Year 6 Teaching Sequence spring S2 – Co-ordinates, translations, rotations and transformations
(five days)
Prerequisites:
 Complete patterns with up to two lines of symmetry (see Year 5 teaching sequence S3)
 Read and plot co-ordinates in the first quadrant (see Year 5 teaching sequence S3 and oral and mental starter bank
S1)
 Draw the position of a shape after a reflection or translation (see Year 5 teaching sequence S3)
Overview of progression:
Children complete shapes and reflect shapes on grids, giving their coordinates. Shapes are moved, the translations
described and new coordinates found. Children rotate shapes on grids and design them to form patterns. Four quadrants are
introduced.
Note that four quadrants are introduced only in the group activities. This knowledge is only necessary for level 5 and relies
on children having a sound understanding of negative numbers.
Watch out for children who find it hard to visualise where new shapes will be after reflections, rotations and translations.
Drawing the shape onto tracing paper may help.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_S2 – Spr – 5days
Objectives:
 Read and plot co-ordinates in the first quadrant
 Use co-ordinates in the first quadrant to draw, locate and complete shapes that meet given properties

Visualise and draw on grids of different types where a shape will be after reflection, after translation, or after rotation through 90 or
180 degrees about its centre or about one of its vertices
Whole class
Group activities
Paired/indiv practice
Draw the following diagram on the board
(preferably using a IWB graph paper background):
Group of 4-5 children
Draw the following diagram on the flipchart (not on
graph paper):
Chn work in pairs and each draw
and label horizontal and vertical
axes on cm2 paper such that each
axis is as long as possible. The
first child imagines a square on
his/her graph paper and draws
three points and the second child
draws a fourth point such that
the four points can be joined to
form a square. They label the
coordinates of each point. They
swap roles, the second child
drawing three points on his/her
paper.
Repeat, this time each drawing a
rectangle.
They then take it in turns to draw
two points and draw a third to
make at least three different
triangles, and then five points and
then a sixth to form a hexagon.
Harder: Chn’s triangles and
hexagons must also be
symmetrical.
y
7
6
A
5
4
B
3
2
1
0
1
2
3
4
5
6
7
8
9 x
What are the coordinates for point A? And B? If
necessary, remind children to go along the x-axis
first before moving up.
A and B are two corners or vertices of a square.
Talk to your partner about where the other two
points might be. Take feedback, marking on chn’s
suggestions and joining them with straight lines.
Now A and B are corners/vertices of a rectangle.
Where might the other two vertices be? What if A
and B are two vertices of a triangle?
This is a picture of two squares. Talk to a partner
about what the coordinates of C might be,
Repeat with the diagrams below:
Ask chn to work in pairs to sketch two axes, draw
on a square and write the four coordinates on the
back. They label two vertices on their diagram and
ask their partner to work out the other two. They
turn over the paper to see if they are in
agreement.
Easier: Chn label three vertices.
Harder: Chn label only one vertex but tell their
partner the length of one side.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Resources
 cm2 paper
Y6 Maths TS_S2 – Spr – 5days
Sketch the following on graph paper:
This is part of a symmetrical shape. Talk to your
partner about where the other two vertices might
be and write their coordinates on your
whiteboards. What is the shape? What are the
angles at each vertex? How do you know?
Group of 4-5 children
Draw horizontal and vertical axes in the centre of
a piece of cm2 paper (or larger piece of paper with
larger squares if you have it), labelled x and y, so
that all four quadrants are visible. Draw a triangle
in the first quadrant and ask chn to write
coordinates by each vertex. The triangle is going to
be reflected in the y axis. Where do you think the
new triangle will be? Invite a child to come up and
draw the reflected shape. We’re going to try and
work out the coordinates of this new shape. Place
numbers 0 to 5 on the x-axis. What whole number
comes before zero? Label -1. What number do you
think goes here? And here? Label the rest of the
x axis. Repeat for the y-axis. Help chn to label the
coordinates of the new shape. What do you notice
about the coordinates of the new shape?
Now we’re going to reflect this new shape in the x-
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Chn draw axes on cm2 paper as in
session one. One child draws a
simple shape (square, rectangle or
triangle) on his/her paper, the
second child draws a horizontal,
vertical or diagonal mirror line.
They both secretly write down
the coordinates of the reflected
shape, and then see if they are in
agreement. When they are, they
draw on the reflected shape
labelling each vertex. They then
swap roles and pieces of paper.
Easier: After the first child has
drawn the mirror line, chn use a
mirror to help them to draw the
new reflected shape and then
identify the coordinates of each
 cm2 paper
 small
mirrors
Y6 Maths TS_S2 – Spr – 5days
Draw the following shape on the board with a
mirror line drawn. Ask chn to discuss in pairs the
coordinates of the triangles reflected in the
mirror line.
Repeat with other simple shapes, reflected in
vertical, horizontal and diagonal mirror lines.
Draw the lower triangle as in the diagram below on
the board, on using an IWB graph paper
background:
Label the coordinates of the lower triangle. The
triangle is then moved to here. Draw on the
triangle in its new position. How could we describe
how it has been moved? Discuss how it has been
moved up three squares and along two squares. Ask
chn to record the coordinates for the new position
and ask them what they notice and why they think
this is. Draw out what has been added to the
original pair of coordinates.
axis. Ask a child to draw the new shape, and
together find the coordinates. Now we’re going to
reflect this shape in the y-axis. Draw and label the
new shape. Now we’re going to reflect this new
shape in x-axis. What do you think will happen?
Chn work in pairs to draw their own axes (showing
all four quadrants) and drawing a simple shape to
reflect in both the x – and y-axes.
Easier: Draw the shapes, but do not find the
coordinates.
vertex.
Harder: Chn draw pentagons or
hexagons.
Group of 4-5 children
Shuffle a set of cards from -10 to 10. Take two
and say that they are the coordinates of a point.
Draw horizontal and vertical axes from -10 to 10
and help chn to mark on the point. Rpt five more
times, and then join the points to make a hexagon.
What shape have we drawn? Give chn two minutes
to write as many facts as they can about the drawn
shape (e.g. it is symmetrical or not, it is irregular,
the numbers of acute and obtuse angles, number of
right angle etc).
Chn repeat this in pairs.
Chn draw axes on cm2 paper. They
draw and cut out a 4cm by 2cm
rectangle and place it on the
graph paper so that it aligns to
the squares on it. They write
down the coordinates. They then
move the rectangle to a new
position, record the translation
(e.g. up 2 squares, 3 squares along
to the right) and its new
coordinates. Each time, they draw
the rectangle on the graph paper.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Cards: -10
to 10
 cm2 paper
Y6 Maths TS_S2 – Spr – 5days
Repeat moving the triangle up and across the same
number of squares and ask chn to predict what the
new coordinates will be. You might see patterns like
this on wrapping paper or material, where one
shape is moved a set distance and repeated to
make a pattern.
Repeat, this time moving a shape a number of
squares up and a number of squares to the left
(keeping it in the first quadrant).
Ask chn to stand and face the front. Play ‘Simon
says’ using instructions about turning clockwise and
anticlockwise. Turn 90 degrees clockwise. Simon
says turn 180 degrees anticlockwise. Turn back.
Draw the following design on squared paper (or
IWB background):
Easier: Draw a four-sided shape in the first
quadrant using cards 0 to 10.
They move the rectangle the
same way each time so as to
create an aesthetic pattern.
Harder: Chn carry out the task in
pairs, one describing the
translation whilst the other
predicts the new coordinates.
They then move the rectangle to
check.
Group of 4-5 children
Cut out a right-angle triangle and draw round it on
the flipchart. Rotate the triangle through 90
degrees around the 90 degree vertex, and draw
round the shape again. Repeat twice more. Show
chn how a protractor can be used to make sure
that the angle between the horizontal side of the
first triangle and the corresponding side of the
new triangle is 90 degrees.
Chn draw and cut out their own shapes and make
their own rotating patterns.
Chn colour in squares to form a
pattern in a 4 by 4 grid of
squares on cm2 paper, using three
different colours. They outline
the grid of 16 squares. They then
rotate their design 90 degrees
clockwise and draw it next to the
original. Then repeat until they
have several lines forming a
pattern, e.g.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Card
 Protractors
 cm2 paper
Y6 Maths TS_S2 – Spr – 5days
The first pattern has been rotated to form the
second. Talk to your partner about how we could
describe this rotation. Take feedback and draw out
the pattern has been rotated anticlockwise
through 90 degrees. Draw what the pattern would
look like if it were rotated through another 90
degrees anticlockwise. Repeat. How else could we
get from the first pattern to the last pattern?
From the first pattern to the third pattern?
Cut out a square from card, and attach it to a piece
of paper with a paper clip as close to one corner as
you can. Draw round the square on the paper.
Rotate the square clockwise through 90 degrees,
and draw round it again. Repeat until the square is
back where it was to begin with.
See diagram below. Draw this.
The shape is going to be rotated 90 clockwise
about point A, that is, the bottom vertex. Sketch
how you think the new shape will look. Ask a child
to come and draw the rotated shape on the board
and ask the others to identify its coordinates.
and so on
Easier: Chn only use right-angled triangles or
rectangles.
Harder: Chn rotate the shape through 45 degrees
each time, e.g.
Easier: Chn use two colours.
Harder: Chn use four colours.
Group of 4-5 children
Cut out an equilateral triangle and put a brass
fastener thro’ its centre, attaching it to another
piece of card. Draw round it. Mark one corner of
the triangle. Ask chn to rotate triangle until it is on
the original drawing. Repeat until it is back to is
original position. We turned this three times, so it
was in three different positions but looked the
same as the original shape, we can say this shape
had rotational symmetry order 3, because we can
rotate it and it looks the same, and we can do this
three times before it goes back to its original
position. Give chn a set of shapes on card attached
with brass fasteners through their centres:
square, rectangle, regular pentagon, regular
Chn draw simple triangles and
quadrilaterals on cm2 paper
(having drawn the x and y-axes
first: these should be as long as
possible so that chn can fit on as
many shapes as possible). They
choose and label a vertex and
rotate the shape through 90
degrees either clockwise or
anticlockwise. They label the
coordinates of each shape. Chn
should use tracing paper if they
find it helpful.
Easier: Chn rotate squares and
rectangles.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Card shapes
as opposite
with brass
fasteners
 cm2 paper
 Tracing
paper
Y6 Maths TS_S2 – Spr – 5days
hexagon and symmetrical but irregular hexagon and
ask them to investigate rotational symmetry.
Easier: Give chn a mix of regular, symmetrical and
irregular and asymmetrical shapes to sort into
those which have rotational symmetry and those
which don’t.
Harder: Chn include other
polygons.
Repeat for the following:
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_S2 – Spr – 5days