Welcome to February's NRICH website. This month the mathematical
themes are Complex Numbers and Transformation Geometry.
Our problems begin with several which focus on different kinds of
transformations. Decide how many quarter turns you need to make
the man look the same as the pictures in the aptly named
Turning Man problem. Or how about looking at our
2 Rings investigation? Can you position the two rings in
different ways and describe how they are arranged? If you want to
take the idea of rotations further, then you'll like
Peg Rotation , which even challenges you to explore a
triangular pegboard.
The three Stage 3 problems are all linked to one another this
month.
Mirror Mirror... is the place to start - can you describe the
single transformation that takes the first flag to the last flag?
This is followed by
...on the Wall which asks you to generalise the single
transformation for any angle between the two mirror lines.
At Stage 4, the three problems are designed to stretch the idea
of number to include new numbers that don't lie anywhere on the
traditional number line, using geometry! Start with
Arrow Arithmetic 1 by trying the additions of the blue
arrows. Can you improve on the arrow?
Arrow Arithmetic 2 does just that - use the interactivities
to understand the new arrows. How could you construct
subtraction?
The interactivity in
Root Tracker and
Cubic Tracker allows you to investigate the roots of
quadratic and cubic equations by varying the graphs and seeing
all the roots both real and complex. This provides an extension
of work at Stage 4 on solving quadratic equations and an
introduction to complex numbers for students who have not met
them before. As well as developing the work on transformations in
this month's Stage 3 problems, the article
What Are Complex Numbers? introduces complex numbers, brings
together some closely related ideas like vectors and the
exponential and trigonometric functions and their derivatives,
and proves that
ei p = -1.
The Education Show
Come along to the Millennium Mathematics Project stand GG84 at
the Education Show, Birmingham NEC, March 22nd-24th.
Easter teacher conferences
Finally, don't forget to book
your place on one of the Easter teacher conferences this year.
Members of the NRICH Team will be running sessions at both
The
Association of Teachers of Mathematics conference in
Loughborough and The
Mathematical Association conference in Keele (follow the
links or click on the images below for details).
