Year 5 Teaching Sequence summer S3 – Symmetry, co-ordinates, reflection and translation (five days)
Prerequisites:
 Describe and identify the position of a square on a grid of squares (see Year 4 teaching sequence S4)
 Recognise reflective symmetry in regular polygons, e.g. know that a square has four axes (lines) of symmetry and an
equilateral triangle has three (see Year 5 teaching sequence S2 and oral and mental starter bank S3)
Overview of progression:
Children complete patterns so that they have two axes (lines) of symmetry. Coordinates are introduced; children identify
the coordinates of vertices of shapes and then their reflections in a vertical mirror line and translations in either a vertical
or horizontal direction.
Note that links could be made to geography and art.
Watch out for children who write the numbers in the squares on the axes as opposed to across the lines.
Watch out for children who get coordinates the wrong way round. Remind them to go along and then up, e.g. ‘along the
corridor, and then up the stairs’ or ‘walk before you fly’.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_S3 – Sum – 5days
Objectives:
 Complete patterns with up to two lines of symmetry
 Read and plot co-ordinates in the first quadrant

Draw the position of a shape after a reflection or translation
Whole class
Group activities
Paired/indiv practice
Launch the ITP Area. Use the four-sided shape tool to draw
a line across the middle of the grid, and a second elastic
band to draw a vertical line in the centre of the grid (drag
the vertices to make the lines). This vertical line is a mirror
line. Ask two chn up to the board. The first clicks on a
square in the top left quadrant. The second child clicks on a
square to the right of the vertical line to create a
symmetrical pattern. They repeat, taking it in turns until
three or more squares are coloured on each side.
Group of 4-5 children
Challenge chn to work in pairs to create
patterns with two lines of symmetry on
pegboards, one horizontal and one vertical,
each crossing the centre of the board.
Easier: Lay two pieces of string across the
board to help chn to see the two lines of
symmetry. They place pegs on one side of
the board to create a pattern with one
line of symmetry, and then reflect this to
create a design with two lines of
symmetry.
Harder: If chn find this easy, challenge
them to use diagonal lines of symmetry.
Chn draw a ten-by-ten grid with
horizontal and vertical lines of
symmetry through the centre.
They work in pairs, each having a
different colour pencil. Chn each
colour in one square in a
different quadrant and then
work together to reflect the
squares in one line of symmetry
and then reflect all four squares
in the other line of symmetry.
Challenge them to colour in other
squares but still keeping the two
lines of symmetry.
Easier: Chn take it in turns to
colour in one square in the top
left quadrant and then work
together to make a design with
two lines of symmetry.
Harder: They take it in turns to
colour one square in each
quadrant and then work together
to make the design symmetrical
in the two lines of symmetry.
This horizontal line is also a mirror line! Challenge the two
chn with help from the rest of the class to colour in squares
below the line to reflect the pattern above. Now this design
has two lines of symmetry!
Click on the squares to clear them and ask four chn up to the
board. The first clicks on a square to the top left quadrant
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Resources
 ITP Area
 Pegboards
and pegs
 String
 cm2 paper
 Coloured
pencils
Y5 Maths TS_S3 – Sum – 5days
and the other three chn click on a square each in their own
quadrant to create a pattern with two lines of symmetry.
Draw the following on the IWB using a squared background:
Ask chn up to the board to make the pattern symmetrical
first in one mirror line and then in both. This pattern now
has two axes or lines of symmetry, the lines of symmetry are
diagonal.
Launch the ITP Coordinates.
Click on the coordinates marker tool on the right and move it
on the grid. The numbers in brackets show the coordinates
of this marker. The coordinates of this point are seven,
three, we go along 7 and then up 3 to get to this point
Move the coordinate marker around to show chn different
positions on the grid. Note that the coordinates label where
Group of 4-5 children
Launch Dino Dig from the Count on
website:
http://www.counton.org/games/virtualmat
hfest/dinosaur.html
Ask each pair of chn to suggest and enter
a pair of coordinates and click check. The
archaeologist will then dig at that spot. If
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Chn each draw axes from 0-10 on
their own piece of paper, and ring
ten points. They then take it in
turns to shuffle a pack of 0-9
cards to create a pair of
coordinates for their partner to
mark on their piece of paper. If
they land on one of their ringed
coordinates, they score a point.
They do this at least ten times
each.
Harder: Chn each draw a square
on their grids, hiding it from
their partners. They take it in
turns to give directions to their
partner to draw the same
rectangle in the same position,
e.g. draw a point at (4, 3), go up
two squares to point (6, 3)… They
check that the drawn rectangle
 ITP
Coordinates
 Access to
the internet
 cm2 paper
 0-9 cards
Y5 Maths TS_S3 – Sum – 5days
two lines cross.
Click on the (x, y) icon to hide the coordinates. Move the
marker around and ask chn to agree in pairs the coordinates
of the new point and to write them on their whiteboards.
Click the (x, y) icon to check. Repeat to give the chn
practice. Remember that we go along first, and then up to
find the coordinates. Discuss how the coordinates (7, 3) and
(3, 7) are very different locations on the grid. Co-ordinates
can be very useful as they can help us to describe the
position of a location on a map.
Draw horizontal and vertical axes from 0 to 10 on a square
background on the IWB. Ring two points: (2, 5) and (6, 1).
Ask chn to write the coordinates of these two points on
their whiteboards. These two points are two of the vertices
of a square. Talk to your partner about where the other two
vertices might be. Agree the coordinates and write them on
your whiteboards.
Repeat, this time giving points (5, 3) and (5, 6) ask chn for
the two possibilities.
Repeat this time using points (3, 1) and (8, 5) explaining that
these are two vertices of a rectangle.
Repeat for points (4, 3) and (8, 8) explaining that these are
two vertices of a right-angled triangles. Challenge chn to
find two possible locations for the third vertex.
a bone appears, he has found part of a
dinosaur, and so the next pair of chn
should suggest a pair of coordinates near
this spot to try and find the rest of the
dinosaur’s skeleton.
Can they find all the dinosaurs?
Easier/Harder: Chn are likely to make
more or fewer mistakes in entering the
coordinates in the correct order
depending on their attainment in this area.
They should become more accurate with
practice.
Group of 4-5 children
Show chn a map of the local area (such as
an ordinance survey map). Find some
locations, which sit exactly on the
intersection between two grid lines and
work out their coordinates (four figures
only). Ask each child to secretly choose a
location and write down its coordinates.
They take it in turns to read out their
coordinates to see if the rest of the
group can correctly guess their location.
Write down a list of coordinates of place
whose first letters spell a word and see if
chn can work out the mystery
word/message.
Harder: Also together work out some
directions to get from one location to
another, using the distance north, south,
west or east. Ask chn to write their own
simple directions to a secret location
having first written down its coordinates,
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
is the same.
Chn draw horizontal and vertical
axes, each from 0 to 10. They
shuffle a pack of 0-9 cards and
each take two. Their pairs of
cards give them one pair of
coordinates each. They mark the
two locations, and then work
together to make these two
vertices of a rectangle. They
draw the rectangle labelling the
coordinates of all its vertices.
Harder: Challenge chn to use
these two points as vertices of a
right-angled triangle. They draw
and label two possibilities for the
third vertex.
 Map of the
local area
 cm2 paper
 0-9 cards
Y5 Maths TS_S3 – Sum – 5days
Draw the following on a squared background but without
labelling the axes:
The left triangle has been reflected in this mirror line. How
could we work out the coordinates of the vertex B? (Point to
the vertex.) How far away is this point from (11, 3)? How do
you know? Agree the coordinates. Work with a partner to
work out the coordinates of A at the top of the triangle.
Repeat this time reflecting a square and then a rectangle.
Draw the following triangle on a squared background:
Ask chn up to the board to label the coordinates for each
point.
This triangle moves two squares to the left. Work with a
partner to agree the coordinates of the triangle in its new
position.
for the rest of the group to guess.
Group of 4-5 children
In advance, draw axes from 0 to 20 on
large squared paper, a line from (10, 0) to
(10, 20) and a triangle on the left of this
line. Draw its refection in the line, and
cover the original triangle with paper.
Challenge chn to work out the coordinates
of the original triangle. Reveal to check.
Ask chn to repeat in pairs. They each draw
triangles on the left of the line and its
reflection in the line. They read the
coordinates of the reflected shape to
their partner who then draws the
reflected shape and works out the
coordinates of the original shape. They
check each other’s results.
Harder: Also draw a reflected triangle
with labelled coordinates on plain paper
without labelled axes and challenge chn to
work out the coordinates of the original
with the squares to help.
Group of 4-5 children
Ask chn to draw axes from 0 to 10 and
label them. They draw a diagonal line at
45° to the x-axis from the original to (10,
10). This is a mirror line. Ask chn to ring
(2, 5) and then to reflect this point in the
mirror line and ring the new point. What
are its coordinates? Ask them to draw a
series of coordinates above the mirror
line, find the coordinates of the reflected
point and describe what they notice. On a
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Chn draw horizontal and vertical
axes, making them as long as
they can, drawing numbers on
each. They draw a vertical line of
symmetry down the middle. They
draw a square, a triangle and
rectangle on the left of the line,
reflect them in the mirror line,
drawing the new shapes and
labelling the coordinates of their
vertices.
Harder: Chn daw a triangle,
pentagon and hexagon.
 Large
squared
paper
 cm2 paper
Each child draws a rectangle on a
grid (axes from 0 to 10), writes
down the coordinates, translates
the shape to a new position (up,
down, left or right a number of
squares) and write the new
coordinates and details of the
translation on a piece of paper
which they give to their partner.
The partner draws the
translated shape and tries to
 cm2 paper
 Coloured
pencils
 Scissors
Y5 Maths TS_S3 – Sum – 5days
Take feedback and draw on the new position of the triangle,
discussing how each point has moved two squares to the left.
We say that this shape has been translated; this just means
that it has moved but kept its original shape and orientation.
Often patterns are translated and repeated to make wall
paper, printed fabrics and wrapping paper.
Repeat with other shapes either moving them up, down, left
or right. Chn sketch the shape on their whiteboards,
labelling the new coordinates of each vertex.
new grid with the same axes and mirror
line, they draw a square above the line and
try and predict the coordinates of its
reflection before drawing it.
Easier: Use this as extra practice in
describing coordinates with individual
practice of reflecting points, but whole
group practice of reflecting a shape.
Harder: Challenge chn to reflect a polygon
with more than four sides.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
work out the coordinates of the
original shape. The pair check
each others’ answers.
Easier: Chn cut out a rectangle
from squared paper so that the
sides align with the lines on the
paper. They draw round this
shape on their grid, so that the
sides align with the lines on the
grid and label the coordinates.
They then slide the shape up
down, left or right, draw round it
and label its new coordinates.
They repeat, drawing round a
new rectangle in a different
colour.
Y5 Maths TS_S3 – Sum – 5days