maths through pattern

Transcription

a teaching resource
Maths
Through
Pattern
01
Maths through Pattern
Maths through Pattern
Introduction
Culture enriches lives. Participation in cultural activities can have a significant impact on
young people’s development. This been shown repeatedly in International studies, and has
also been backed up by recent evaluations of major programmes such as Creative
Partnerships and Museums’ Strategic Commissioning. What these evaluations have shown
is that culture can help young people achieve all of the Every Child Matters outcomes.
(Find Your Talent http://www.findyourtalent.org/)
Turner Contemporary, Stour Valley Arts and Canterbury City Council Museums
and Galleries Service are delighted to launch Maths Through Pattern, a resource
that explores how to use pattern in contemporary and historical art, museum
specimens and the natural environment to teach maths.
We believe that teachers and other educationalists should feel confident about
making use of our collections, exhibitions and environments and that the ideas
included in this resource can help to ignite children’s enthusiasm for learning,
using their local area.
Whilst Superabundant: A Celebration of Pattern at Turner Contemporary was a
temporary exhibition running from 24 January to 22 March 2009) we hope we have
made a resource with a long life span. We have included a broad range of artists’
work, including commissions by Stour Valley Arts, resources found in museums
and the natural and built environment in addition to extensive weblinks, in the
hope of encouraging a creative way of looking and thinking which can be used
beyond the constraints of a specific project. Should you wish, however, to visit and
see something specific mentioned in this resource, please phone the venue
beforehand to make arrangements.
Turner Contemporary, Stour Valley Arts and Canterbury City Council Museums
and Galleries Service all believe in placing artists at the heart of what we do,
and are continuously surprised and delighted by the way artists see the world.
We are grateful to artist Katy Beinart for the creation of this inspiring and
imaginative resource.
We are also grateful to enquire for providing the funding that has enabled us to
develop both this resource and our collaboration. The enquire programme is
funded by the Department for Culture, Media and Sport and the Department for
Children, Schools and Families as part of the Strategic Commissioning Programme
for Museum and Gallery Education, and by the Foyle Foundation. The enquire
programme is managed by engage and has been developed in association with
Arts Council England.
01
Images of objects in Canterbury Museums Service collections all copyright reserved 2009 ©
General information
Visiting Information
Turner Contemporary
Opening Hours:
visit www.turnercontemporary.org
Booking your visit is essential
Please contact Turner Contemporary on:
T: 01843 280261
E: [email protected]
Turner Contemporary’s new building will open in 2011. Schools can currently visit
our visitor centre, Droit House, or offsite projects. Our Project Space is now closed
Gallery charges
Admission to all Turner Contemporary exhibitions is free
Stour Valley Arts
Opening hours:
Stour Valley Arts is based at King’s Wood, Challock, near Ashford and is an open
access site.
PLEASE NOTE ALL GROUPS VISITING THE FOREST NEED TO OBTAIN PERMISSIONS
Book an Education Workshop
Stour Valley Arts offer education workshops to schools, youth or community
groups, and further education colleges.
We can tailor your visit to suit you and to support class based activities, projects
and the curriculum. We have a range of artists, photographers, poets, ecologists
and environmentalists trained to work in the forest to choose from.
Half-day visits can also be arranged to view the sculptures.
Please ring Lucy Medhurst on 01233 740040 or email education@stourvalleyarts.
org.uk to discuss your needs or book a visit.
In order to ensure safe planning and coordination of visits and to conform to
forestry requirements all groups planning a visit to King’s Wood should contact
the SVA office well in advance. We will provide you with a forestry approved risk
assessment.
All SVA staff and artists are trained, CRB checked and have specialist knowledge of
the site and works of art
Workshop Charges 2009/10
Walks and guided tours £100
Artist led workshops    £200
02
Canterbury City Council Museums and Galleries Service
operates six museums across the district: Canterbury Royal Museum and Art
Gallery (Beaney), Museum of Canterbury, Roman Museum and West Gate Towers
in Canterbury; Herne Bay Museum; and Whitstable Museum.
Canterbury Royal Museum and Art Gallery (Beaney)
Closed for extension and improvement works, reopening in 2011. Some of the
collections have been moved and displayed at the Museum of Canterbury, the
remainder are in store.
Museum of Canterbury
Housed in one of the country’s finest medieval buildings, in Stour Street. Explores
the story of the city from prehistoric times to the present. Admission charge.
Roman Museum
Built around the remains of a Roman town house with mosaic floors.
Admission charge.
West Gate Towers
Medieval fortified gatehouse used later as a prison. Admission charge.
Herne Bay Museum and Whitstable Museum
Tell the stories of these seaside towns; admission is free to both.
There is an extensive programme of events and activities across the museums and
an outreach programme of work with schools and community groups.
Group visits to the museums are welcome but must be booked in advance.
Handling sessions (teacher-led or led by museum staff) can be arranged at a small
extra charge. This can include viewing of items in the Museum Collections
included in this resource (many of which will be on display in the new Beaney
from 2011).
FOR FURTHER DETAILS, OPENING TIMES AND ADMISSION CHARGES
visit the museums website www.canterbury-museums.co.uk
or contact the museums office:
T: 01227 452 747
E: [email protected]
03
Natural Systems: Solar Patterns
Emily Robertson Aspect 2004
Topic/maths subjects
Solar patterns, Measures, Time
Locations
l Stour Valley Arts
l Exhibited in ‘Superabundant’, Turner Contemporary, Spring ‘09
Canterbury Museums
l Roman Museum
l Beaney
l Museum of Canterbury
l Museum Collections
Artists
Emily Richardson
Susan Derges
Lukasz Skapski
Chris Drury
Objects in the collections
Sundials
Objects in everyday life
Watches
Clocks
Sundials
Photographs
Curriculum Links
Foundation Stage Early Learning Goals
l
Problem Solving, Reasoning and Numeracy
Use everyday words to describe position.
l
Knowledge and Understanding of the World
Find out about, and identify, some features of living things, objects and
events they observe.
01
KS1: Ma3 Shape, Space and Measures
2a: Describe properties of shapes that they can see or visualise using the
related vocabulary
3a: Observe, visualise and describe positions, directions and movements using
common words
4a: Estimate the size of objects and order them by direct comparison using
appropriate language; put familiar events in chronological order; compare and
measure objects using uniform non-standard units [for example, a straw, wooden
cubes], then with a standard unit of length (cm, m), weight (kg), capacity (l) [for
example, ‘longer or shorter than a metre rule’, ‘three-and-a-bit litre jugs’];
compare the durations of events using a standard unit of time
2b: Visualise and describe 2-D and 3-D shapes and the way they behave, making
more precise use of geometrical language, especially that of triangles,
quadrilaterals, and prisms and pyramids of various kinds; recognise when shapes
are identical
3a: Visualise and describe movements using appropriate language
4d: Read the time from analogue and digital 12- and 24-hour clocks; use units
of time - seconds, minutes, hours, days, weeks - and know the relationship
between them
Learning Objectives
l
To understand the use of solar patterns to tell the time
l
To explore how light can create shapes and shadows
l
To visualise and describe movements
Activities
F / KS1 / KS2
horizon line
20.41ʼ 00”
20.42ʼ 50”
20.44ʼ 15”
3m
5°
5m
8.5 m
20.57ʼ 50”
20.59ʼ 09”
21.00ʼ 33”
x
21.15ʼ 42”
summer time y.2000
Lukasz Skapski: Via Lucem Continens, 2000
Make a Sundial (outdoor activity) VisibiltyofheSunitave
from the observation point X
drawing
approximate
Find a place in your school groundsProportions
whereof the
you
can
install a post. Draw a line
l
on the ground where the shadow ofŁukasz
theSk?pski
post falls at each hour of the day.
l
You can use the sundial to tell time.Via Lucem Continens A.D. MM (Time Walk)
Stour Valley Art Project
l
* How does the length of the shadow
differ
Curator:
Sandra at
Drewdifferent times of year?
Explore solar patterns and the way the sun changes in its position through
the year.
l
* Have a go at making a mini sundial: look at the resources section for ideas.
Equipment: Post/stick
02
Susan Derges Oak No 1
Susan Derges Kingswood No 7
Sun Prints
l
Look at Susan Derges’s photographs from King’s Wood. What shapes can
you see?
l
Use light-sensitive paper to make exposures of natural objects like leaves or
seeds. Leave the paper out in the sun for different lengths of time and see
what the effect is.

What kind of shapes can you see in your images?
Equipment: Light sensitive paper (for sources see resource section)
KS1 / KS2
Pinhole Cameras
l
Use a cardboard tube (e.g. empty Pringles canister) and cut off a piece about
5 cm long. Make a small hole in the solid end with a pin. Then put the lid
back on the other end, first covering it with some white tissue. Then tape the
piece you cut off on top of the lid and cover the whole tube with black paper
or tin foil.
l
Go outside and look into the tube - you should see upside down pictures on
the screen.
Equipment: Cardboard tube, scissors, knife (for teacher use) pin, tape, white tissue,
black paper, tin foil
KS2
Pinhole Cameras
l
* You could also try making a pinhole camera that uses photographic paper.
You will need access to a darkroom. For instructions, see the resources
section.
Equipment: Cardboard tube, scissors, knife (for teacher use) pin, tape, white tissue,
black paper, tin foil
03
Other artists and resources
Nancy Holt, Sun Tunnels
http://www.earthworks.org/tunnels.html
Francis Alÿs Zocalo May 20 1999
http://www.tate.org.uk/modern/exhibitions/timezones/artists.shtm
Man Ray- Rayographs
http://www.geh.org/amico2000/htmlsrc/index.html
http://www.manraytrust.com/
Cyanotype Photogrpahy and Anna Atkins
http://www.vam.ac.uk/vastatic/microsites/photography/
processframe.php?processid=pr012
Light Sensitive paper/sun print paper is available from:
http://www.rapidonline.com
http://www.hawkin.com
Making sundials
http://www.sundials.co.uk/
http://www.bbc.co.uk/norfolk/kids/summer_activities/make_sundial.shtml
Make a Pinhole Camera
http://www.kodak.com/global/en/consumer/education/
lessonPlans/pinholeCamera/pinholeCanBox.shtml
Emily Richardson
http://www.emilyrichardson.org.uk/
Lukasz Skapski
http://www.stourvalleyarts.org.uk/commissions/vialucem/
Notes on images of objects in the collections
Anglo-Saxon sundial
Pocket sundial dating from 950AD, found in Canterbury Cathedral (electrotype
copy in museum collection). Indicated times of Cathedral services and believed
to have belonged to a monk. To use it you would face the sun and the gnomen
(sundial upright) would cast a shadow down the front of the dial.
Eighteenth century sundial
Wooden pillar sundial with initial letter of months around the base; the attached
metal gnomen can be rotated to point to each month; interval lines marking each
hour curve around the pillar. Probably a shepherd’s sundial for use when far from
a church clock.
04
© Canterbury Museums Service
Natural Systems: Mass Productions
Mass-produced 1950s and 1960s objects
Number Values, 2-D and 3-D Shapes
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Daniel Sturgis
Jim Drain
Richard Woods
Henna Nadeem
Lesley Halliwell
Wim Delvoye
Jacob Dahlgren - stripey tops and Life is Art is Life
Ceramics at Beaney
Mass produced objects (1950s and 60s)
Medieval Seal and Mould
Pilgrim Badges
Games counters
Games counters
Mass produced objects
Food packaging
Hand-made objects e.g. crafts
Games
Photographs
01
Curriculum Links
l
l
Talk about, recognise and recreate simple patterns.
l
l
Look closely at similarities, differences, patterns and change.
l
Creative Development
l
Explore colour, texture, shape, form and space in two or three dimensions.
KS1
Ma2 Number
1e: Use the correct language, symbols and vocabulary associated with number
and data
1f: Communicate in spoken, pictorial and written form, at first using informal
language and recording, then mathematical language and symbols
Ma3 Shape, space and Measures
1e: Recognise simple spatial patterns and relationships and make predictions
about them
2c: Create 2-D shapes and 3-D shapes
KS2
Ma2 Number and Algebra
1a: Make connections in mathematics and appreciate the need to use numerical
skills and knowledge when solving problems in other parts of the mathematics
curriculum
1f: Organise work and refine ways of recording
Ma3 Shape, Space and Measures
2d: Visualise 3-D shapes from 2-D drawings.
3c: Identify and draw 2-D shapes in different orientations on grids
Learning Objectives
l
Use ICT to understand number values and patterns
l
Communicate using numbers and number values
l
Explore shape through hand-made and ICT-based processes
Activities
F
Patchwork quilt
l
Collect labels from food packaging, sweet wrappers etc.
l
Each child has a square of paper on which they can create a design by hand.
l
Make a patchwork, alternating the mass-produced packaging with the hand
made designs.
Equipment: Paper, pens or paint, food packaging/labels.
KS1 / KS2
Hand-made
Jim Drain,
Hex
2008
l
Look at work by the artists Daniel Sturgis, Jim Drain, Richard Woods,
Henna Nadeem, Wim Delvoye and Lesley Halliwell. Their work is all
hand made and takes many hours to produce.
02
Lesley Halliwell
l
Create a games board by hand. Make a board from squares and create
circular counters, each one should be hand made and different. You could
use, paint, collage, crayons or pens.
Equipment: Card, scissors, paint, magazines, glue, pens, crayons.
Mass-Produced
l
Look at the work of Jacob Dahlgren. He uses a computer to design his
installations, uses mass produced objects to make his sculptures (food cans,
weighing scales) and observes repetition of mass-produced objects in
everyday life (stripy jumpers).
l
Look at the seal and mould. Seals were mass-produced by pressing wax into
moulds. The Medieval lead Pilgrim badges were made the same way,
hammering soft lead into moulds.
l
Create your own sculpture using mass produced objects.
l
Create a games board on the computer. Create counters on the computer.
Print and cut them out.
Equipment: Paper, scissors.
Game, set and match!
l
Mix up the two games, so you pitch the mass produced counters against the
hand-made. Who wins?
Jacob Dahlgren, Signes d’Abstraction
Art to Life to Art, 2009
03
Jacob Dahlgren Heaven is a Place on Earth 2006–9
KS2
Product Design
l
Make a drawing of one of the artists’ work. Now give each colour a number
and label all the sections of the drawing. Now change the colour value of
each number, and colour in the drawing to create a new drawing.
l
Do the same activity on the computer. How different do the end results look?
l
Give each number a height value, and create a 3-D model using the drawing
as a base. Try creating the model on the computer. Does your hand-made
model look like your computer model?
Equipment: Paper, pens, paint, card, scissors, glue.
Jacob Dahlgren, Sketch for installation at Turner Contemporary
Andy Warhol: Campbells Soup series
210 Coca Cola Bottles, 1962
http://www.tate.org.uk/modern/exhibitions/warhol/
Pop Art
http://en.wikipedia.org/wiki/Pop_art
Sonia Delaunay -Atelier Simultane
http://www.exporevue.com/magazine/fr/s_delaunay.html
04
Eduardo Paolozzi, A formula that can shatter into a million glass bullets (Universal
Electronic Vacuum), 1967
http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999973&workid=11076&sea
rchid=9283&tabview=subject
Omega Workshops
http://www.tate.org.uk/archivejourneys/bloomsburyhtml/art_omega.htm
Daniel Sturgis
http://www.danielsturgis.co.uk/
Jim Drain
http://www.greenenaftaligallery.com/artist/Jim-Drain
Richard Woods
http://www.richardwoodsstudio.com/
Henna Nadeem
http://www.axisweb.org/seCVPG.aspx?ARTISTID=10089
Lesley Halliwell
http://www.lesleyhalliwell.co.uk/
Wim Delvoye
http://www.wimdelvoye.be/
Jacob Dahlgren
http://www.jacobdahlgren.com/
Medieval seal and two-part mould
Double-sided seals were made by pouring wax into a two-part mould or ‘matrix’.
This Medieval matrix has a general view of Canterbury on one side and originally
had a scene of Thomas Becket’s murder on the other. But during the Reformation
Thomas Cromwell, Henry VIII’s chief minister, ordered images of Becket to be
destroyed and the local bell-founder was paid by the city of Canterbury to make
a replacement matrix bearing the city’s coat of arms.
Norman bone gaming counters
Norman (12th century) bone gaming counters from Canterbury, incised with
repeating circular patterns. The counters, made from a cow’s jaw bone, were used
for a game called tabula, which is similar to modern backgammon.
Medieval Pilgrim badges
Pilgrims to holy shrines like Canterbury collected badges to show they had been
on pilgrimage to those shrines. Canterbury Pilgrim badge images included heads
and hands of Thomas Becket. Badges for Compostella in Spain were usually cockle
shells, the symbol of St James of Compostella (‘coquilles St Jacques’).
05
Natural Systems: Fractals
Fern fossil, Carboniferous era
Fractals, Chaos theory, Fibonacci series,
Euclidean/Non-Euclidean Geometries, Scale
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Jim Drain
Carboniferous ferns and plants
Dendritic Flint
Clouds
Rivers
Plants
Curriculum Links
l
l
l
l
Observe, find out about and identify features in the place they live and the
natural world.
01
about them.
2a: Describe properties of shapes that they can see or visualise using the related
vocabulary.
2b: Observe, handle and describe common 2-D and 3-D shapes; name and describe
the mathematical features of common 2-D and 3-D shapes, including triangles of
various kinds, rectangles including squares, circles, cubes, cuboids, then hexagons,
pentagons, cylinders, pyramids, cones and spheres.
2c: Create 2-D shapes and 3-D shapes.
common words.
1h: Use mathematical reasoning to explain features of shape and space.
are identical.
2c: Make and draw with increasing accuracy 2-D and 3-D shapes and patterns;
recognise reflective symmetry in regular polygons; recognise their geometrical
features and properties including angles, faces, pairs of parallel lines and
symmetry, and use these to classify shapes and solve problems.
3a: Visualise and describe movements using appropriate language.
Learning Objectives
l
Understand what a fractal pattern is
l
Explore ideas of different kinds of shapes and patterns (different geometries)
Activities
F / KS1 / KS2
Flat fractals
l
Use two pieces of stiff card, glass or plastic. Put a blob of paint on one piece
and press the other one on top of it. Pull off the top piece quickly, and you
should get a pattern which looks a bit like a river delta (see illustration). You
can try making a print from this by placing a piece of paper gently on top
and pulling it off slowly.
Equipment: Card, glass or plastic sheets, paint, paper
KS1 / KS2
Natural fractals
Dendritic flint
l
Draw a fern leaf using a magnifying glass to zoom in. What do you notice
about the pattern repeat?
02
l
Discuss how fractal geometry makes this pattern by repeating the same
shape joined onto the previous one, but at a different scale. Notice how the
pattern unit does not lose its detail at a smaller scale.
l
Look at other examples in nature: e.g. clouds, rivers, edges of land, the river
like pattern that manganese has made in the flint sample. How are they
different from the regular solids that we draw in our maths classes?
l
Explore making a Sierpinski triangle. Draw a large equilateral triangle.
Measure the mid-point of each line and use these points to construct another
triangle upside down inside it. Continue this process until you run out of
space. How is this similar to the pattern in the fern? How is it different?
Equipment: Magnifying glass, paper, pencil, ruler, protractor.
KS2
Chaos theory *
l
Artist Jim Drain uses pattern randomly, imitating ideas of chaos theory.
l
Use ICT to find out more about chaos theory and Mandelbrot sets. See if you
can create your out Mandelbrot design pattern.
Jim Drain Hex 2008
Introducing Fractal Geometry (2000) N. Lesmoir-Gordon, W. Rood, R Edney, Icon Books
Mathematics in Nature (2003), J.A. Adam, Princeton University Press
Sacred Geometry (2006), S. Skinner, Gaia Books
Mandelbrot sets
http://www.math.utah.edu/~pa/math/mandelbrot/mandelbrot.html
Fractals activities:
http://www.rigb.org/christmaslectures06/pdfs/fascinating_fractals_p1.pdf
http://www.shodor.org/interactivate/activities/FlakeMaker/
03
www.numberspiral.com
Jim Drain
http://www.greenenaftaligallery.com/artist/Jim-Drain
Carboniferous ferns and plants
Kent was once covered by luscious tropical forests. The trees and plants fell and
were compressed over millions of years by other layers of rock formed above,
forming coal. Fossils of some tree bark and plants can be found in the coal. These
examples come from the East Kent coalfield that spanned the Canterbury and
Dover districts.
Dendritic flint
Manganese oxide has made this pattern in the rock as it was forming. This sample
came from Chartham Quarry, near Canterbury.
04
Natural Systems: Crystal Structures
Fluorite crystals
2-D and 3-D Shapes, Scale
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Susan Derges
Fluorite and Galena crystals
Tortoiseshell
Coral
Sugar
Salt
Sand
Curriculum Links
l
l
Use language such as ‘circle’ or ‘bigger’ to describe the shape and size of solids
and flat shapes.
l
l
natural world.
01
about them
vocabulary
various kinds, rectangles including squares, circles, cubes, cuboids, then
hexagons, pentagons, cylinders, pyramids, cones and spheres
2b: Visualise and describe 2-D and 3-D shapes and the way they behave, making more
precise use of geometrical language, especially that of triangles, quadrilaterals, and
prisms and pyramids of various kinds; recognise when shapes are identical
symmetry, and use these to classify shapes and solve problems
Learning Objectives
l
To observe shapes at different scales
l
To explore natural structures
Activities
F / KS1 / KS2
Crystals up Close
Look at sugar and salt crystals (or snowflakes in winter) through a magnifying
glass and/or under a microscope. What patterns and shapes can you see?
Equipment: magnifying glass/microscope
Inter-grown Fluorite crystals on Galena
KS1 / KS2
Make a Crystal
l
Dissolve washing soda, salt or sugar in a a glass jar of very hot water (teacher
may need to demonstrate/supervise). Hang a paper-clip on some thread from
a pencil, so that it hangs in the water. Leave the jar for a few days and see
what happens. Crystals should form on the paper-clip.
l
Use a magnifying glass to look at the crystals. What shapes and patterns can
you see? Draw the shapes you see.
Equipment: Glass jar, washing soda, water, pencil, thread, paper-clip, pencil, paper
02
KS2
Make a Crystal
l
Try making a 3-D model of the crystals using cardboard.
Equipment: Glass jar, washing soda, water, pencil, thread, paper-clip, card, glue,scissors,
pencil, paper
From Atoms to Patterns *
l
Look at the patterns on a leaf, a tortoiseshell, and coral. How are they similar
and different? What happens if you magnify a leaf?
l
Draw a magnified part of a leaf, and use it to create pattern design for
wallpaper, a carpet or a dinner plate. Simplify the shapes you see and change
the colours. You could also use a computer to do this.
l
You could use this activity to explore scale, by looking at zooming in on a
leaf or other object to see its structure. The Atoms to Patterns website has
some good examples of molecular structures (see resource section).
Equipment: Paper, magnifying glass, pens and pencils
Koo Jeong-a, Cedric, 2003
http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999875&workid=93375&sea
rchid=13859&tabview=display
From Atoms to Patterns: Crystal Structure designs from the 1951 Festival of Britain (2008), L.
Jackson, Richard Dennis Publications
From Atoms to Patterns exhibition at the Wellcome Gallery
http://www.wellcomecollection.org/exhibitionsandevents/
pastexhibitionsandevents/fromatomstopatterns/index.htm
Fluorite crystals
Both examples have transparent crystals but in the darker sample they are on a
bed of Galena and covered with Pyrite; found in Derbyshire.
Galena crystals
Cubo-octahedral crystals coated in Dolomite, found in Cumbria.
Coral
The illustrated example is known as Brain Coral because of the pattern resembling
a human brain that is created as the coral grows.
03
Natural Systems: Fibonacci
Inter-grown Fluorite crystals on Galena
2-D and 3-D Shapes, Scale
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Daniel Sturgis
Tim Norris
Ammonites and nautiloids
Ferns
Leaves (arrangement on plants)
Petals (arrangement on flowers)
Pine Cones
Sunflowers
Romanesque Broccoli/Cauliflower
Leaf arrangement on plants
Petal arrangement on flowers
Curriculum Links
l
l
l
l
natural world.
01
about them.
Learning Objectives
l
To recognise simple patterns and and relationships
l
To use reasoning to make predictions about these patterns
Activities
F / KS1 / KS2
Pine cone patterns
l
Look at a pine cone. Colour in the kernels with one paint colour to see the
spirals which come out from the centre. (you could also do this activity with
sunflower head)
Equipment: Pine cone, paints or pens
Herb Spiral
l
Outdoor Activity: Create a herb spiral in your school grounds. Use bricks or
logs to build the spiral shape, which gets lower as it spirals out. Then fill it
with earth and plant herbs in it. (Worksheet available from Centre for
Alternative Technology-see link at end of sheet)
Equipment:Bricks or logs, earth, plants or seeds
KS1
Snail Shell Spirals
l
Look at a snail or nautilus shell. Use the template of the Fibonacci number
sequence. Join the dots at the corner of the squares to make a spiral.
l
Then use collage of different colour shapes cut out to create a snail shell like
Matisse's The Snail.
* Use this activity to discuss the idea of a number sequence.
l
Equipment: Template, pencils, pens, coloured paper, scissors, glue
02
Nautilus fossil, polished interior (Cenoceras)
Nautilus shell, interior
03
Petal Patterns
l
Look at Daniel Sturgis's painting, Clean Life. Daniel uses hand-cut templates
of a petal to create his paintings. Design a leaf or petal template, and then
use it to create a pattern which looks like a plant viewed from above, or a
flower’s face.
Equipment: card, glue, scissors, paint
Daniel Sturgis Clean Life 1998–9
KS2
Snail Shell Spirals
l
Use the template of the Fibonacci number sequence to draw a spiral. You
could try sticking it on to a bigger sheet of paper, and continuing the
sequence, and making your spiral bigger.
l
* Use the Fibonacci sequence to construct a template yourself, and then draw
a spiral. The sequence is made by adding each number to the previous
number, i.e., 1, 1, 2, 3, 5, 8, 13, 21. These form squares which are added onto
the previous square's side.
l
* Use this activity to discuss the ideas of the Fibonacci series in nature, and
the golden ratio (1·618034 )
l
* Look at an image of a cross-section of a Nautilus sea shell. Draw a line from
the centre out in any direction and find two places where the shell crosses it
so that the shell spiral has gone round just once between them. The outer
crossing point will be about 1.6 times as far from the centre as the next
inner point on the line where the shell crosses it. This shows that the shell
has grown by a factor of the golden ratio in one turn. You could lead this
activity onto looking at examples of the Golden Section in Architecture and
Art – see links at end of sheet.
Equipment: Template, pencils, pens
Matisse: The Snail, 1953
http://www.tate.org.uk/imap/pages/animated/cutout/matisse/snail.htm (animation
of the artwork)
Work is on display in Tate Modern permanent Collection
Robert Smithson: Spiral Jetty, 1970
http://www.robertsmithson.com/earthworks/spiral_jetty.htm
Leonardo da Vinci (Golden Section)
http://brunelleschi.imss.fi.it/menteleonardo/
04
Tim Norris
http://www.timnorris.co.uk/
http://www.timnorris.co.uk/html/sculptures5.htm
Daniel Sturgis
Create A Herb Spiral worksheet
http://www.cat.org.uk/catpubs/pubs_content.tmpl?subdir=catpubs&sku=PUBS_20/0
8&key=ts_hs
Fibonacci numbers and the Golden Section website
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
Ammonites
Similar to nautiloids but now extinct; the exterior view is of Dactylioceras,
the polished interior sample is Asteroceras, the polished interior fragment
is Phylloceras.
Nautilus and Nautiloid shells
Modern nautiloid shells and fossil ancestors
05
Repetition: Repeating Patterns
Paul Moss Danger Painting 1-6 2003
Repeating Patterns, Translation, Position and Movement
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Paul Moss
Richard Woods
Lesley Halliwell
Medieval seal and mould
Roman imprinted relief pottery
Roman tile impressed with pattern
Wooden carved paddle
Imprinted and relief pottery
Sweet wrappers
Food labels
Pottery and ceramics
Curriculum Links
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01
common words
3b: Recognise movements in a straight line (translations) and rotations, and
combine them in simple ways [for example, give instructions to get to the head
teacher’s office or for rotating a programmable toy]
3a: Visualise and describe movements using appropriate language
3b: Transform objects in practical situations; transform images using ICT; visualise
and predict the position of a shape following a rotation, reflection or translation
Learning Objectives
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To create simple repeating patterns
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To identify pattern networks
Activities
F / KS1
Printing patterns
Wax seal
Carved wooden paddle
Roman pottery
Roman pottery
l
Look at the patterns on the pottery and wooden paddle in the museum
collection. How many times is the pattern repeated?
l
Look at the Medieval seal and its two-part mould. Lots of seals could be made
using the mould. The pattern on the Roman tile was made with a roller on
damp clay.
l
Make a printing roller. You could either use a foam sheet stuck onto a toilet
roll or a cotton reel covered in clay or play dough. Stick a pencil or a bamboo
skewer through the centre (you will have to make ends for the toilet roll).
Alternatively a paint roller could be used.
02
l
Cut into the foam or draw into the clay/dough with a pencil to make a
pattern. Now dip it into paint and see how the pattern repeats. What
happens when you join more than one line of the pattern together?
l
You could also try making a repeating pattern using block printing. Create
designs on blocks of clay or foam, or use potatoes, and then dip in paint and
print onto paper in your pattern.
l
Look at examples of fabric design in other cultures. What shapes do you see?
Equipment: Cardboard tubes, cotton reels, bamboo skewers (for older children), pencils, foam
sheet, clay, play dough, paint, paper
KS1 / KS2
Wrapping patterns
l
Look at Paul Moss's artwork, Danger Painting. What has he used to create the
repeating pattern?
l
Use food labels or sweet wrappers to see what patterns you can create based
on a repeating object.
l
You could try covering a 3-D shape in the wrappers. What happens at the
edges?
Equipment: Paper, card, wrappers or labels, glue, scissors
Paul Moss Danger Painting 1 (detail) 2003
03
Indian fabric designs
Indian Textile Prints CD-ROM and Book, Pepin Press (available from Dover Books
http://www.doverbooks.co.uk/)
African fabric designs
http://afribatik.co.uk/fabrics.php?group=Fabrics&piece=2
Shack Chic
http://news.bbc.co.uk/1/hi/world/africa/2196254.stm
Richard Woods
Paul Moss
http://www.workplacegallery.co.uk/artists/_Paul%20Moss/
Lesley Halliwell
http://www.lesleyhalliwell.co.uk/
Shack Chic: Innovation in the Shack-lands of South Africa (2002), C. Fraser,
Thames and Hudson
Andy Warhol: Campbells Soup series
210 Coca Cola Bottles, 1962
http://www.tate.org.uk/modern/exhibitions/warhol/
Medieval seal and two-part mould
Double-sided seals were made by pouring wax into a two-part mould or ‘matrix’.
This Medieval matrix has a general view of Canterbury on one side and originally
had a scene of Thomas Becket’s murder on the other. But during the Reformation
Thomas Cromwell, Henry VIII’s chief minister, ordered images of Becket to be
destroyed and the local bell-founder was paid by the city of Canterbury to make
a replacement matrix bearing the city’s coat of arms.
Roman tile impressed with roller pattern
Fragment of a ‘voussoir’ or roof tile from a Roman bath-house in Kent (Plaxtol,
near Sevenoaks), impressed with a pattern that is actually an inscription saying
‘I, Cabriabanus made this wall tile (Parietalem Cabriabanu Fabricavi) – you can see
‘CABR’ in the bottom right corner. Grooved rollers were run over damp clay tiles,
creating a rough surface to which wall plaster would stick. In this case the maker
carved an inscription into his wooden roller instead of the usual grooves.
Roman imprinted relief pottery
Red clay pottery known as Samian ware was often decorated with reliefs by
pressing the clay against a mould that could be repeated all round
Imprinted and relief pottery
The jugs include patterns made by incised or imprinted lines, relief additions
made in moulds (some made separately then attached to the jug body), and
painted lines.
Wooden carved paddle
Wooden carved paddle from the Pacific islands (Friendly Islands?) collected by
nineteenth century traveller Henry Lansdell
04
Repetition: Rotation
Floor of Beaney
Translating through Angle, Rotation
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Jacob Dahlgren
Jacqui Poncelet
Medieval tiles
Roman mosaics
Beaney floor pattern (terrazzo)
Tiles
Wallpaper
Pottery
Curriculum Links
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01
about them
common words
combine them in simple ways
4b: Understand angle as a measure of turn using whole turns, half-turns and
quarter-turns
2a: Recognise right angles, perpendicular and parallel lines; know that angles are
measured in degrees and that one whole turn is 360 degrees and angles at a point
total 360 degrees, then recognise that angles at a point on a straight line total 180
degrees; know that the sum of the angles of a triangle is 180 degrees
2b: Visualise and describe 2-D and 3-D shapes and the way they behave, making more
precise use of geometrical language, especially that of triangles, quadrilaterals, and
prisms and pyramids of various kinds; recognise when shapes are identical
4c: Recognise angles as greater or less than a right angle or half-turn, estimate
their size and order them; measure and draw acute, obtuse and right angles to the
nearest degree
Learning Objectives
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To recognise simple spatial patterns which use rotation
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To recognise different angles
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To understand properties of rotation and what happens when a shape is
translated through angle
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To learn about different types of pattern networks
Activities
F /KS1 / KS2
Window Patterns
l
Make a window pattern based on rotation through angle, using see-through
acetate or tissue. Cut out eight rectangles of the same size and then place
them as shown in illustration 2. This will make an 8 pointed star pattern.
You could also try some of the other placing rules, and experimenting
with different shapes and sizes of rectangles, and with using different
coloured paper.
02
l
This activity could be developed further with KS1 and KS2 by exploring
properties of angle and using it to calculate the different angles in the
pattern. You could also try creating a pattern on the computer by rotating a
simple shape.
Equipment: Tissue paper or acetate, scissors, glue or sticky tape
KS1 / KS2
Roman mosaics
Pattern Networks
l
Find the repeating pattern and pattern network in Jacob Dahlgren’s Heaven is
a Place on Earth or Jacqui Poncelet’s merry go round (Pattern network types:
Square, Brick or Half-drop, Diamond, Triangle, Ogee, Hexagon, Circle, Scale)
l
Find the pattern network in medieval tiles, or in everyday objects like floors,
plates, fabrics, wallpaper etc.
l
Identify whether the pattern is made by rotation, reflection or another
means of translation.
l
Look at the Medieval tiles. Create your own pattern square and then rotate
and repeat it to create a new pattern. You could also do this on the computer.
Equipment: paper, pencils
Jacqui Poncelet merry go round (detail) 2009
03
KS2
Metamorphs*
l
Make a Metamorph from the template. Cut out each side and decorate with a
pattern (simple geometric patterns work well). Then glue the sides together
and cut along the solid lines, and score along the dotted lines.
l
Now experiment with folding the pattern in different ways, creating new
arrangements of patterns. Push the centre of the pattern in to see how it
rotates (see illustration).
l
Find out more about metamorphs, and who invented them.
Equipment: Template, scissors, pens, glue
Helio Oiticica: Metaesquema (various)
04
http://www.tate.org.uk/modern/exhibitions/heliooiticica/rooms/room2.shtm
Frank Stella, Flin Flon 1970
http://cs.nga.gov.au/Detail.cfm?IRN=37841
Malevich, Dynamic Suprematism 1915 or 1916
http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999961&workid=9205&sear
chid=10709
Principles of Pattern Design (1969), R. Proctor, Dover Publications Inc.
Metamorphs: Transforming Mathematical Surprises (2008), R. Brynes, Tarquin
Publications
Mathematical Window Patterns (1999), W. Gibb, Tarquin Publications
Paul Schatz and the Invertible Cube
http://www.paul-schatz.ch/en/invertiblecube.htm
J R Soto, Spiral, 1956
http://www.jr-soto.com/
Jacob Dahlgren
Jacqui Poncelet
http://www.poncelet.me.uk/
Medieval tiles
Made at kilns on Tyler Hill, Canterbury, and found at medieval sites throughout
the city, including the Poor Priests Hospital (Museum of Canterbury) and old
Marlowe Theatre. Some have individual designs while others make up groups or
pattern networks of four, nine or sixteen tiles (like the example from Rievaulx
Abbey, North Yorkshire, which used tiles made locally to that abbey).
Roman Mosaics
Decorative panels inserted into areas of plainer tiles on the floors of a Roman town
house in Canterbury and preserved where they were found
Floor of Beaney
Made of terrazzo, a concrete flooring containing small coloured stones that can be
arranged into intricate patterns and took its name from Italian use; corners of
rooms have repeat patterns, as do the centres.
05
Repetition: Tessellation
Richard Woods re-brand 2009
Tessellation, Measure, Angles, Scale
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Richard Woods
Jacob Dahlgren
Wim Delvoye
Daniel Sturgis
Henna Nadeem
Guiliano Mauri
Chinese Pangolin
Seed pod
Tortoiseshell
Rattlesnake tail
Roman mosaics
Seed pods
Brickwork
Wallpaper
01
Curriculum Links
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about them
vocabulary
hexagons, pentagons, cylinders, pyramids, cones and spheres
1c: Approach spatial problems flexibly, including trying alternative approaches to
overcome difficulties
are identical
Learning Objectives
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To recognise patterns that use tessellation
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To understand why some shapes tessellate and not others
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To explore creating tessellating patterns
Activities
F / KS1 / KS2
Mosaic Making
l
Have a look at the Roman mosaics that were found in Canterbury. In Latin,
tessella was a small cubical piece of clay, stone or glass, used to make mosaics.
A tiny cube was a tessella; from this we have the word tessellation. What do you
notice about the mosaics? Can you see any spaces between the tiles?
* Discuss the meaning of tessellation.
l
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Try making a mosaic from small pieces of coloured paper cut into squares.
Equipment: Coloured paper, glue, scissors.
l
Whole class activity: design and make a mosaic for the school grounds.
Equipment: mosaic tiles, cement, wood (for frame).
02
Daniel Sturgis Clean Life 1998–9
Richard Woods, Sketch (detail), 2009
Guiliano Mauri Imprints
KS1 / KS2
Tessellating shapes
l
Look at the work of Jacob Dahlgren, Richard Woods, Daniel Sturgis
and Guiliano Mauri. What different tessellating shapes can you see?
l
Why can some shapes tessellate but not others? Experiment with trying to
tessellate squares, triangles, pentagons, hexagons. Which ones will
tessellate? Why do you think they do?
l
Use collage to create a tessellating pattern using a regular polygon.
Equipment: Paper, pencils, rulers, protractor, magazines, glue, scissors
Tessellation Templates
l
Draw the pattern you see in a seed pod, Tortoiseshell, Rattlesnake tail or
Pangolin. Are the shapes regular or irregular?
l
Draw one tessellating shape on a larger scale. Use this as a template to cut
out lots of the same shape using different fabrics, magazines etc.
l
Collage the shapes together and find out what new patterns you can create.
Equipment: Paper, pencils, ruler, magazines, glue, scissors
Chinese Pangolin detail
Rattlesnake tail
03
Ivory nut pod
KS2
Tessellation Templates
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* Look at the work of Roger Penrose, a mathematician who found a way of
making a tessellating pattern which didn't repeat (see resources section).
Equipment: Paper, pencils, ruler, magazines, glue, scissors
Figure Ground*
Henna Nadeem Sherbert Sunset 2005
Wim Delvoye Marble Floor #86 1999
l
Look at the work of artists Wim Delvoye and Henna Nadeem. What happens
in the space behind the pattern? Discuss the idea of figure/ground.
l
Look at examples of Arabic art and trace the patterns. Colour in different
elements of the pattern in solid colours to explore the tessellating shapes.
l
Create a figure/ground design of your own. Try to make a pattern which
tessellates with a strong colour in the foreground and a lighter colour in the
background.
Have a look at this site for ideas: http://britton.disted.camosun.bc.ca/jbescher3.htm
Equipment: Paper, pencils, tracing paper, pens or paint
04
Escher
http://britton.disted.camosun.bc.ca/jbescher.htm
http://www.mcescher.com/
Toby Zeigler, The Subtle Power of Spiritual Abuse, 2007
http://www.patrickpainter.com/artists/Ziegler_Toby/index.html
Wallpaper patterns
http://en.wikipedia.org/wiki/Wallpaper_group
Examples of Arabic and other historical patterns using tessellations
http://www2.spsu.edu/math/tile/grammar/index.htm
http://fiveprime.org/hivemind/Tags/tessellation,tiling
Other activities and examples:
http://tessellations.org/
Roger Penrose and tessellations:
http://nrich.maths.org/public/viewer.php?obj_id=1268&part=index
Figure Ground
http://en.wikipedia.org/wiki/Figure-ground_(perception)
Richard Woods
Jacob Dahlgren
Wim Delvoye
Daniel Sturgis
Henna Nadeem
The Magic Mirror of MC Escher (1985), B. Ernst, Tarquin Publications
Godel, Escher, Bach (1979), D. Hofstadter, Penguin Books
Chinese Pangolin
Pangolins live in South and West Africa, India, China and South East Asia – all are
endangered species
Rattlesnake tail
Rattle from a rattlesnake, found in North America and brought back by a traveller
in the nineteenth century
Roman Mosaics
house in Canterbury and preserved where they were found
Ivory-nut palm fruit
Outer skin of the one-seeded fruit from an Ivory-nut palm, which resembles a
closed pine cone (grows in the Caroline Islands of Micronesia)
05
Repetition: Symmetry
Scallop shell
Symmetry, Translating through Reflection
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Jacqui Poncelet
Wim Delvoye
Henna Nadeem
Susan Derges
Butterflies
Shells
Sea urchin fossils
Indian shields and mace
Handle of carved paddle
Anglo-Saxon brooches
Medieval Roof inside Museum of Canterbury
60s and 70s clocks, lampshades
Medieval tiles
Floor of Beaney
Roman mosaics
Leaves
Fossils
01
Tiles
Leaves
Animals
Faces
Bodies
Curriculum Links
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natural world.
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2d: Recognise reflective symmetry in familiar 2-D shapes and patterns.
Learning Objectives
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To be able to recognise examples of symmetry in 2-D shapes
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To use reflective symmetry to create a pattern
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To use ICT to explore symmetry
Activities
F
Mirror Prints
l
Fold a piece of paper in half, and open it out again. Coat a piece of string
with paint and lay it onto one side of the paper. Then fold the paper over the
string, hold it in place and pull the string out. When you open it up you will
have a symmetrical print.
Equipment: Paper, paint, string
02
Pecten (scallop) shell
Butterfly
KS1 / KS2
Natural Symmetry
l
Look at a leaf and find the line of symmetry. Now try changing the line of
symmetry and use a mirror to imagine what the leaf would look like. Draw
the new 'leaf' pattern based on this new line of symmetry.
l
Look at lines of symmetry in shells, sea urchins and butterflies. Try placing
the mirror on a different line and seeing what new 'animal' you can make.
Where else do you find symmetry in nature?
Equipment: mirror, paper, pencil.
Kaleidoscope
l
Use an on-line programme to explore making your own kaleidoscope.
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http://www.krazydad.com/kaleido/
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http://www.vam.ac.uk/vastatic/microsites/moc_kaleidoscope/
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What kind of symmetry does a kaleidoscope use?
KS2
Natural Symmetry
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Where else do you find symmetry in nature?
l
Discuss how lines of symmetry are different on different shapes (eg. Square,
pentagon, hexagon)
l
Explore the symmetry of your face. Take a portrait photograph of everyone
in the class. Use ICT to scan the photo and reflect one side back on itself.
How are the two sides of your face different from each other? Are some
people more symmetrical than others?
Reflective Patterns
Anglo-Saxon pendant
Indian shield
l
Look at patterns by the artists – how have they used symmetry to create a
pattern? What else do you notice about their patterns? (scale)
l
Look at brooch designs in the Museum of Canterbury and look at other
objects that have reflection in their patterns (such as snow flakes). Can you
find the lines of symmetry?
03
Henna Nadeem Four Sunsets 2005
Wim Delvoye Marble Floor #86 1999
l
Create a brooch design, or a design for wallpaper or a mosaic, using
reflective symmetry. Base your design on collage or block colours.
Equipment: Paper, pens, magazines, glue, scissors
Kaleidoscope
l
* You could try making your own kaleidoscope. You can find instructions at:
http://www.kaleidoscopesusa.com/makeAscope.htm
Dan Graham - mirror pavilions
http://www.upprojects.com/portavilion/dan_graham.htm
http://www.diaart.org/exhibs/graham/rooftop/
Dieter Roth
http://www.tate.org.uk/tateetc/issue9/symmetry.htm
http://www.tate.org.uk/servlet/ArtistWorks?cgroupid=999999961&artistid=1870&pa
ge=1
The Symbol of Beauty
http://www.art.net/~coffin/WRITINGS/BEAUTY/beauty.html#Subject8
Kaleidoscopes
http://www.gogeometry.com/wonder_world/haeckel_kunstformen_ascidiae_1.html
Jacqui Poncelet
Wim Delvoye
Henna Nadeem
Snowflakes
The Art of the Snowflake by Kenneth Libbrecht (Motorbooks International, 2007)
Snowflakes by Kenneth Libbrecht (Voyageur Press, 2008)
and other books by the same author who has made a lifetime study of snowflakes,
looking at them under microscopes (and finding no two the same).
04
Butterflies
Tropical butterflies from cabinets put together by various nineteenth century
collectors.
Shells
Scallop shells (British) collected in the nineteenth century
Sea Urchin fossils
Shells of soft-bodied Sea Urchins, which lived when southern England was covered
by tropical seas and have turned into rock (flint) over millions of years to become
fossils, known as an Echinoids.
Indian shield and mace
Metal decorated with incised and inlaid patterns; collected in the nineteenth
century by a traveller and brought back to Canterbury
Wooden carved paddle from the Pacific islands (Friendly Islands?) collected by
nineteenth century traveller Henry Lansdell. The handle has a pattern of small
heads carved around the outside.
Anglo-Saxon jewellery
Cross and Pendant found in Canterbury. The Pendant incorporates the Christian
symbol of a cross in a traditional Kentish style of brooch, with coloured enamel
infilling gold filigree wire patterns.
Medieval roof interior of the Museum of Canterbury
The Museum of Canterbury is housed in the medieval hospital for poor priests and
has original wooden roof structures inside
Medieval tiles
Made at kilns on Tyler Hill, Canterbury, and found at medieval sites throughout
the city, including the Poor Priests Hospital (Museum of Canterbury) and old
Marlowe Theatre.
Floor of Beaney
Made of terrazzo, a concrete flooring containing small coloured stones that can be
arranged into intricate patterns and took its name from Italian use; corners of
rooms have repeat patterns, as do the centres
Roman Mosaics
Decorative panels inserted into areas of plainer tiles on the floors of a Roman
town house in Canterbury and preserved where they were found
05
Repetition: Scale
Elizabethan painted wall
Scale, Measure, Translation
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Henna Nadeem
Jacqui Poncelet
Jacob Dahlgren
Lukasz Skapski
Rosie Leventon
Susan Derges
London Fieldworks
Peter Fillingham
Leaves
Trees
King’s Wood
Leaves
Trees
Maps and plans
Murals
01
Curriculum Links
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Use developing mathematical ideas and methods to solve practical problems.
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natural world.
KS1
4c. Choose and use simple measuring instruments, reading and interpreting
numbers, and scales to the nearest labelled division
KS2
3b. Transform images using ICT; visualise and predict the position of a shape
following a rotation, reflection or translation
4b. Interpret numbers and read scales with increasing accuracy
Learning Objectives
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Understanding scale
l
Using simple measuring instruments and units
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Transforming the scale of a 2-D shape
Activities
F / KS1 / KS2
Classroom Mural
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Whole class activity: each person designs a small tile. Then choose a wall of
the classroom and cover in paper. Divide it up into squares and ask each
child to transfer their design onto a square, by scaling it up. (For F/KS1 the
teacher may need to trace out the pattern and the children can then colour
it in)
Equipment: paper, pencils, paint, large sheets of paper and sticky tape.
F
Enlarging Nature
Susan Derges Fruitbody No.17
Susan Derges Fruitbody No.17
l
Look at Susan Derges’s photographs of leaves, bluebells and fungi. What can
you see in her photos? Discuss ‘bigger’ and ‘smaller’ things you find in
nature.
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Use leaves to create a collage of a leaf or tree, or make a big drawing of a leaf.
What happens when you make something small big, and something big small?
Equipment: paper, pencils, pens, paint
02
KS1
Micro and Macro
l
Look at Henna Nadeem’s collages. Can you see the different images she has
used to make her patterns? Nadeem combines micro (zoomed in) views of
nature with macro (zoomed out) views.
l
Choose a photograph and use ICT to zoom into it, and select a small section.
Print this out at a larger scale, and cut out a pattern. Overlay the pattern on
the original picture.
Equipment: glue, scissors
Enlarging Nature
l
Look at Susan Derges’s photographs of leaves, bluebells and fungi. What
kind of details do you see in her photos?
l
Collect leaves. Experiment with enlarging objects – use measure to make a
large-scale drawing of a leaf. Use measure to make a small scale drawing of
a tree or large object (draw something you can find in the school grounds).
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What happens when you make something small big, and something big
small? What happens when you combine scaled-up and scaled-down
drawings in one picture? How do patterns make the scale of something
look different? (Jacqui Poncelet)
Equipment: paper, pencils, ruler
KS2
Enlarging Nature
l
You could try stretching an image by changing the scale in one dimension
but not another.
l
Try using the drawings you have made to create a pattern and use this to
cover an everyday object (e.g. a folder).
l
How do patterns make the scale of something look different? (Jacqui
Poncelet)
Equipment: paper, pencils, ruler
03
Rosie Leventon, B52, 2003
Scale Models
l
Explore how artists use scale to design large-scale pieces of artwork. Look at
the drawings by London Fieldworks and Lukasz Skapski; how do you know
what size the finished artwork will be? Look at B52 by Rosie Leventon and
discuss how she would have planned it out. Look at Peter Fillingham’s
artwork- how do you think he designed it?
l
Make a scale model of your classroom or your bedroom. First measure the
walls and floor of the room. Then draw out a plan and elevations of the walls
onto paper, at a scale of 1:100 (so 100 cm in real life = 1 cm on the drawing).
Then using the drawings, transfer the individual parts of your plan (walls,
floor etc) onto card. Cut out the pieces and assemble the model. You could
add furniture, windows, etc. You could also try this with other objects (See
Claus Oldenburg).
Equipment: card, glue, scissors, ruler
London Fieldworks Superkingdom 2008
04
Claus Oldenburg
www.oldenburgvanbruggen.com/lsp.htm
Langlands and Bell: Ivrea, 1991
http://www.langlandsandbell.com/ivr01.html
Works are on display in Tate Modern permanent Collection
Murals & Frescoes
http://en.wikipedia.org/wiki/Mural
http://en.wikipedia.org/wiki/Fresco
Diego Rivera
http://diegorivera.com/index.php
Henna Nadeem
Jacqui Poncelet
Jacob Dahlgren
Found in a building on Old Dover Road in Canterbury, preserved under later
surfaces. The plant decoration spreads across the timber frame and the
plaster infills.
05
Architecture: Construction
Wasps’ nest interior
2-D and 3-D Shapes
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
London Fieldworks
Guiliano Mauri
Richard Harris
Chris Drury:
Wasps’ nests
Birds’ nests
Pumice stone
Tortoiseshell
Sea Urchin fossil
Trees - cell structures
Tree rings
Roman underfloor heating
Beaney façade (corner turrets, stairs)
Buildings
Homes
Birds’ nests
Honeycombs
Packaging, e.g. egg boxes, fruit trays
Soap bubbles
01
Curriculum Links
l
l
Use language such as ‘circle’ or ‘bigger’ to describe the shape and size of
solids and flat shapes.
l
l
Select the tools and techniques they need to shape, assemble and join
materials they are using.
l
Build and construct with a wide range of objects, selecting appropriate
resources and adapting their work where necessary.
l
l
vocabulary
hexagons, pentagons, cylinders, pyramids, cones and spheres.
quadrilaterals, prisms and pyramids of various kinds; recognise when shapes are
identical.
2d: Visualise 3-D shapes from 2-D drawings
Learning Objectives
l
To identify 2-D and 3-D shapes
l
To use language to describe the shape/size of 2-D and 3-D shapes.
l
To mentally visualise shapes
l
To construct 3-D shapes
Activities
F / KS1 / KS2
Animal Homes:
02
Wasps’ nest
Goldfinch or Linnet’s nest
l
Imagine what it would be like to live inside Superkingdom. Describe and draw
the shapes you can see inside the installations.
l
Imagine you are an insect or animal, draw or make your ideal home or use
ICT to design it.
Equipment: pencils, pens, paper
l
Looking at the homes of animals and insects, imagine a whole city of these
homes. Each home can be made up of different shapes (like the Beaney
façade). Construct a cityscape of different shapes and sizes (this could be
done as a whole class activity).
Equipment: Card, scissors and glue, packaging material
l
Outdoor project: Look at Richard Harris and Guiliano Mauri's sculptures. Use
willow to construct a home for an animal in your school grounds (this could
be done as a whole class activity).
Equipment: withies, hemp string, secateurs (for teacher usage)
Wasps’ nest
03
F
Making Shapes:
l
Use Lego or stickle bricks to make shapes. What shapes can you make? Join
the shapes together to make new shapes. What new shapes can you make?
Can you stack the shapes (like Roman under-floor heating stacks)?
l
Look at soap bubbles. What shapes can you see? How do they join together?
Equipment: Lego, soap, water
KS1
Making Shapes:
l
Use packaging material (e.g. egg cartons, fruit trays) to construct a shape.
What shapes can you find in the packaging? What new shapes can you make
with it?
l
* Imagine the shape you have made is a building. Draw the outside and the
inside of the building. Do this on the computer, or using a pencil and paper.
Equipment: packaging materials, glue, sticky tape, paper, pencils
KS2
04
Making Shapes:
l
Construct a 3-D Hexagonal cell from the template (this can be photocopied
onto card or paper). Now construct several more of the same shape. How
easily do the shapes fit together? Try gluing the shapes together in different
combinations to make a new shape. You could look at a Tortoiseshell or Sea
Urchin.
l
Construct an Octahedron from the template. Make several more and explore
sticking them together to make new shapes. Explore where the lines of
symmetry are in the new shape.
l
Imagine the shape you have made is a building. Draw the outside and the
inside of the building. Do this on the computer, or using a pencil and paper.
l
* Use ICT to generate another pattern for a 3-D shape. Print this out and
construct it as you did with the previous one.
l
Compare the pattern of the Wasps nest (regular hexagons) with Pumice
stone (similar but more random shapes made by air bubbles).
l
* Try using cylinders to make a wall, like Chris Drury's Coppice Cloud Chamber.
How easily do they stack together? What kind of spaces are left between the
cylinders? Look at buildings in your neighbourhood. Can you see how they
are constructed? Why do you think some shapes are better for building with
than others? You could also look at tree rings and tree structures. How are
trees constructed? Can you use cylinders to construct a ‘tree’ shape?
Equipment: card, scissors, glue, paper, pencil
Langlands and Bell, Ivrea, 1991 http://www.langlandsandbell.com/ivr01.html
Vladimir Tatlin, Monument to the Third International
http://en.wikipedia.org/wiki/Tatlin’s_Tower
Model is in Moderna Museet, Sweden
Sol LeWitt, Five Open Geometric Structures, 1979
http://www.tate.org.uk/servlet/ViewWork?workid=21766&roomid=3669
Loop PH, Metabolic Media, 2008
http://www.loop.ph/bin/view/Loop/WebHome
Jeremy Deller, Bat House Project
http://www.bathouseproject.org/
Toby Zeigler, Study for True North, 2007
http://www.patrickpainter.com/artists/Ziegler_Toby/index.html
Guiliano Mauri, Cattedrale Vegetale , 2001
http://arengario.net/momenti/momenti69.html
Make Shapes 1, Jenkins & Wild, Tarquin Books
05
Wasps’ Nests
Images of Wasps’ nest interior (hexagons) and exteriors. Wasps build layers of
hollow hexagons in which to hatch new wasps. The solid hexagons are filled with
wasp grubs and food for them. The exterior is made of small semicircular layers of
paper or other material chewed and regurgitated by the wasps.
The small round nest (B) was attached to a curtain and only had a few wasps. The
large nest (A) was built by a swarm of wasps in the roof of a Canterbury house.
Birds’ Nests
Reed Warbler’s nest (British), constructed on reeds.
Weaver Bird’s nest (African), woven; the bird enters via the long tube at the base.
Leafy nest of a Goldfinch or Linnet (British), made of leaves, grass, twigs, ivy, moss.
Roman under-floor heating
Stacks of clay tiles on top of which the floor of the house was built, allowing warm
air from a fire at one side to circulate below the floor. Part of the flooring of a
Roman town house preserved where it was found in Canterbury, around which the
Roman Museum has been built.
Beaney façade
The Beaney Institute, which houses the museum, gallery and library, was designed
and built in the late 19th century, imitating Tudor styles. The front incorporates
corner turret rooms and rounded front stairs.
Tortoiseshell
Home of a soft-bodied tortoise; made of interlocking pentagons, created as the
tortoise and its shell grew.
Sea Urchin fossil
Shell home of a soft-bodied Sea Urchin, which lived when southern England was
covered by tropical seas and has turned into chalk rock over millions of years to
become a fossil, known as an Echinoid. Constructed of interlocking hexagons,
each of which had a spine in the centre (where round bosses have remained when
the spines broke away).
Pumice stone
Stone made of volcanic lava that contained lots of air bubbles.
06
Architecture: Façades
Beaney exterior detail
2-D and 3-D Shapes and Area
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Richard Woods
Jacob Dahlgren
Paul Moss
London Fieldworks
Façade of the Beaney
Façade of the Museum of Canterbury
Façade of Turner Contemporary Project Space
Roman Mosaics
Drawings of buildings
Trees
Leaves
Buildings
Graffiti patterns
Murals
01
Curriculum Links
l
l
Use language such as ‘circle’ or ‘bigger’ to describe the shape and size of
solids and flat shapes.
l
l
l
Observe, find out about and identify features in the place they live and
the natural world.
l
l
about them.
vocabulary.
hexagons, pentagons, cylinders, pyramids, cones and spheres.
2c: Create 2-D shapes and 3-D shapes.
quadrilaterals, prisms and pyramids of various kinds; recognise when shapes are
identical.
4e: Find perimeters of simple shapes; find areas of rectangles using the formula,
understanding its connection to counting squares and how it extends this
approach; calculate the perimeter and area of shapes composed of rectangles.
Learning Objectives
l
To identify 2-D shapes
l
To use language to describe the shape/size of 2-D shapes.
l
To mentally visualise shapes
l
To create patterns by arranging shapes
Activities
F / KS1 / KS2
Surface lines
l
Look at tree bark. Draw the patterns you can see in the bark. You could also
draw the patterns you see in your skin, or on leaves. Colour the sections in
different, contrasting colours. How many colours do you need so that none
of them touch the same colour?
Equipment: Paper, pencils, crayons, pens
F
Handprints
l
Class activity: everyone makes a hand print using different colours. Cut out
the hand prints and add them to one wall of the classroom. Use the hand
prints to make a pattern. How do they change the way the classroom feels?
Equipment: Paper, paint, scissors
02
KS1 / KS2
Wall Patterns
Beaney exterior view
Museum of Canterbury exterior
Stour Valley Arts’ hut
l
Draw one outside wall of your school. What patterns can you find?
l
Now create a new pattern which would transform the façade of the school.
Use a repeating pattern of a simple shape in different colours. You can do
this using paper and pens or you could use the computer.
l
Using the photograph, design a new façade for the hut at Stour Valley Arts.
l
Look at the façades of the Beaney, Museum of Canterbury and re-brand by
Richard Woods. Look at the patterns on the Superkingdom installations, in the
mosaics in the Roman Museum and Jacob Dahlgren’s work. What patterns
can you find? (visit activity or from photos)
l
Trace a façade or artwork and try decorating your drawing using different
colours.
Equipment: Paper, pencils, tracing paper, pens
KS2
l
Link the above activity into ‘area’. Calculate the area of the wall from one
brick/one repeat of pattern.
Equipment: Paper, pencils, ruler, tracing paper, pens
Richard Woods re-brand 2009
03
Paul Moss Danger Painting 1-6 2008
Wrapping walls
l
Look at Danger Painting by Paul Moss. What do you think he has used to
create this effect?
l
Make a model of your classroom. Now try wrapping the walls with different
types of fabric, or collaging with coloured paper. How does this change your
perception of shape? You could also create a model on the computer and add
different patterns or textures to the model.
l
Use images of graffiti to transform a surface. What shapes and repeats can
you find in the graffiti? Cut up the graffiti and layer it to create patterns.
(Use ICT to find images and print them out).
Equipment: card, glue, fabric, magazines, scissors
Christo - wrapped buildings
http://www.christojeanneclaude.net/
Tim Otto Roth- “I see what I see not”
http://www.kunstfassade.de/tor/vernissage.html
Richard Woods
Jacob Dahlgren
Paul Moss
http://www.workplacegallery.co.uk/artists/_Paul%20Moss/
Façade of the Beaney
Decorated with patterns in wood, brick, terracotta (red unglazed ceramic)
sculptures and mouldings, coloured stone, and plasterwork, imitating Tudor styles
in a late-nineteenth century building.
Façade of the Museum of Canterbury
Medieval timber-framed building, which was a hospital or home for poor priests,
decorated with ‘knapped’ flints in traditional Kentish style. Later additions in brick.
Roman Mosaics
house in Canterbury and preserved where they were found.
04
Architecture: Plans
London Fieldworks Superkingdom Sketch 2008
Area and Perimeter, Measures, Axis & Coordinates, Scale
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Henna Nadeem
Jacob Dahlgren
London Fieldworks
Chris Drury
Lukcas Skapski
Bark Beetle markings
City street patterns Elizabethan Canterbury
Canterbury water supply map
Map of bombing in Canterbury
Plan of Roman Amphitheatre, Canterbury
King’s Wood map
Beaney Institute and Turner Contemporary architectural plans
Buildings
Maps
01
Curriculum Links
l
l
natural world.
l
Find out about their environment, and talk about those features they like
and dislike.
4c: Estimate, measure and weigh objects; choose and use simple measuring
instruments, reading and interpreting numbers, and scales to the nearest labelled
division.
2d: Visualise 3-D shapes from 2-D drawings.
3c: Identify and draw 2-D shapes in different orientations on grids; locate and
draw shapes using coordinates in the first quadrant, then in all four quadrants.
4b: Recognise that measurement is approximate; choose and use suitable
measuring instruments for a task; interpret numbers and read scales with
increasing accuracy; record measurements using decimal notation
Learning Objectives
l
To use simple measuring tools
l
To calculate area
l
To gain an understanding of scale
l
To explore using an axis and coordinates
Activities
F
Classroom Map
l
Teacher draws out a map/plan of the classroom. Get each child to draw their
face onto a paper plate and then work out as a group where everyone should
go on the map.
l
Use pacing to work out how big the classroom is: ask the children to find out
how many paces wide and long it is.
l
Talk about other maps they have seen (eg. Playmat maps).
Equipment: Paper, pencils, pens, paper plates, blu tac.
Bird’s eye view of Elizabethan Canterbury
KS1 / KS2
Classroom Map
l
Make a map of your classroom. Measure the classroom and plot it out onto a
sheet of paper. Then measure and draw on the tables and chairs. Now try to
draw the route you usually take around the classroom. Try using ICT to make
the map.
l
Visit a gallery, library or other space to compare. Is it larger or smaller than
the classroom? Why do you think so? (e.g. judging by comparison). Measure
and draw the space to see if you were correct.
02
l
Playing with scale: Put people into your map. Use different sizes of drawings
or collage to explore what different scales look like (refer to Henna Nadeem,
and Superkingdom concept sketches) Use the computer to try this as well.
l
Look at the Bark Beetle markings, what do you think these show? What if we
left a trail behind us when we moved around? Trace the usual journey you
make in your classroom onto the map.
Equipment: Paper, ruler, tape measure, pencils, magazines
Mini Museums
l
Look at the plans by Jacob Dahlgren, London Fieldworks-Superkingdom, Chris
Drury, Coppice Cloud Chamber and Lukasz Skapski, Via Lucem and look at the
images of the finished 3-D artworks.
l
Draw a plan for an imaginary exhibition / forest / museum. Then create it in
a shoebox. Use dolls house furniture, twigs as trees, etc for scale
Equipment: Paper, pencils, card, natural materials, found objects, collage materials, glue,
scissors
horizon line
20.41ʼ 00”
20.42ʼ 50”
20.44ʼ 15”
3m
5°
5m
8.5 m
20.57ʼ 50”
20.59ʼ 09”
21.00ʼ 33”
x
21.15ʼ 42”
summer time y.2000
Lukasz Skapski, Via Lucem
Visib
iltyo
fh
eSu
n
itave
from the observation point X
Proportions of the drawing approximate
Łukasz Sk?pski
Via Lucem Continens A.D. MM
Stour Valley Art Project
Curator: Sandra Drew
(Time Walk)
Chris Drury, Coppice Cloud Chamber
03
Map of bombing in Canterbury, 1942
KS2
Map Plotting*
l
Look at the map showing where the bombs landed in Canterbury.
l
Create a grid with an axis. Use coordinates to plot the colours in Jacob
Dahlgren’s artwork onto the grid. Give each colour a number value. You
could use a computer to do this. What new pattern do you end up with?
Equipment: ruler, pencil, coloured pen
Mark Bradford, Los Moscos  2004
http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999961&workid=88775&se
archid=10545
On the Map: Artists inspired by maps
http://www.northhousegallery.co.uk/exhibitiondetail.asp?exID=27
Richard Long, A line made by walking, 1967
http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999961&workid=76954&s
earchid=9755&tabview=text
City street pattern (Elizabethan Canterbury)
Shows the city walls, River Stour, Cathedral and streets in Shakespeare’s time; the
street pattern is still very similar today.
Henna Nadeem
Jacob Dahlgren
From a book about cities published in Cologne in 1588, and believed to be the
oldest known map of Canterbury. Shows the city walls, River Stour, Cathedral and
streets in Shakespeare’s time; the street pattern is still very similar today.
Canterbury waterworks plan
12th century plan of waterworks improvements for Canterbury Cathedral carried
out for Prior Wibert, who was in charge of the Cathedral and its monastery
between 1155-1167. He arranged for a clean water supply by having water brought
via lead pipes into the Cathedral from cisterns on the hill above Canterbury. The
round Water Tower and some of this piping survive today. The magnificent
original drawing is in Cambridge (reproduced courtesy of The Master and Fellows
of Trinity College Cambridge) and there is a nineteenth century drawn copy in
Canterbury Cathedral Archives.
04
Map of bombing in Canterbury
Detail of plan showing where bombs fell during the German air raid on
Canterbury in June 1942. Buildings destroyed included a newspaper office, two
churches, several drapery stores, two banks, three insurance offices, four schools,
a large garage, a nursery and many scores of houses in residential areas.
Plan of Roman Theatre, Canterbury
Conjectural plan of the Roman Theatre in Canterbury, based on archaeologists’
finds of wall parts (the solid black areas on the plan). (Reproduced courtesy of
Canterbury Archaeological Trust.)
Beaney Institute plan
Plans, by architect A. H. Campbell, of the ground and first floors of the Beaney
Institute, built ‘for the education of working men’ in 1897-99. The building,
housing museum, gallery and library, was extended in the 1930s and is about to
be renovated and extended again (see www.futurebeaney.com).
05
Illusion
Terrazzo floor of Beaney
Illusion: Symmetry, Transforming Shape through Angle
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Richard Woods
Wim Delvoye
Henna Nadeem
Jacqui Poncelet
Moth and Butterfly wings with camouflage patterns
Tree Rings
Floor of Beaney (Terazzo)
Camouflage clothing/fabric
Carpets/rugs (with patterns)
Floor patterns
Wallpaper patterns
Animals, insects and plants which use camouflage
Curriculum Links
l
l
l
lLook closely at similarities, differences,
patterns and change.
01
KS1
1e. Recognise simple spatial patterns and relationships and make predictions
about them
2d. Recognise reflective symmetry in familiar 2-D shapes and patterns.
3b. Recognise movements in a straight line (translations) and rotations, and
KS2
1h. Use mathematical reasoning to explain features of shape and space
2c. Make and draw with increasing accuracy 2-D and 3-D shapes and patterns;
3b. Transform objects in practical situations; transform images using ICT; visualise
Learning Objectives
l
To understand basic concepts of optical illusions
l
To understand how an object or shape can be transformed through pattern
l
To recognise symmetry in patterns
l
To understand and think about similarities and differences between patterns
and shapes
Activities
F
Butterfly Camouflage
l
Use the butterfly template and collage onto it a camouflage disguise. Try
using strips or shapes ripped from wrapping paper or magazines and moving
them around to create a pattern on the butterfly’s wings. Can you disguise
the butterfly as something else, like the ones in the picture?
Equipment: Template, wrapping paper or magazines, scissors, glue
KS1 / KS2
Rotating illusion
Butterfly
Moth
l
Cut out two circles on card (use template provided) and decorate them
both with different patterns. You could use circles, straight lines or an
abstract pattern. Then cut a line from the centre to the edge, where
shown. Cut around the inner circle on the top layer, where shown (do not
cut all the way round!) Attach a paper fastener through the centre of both
circles. Now try sliding one circle over the other. How does this affect the
pattern?
Equipment: Template, card, paper fasteners, scissors, pens/crayons/pencils
02
02
Hidden Pictures
l
Look at Henna Nadeem's work. How many different pictures can you see in her
work? What do you see first, a pattern or a photograph? Cut pictures of
everyday objects from magazines. Then use other pictures to disguise the
original object by cutting out patterns and layering them over the first picture.
Ask other people to see if they can work out what the original object was.
Equipment: magazines, scissors, glue
KS2
l
Choose a photo, and, using ICT, create another design on top of it, which
disguises the first picture.
l
Look at Wim Delvoye's Marble Floor # 86. What is it made of? Trace a
pattern from a design for a carpet or wallpaper. Now use paint or collage
to transform the original pattern. How is it different from your original
pattern?
Equipment: tracing paper, pencil, paint or magazines/coloured paper, scissors, glue
l
Look at Richard Woods' Flat Stack Sculpture and the Beaney floor details.
Try using 3-D objects (e.g. junk modelling, packaging) to create a pattern.
How does the pattern look when viewed from different angles? Draw the
pattern from above and from the side. What do you notice about the
different views?
Equipment: 3-D packaging/junk, glue or wire, scissors, paper, pencils
03
Bridget Riley
http://www.tate.org.uk/servlet/ArtistWorks?cgroupid=999999961&artistid=1845&pa
ge=1
Victor Vasarely
http://www.vasarely.com/
Marcel Duchamp, Roto Reliefs
http://www.aqualoop.com/aqua_sound/delia/Duchamp.html
M.C. Escher
http://www.mcescher.com/
Trompe L’oeil
http://en.wikipedia.org/wiki/Trompe_l’oeil
Richard Woods
Wim Delvoye
Henna Nadeem
Jacqui Poncelet
Moth and Butterfly wings
(A) Moths with camouflage patterns that disguise wing shape
(B) Butterfly with camouflage pattern to look like the eyes of a large bird (owl?)
(C) Moths with pattern on tips of wings looking like beaks of birds or snakes
(D) Top and underside of a tropical butterfly ‘Crameri’, with camouflage patterns
Floor of Beaney
Made of terrazzo, a concrete flooring containing small coloured stones that can
be arranged into intricate patterns and took its name from Italian use.
04
Time
Jem Finer Score for a Hole in the Ground 2006
Time: Telling the Time
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Rodney Glick & Lynette Voevodin
Guiliano Mauri
Susan Derges
Chris Drury
Stephen Turner
Jem Finer
Emily Robertson
Agate rings
Mammoth tusk
Shells
Shells
Tree rings
Decommissioned work at Stour Valley Arts
Clocks
Watches
01
Curriculum Links
l
l
Find out about past and present events in their own lives, and in those
of their families and other people they know.
4a: Estimate the size of objects and order them by direct comparison using
appropriate language; put familiar events in chronological order; compare and
measure objects using uniform non-standard units [for example, a straw, wooden
cubes], then with a standard unit of length (cm, m), weight (kg), capacity (l) [for
example, ‘longer or shorter than a metre rule’, ‘three-and-a-bit litre jugs’]; compare
the durations of events using a standard unit of time
4d: Read the time from analogue and digital 12- and 24-hour clocks; use units of
time - seconds, minutes, hours, days, weeks - and know the relationship between
them
Learning Objectives
l
To understand different ways of measuring time
l
To explore cycles and rhythms of nature and natural systems
l
To understand ideas of growth and decomposition over time
Activities
F / KS1 / KS2
Decomposing
l
Guiliano Mauri's work was made with the intention of it going back into the
forest, gradually decomposing and retuning to where it had come from.
Stephen Turner's tree rings document the natural cycles and decomposition
on the forest floor over time.
l
Make a sculpture that can decompose, from natural objects like fruit,
vegetables or plants. Either draw it every day to record how it changes, or
use digital photographs to document it and put them into an animation on
the computer.
l
How long does the object take to decompose?
Equipment: fruit/vegetables/plants, camera, paper, pencils
Guiliano Mauri Imprints 1999
Stephen Turner Tree Rings 2002
02
KS1 / KS2
Growing
l
Look at the photographs by Jem Finer. How does the forest change in the
photographs? Can you tell what time of year it is?
l
How do we record growth and change - look at the tree rings, agate rings,
Rattlesnake tail and Mammoth tusk. Are all the layers the same?
l
Make a flip book which shows something growing. You could choose a plant,
a flower, an animal, or a person. Using the template, make a slight addition
to your drawing in each frame. Then cut them out and make holes where
shown. Tie it together with string, and tape around the string to hold it
securely in place. When you flick through you should be able to see a 'minimovie' of your growing object.
l
You could also try doing this on the computer, or using an animation
programme to show something growing.
Equipment: Template, pens, pencils, scissors, string, sticky tape
03
Rodney Glick Down on his Luck 2006-2008
Natural Rhythms – A day in the life...
l
Susan Derges spent a year observing the forest, Emily Robertson filmed over
a whole year and condensed it down to a few minutes, Rodney Glick filmed
for a whole day and condensed it to an hour.
l
Make a record of a whole day from your classroom window, or in your
school grounds. Record any changes in the weather, people, and other things
you see. This could be written, drawn or photographed.
l
Take a series of photos or make a series of drawings of the same place every
day for a month. Stick your drawings or photographs up on the wall, as you
go. How does it change over time?
l
Try making a water clock; instructions can be found at:
http://www.nationalgeographic.com/ngkids/trythis/try10.html
l
Visit Activity. Explore forest life cycles at Stour Valley Arts. How do the
woodland management team keep the forest healthy?
Equipment: Paper, pencils, camera
Life Cycles
Emily Robertson Aspect 2004
l
Aspect is filmed in a forest over the period of a year. The forest year is
condensed into a few minutes. Tree rings and layers in the Mammoth Tusk
show how a tree or tusk has grown and shells reveal their own growth with
gradually larger additions.
l
Think about how much you have grown since you were born, and how you
have changed.
l
Bring in family photos that show you at different ages and make a time line
of your life. You could also make a family tree with photos or drawings of
your mum, dad, sisters, brothers, grandparents.
l
Can you imagine what you will look like at different ages? Draw a self
portrait of yourself at the age of 20, 30, 40…etc.
l
Make an autobiography of your life so far, this could be written, drawn or
made using collage.
l
Visit activity: at the Roman Museum in Canterbury, each step down from
street level takes you back 100 years. Can you imagine what life was like in
Roman Canterbury? How has it changed? How is it similar?
Equipment: paper, pencils, magazines, photographs, glue, scissors
04
Sam Taylor Wood, Still life, 2001
http://www.bbc.co.uk/collective/gallery/2/static.shtml?collection=samtaylorwood&
image=6
Eadweard Muybridge
http://www.bbc.co.uk/photography/genius/gallery/muybridge.shtml
Francis Alÿs, Zocalo, May 20 1999
http://www.tate.org.uk/modern/exhibitions/timezones/artists.shtm
Christian Boltanski
http://en.wikipedia.org/wiki/Christian_Boltanski
http://www.moma.org/collection/browse_results.php?criteria=O%3AAD%3AE%3A6
49&page_number=2&template_id=1&sort_order=1
Cindy Sherman
http://www.tate.org.uk/servlet/ArtistWorks?cgroupid=999999961&artistid=1938&p
age=3&sole=y&collab=y&attr=y&sort=default&tabview=worklist
http://www.temple.edu/photo/photographers/cindy/mannequins/sherman.htm
Feliks Topolski, Autobiography 1973
http://www.tate.org.uk/servlet/ViewWork?cgroupid=999999961&workid=14368&se
archid=10247&tabview=image
http://www.emilyrichardson.org.uk/
Telling the time- early devices
http://physics.nist.gov/GenInt/Time/early.html
Agate
Made of very fine quartz that crystallises in air pockets within volcanic rock.
Different minerals in the quartz crystallise at different rates, depositing layers of
different colours, the outermost deposited first and innermost last.
Mammoth tusk
In cross-section a mammoth tusk looks like a tree, with rings of growth from the
centre outwards. In longitudinal section you can see the pointed ends getting
longer with each additional growth inside. Mammoths once lived in Kent: this
tusk was found on the lower beach at Long Rock, Swalecliffe, near Whitstable.
Shells
Shells are the homes for soft-bodied animals and grow as the animal gets larger.
You can see the progression in size relating to growth. The Tellin shell has dark
growth rings.
05
Waves and Sound
Jem Finer, study for Score for a Hole in the Ground 2006
Waves: Geometry
Locations
l Stour Valley Arts
Canterbury Museums
l Roman Museum
l Beaney
Artists
Jem Finer
Richard Harris
Elizabethan Canterbury
Canterbury water supply map
Water
Sound
Curriculum Links
l
l
Investigate objects and materials by using all of their senses as appropriate.
l
Build and construct with a wide range of objects, selecting appropriate
resources and adapting their work where necessary.
l
natural world.
l
l
Respond in a variety of ways to what they see, hear, smell, touch and feel.
01
1d: Use the correct language and vocabulary for shape, space and measures.
about them.
common words.
3a: Visualise and describe movements using appropriate language.
* 4c: Recognise angles as greater or less than a right angle or half-turn, estimate
their size and order them; measure and draw acute, obtuse and right angles to the
nearest degree
Learning Objectives
l
To explore the properties of sound and water
l
To understand the idea of waves (sound and water)
l
To understand why waves make different patterns
Activities
F
Make a sound machine
l
Ask children to build sound machine using natural/found materials eg.
dripping water, sticks striking, stones dropping onto different surfaces.
What different sounds can you make? What do the sounds look like? Use
different words to describe the sounds.
Equipment: water, sticks, stones, different surfaces
KS1 / KS2
Seeing Sound Waves
l
What does sound look like? These activities explore how sound makes patterns.
Kaleidophone
l
Make a Kaleidophone: use a knitting needle, with a silver bead fixed to one end.
Hold it fast at one end in a vice or between two tables. Set up a screen behind it,
then shine a bright light onto the needle. If you hit the needle you should see
wave patterns as the needle moves. What kind of shapes do you see?
Equipment: knitting needle, beads, screen
02
© Master and Fellows of Trinity College Cambridge
Chladni patterns
l
Cut off half a large balloon, and stretch it over an open tin can. Hold it in
place with rubber bands. Sprinkle salt onto the balloon.
l
Try playing different sounds to the balloon and see what happens to the
salt. It should move into patterns. Try downloading the sound from Jem
Finer's artwork and playing it. What pattern does it make?
l
Draw the pattern you see. Experiment with different sounds to see what
kind of patterns they make. What do you notice about louder or softer
sounds, higher or lower notes?
Equipment: Balloon, can, rubber band, paper, pencils
Richard Harris Untitled 1994
Water and waves
l
Look at Richard Harris's sculpture. What does the shape remind you of?
Look at the Narwhal tusk - what does its shape have in common with water?
l
Water is also essential to Jem Finer's piece, as it makes the sound. Have a
look at the Elizabethan Canterbury and Canterbury water supply maps.
What do you know about the properties of water?
l
Fill a plastic tray with water. What happens when you drop a small drop of
water into it? What happens when you disturb one side with a stick?
Explore the idea of waves and the way water behaves. Try drawing the
different patterns you see in the water
l
* Look at a picture of a river. Does it flow in a straight line? Some facts about
rivers include:
l
No river, regardless of size, runs straight for more than 10 times its width.
l
The radius of the bend is nearly always 2-3 times the width of the river at
that point.
l
The wavelength (distance between points of bends) is 7-10 times the
average width.
The technical name for the pattern a river makes is meander geometry. The
shape it makes is an irregular waveform. Discuss the difference between
regular and irregular waves. Use maths to explore the geometry of a river
pattern.
Equipment: Tray, water, paper, pencils
03
Naum Gabo, Linear Construction No. 2 1970-71
http://fusionanomaly.net/naumgabo.html
Musical Minimalism
http://en.wikipedia.org/wiki/Minimalism
Kaleidophones
http://physics.kenyon.edu/EarlyApparatus/Acoustics/Kaleidophone/Kaleidophone.
html
http://www.interactivearchitecture.org/kaleidophone-christian-moller.html
Chladni Patterns
http://www.phys.unsw.edu.au/jw/chladni.html
Harmonograph: A visual guide to the mathematics of music (2001), A. Ashton,
Wooden Books
Godel, Escher, Bach (1979) D. Hofstadter, Penguin Books
Living Water (1976), Olof Alexandersson, Gateway Books
Flowforms
http://www.doc.ic.ac.uk/~gzy/heart/flowforms/flowforms.htm
http://www.flowformsdotcom.pwp.blueyonder.co.uk/
River Meanders
http://www.cleo.net.uk/resources/displayframe.php?src=309/consultants_
resources%2F_files%2Fmeander4.swf
Shows the city walls, River Stour, Cathedral and streets in Shakespeare’s time. The
river was diverted to build mills powered by water and there were also.tanneries,
parchment works and similar that used water for industrial production.
12th century plan of waterworks improvements for Canterbury Cathedral carried
out for Prior Wibert, who was in charge of the Cathedral and its monastery
between 1155-1167. He arranged for a clean water supply by having water brought
via lead pipes into the Cathedral from cisterns on the hill above Canterbury. The
round Water Tower and some of this piping survive today. The magnificent
original drawing is in Cambridge (reproduced courtesy of The Master and Fellows
of Trinity College Cambridge) and there is a nineteenth century drawn copy in
Canterbury Cathedral Archives.
04

maths through pattern

Transcription

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