Year 6 Teaching Sequence Autumn S1 – 2D and 3D shape and angles (five days)
Prerequisites:
 Estimate, draw and measure acute and obtuse angles using a protractor and calculate angles in a straight line (see
Year 5 teaching sequence S1)
 Use knowledge of properties to draw 2-D shapes (see Year 5 teaching sequence S1 and Year 6 oral and mental starter
bank S1)
 Recognise parallel and perpendicular lines in shapes (see Year 5 teaching sequence S2)
 Recognise reflective symmetry in regular polygons, e.g. know that a square has four axes of symmetry and an
equilateral triangle has three (see Year 5 teaching sequence S2)
 Identify, visualise and describe properties of rectangles, triangles, regular polygons and 3-D solids; use these
properties to classify 2-D shapes and 3-D solids (see Year 5 teaching sequence S2 and Year 6 oral and mental starter
bank S1)
 Make 3-D shapes with increasing accuracy (see Year 5 teaching sequence S2)
 Identify and draw nets of 3-D solids (see Year 5 teaching sequence S2)
 Use Venn and Carroll diagrams to sort shapes and show information about shapes (see Year 5 teaching sequence S2
and Year 6 oral and mental starter bank S1)
Overview of progression:
Children identify and draw acute, obtuse and reflex angles. They use the fact that angles in a triangle add up 180° to work
out missing angles. Children draw 2D shapes according to given properties. Quadrilaterals including kite, rhombus, trapezium
and parallelogram are introduced and children sort them according to their properties including pairs of parallel sides.
Children identify nets of closed cubes and make other 3D solids, recording their properties including pairs of parallel faces.
Note that using the term vertex rather than corner can, surprisingly, be less confusing when describing 3D shapes. This is
because some children can confuse a ‘corner’ with where the sides of two faces meet, rather than a point where the
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_S1 – Aut – 5days
vertices of at least three faces meet. Likewise it is better to use the term ‘side’ when describing 2D shapes, and the terms
‘faces’ (rather than sides) and ‘edges’, which are where sides of faces meet, when describing 3D shapes.
Note that it is more important that children can describe the properties of shapes rather than remember their names.
Note that rectangles are four-sided shapes with four right angles and so a square can be thought of as a special kind of
rectangle. Rectangles, which are not square, are also called oblongs.
Watch out for children who find it difficult to visualise 3D shape from 2D drawings.
Watch out for children who only recognise regular pentagons, hexagons, heptagons and octagons.
Watch out for children who do not align the protractor properly when measuring angles.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_S1 – Aut – 5days
Objectives:
 Describe, identify and visualise parallel and perpendicular edges or faces
 Use the properties of 2D and 3D shapes to classify 2D shapes and 3D solids
 Visualise 3D shapes from 2D drawings and identify different nets for a closed cube
 Use Venn and Carroll diagrams to show information about shapes
 Sort and classify quadrilaterals using criteria such as parallel sides, equal sides, equal angles and lines of symmetry
 Make and draw shapes with increasing accuracy
 Estimate angles and use a protractor to measure these
 Draw angles, using a protractor, on their own and in shapes
 Calculate angles on a straight line, in a triangle or around a point
Whole class
Group activities
Paired/indiv practice
Resources
How many degrees are in a right angle? What do we
call an angle less than 90°? Draw a right angle and an
acute angle on your boards. What do we call an angle
that is more than 90° but less than 180°? Draw an
obtuse angle on your boards. An angle that is more
than 180° is called a reflex angle. Sketch one on the
board to show this. Also sketch an acute angle and
an obtuse angle. Discuss the reflex angle. Do you
think that this is more than three right angles? How
many degrees would be in three right angles? Ask
children to make an estimate of the number of
degrees. Use a 360° IWB protractor to show how to
measure the angle. Pay particular attention to lining
up one of the drawn lines with the diameter of the
protractor and the centre cross at the tip of the
angle. If your school protractors have numbers in
both directions ask them to beware of this! Repeat
with the second angle.
Draw other reflex angles and ask children up to the
board to measure them, pointing out how they are
Group of 4-5 children
Draw a quadrilateral with two acute angles on
your whiteboards. Share children's responses.
What are the other two angles? Acute or
obtuse? Is it possible to have one of each? Now
draw a quadrilateral with one reflex angle. This
is called a concave shape, is it ‘caves’ in. What
are the other angles? Obtuse or acute?
Ask children to work in pairs to find the
numbers of acute, obtuse and reflex angles
that are possible in quadrilaterals.
Easier: Ask children to draw five different
looking quadrilaterals and then label each
according to the number of obtuse, acute and
reflex angles. Discuss what they notice.
Harder: Children could also investigate what
numbers of acute, obtuse and reflex angles are
possible for pentagons, after first making a
prediction. Remind them to include irregular
pentagons.
Ask children to use a protractor
to draw the following angles:
49°, 95°, 185° and 265°. They
label each acute, obtuse or
reflex. They then turn this piece
of paper face down.
They work in pairs to shuffle a
pack of cards (see resources),
take one and each try and draw
an angle measuring this number
of degrees. They use a
protractor to measure their
angle; the closest person wins a
point. Repeat. Ask them to
discuss if their estimates are
improving with practice.
Easier: Children use their
original five angles to help, and
measure to the nearest five
degrees.
 Cards made
from activity
sheet (see
resources)
 360°
protractors
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_S1 – Aut – 5days
aligning the protractor. Ask children to write acute,
obtuse or reflex on their whiteboards for each
angle.
Ask children to use a ruler to draw a triangle on
paper. Try and make yours look different from your
neighbours. Now measure the size of each angle, and
then find the total. What do you notice? Children’s
answers might not total 180° exactly, but with
enough examples, they may realise that if they could
measure the angles very accurately (which is
difficult) they should do. Try and draw a triangle
that has a different total. Take feedback and agree
that the total is always 180°.
Ask children to cut their triangles out, and then to
tear off each corner. They should then stick the
corners together. What happens? So all the
triangles that we have drawn have three vertices
that can be put together so that the total angle is
180°. This is a useful fact as we can now use this to
find one angle in a triangle if we know the other two.
Draw a right-angled triangle on the board, marking
the right angle with a square. This angle is a right
angle, this is the symbol we use, and so it measures
90 °, so what is the total of the other two angles?
Draw a regular hexagon on your whiteboards. Now
draw an irregular hexagon. Compare it to your
Harder: Their measurements of
angles should be more accurate.
Group of 4-5 children
Ask children to draw a horizontal line 5cm long.
They then use their protractor to measure 60°
from each end, drawing the two lines so that
they cross.
60°
60°
What
type of triangle have you drawn? Measure the
third angle to check.
Repeat this time asking children to measure
50° from each end, then 40°, 30° and so on.
They should work out, then check the third
angle each time
What happens to the triangle? What word
could you use to describe all of these
triangles? What will an isosceles triangle look
like with two angles each measuring 70°? 80°?
Harder: Challenge children to draw an isosceles
triangle where only one angle measures 40°.
What will the other two angles be? Repeat for
triangles with one angle measuring 20°, 80° and
120°.
Group of 4-5 children
Draw three lines of the same length meeting at
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Ask children to work out the
missing angles in a triangular
jigsaw (see resources), and then
use a protractor to check.
Easier: Ask children to draw at
least six right-angled triangles.
Each triangle must be different.
They use the protractor to
measure one of the acute angles,
and then subtract this from 90°
to find the other. They use a
protractor to check.
 Activity
sheet of a
triangular
jigsaw (see
resources)
Children make shapes on
geoboards and copy them onto
 Protractors,
rulers
Y6 Maths TS_S1 – Aut – 5days
partner’s. Is it symmetrical? Does it have any reflex
or obtuse angles?
Now draw an irregular but symmetrical pentagon.
Compare it to your neighbour’s. What’s the same and
what’s different?
Draw an irregular heptagon that is not symmetrical.
Draw an irregular octagon with two lines of
symmetry.
Draw the following quadrilaterals on the board:
square, rectangle, kite and rhombus. Take each in
turn and ask children to describe them. Rectangles
have four right angles, and so technically a square is
a special rectangle, special because all sides are also
the same length. We can call a rectangle that is not
square an oblong (a shape which is longer than it is
wide), but often they are just called rectangles.
This is a bit like saying that a circle is a special kind
of oval.
Point out that the kite has two pair of sides of equal
length like a rectangle, but they are adjacent not
opposite, and the angles are not 90°. Tell children
that this shape is called a kite, easy to remember as
it looks kite-shaped! Draw out that the rhombus has
four equal sides like a square, but that the angles
are not 90°. What do you notice about the angles?
Draw out that opposite angles are the same. This
shape is called a rhombus, it’s a diamond shape. We
could say that a rhombus is a special sort of kite
with all sides of the same length, and a square is a
special kind of rhombus with all angles of 90°!
Draw an inverted kite (delta).
a point so that there is 120° between each pair
of lines:
If I join the ends of the lines, what shape will
it make? I’ve drawn a line every 120° round a
point. If I draw four lines equally spaced
around the point, what shape will I get? What
will the central angles be? Why? Try it. Discuss
that if every line is the same, then a square is
drawn, if the lines are of different lengths,
other quadrilaterals can be drawn.
How could I use this way to draw a pentagon?
How can I find what the central angle needs to
be? Divide 360° by 5 to work out what angle
you need to measure to draw five equally
spaced lines.
Repeat with six lines and eight lines, discussing
what shapes emerge.
Easier: Ask children to draw an equilateral
triangle, square, regular pentagon and hexagon
and investigate the number of diagonals in
each, pointing out that a diagonal is a line
joining any two vertices that are not next to
one another. (Some children may think that a
diagonal is the same as a line of symmetry.)
Harder: Point out that each shape is made of
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
‘spotty’ paper according to given
properties (see resources). They
number and name each.
Easier: Children take in turns to
choose a shape (see resources).
They describe it to their
partner who has to guess which
shape was chosen. Together they
copy the shape and record its
name and the properties that
helped them to identify the
shape by the side. They swap
roles and repeat.
 Activity
sheet of
properties
 Geoboards,
elastic bands
and spotty
paper
 Activity
sheet of
shapes to
guess (see
resources,
easier version
only)
Y6 Maths TS_S1 – Aut – 5days
isosceles triangles, and so the angles at each
vertex of each shape can be worked out. Ask
children to do this for the pentagon, hexagon
and octagon, and use a protractor to check to
see if they are correct.
What do you think this shape is? Draw out that it is
a kite as it has two pairs of sides of the same
length, and explain that we call this an inverted kite
(or delta) because of the reflex angle. It’s shaped
like an arrowhead.
Leave the labelled quadrilaterals on the board for
reference during the practice activity.
Draw a parallelogram and trapezium on the board.
Ask children to describe each including what is the
same about them and what is different. Discuss how
neither is symmetrical (depending on the trapezium
you have drawn), and both have a pair of sides that
are the same distance away from each other, like a
pair of train tracks. Remind children that we call
these parallel lines. The first shape has two sets of
parallel lines and is called a parallelogram. The
second has just one pair of parallel sides and is
called a trapezium.
Draw a square and a rectangle and draw in the
diagonals in the square, rectangle and parallelogram.
What do you notice about these diagonals? Draw out
that the diagonals in the square cross each other at
right angles. Remind children that we call two lines
that are at right angles to one another
perpendicular. They might also notice that each of
the pairs of diagonals cross each other in the middle
of the lines – they bisect each other, or cut one
Group of 4-5 children
Ask children to investigate which quadrilaterals
have diagonals that are perpendicular, bisect
one another, both and neither. What diagram
could we draw to show this? Agree that you
could draw either a Venn diagram or a Carroll
diagram. Ask children to work in pairs to draw
whichever one they prefer.
Easier: Ask children to use the pre-drawn
shapes in the Activity sheet for the practice
activity (see resources). Show them the outline
of a Venn or Carroll diagram rather than asking
them to come up with their own.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Children use a sorting tree to
sort quadrilaterals, and then
draw their own Venn diagram to
sort them.
Easier: Children use an easier
sorting tree, and then place
shapes on the following Carroll
diagram:
Has at
least one
right
angle
 Activity
sheet of
quadrilateral
sorting tree
(see
resources)
Has no
right
angles
Has at
least one
line of
symmetry
Has no
lines of
symmetry
Y6 Maths TS_S1 – Aut – 5days
another in half. Do the diagonals of a trapezium do
this? Draw one on your whiteboard to find out.
Draw one each of square, rectangle, parallelogram,
trapezium, rhombus and kite. Draw a blank Venn
diagram (making you sure you include the outside
rectangle as well as two interlocking sets). What
criteria could we use to sort these quadrilaterals?
Take some suggestions, e.g. at least one pair of
parallel sides, at least one line of symmetry, and ask
children to help you to sort the shapes accordingly.
Show a net of a cube and ask children to sketch it
on paper. Point to one of the faces. This face is
going to be at the bottom when I make it. Which
face do you think will be parallel to this face when I
make the shape? Ask children to mark on their
copies of the net. Take suggestions, if there is
consensus, colour in that face and the base, and
make the cube to check.
Unfold it again. Point to the base again. Which faces
do you think will be perpendicular, at right angles, to
this face when I make it up again? Mark them with
a cross on your net. Take feedback, mark the four
faces with a cross, and make up the cube to check.
Show children a collection of 3D shapes and sort
them according to a secret criterion, e.g.
regular/not regular. Ask them to guess what
criterion you have used.
Group of 4-5 children
Ask each child to choose a 3D shape to make
(see resources for nets) and together record
the number of faces, vertices and edges for
each in a table, e.g.
Faces
Vertices
Edges
cube
6
8
12
tetrahedron
4
4
6
triangular
5
6
9
prism
Can you spot a relationship between the
numbers? If children struggle to see this,
suggest they add the number of faces and
vertices together; they should then notice that
this total is always 2 more than the number of
edges.
Choose another 3D shape and count the number
of faces and vertices. Use the formula to work
out the number of edges and then check by
counting.
A Swiss mathematician called Euler wrote
about this in the mid 1700s and showed that
this was true for any polyhedron (3D shape
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Children identify which nets
which will make a cube. They
choose one of them and record
its properties including how many
pairs of parallel faces it has.
They work in groups to make a
collection of other 3D solids,
record their names, and
properties including whether
they are regular or irregular,
the number and shapes of faces,
vertices and pairs of parallel
faces. They can either use paper
nets (see recourses) or a
resource such as Polydron or
Clixi.
Easier: /Harder: Arrange
children in mixed ability groups,
and encourage those who are
most dexterous to make the
more difficult shapes,
particularly the dodecahedron!
 Activity
sheet of
pictures of
3D shapes
and nets (see
resources)
 Polydron/Clixi
(optional)
 Scissors
 Glue sticks
Y6 Maths TS_S1 – Aut – 5days
with flat surfaces, so not cones, cylinders or
spheres) that is not concave (so it doesn’t have
any corners that point inwards). It became
known as Euler’s formula.
Easier: Give the simpler nets to children who
find this kind of activity more difficult.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_S1 – Aut – 5days