| After
the highly successful SUMIT week last year we held a similar
event in January 2002.
Sumit
2(002)
At the beginning of the term,
students in the Lower School were able to experience a variety
of activities.
Sets F, O an R in Year 9 studied
work on Loci - initially using lots of cut out circles - then
doing (hopefully) accurate diagrams using rulers, compasses,
sharp pencils and much rubbing out of errors!
The word Loci comes from the
Latin word Locus meaning a point or a place. The word itself
is plural, so therefore lots of points infer a path. Other
derivations include "locum" - a doctor who stands
in when the your own doctor is on holiday - and "in loco
parentis" - people who temporarily are taking the place
of the parents - teachers for example!
The first two investigations
involved finding the loci of points which equidistant from
a point, then from a line. LOCI
1 (Word)
Pupils'
Comments
"I have improved very much at my geometry skills
like drawing perfect circles etc."
"My favourite activity during the week was using my
compasses as I felt that my skills are improving. I feel
that I have learned many new skills."
This was then extended to
finding loci of points, which were equidistant from two points,
then from two lines. LOCI
1
(Word)
These last two investigations
form the basis of two very important geometric constructions.
Loci of points from two points give the perpendicular bisector
of a line, whilst the loci of points equidistant from two
lines gives the angle bisector.
Pupils'
Comments
"I have that doing the accurate drawing of a parabola
was the most interesting construction that we did"
"I probably found the third investigation the most
interesting. I heard the term parabola for the first time.
I have learnt a lot from this week and I enjoyed it!"
What do we get if we find
the loci of points, which are equidistant from both a point
and a line? Well the answer is we get a curve - in this case
it is the PARABOLA.
LOCI 1
(Word)
Graphs of this kind have the
formula y = x2
Interesting things happen
to the curve if you start altering distances - print the sheets,
follow the instructions and try them for yourself.
Pupils'
Comments
"I enjoyed the tree and the wall exercise the best"
The second investigation - "GRAZING
THE GOAT" - involved finding the area of
grass, which a goat can graze when it has been tethered at
different points on the wall of a shed.
Pupils'
Comments
"I found the last one the most interesting - where
we had to devise our own huts and place the goats so they
wouldn't fight"
"I enjoyed working out the Loci and the amount of space
that the goat would have"
This investigation required
- in fact demanded from the students- a high degree of accuracy
when using their geometrical equipment.
Again print the sheets, follow
the instructions and try them for yourself.
Year 8 Set N were asked to
look at Ponds & Borders - is there a connection between
the dimensions of a pond and the number of 1 metre square
paving slabs required to surround each of the ponds?
The first investigation was
based on the STANDARD Pond - square in shape - and the second
investigation was based on the LONGLEY Pond - rectangular
in shape. Click on PONDS
& BORDERS to access the investigation.
The students were able to
find a connection between the dimensions of the ponds and
the number of paving slabs required to place a border around
the pond.
They were then asked to consider
differently shaped ponds - the LABRADOR and the ZIG - ZAG.
These proved to be more challenging for the students, but
they produced some good work. Again click on PONDS
& BORDERS to access the investigation.
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