in
Wrestle with re
up to, er, square ctangles, and square
s wit
cross-Key Stageh Mike Askew's
conundrums...
goS od
HAPE
T
hese activities
are aimed at he
lping
children develo
p appropriate
an
d
accurate langua
ge of shapes.
A
common featur
e to the activiti
es is the use
of a collection
of objects: unde
rstanding of
properties of sh
ape develops as
much
through lookin
g at the differe
nces and
variation betw
een shapes as
through lookin
g at the proper
ties of
individual shap
es.
One aspect to
look out for in
these
activities is child
ren 'over-defin
ing' shapes.
For example, it'
s often the case
that
children will de
fine a rectangl
e as a shape
Behind the wa
ll
LO
W
E
R
K
E
Y
S
T
A
G
E
2
KEY STAGE 1
I introduce this
activity by playin
g a 'guess the
whole class. Pr
shape' activity
eparation involve
with the
s cutting out a
from thin card.
number of 2D
Using a large bo
shapes
ok to hide them
the shape to 'p
behind I allow
op' up from be
part of
hi
nd
the book. Can
what the shape
the children de
is? When are th
cide
ey
ce
rtain? As well as
regular shapes
I make sure to
using the usua
include less ob
l
Not only do th
vious versions of
ese 'fool' the ch
shapes.
ildren into thin
shape must be
king they know
, they also chall
what the
enge the idea th
must be regular
at, say, all pent
, or that all trape
agons
ziums must look
like 'roofs'.
Next, I give pairs
of children a sm
all collection of
making sure th
2D or 3D shap
at there are mat
es,
ching pairs of ea
book to stand
ch shape. They
up as a 'wall' be
find a
tween them. Th
put four or five
ey take it in turn
of the shapes to
s to
gether to create
'wall' and hidd
a design behind
en from their pa
the
rtn
er.
Can they describ
that their partn
er can re-create
e their design so
it? As well as us
naming shapes
ing the languag
this helps child
e of
ren to develop
language. Ofte
their use of po
n their initial in
sit
io
nal
str
uc
tions can be qu
“Put the triangl
ite ambiguous
e on top of the
(does
sq
ua
re
or position the
” mean literally
triangle further
stack them up
away than the
children to sit on
square?). I enco
their hands whe
urage
n they are desc
hands-on appr
ribing to stop a
oach to sorting
out any comm
unication difficu
lties.
22
with four right
-angles and tw
o pairs
of equal sides.
Actually, just ha
ving four right
angles is sufficie
nt information
to fix a shape
as a rectangle
(and gets over
the thorny issue
of whether or
not a square is
a rectangle.
Squares have fo
ur right-angles
and so, by
definition, are
rectangles).
As children mov
e into KS2, they
develop their lan
2D and 3D shap
guage to describ
es, making mor
e
e
precise use of ge
Using tree diag
ometrical terms.
rams to sort a sm
all collection of
is a good way bo
geometrical shap
th to assess wha
es
t language child
help them deve
ren know and
lop accurate us
to
e of it.
Tree sorts
I introduce the
idea of tree sorts
by working with
Inviting four ch
the whole class
ildren to the fro
.
nt we play 'Gue
children I am se
ss who'. I tell th
cretly thinking
e
of one of the fo
front, and the cla
ur standing at th
ss have to ask qu
e
estions with ye
find out who I'm
s/no answers to
thinking of. For
example, are th
trainers? Or, do
ey wearing
they wear glasse
s? We talk abou
question is, look
t what a good
ing for those th
at separate the
two groups of
group of four in
two and then sp
to
lit the pairs. Us
questions I draw
ing appropriate
a tree sorting di
agram on the bo
invite children to
ard and then
take turns in se
cretly thinking
and have questio
of one of the fo
ns directed to th
ur
em to find out
person is.
who their myste
ry
Are they wearin
g
YES
Are they a girl?
YES
NO
Sally
Tom
trainers?
NO
Are they a girl?
YES
Aisha
NO
Joe
Working in pairs
, I give the child
ren a small colle
create their ow
ction of shapes
n tree sorting di
to
agrams. Four or
good number.
eight shapes is
They draw up
a
th
eir
tre
turns to secret
e diagrams and
ly think of a sh
take it in
ape and check
works by getting
their sorting di
other children
agram
to work throug
h the questions
.
MATHS
Find out more
Mike Askew is
professor of pr
imary
education at M
onash Univers
ity,
Melbourne and
a freelance prim
ary
maths consulta
nt. For further
information on
his work, visit
mikeaskew.net
UPPER
K
E
Y
S
T
A
G
E
2
Towards
the end of
primary school
children need to
be
confident in m
aking and draw
in
g
with increasing
2D shapes, and
accuracy
classifying shap
es using proper
angles and pairs
tie
s
that include
of parallel lines
. Usually this is
children a colle
done by giving
ction of shapes
and asking them
properties. 'In th
to describe the
e square' turns
this around: by
properties and
being given
having to create
shapes children
think about po
are challenged
ssibilities (and im
to
possibilities).
parallel sides. Fo
r example,
the centre cell
must contain
a quadrilateral
with exactly
one pair of equa
l sides and
one pair of para
llel sides (a
symmetrical tra
pezium,
for example).
■ Can
they name th
eir quadrilater
■ Are
there any cells
als?
th
at
ca
n contain mor
type of quadril
e than one
ateral?
This question fo
cuses the child
ren's attention
some quadrilat
on the fact that
erals that we gi
ve different nam
common proper
es to still share
ties. For exampl
e, a non-rectan
and a rectangle
gular parallelogr
both satisfy the
am
condition of tw
sides and two
o pairs of para
pairs of equal sid
llel
es.
In the square
Working in sm
all groups, child
ren are given a
this table:
large version
of
PAIRS OF EQUA
L SIDES
0
PAIRS OF 0
PARALLEL
SIDES 1
1
2
2
Their challenge
is to create quad
rilaterals to fill as
cells as possible,
many of the
with the given
number of pairs
of equal and
■ Wha
t about a squa
re? Does that
of equal sides
count as having
given that all
two pairs
four sides are
equal?
There are some
cells that are im
possible, for ex
quadrilateral ca
ample, a
nnot have two
pairs of paralle
equal sides. W
l sides and no pa
hen the childre
irs of
n begin to thin
solutions they us
k some cells ha
ually want conf
ve no
irmation from m
right. I resist te
e that they are
lling them whe
ther they are co
the class togeth
rrect or not, bu
er to share their
t bring
results and disc
why they think
uss the reasons
quadrilaterals ar
for
e
no
t possible for so
The main point
me cells.
with this task is
not so much th
the shapes as w
e creating of
orking with the
children on deve
of their 'argum
loping the quali
ents' for why ce
ty
rtain shapes be
cells and why so
long in particular
me are imposs
ible.
23