SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Imaginings in shape and space
TYPE:
Main
OBJECTIVE(S):
Begin to identify and use angle, side and symmetry properties of triangles
and quadrilaterals; solve geometrical problems involving these properties,
using step-by-step deduction and explaining reasoning with diagrams and
text; use 2-D representations to visualise 3-D shapes and deduce some of
their properties.
DESCRIPTION:
3 screens. 1 shows a square which is 'cut' to make other shapes
(tangram). 2 shows 8 shapes and you are asked which could be views of a
square. 3 shows a square with beads constrained to move on its edges
where you have to make shapes.
OVERVIEW:
Tangrams, square shapes and shapes in a square.
EQUIPMENT:
A search of Google (www.google.co.uk) using 'Tangram' will give many
interesting sites, both in the UK and abroad. A balloon with a square
drawn on it may be useful for screen 2. Geogebra is very useful for screen
3 where you can also use pinboards or geoboards. Commercial tangrams
are available (magnetic ones can work well).
Teacher notes include a photocopiable master of an 8 cm by 8 cm and
16cm by 16 cm tangram and another two masters give the silhouettes for
the shapes here based on the 8 by 8 cm square. A final master provides 5
grids to draw shapes for the 'inside a square' activity.
TYPE:
Plenary
OBJECTIVE(S):
Begin to identify and use angle, side and symmetry properties of triangles
and quadrilaterals; solve geometrical problems involving these properties,
using step-by-step deduction and explaining reasoning with diagrams and
text; use 2-D representations to visualise 3-D shapes and deduce some of
their properties.
DESCRIPTION:
4 screens. 1 works through constructing Tangram pieces on a square grid.
2 works through constructing Tangram pieces by folding a square piece of
paper. 3 allows pupils to construct polygons by moving 4 connected,
variable points on a square frame.
OVERVIEW:
Tangrams, square shapes and shapes in a square.
EQUIPMENT:
None specific.
Imaginings in shape and space ................................................................................................... 1
Main Whiteboard and Screen information ................................................................................ 2
Plenary Whiteboard and Screen information ............................................................................ 5
Tangrams 1 .............................................................................................................................. 9
Tangrams 2 ............................................................................................................................ 10
Tangrams 3 ............................................................................................................................ 11
Inside a square ....................................................................................................................... 12
Spire Maths interactive files available in a flash format at: https://spiremaths.co.uk/ia/
Unfortunately they will not work on iPads or iPhones.
http://jamtecstoke.co.uk/
Page 1 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Main Whiteboard and Screen information
Screen 1: The tangram
A square made of seven parts is shown on screen. After a short while the seven parts move to
the edge one at a time to form a candle with flame. You are then shown the silhouette of a
runner. You can drag and drop the pieces onto the runner to make it without overlap. Pieces
are dragged by holding at the centre and rotated by dragging near the corner. There are 4
other shapes a cat, cat's head, house and figure three. The last of these can create a problem
if pupils place the square at the top of the shape since the parallelogram then cannot be put
there (and this is where it belongs) - this may not be a problem if pupils have cut out shapes
since the parallelogram can then be turned over and will fit at the bottom of the shape.
Key points: pupils enjoy making and using their own tangram (the instructions for folding and
drawing are in the plenary); have pupils discuss this and try to visualise how to do it without
any of the parts; some pupils will require the silhouettes visible to be able to complete these;
some pupils will need the exact size silhouettes, some will manage with half size silhouettes
while a few will be able to get by without either; one or two pupils may be able to visualise
how to put the shapes together and do it very quickly.
http://jamtecstoke.co.uk/
Page 2 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Screen 2: Square shapes
You are given 8 shapes: rectangle, ellipse, trapezium, kite, isosceles trapezium, circle,
rhombus and square (45 degrees from the horizontal) and asked to state which could be a
view of a square. When you have decided the shapes are moved to the side and it is
suggested that you use a square with the data projector to attempt to make the given shapes.
It is not easy to show any of these with the data projector, so practice first. For one or two of
the shapes you may be able to draw a square on the screen with the pen and then use the
'keystone' features of your projector.
Key points: do not move too quickly from the initial screen since you want pupils to think
about the problem and how to try to demonstrate that any of these might be a view of a
square; discussion is the key to this; some of your pupils may be aware of the distortion
caused by an overhead projector when you project things well above the level of the projector
lens; many pupils may be happy to exclude the ellipse and circle, but you could ask what the
square would look like drawn on a balloon and then blown up (and then do it); all the rest are
possible, but it does depend on the square (whether it is rigid or not); note that when you use
anything square shaped with the projector you are probably technically using a square based
prism.
http://jamtecstoke.co.uk/
Page 3 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Screen 3: Inside a square
A 6 by 6 square is shown. On each side of the square is a bead (a moveable point) that is
constrained to move along the one side of the square. Each bead starts at the midpoint of the
side and each bead is joined to the two beads that are closest to it (so they are joined to make
a square at the start). Each bead can be moved independently along its side. You are asked to
make and describe the shapes you have made.
Key points: have pupils discuss this and try to visualise what shapes can be made; some pupils
will find this easy, others will not; you may wish to set the task asking which quadrilaterals can
be made (and how); also which triangles can be made (once someone has suggested that this
is possible); all quadrilaterals except the arrowhead can be made - though some pupils will
have problems with another square (excluding the 6 by 6 and the start) and a rectangle; in all
cases ask 'how do you know it is what you say it is' to help improve reasoning; a good
individual activity on Geogebra; you can also use pinboards or geoboards to help with this; you
may want pupils to record the work, but it is much less interesting if you just ask pupils to do
it on paper and pupils are likely to gain less from it.
http://jamtecstoke.co.uk/
Page 4 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Plenary Whiteboard and Screen information
Screen 1: Drawing a tangram
Pupils are invited to work through the construction of a tangram on an 8 by 8 square grid. An
animated construction, superimposed on the grid, is revealed by clicking '>' The animation can
be stopped and started at any time by using '>' as a toggle. A line by line solution can be
revealed by using '>>' and a complete solution by using '>|'. Steps can be reversed in a
similar manner. At each stage, brief notes explain what is happening in the animation. The use
of colour highlights the work in process. At the end the 7 piece tangram is shown on the
screen, all pieces coloured differently and without grid lines.
Key points: pupils enjoy making and using their own tangram and should be encouraged to
work through the process; accuracy and discussion of symmetry should be encouraged.
http://jamtecstoke.co.uk/
Page 5 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Screen 2: Folding a tangram
Pupils are invited to work through the construction of a tangram by folding an 8 by 8 square.
An animated construction, representing the various folds of the paper, is revealed by clicking
'>' The animation can be stopped and started at any time by using '>' as a toggle. A line by
line solution can be revealed by using '>>' and a complete solution by using '>|'. Steps can be
reversed in a similar manner. At each stage, brief notes explain what is happening in the
animation and clarify the folding process. The use of colour highlights the work in process and
the nature of the folds. At the end the 7 piece tangram is shown on the screen, all pieces
coloured differently.
Key points: pupils enjoy making and using their own tangram and should be encouraged to
work through the process; accuracy and discussion of symmetry should be encouraged.
http://jamtecstoke.co.uk/
Page 6 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Screen 3: Inside a square
A 6 by 6 square is shown. On each side of the square is a bead (a moveable point) that is
constrained to move along the one side of the square. Each bead starts at the midpoint of the
side and each bead is joined to the two beads that are closest to it (so they are joined to make
a square at the start). Each bead can be moved independently along its side. You are asked to
make and describe the shapes you have made.
Key points: have pupils discuss this and try to visualise what shapes can be made; some pupils
will find this easy, others will not; you may wish to set the task asking which quadrilaterals can
be made (and how); also which triangles can be made (once someone has suggested that this
is possible); all quadrilaterals except the arrowhead can be made - though some pupils will
have problems with another square (excluding the 6 by 6 and the start) and a rectangle; in all
cases ask 'how do you know it is what you say it is' to help improve reasoning; a good
individual activity on either Geometer's SketchPad or Cabri Geometre; you can also use
pinboards or geoboards to help with this; you may want pupils to record the work, but it is
much less interesting if you just ask pupils to do it on paper and pupils are likely to gain less
from it.
http://jamtecstoke.co.uk/
Page 7 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Screen 4: Vocabulary
Vocabulary present: 2D, 3D, Axes, Circle, Concave, Construct, Convex, Cube, Cuboid, Cylinder,
Delta, Distance, Draw, Edge, Equilateral, Face, Hemisphere, Irregular, Isosceles, Kite,
Measure, Net, Parallelogram, Perpendicular, Polygon, Prism, Protractor (angle measurer),
Pyramid, Quadrilateral, Rectangle, Regular, Rhombus, Right-angled, Ruler, Scalene, Set
square, Sketch, Sphere, Square, Tetrahedron, Trapezium, Triangle, Vertex, Vertices.
Spire Maths interactive files available in a flash format at: https://spiremaths.co.uk/ia/
Unfortunately they will not work on iPads or iPhones.
http://jamtecstoke.co.uk/
Page 8 of 12
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Tangrams 1
http://jamtecstoke.co.uk/
Page 9 of 12
https://spiremaths.co.uk/ia/
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Tangrams 2
http://jamtecstoke.co.uk/
Page 10 of 12
https://spiremaths.co.uk/ia/
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Tangrams 3
http://jamtecstoke.co.uk/
Page 11 of 12
https://spiremaths.co.uk/ia/
SPIRE MATHS
Stimulating, Practical, Interesting, Relevant, Enjoyable Maths For All
Inside a square
Shape name
Shape name
Shape name
Shape properties
Shape properties
Shape properties
Shape name
Shape name
Shape properties
Shape properties
http://jamtecstoke.co.uk/
Page 12 of 12
https://spiremaths.co.uk/ia/