Year 3 Teaching Sequence summer S4/D5 – Shape, right angles and data handling (five days)
Prerequisites:
 Know properties of 3D solids; describe, visualise, classify and make the shapes (see teaching sequence S3 and oral
and mental starter bank S4/D5)
 Relate 3D solids to drawings of them (see teaching sequence S3)
 Know properties of 2D shapes; describe, visualise, classify and draw and make the shapes (see teaching sequence S1
and oral and mental starter bank S/4D5)
 Begin to use Venn or Carroll diagrams to sort data and objects using more than one criterion (see teaching sequence
D4)
Overview of progression:
Children count and begin to predict the number of faces, edges and vertices of pyramids with different shaped bases. They
use Venn diagrams to sort 3D shapes according to different criteria. Set squares are used to identify right angles and to
draw shapes with right angles. Carroll diagrams are used to sort 2D shapes according to different criteria including right
angles.
Note that children may not find counting faces, vertices and edges easy! It’s important to have a way of keeping track of
which have been counted.
Watch out for children who only recognise solids of the same proportions of those in sets of 3D shapes.
Watch out for children who use the term side rather than face to describe the faces of 3D shapes as this may lead to
confusion when describing sides of 2D shapes.
Watch out for children who only recognise right angles when they are between a pair of horizontal and vertical lines, but
not when they are between diagonal lines.
Watch out for children who don’t understand that the pairs of headings in Carroll diagrams are mutually exclusive (the
opposite of one another) and incorporate all possibilities, unlike the headings in Venn diagrams where an object can be in one
category, both categories or neither (but still inside the surrounding box, the universal set).
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS_S4/D5 – Sum – 5days
Objectives:
 Relate 2D shapes and 3D solids to drawings of them
 Know properties of 2D shapes; describe, visualise, classify and draw and make the shapes
 Know properties of 3D shapes; describe, visualise, classify and draw and make 3D shapes
 Use a set square to draw right angles and to identify right angles in 2D shapes
 Compare angles with a right angle
 Recognise that a straight line is equivalent to two right angles

Use Venn or Carroll diagrams to sort data and objects using more than one criterion
Whole class
Group activities
Paired/indiv practice
Resources
Show chn a picture of an Egyptian pyramid (e.g. sourced from
the internet). What shape is this? Pass several square-based
pyramids round the class. Describe this to your partner. Ask
chn to share their descriptions, draw out the type and number
of faces as well as numbers of vertices (corners) and edges.
Draw the following table:
Shape
Number
Number
Number
base
of faces
of
of edges
vertices
Group of 4-5 children
Ask chn to work in pairs to make a squarebased pyramid from a construction set such
as Polydron. How a many faces are there?
And how many vertices? How many edges?
Record this information in a table.
How many faces do you think there might
be on a pentagonal-based pyramid? Try and
imagine what it would look like, one
pentagon at the bottom. How many
triangles would be round the sides, meeting
at a point at the top? Make one to check
your ideas. How many faces? Vertices?
Edges?
How many faces do you think a hexagonal
pyramid might have? Why? Make one and
find out. Chn also find the number of
vertices and edges.
Ask chn to predict the number of faces for
an octagonal-based pyramid, and to look for
a pattern in the table to help them to
predict the number of vertices and edges.
Harder: Chn also predict the number of
vertices.
Chn work in pairs to cut out
nets of pyramids (see
resources) and use them to
make pyramids with different
shaped bases. They work
together to count the
number of faces, vertices
and edges and record this in
a table as in the whole class
teaching.
Easier: Chn may need to use
sticky labels to help the
shape hold together in order
to be able to count the
number of edges and
vertices.
Harder: Ask chn also to
predict the number of faces
a pyramid with a nine-sided
base might have.
 Pyramids with
different
shapes bases
 Activity sheet
of pyramid
nets (see
resources)
 Scissors
 Sticky labels
Pass round pyramids with other shaped bases and discuss how
they are all pyramids with a number of triangular faces, but
the bases are different shapes. Do not draw out the numbers
of faces, vertices and edges at this point.
Show chn a net for a square-based pyramid (enlarged from the
Activity sheet). Show chn how the triangles can be gathered
up to form a square-based pyramid. Explain that each of the
nets on the Activity sheet will form pyramids in a similar way.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS_S4/D5 – Sum – 5days
Show chn as many different looking 3D shapes as possible and
revise the names for each. Ask chn to describe the number
and shape of faces of each shape.
Ask chn to close their eyes whilst you take one shape or else
hold it behind the f/c. This shape has a square face. What
could it be? What can’t it be? It also has a rectangular face.
What do you think it might be now? What can’t it be? Chn open
their eyes to see the shape.
Repeat with other shapes.
Place two overlapping hoops on the floor, one labelled ‘has a
square face’ and the other ‘has a triangular face’. Ask chn to
help you to sort shapes into the correct set, including those
which belong outside the sets. Discuss how the square-based
pyramid belongs in both sets.
Draw a range of four-sided shapes on the board in advance,
making sure that some are squares and rectangles with right
angles and some look like they might be but when checking with
a set square, it can be seen that the corners are not ‘square'.
Which of these shapes do you think are squares? Take chn’s
suggestions and put ticks in those that they think are squares
and question marks in those if chn are not sure. What’s special
about a square? Draw out that all sides and angles are equal,
and that all the angles are 90°, i.e. a right angle. How can we
check that the sides are the same length? We can check that
the angles are right angles by using a set square. Show chn a
set square (preferably large) and show how it has a ‘square’
corner which measures exactly 90°. Ask chn up to the board to
use this to check that the squares are indeed square. Show
chn how we mark an angle as a right angle.
Repeat for rectangles.
Draw a series of acute, obtuse and right angles on the IWB.
Ask chn to help you sort them into right angles, angles which
are more than 90° and those which are less than 90°, using the
set square to check.
Where can you see right angles in the classroom? Make a list
Group of 4-5 children
Show chn 2 hoops labelled curved face and
circular face. Ask chn to think of shapes
that would go in each set, in both and also
in neither. Help chn to draw an example to
go in each, and label them, explaining that
it is not easy to draw 3D shapes!
Afterwards show chn shapes from the
whole class teaching and look to see if they
missed any possibilities.
Repeat with headings: ‘square face’ and
‘pentagonal face’.
Easier: Show chn a selection of shapes and
ask them to sort into the sets as above.
Group of 4-5 children
Ask chn to help you to program a Roamer to
draw a rectangle. What’s important about a
rectangle? So what do we need to
remember when writing the instructions?
Harder: Also challenge chn to program the
Roamer to draw an ‘L’- shaped hexagon
using only 90° turns left or right.
Chn cut and stick pictures of
3D shapes (see resources) in
Venn diagrams using the
following pairs of criteria:
Has a circular face, has a
square face
Has a triangular face, has a
hexagonal face
Easier: Chn sort real 3D
shapes rather than drawings
of them.
 A range of 3D
shapes
 Two hoops
 Activity sheet
of drawings
of 3D shapes
 Scissors and
glue sticks
Chn use a set square to
identify right angles in 2D
shapes (see Activity sheet).
Harder: Chn add several
shapes of their own that have
right angles (no squares’ or
rectangles).
 Roamer
 Large set
square
 Activity sheet
of 2D shapes
(see
resources)
 Set squares
Group of 4-5 children
Ask chn to work in pairs to use elastic
bands on geoboards to make different
looking quadrilaterals with at least one
right angle. They investigate where it is
Chn roll a dice and use a set
square to draw a square
whose sides measure that
number of centimetres.
Harder: Chn roll two dice to
 Geoboards
and elastic
bands
 Set squares
 Dice
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS_S4/D5 – Sum – 5days
of chn’s suggestions and ask chn to check that they are right
angles (if they can reach!).
Place two set squares together so that the two right angles
form a straight line. What happens when we put two right
angles together? Draw out that they form a straight line and
explain that this angle is 180°. What would happen if we put
four right angles together? Remind chn that a right angle is a
quarter of a whole turn, so four right angles make a complete
turn, 360°.
Demonstrate how to use a set square to draw a rectangle,
discussing how it can also be used as ruler.
Ask chn to help you to sort a range of plastic 2D shapes
according to whether they have a right angle or not, placing
them under the headings ‘has at least one right angle’ and ‘has
no right angles’. If the set of shapes only has squares and
rectangles as examples of quadrilaterals, make some extra
shapes from cards (e.g. a rhombus, trapezium, a parallelogram
and a quadrilateral with a right angle that is not a square or a
rectangle).
Now we’re going to sort these shapes again. Write two
headings at the side so that you from a Carroll diagram: ‘is a
triangle’; 'is not a triangle’ and ask chn to help you to sort each
of the two groups of shapes. Point out the shapes that are
both triangles and have right angles. Not surprisingly we call
these right-angled triangles!
Draw the Carroll diagram below on a large piece of paper:
Point to the first cell. Can you think of a shape that will go
here?
possible to draw quadrilaterals with one,
two, three or four right angles. (It is not
possible to draw a quadrilateral with three
right angles.) As they do so, copy the
quadrilaterals made under heading ‘one
right angle’ two right angles’, ‘three right
angles’, four right angles’. What can we say
about all the four-sided shapes with four
right angles? Could you make a four-sided
shape with three right angles? What
happened? Do you think you could make a
five-sided shape with three right angles?
Try and see. What do we call a five-sided
shape?
Easier: Roll a dice (rolling again if you roll a
1 or 2) and ask chn to make a shape with
that number of sides. Chn score points for
the number of right angles in their shapes.
Group of 4-5 children
Draw a blank Carroll diagram on a large
piece of paper. Sort a set of 2Dshapes
according to secretly chosen criteria (e.g.
red, has a right angle). Ask chn to suggest
what the criteria might be. As you continue
to sort the shapes ask them what the titles
could/couldn’t be.
Give a shape to a child and ask them to
predict where you will put it as a way of
testing out their ideas about the headings.
Repeat with other criteria, e.g. has a right
angle, does not have a right angle, is
symmetrical, is not symmetrical.
Harder: Ask chn to take turns in pairs to
secretly sort 2D shapes and challenge the
rest of group to work out how this is done.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
give the dimensions of a
rectangle.
Chn sort 2D shapes (see
resources) and place them in
the Carroll diagram
(photocopy resource onto
A3).
Easier: Suggest that chn fold
each shape in half to see if it
is symmetrical.
Harder: Chn draw another
shape in each cell.
 A range of
plastic 2D
shapes
including a
range of
quadrilaterals
 Activity sheet
of 2D shapes
to cut out and
use in Carroll
diagram (see
resources)
 Scissors and
glue sticks
 Set squares
Y3 Maths TS_S4/D5 – Sum – 5days
Ask chn to place shapes in the correct cells. Discuss the
diagram afterwards.
Has at
Has no
least one
right angles
right angle
Has four sides
Does not have
four sides
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y3 Maths TS_S4/D5 – Sum – 5days