Year 4 Teaching Sequence autumn S1 – Symmetry and properties of 2D shapes (five days)
Prerequisites:
 Describe, visualise, classify and draw 2D shapes (see Year 3 autumn teaching sequence S1 and oral and mental starter
bank S1)
 Draw and complete 2D shapes with reflective symmetry; draw the reflection of a shape in a mirror line along one side
(see Year 3 autumn teaching sequence S1)
 Identify right angles in 2D shapes (see Year 3 summer teaching sequence S4/D5)
 Use Venn or Carroll diagrams to sort data and objects using more than one criterion (see Year 3 summer teaching
sequence S4/D5 and oral and mental starter bank S1)
Overview of progression:
Children learn the name heptagon and draw as many different looking heptagons as they can. They name and describe a
range of polygons, for example if they regular or irregular, symmetrical or not, have right angles or not. The terms
equilateral and isosceles are introduced; children sort triangles according to their properties and use equilateral and rightangled triangles to make symmetrical patterns. They imagine and draw polygons and investigate the numbers of lines of
symmetry particular polygons can have, reaching a generalisation. They create patterns with one then two lines of symmetry.
Note that in this sequence children draw and describe a range of irregular polygons and this should help them to clarify
what makes a shape a pentagon, hexagon, heptagon or an octagon as otherwise some children only recognise regular
pentagons, hexagons, heptagons and octagons.
Watch out for children who only recognise isosceles triangles and right-angled triangles when they are shown as the first
two below, as opposed to in different orientations as the second pair.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS_S1 – Aut – 5days
Objectives:
 Recognise and understand properties of 2D shapes
 Draw polygons and classify them, identify their properties including line symmetry, right angles and whether they are regular or
not
Whole class
Show a picture of a 50p coin (or a large mock
50p coin). How many sides does it have? A shape
with seven straight sides is called a heptagon.
The 50p coin is not quite a heptagon because the
corners are very rounded. Can you think of
another coin with seven sides? (20p). Draw a
heptagon on your whiteboard; try to make it look
different from your neighbour’s. Describe it to
your partner, for example say whether it is
regular or irregular, has any right angles or lines
of symmetry. They look different but all have
seven straight sides and seven vertices so are all
heptagons.
Take feedback and share some of the children's
boards and their descriptions.
NB Occasionally heptagons are also referred to
as septagons.
Group activities
Group of 4-5 children
Cut out 2D shapes (see resources, the
same sheet as for paired/indiv
practice), and give several to each
child. Draw the following Carroll
diagram on the board:
Has at
Has no
least one
right
right angle angles
Has at
least one
line of
symmetry
Has no
lines of
symmetry
Ask children to stick their shapes one
by one in the correct place on the
diagram, discussing and naming each as
you do so.
I’m thinking of a polygon. It has five
sides is symmetrical and has two right
angles. Draw what it might look like.
Repeat with similar descriptions.
Harder: Instead of giving children
shapes, ask them to draw shapes on
Post-its to go in each cell. Their
drawings must include at least one
Paired/indiv practice
Resources
Children write the names and
properties of shapes (see
resources).
Harder: Children cut out the shapes
and choose a way of sorting them
into two overlapping sets.
 Activity
sheet of
polygons (see
resources)
 Blu-tac™
 Post-its™
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS_S1 – Aut – 5days
pentagon, hexagon, heptagon and
octagon.
Draw the following triangles on the board:
Ask children to discuss what is the same and
what is different about these shapes.
What is the difference between the first two
triangles? Agree that they are both
symmetrical, but the second has all sides of
equal length. This first is called an isosceles
triangle. You might like to explain that the name
comes from the Greek iso (same) and skelos
(leg). The second is a special sort of isosceles
triangle as all sides are equal; we call it an
equilateral triangle. We can describe it as
regular as all sides and angles are equal. Sketch
it on your board and find how many lines of
symmetry it has. (You may need to fold a paper
example.)
What is the difference between the two rightangled triangles? Agree that one is symmetrical
and one is not. So one is not only right-angled,
but also isosceles.
What do you notice about the last triangle?
Draw out that it neither symmetrical nor has a
right angle. We call these completely irregular
Group of 4-5 children
Draw this Carroll diagram on the
flipchart:
Has a
Has no
right angle right
angles
Has at
least one
line of
symmetry
Has no
lines of
symmetry
Give each child a Post-it. Ask them to
draw a triangle on it which belongs on
the first cell of the diagram. Repeat
for each cell.
What do you notice about the triangles
which have at least one of symmetry?
Draw out that they are isosceles and
equilateral if they have three lines of
symmetry. Can you draw a triangle with
two lines of symmetry? (No!)
What do you notice about the
symmetrical right-angled triangles? Can
you draw a right-angled triangle with
more than one line of symmetry?
Discuss how all three angles and sides
must be same for the triangle to have
three lines of symmetry, and this is not
Children label properties by the
side of triangles (see resources).
Encourage them to use a ruler to
check that triangles are isosceles
or equilateral. They could use the
corner of a page or set square to
check the right angles.
Children copy the following Venn
diagrams from the board, and draw
at least two triangles to go in each
set:
Isosceles
Equilateral
 Post-its™
 Activity
sheet of a
range of
triangles (see
resources)
 Scissors, glue
sticks
 Rulers
 Set squares
(optional)
Right-angled
Right-angled
They write what they notice (there
are no equilateral right-angled
triangles so the centre section in
the second diagram will remain
empty), then work in pairs to sort
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS_S1 – Aut – 5days
triangles scalene. Try and draw one on your
whiteboards. Children may find this quite
difficult as we naturally seem to want to draw
right-angled or isosceles triangles!
How could we sort these triangles into two sets?
Move them according to children’s suggestions,
e.g. those with right angles and those without, or
those which are symmetrical and those which
are not.
Imagine a square. Now imagine that one corner
as been cut off. Now another corner has been
cut off. Draw the shape of the paper that is
left. What is the name of this shape? Compare it
to your neighbour’s. Do you have the same
shape? How many sides does your shape have?
Imagine a square. Imagine that it is folded in
half. Now a corner is cut off, and finally the
paper is opened out. Draw what you imagined.
What shape is it? Count the sides to establish
the name of the polygon. Compare it your
neighbour’s.
Imagine an equilateral triangle. Another one now
joins it, so that the sides touch along their
length. Draw what you’ve imagined. What shape
is it? Compare it with your neighbour’s. Now ask
children to try this out by actually drawing it!
What shape do they get? Were they right?
Repeat with:
Imagine three equilateral triangles touching so
their sides touch along their length.
Now imagine four equilateral triangles touching.
Draw what you imagine. What shape have you
drawn? Is it different to your neighbour’s?
possible with a right-angled triangle, as
it isn’t possible to draw a triangle with
more than one right angle.
Easier: Give children triangles to sort
from activity sheet (indiv/paired
practice task).
triangles in two different ways (see
resources)
Harder: Children label and describe
each triangle, and then sort them in
a Carroll diagram with titles of
their choice.
Group of 4-5 children
Ask children to work in pairs to make a
symmetrical pattern using between 3
and 7 flat plastic triangles. They can
choose to use only one type, or several.
Ask each pair to show where the line of
symmetry is. Can you take away one
triangle so that your pattern is still
symmetrical? Can you remove another
triangle so that it is still symmetrical?
And another? Can you add a triangle in
a different place and still keep the
pattern symmetrical?
Repeat with different patterns made
from triangles.
Easier: Ask children to use equilateral
triangles.
Harder: Challenge children to create a
pattern with three lines of symmetry.
Ask children to work in pairs to
make as many symmetrical patterns
as they can using four identical
triangles, first equilateral triangles
and then right-angled triangles.
Give children isometric and cm2
paper to help.
Harder: Challenge children to also
see if they can come up with some
patterns which have two, three or
four lines of symmetry.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Plastic
triangles
 Isometric
and cm2
paper
Y4 Maths TS_S1 – Aut – 5days
Ask children to draw a hexagon on their boards,
so that it looks different to their neighbours.
Make sure that they are not all regular. Ask
them to draw on any lines of symmetry. They
swap boards and their partner checks to see if
there are any more. Take feedback. Did anyone
have a hexagon with no lines of symmetry? Show
the board. If not ask children to try and draw
one. So this hexagon is not symmetrical. Did
anyone have one line of symmetry? Continue in
this way until you have discussed numbers of
lines of symmetry from 0 to 6. It is not possible
to draw hexagons with 4 or 5 lines of symmetry.
It’s quite likely that no child has drawn a
hexagon with three lines of symmetry, but it is
possible, e.g.
Group of 4-5 children
Ask children to work in pairs to look in
books or on the internet to try and find
flowers with one, two, three, four, five
and six lines of symmetry. They make a
sketch of each that they can find,
drawing on lines of symmetry. What
numbers of lines of symmetry did they
manage to find?
Easier: Use mirrors to help.
Harder: Also challenge children to draw
their own flower with three lines of
symmetry.
Ask children to work in pairs to find
out the maximum number of lines of
symmetry possible for
quadrilaterals, pentagons, hexagons,
heptagons and octagons. They then
write a generalisation, saying the
maximum number of lines of
symmetry that any polygon can
have. They will discover that
regular polygons have the most lines
of symmetry and this is the same as
the number of the sides.
Easier: Give children a copy of each
regular polygon (see resources).
Harder: In addition children find
the numbers of lines of symmetry
possible for each polygon. They
should record this information in a
table.
 Access to
books on
flowers or
the internet
 cm2 paper
 Coloured
pencils
 Plastic
mirrors
 Activity
sheet of
regular
polygons (see
resources)
for easier
version only.
Launch the ITP Area, choose a five-by-five grid
and colour squares to create a pattern:
Group of 4-5 children
In advance draw a design on a paper
plate such that it has two lines of
symmetry.
Is this design symmetrical? Where
could we draw a line of symmetry? Use
a mirror to check if necessary. Are
there any more lines of symmetry?
Ask children to design their own plate
patterns with two lines of symmetry.
Easier: Children make a design with one
line of symmetry.
Harder: Children make a design with
four lines of symmetry.
Ask children to complete the
symmetrical patterns (see
resources). Then ask them to work
in pairs to draw a six-by-six grid on
cm2 paper with a vertical line of
symmetry. They take it in turns to
colour in a square on their own side
of the line of symmetry. The
partner must colour in a square on
their side to make the pattern
symmetrical. They use a total of
three different colours.
Repeat, this time drawing a diagonal
line of symmetry.
 ITP Area
 Paper plates
 Activity
sheet of
symmetrical
patterns to
complete
(see
resources)
 cm2 paper
 Coloured
pencils
This is a symmetrical pattern. Where could we
draw a line of symmetry? Change the colour of
one square. To keep the pattern symmetrical,
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS_S1 – Aut – 5days
what do you we need to do now? Repeat.
Reset and create a pattern as below:
Easier: When working in pairs
children draw first a vertical line of
symmetry, and then a horizontal
line of symmetry.
Harder: When working in pairs,
children draw two lines of
symmetry, one vertical and one
horizontal.
Where can we draw a line of symmetry on this
pattern? Draw out that this pattern has 2 lines
of symmetry. Change the colour of a square, and
ask what other squares must be changed to
preserve two lines of symmetry. Try out
children’s suggestions.
Reset and use triangles and squares to create
the following pattern:
Explain that this is a partly completed pattern
which has a diagonal line of symmetry form top
left to bottom right. Ask children to help you to
complete the pattern. Can you see another line
of symmetry?
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y4 Maths TS_S1 – Aut – 5days