH Team.
--
Liz Pumfrey
NRICH Primary Coordinator
University of Cambridge Centre for Mathematical Sciences
Wilberforce Road
Cambridge
CB3 0WA
01223 764246
www.nrich.maths.org
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