Year 5 Teaching Sequence Autumn S1 – 2D shapes and angles (five days)
Prerequisites:
 Draw polygons and classify them by identifying their properties including their line symmetry (see Year 4 teaching
sequence S4)
 Know that angles are measured in degrees and that one whole turn is 360°; compare and order angles less than 180°
(see Year 4 teaching sequence S4)
 Add and subtract pairs of two-digit numbers mentally (see oral and mental starter bank S1)
Overview of progression:
Children learn how to use a protractor, and after some experience make estimates before measuring angles which they
classify as acute or obtuse. They use the facts that angles on a straight line total 180° to find and check totals of angles.
They draw and describe polygons according to properties including numbers of acute and obtuse angles. Triangles are drawn,
described and classified, including whether they are scalene, equilateral, isosceles and/or right-angled. Children measure
the angles of regular polygons and use this information to predict which will fit round a point and so might tessellate.
Note that children are likely to find using a protractor accurately quite difficult to begin with, and so may be measuring to
the nearest five degrees initially. In Year 6 they are expected to measure to the nearest degree.
Watch out for children who 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.
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.
Y5 Maths TS_S1 – Aut – 5days
Objectives:
 Estimate, draw and measure acute and obtuse angles using a protractor
 Calculate angles in a straight line
 Use knowledge of properties to draw 2D shapes

Classify triangles (isosceles, equilateral, scalene) using criteria such as equal sides, equal angles and lines of symmetry
Whole class
Group activities
Paired/indiv practice
How many degrees are in a right angle? Draw a
right angle on your boards. Now draw an angle that
is smaller than this. We call angles less than 90°
acute, they are ‘sharp’. Now draw an angle that is
bigger than a right angle, but less than two right
angles, i.e. an angle between 90° and 180°. We call
these angles obtuse, they are ‘blunt’. Ask a child
to come up to the board and draw an example of
each. Discuss the first. Do you think this is less or
more than half a right angle? Ask children to make
an estimate of the number of degrees. Use an
IWB protractor to show how to measure the
angle. Pay particular attention to lining up one of
the drawn lines with the base line on 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 angles and ask children up to the
board to measure them, pointing out how they are
aligning the protractor. Ask children to write
Group of 4-5 children
Draw a triangle with three acute
angles on your whiteboards. Share
children's responses. Now draw a
triangle with one obtuse angle and
two acute angles. Now draw a triangle
with two obtuse angles and one acute
angle. What happens? Draw out that
this is not possible.
Ask children to work in pairs to find
the numbers of acute and obtuse
angles possible in quadrilaterals.
Easier: Ask children to draw five
different looking triangles and then
label each according to the number of
obtuse and acute angles. Repeat with
quadrilaterals. Discuss what they
notice.
Harder: Children could also
investigate what numbers of acute
and obtuse angles are possible for
Ask children to use a protractor
to draw the following angles:
45°, 100°, 15° and 170°. They label
each acute and obtuse. They also
draw a right angle, labelling it
90°, ‘right angle’. 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.
Harder: Children draw angles of
47°, 98°, 13° and 172°. Their
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Resources
 Cards made from
activity sheet (see
resources)
 Protractors
Y5 Maths TS_S1 – Aut – 5days
acute or obtuse on their whiteboards for each
angle.
What is the sum of two right angles? Imagine two
corners of a page being torn off and the two right
angles put next to one another. Draw this angle.
Draw out that it is a straight line, and that the
angle is 180° as on the protractor they were using
in the previous session. What if we put four right
angles together? Remind children that one whole
turn is 360°.
Launch the CalcAngles ITP. Choose to show angles
along a straight line, choose a quadrilateral. Point
to the question mark on the angle of the yellow
shape. What angle do you think this might be? Is
it an acute or an obtuse angle? Click to reveal the
angle.
Point to the angle which is the complement to
180°. What is this angle? The total of the two
angles must be 180°as they lie on a straight line.
pentagons, after first making a
prediction. Remind them to include
irregular pentagons.
Group of 4-5 children
Ask children to each draw five
different looking triangles. They use
a protractor to ensure the three
angles in each, and find the total.
What do you notice?
Draw a triangle and cut it out. Rip off
the three corners and stick them
together to show the total of 180°.
Challenge children to draw triangles
whose angles don’t add up to 180°!
Draw out that this is not possible
(unless their measuring is
inaccurate!).
Easier: Children may need more
support in measuring the angles
accurately.
Harder: Also investigate the sum of
angles in quadrilaterals, first making a
prediction.
measurements of angles should be
more accurate.
Ask children to work in pairs to
draw two circles (e.g. by drawing
round a pencil pot or using a pair
of compasses. They fold each in
half and cut them to form four
semi-circles. They fold each in
half, open out and draw a line
from where the centre of the
circle was to the outside edge.
They do this to each semi-circle,
so that each one looks different.




CalcAngles ITP
Scissors
Protractors
Rulers
They then cut long these lines to
divide each semicircle into two
pieces. They shuffle the pieces,
measure the angle of each, and
then check their measurements
by finding the piece that goes
with each to make 180°.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_S1 – Aut – 5days
Agree an answer with your partner. Click to reveal
the angle.
Repeat with different shapes. (Each time you
reset and choose a quadrilateral, it will be a
different one giving you a variety of obtuse and
acute angles.)
Display the Game board activity sheet (see
resources). Choose one of the shapes. How could
you describe this shape? Ask children to work in
pairs to write as many facts about it as they can.
Can they write more than five facts about it?
Take feedback, draw out that it is a polygon, and
list other properties to include regular/nonregular, number of vertices and sides, number of
obtuse and acute angles, lines of symmetry and
also its name.
Repeat with another shape to give children
opportunity to practise the vocabulary used to
describe the properties of polygons.
Secretly choose one polygon, and challenge the
children to work out which it is by asking questions
about its properties, to which you can only answer
‘yes’ or ‘no’.
Harder: Children cut each semicircle into three different sized
pieces.
Group of 4-5 children
Ask children to investigate how many
different polygons they can make by
drawing five equilateral triangles next
to one another (on isometric paper).
They compare their shapes with
others, and eliminate any repeats
(reflections and rotations). They
name each and decide whether it is
regular or not, and if not if it is
symmetrical or not.
E.g.
Children play Guess the shape.
One child chooses a polygon (see
resources for game board) and
the other child has to guess which
one it is by asking questions about
its properties. The first child can
only answer ‘yes’ or ‘no’. The first
child crosses out shapes on the
board according to the answers
given until it is possible to deduce
which polygon was chosen. They
swap roles.
Easier: / Harder: The level of
children’s vocabulary will vary
according to their attainment in
this area.
 Activity sheet for
Guess the shape (see
resources)
 Isometric paper
An irregular pentagon, not
symmetrical.
Easier: Children draw four equilateral
triangles.
Harder: If you introduce the concept
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_S1 – Aut – 5days
Draw an isosceles triangle on your whiteboard.
What makes it isosceles? Now draw an isosceles
triangle with a right angle. Now draw an isosceles
triangle with an obtuse angle.
Drawn an equilateral triangle on your board. What
makes it an equilateral triangle? Now draw an
equilateral triangle with a right angle. Draw out
that this is not possible; a triangle cannot have
three right angles. Do you think you can draw an
equilateral triangle with an obtuse angle? Why
not? Display at least two different-sized
equilateral triangles and measure the angles to
show that they are always 60°.
Draw a scalene triangle. What makes it scalene?
Draw a scalene triangle with a right angle. Now
draw a scalene triangle with an obtuse angle.
Draw the following Venn diagram on the board:
Have a right angle
Have an obtuse angle
of reflex angles, children could also
describe what sort of angles each
shape has.
Group of 4-5 children
Give each child a sheet of octagons
(see resources) and ask them to join
three vertices of the first octagon to
make a triangle. Join different
vertices to your neighbour. Discuss
what sorts of triangles have been
drawn – scalene, equilateral, isosceles,
obtuse-angled, right-angled, and
acute-angled.
Now try and draw two different
isosceles triangles.
Now draw two different right-angled
triangles. Use a protractor to check.
Ask children to investigate what
other types of triangles are possible,
including scalene or equilateral,
obtuse and acute-angled triangles.
Point out that they could just join two
vertices, and use two sides of the
octagon to from two sides of a
triangle.
Easier: Challenge children to draw as
many different looking triangles as
possible, and to describe each
according to their properties.
Children cut out triangles and
stick them onto two Venn
diagrams (see resources, they will
need two copies of the triangles)
Easier: Children sort by angle and
side length (see resources).
Harder: Children also make up
their own way to sort the shapes.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Protractors
 Rulers
 Activity sheet of
regular octagons (see
resources)
 Activity sheet of
triangles to sort and
Venn diagrams (see
resources)
 Scissors
 Glue sticks
Y5 Maths TS_S1 – Aut – 5days
Invite children up to the board to draw as many
different looking triangles in the first set as
possible. Draw out that this set includes scalene
and isosceles triangles but no equilateral triangles.
Repeat with the second set. Ask children to draw
triangles that have both an obtuse angle and a
right angle, and draw out that this is not possible,
so the intersection will be empty.
Now draw triangles that belong in neither set.
Explain that we draw these in the rectangle (which
is the set of all triangles) but not in either of the
two rings. Examples should include equilateral
triangles and acute –angled scalene and isosceles
triangles.
Show the following pattern:
What are these shapes? And what’s special about
these hexagons? Draw out that they are regular.
We can tessellate using regular hexagons; that
means we can cover a space with them without
them overlapping or leaving spaces. Where might
you have seen this pattern?
Harder: Children could also
investigate what polygon would make
it possible to draw an equilateral
triangle (e.g. a hexagon).
Group of 4-5 children
Show children a card square. Cut out
a shape from one side. If I stick this
shape on the opposite side, the new
shape will still tessellate. Repeat, this
time cutting out a shape from the top
side and sticking it to the bottom
side of the square. Now we have a
more interesting shape that will still
tessellate. Draw round the shape
several times to show that this is the
case.
Where tessellations might be used?
Discuss how it used in tiling patterns,
mosaics, wallpapers and fabrics for
Children use plastic shapes to
investigate which regular polygons
will fit round a point without
overlapping/leaving gaps, and then
which of these will tessellate.
They can then find a pair of
shapes which tessellate.
Harder: Children find
combinations of two shapes that
will fit round a point, and will
tessellate. They may even be able
to find three shapes that
tessellate (squares, hexagons and
triangles).
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Plastic regular polygons
(to include at east
equilateral triangles,
squares, pentagons,
hexagons and octagons)
 Protractors
 Card, scissors,
coloured pencils
Y5 Maths TS_S1 – Aut – 5days
Draw a spot where three vertices of three
neighbouring hexagons meet. How many meet at
this point? And how many degrees are around a
point? So what to do you think each angle might
be? Use a protractor to show the angle to be 120°.
If we put just two hexagons together, what angle
would be left? What else could we fit in this
space? Draw out that we could fit two equilateral
triangles. It might be possible to tessellate a mix
of hexagons and equilateral triangles. Sometimes
however, you can fit some shapes around a point,
but then have problems at another point, so you
will have to try and see if this works!
Show a regular pentagon and measure one of the
angles. Do you think these will fit round a point
leaving no gaps or overlapping? Show that this is
not possible with regular pentagons. If we put two
or three together, perhaps we can fit another
shape between.
clothing, curtains and soft
furnishings.
Ask children to create their own
tessellating shape and then use it to
tessellate.
Harder: Children investigate what
other polygons will also work like this.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_S1 – Aut – 5days