Year 5 Teaching Sequence autumn M1 – Measuring lines, area and perimeter (four days)
Prerequisites:
 Draw rectangles, and measure and calculate their perimeters; find the area of rectilinear shapes drawn on a square
grid by counting squares (see Year 4 teaching sequence M5)
 Know multiplication and division facts for the 2, 3, 4, 5, 6, 9 and 10 times tables (see oral and mental starter bank M1)
Overview of progression:
Children draw a range of rectangles with a given perimeter, and multiply the length by the width to find their areas. They
learn to find the areas of right-angled triangles and use this to help to find the area and perimeters of irregular polygons
drawn on squared paper. They also find the perimeters of regular polygons by multiplying the length of one side by the
number of sides. Square metres, kilometres and millimetres are discussed including when each would be appropriate and
children are asked to estimate the areas and perimeters of simple shapes.
Note that experience of activities in this sequence should help children to realise that area does not always increase with
perimeter.
Note that names of polygons are also revised in preparation for Teaching Sequence S1.
Watch out for children who confuse the units of measurement for area and perimeter. This can occur because children
count the squares around a shape in order to measure its perimeter, and so think perimeter is measured in square units.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_M1 – Aut – 4days
Objectives:
 Draw lines to nearest centimetre and millimetre
 Measure lines to nearest millimetre and centimetre
 Measure and calculate the perimeter of regular and irregular polygons
 Use the formula for the area of a rectangle to calculate the rectangle’s area
Whole class
Group activities
Paired/indiv practice
Resources
Draw a rectangle on the board with sides
between 20 and 30cm long. How can we find
the perimeter of this rectangle? Remind
children that the perimeter is the distance
round the outside of the shape. Take
feedback, and measure each of the four sides
to the nearest millimetre and add up the four
distances using a calculator. Did I need to
measure all four sides? Why not? What do we
know about rectangles? Draw out that opposite
sides are the same length, and so we only need
to measure two sides. So if we know the length
of two sides, how can we find the perimeter?
Draw out that we can double the total of two
sides (one longer and one shorter) as this will
give us the total of the two shorter sides and
the two longer sides.
Show children a rectangle on square paper, e.g.
8 squares by 5 squares (preferably an IWB
background so that the squares are large
enough to be seen). What is the area of this
rectangle?
Group of 4-5 children
Give a book to each child. Show children
a book with a dust jacket. Remove the
jacket and discuss how it is made and
how children could make dust jackets
for the books they have been given.
What measurements will we need to
make? Draw out that children need to
measure the width of the front cover,
the spine, the back cover, and add on an
amount for each flap. They also need to
measure the height of the book, and
add on a few millimetres so that the
dust jacket slightly overlaps the book.
Give children large sheets of paper to
make dust jackets. They should write
the title and author’s name on both the
front cover and the spine, and decorate
the jacket. Afterwards cover the
jackets with sticky backed plastic
before placing the jacket round the
book and securing the flaps to the
Children draw as many rectangles
as they can with a perimeter of
48cm on squared paper. They find
the area of each, using a
calculator where the sides do not
measure a whole number of
centimetres.
Easier: Explain that a long and a
short side will need to add up to
24cm.
Harder: Say that each side is not
a whole number of centimetres.
 Large sheets
of paper
 Coloured
pencils/felttipped pens
 Sticky-backed
plastic
 Stapler and
staples or
sticky tape
 Rulers marked
in cm and mm
 5/6 books,
including one
with a dust
jacket
 cm2 paper
 Rulers marked
in cm and mm
 Calculators
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_M1 – Aut – 4days
sections covering the front and back
covers (with small staples or sticky
tape).
Easier: Children round measurements to
the nearest half centimetre.
Remind children that the area is the amount of
surface covered by the shape. Draw out that
we can count the number of squares covered
by the rectangle. Do we need to count the
number of square in each row? Why not?
Discuss how we can find the number in one row
and then multiply by the number of rows. If
each square was one centimetre long, what
would the length of this rectangle be? And
what would be the width?
Sketch a rectangle and label the sides as 7cm
and 3cm. The sides don't really measure 7cm
and 3cm, but if they did how many square
centimetres would be inside this rectangle?
How do you know? So if we are trying to
measure the area of a rectangle not drawn on
squared paper, how could we work out the
area? Draw out that we can multiply the length
by the breadth. What units of measure would
we use? Remind children that the squares
measuring 1cm by 1cm are called square
centimetres, and written as cm2.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_M1 – Aut – 4days
Go back to the original rectangle. How could
we find the area of this rectangle? Show
children how to enter the measurement of the
sides in just centimetres into the calculator to
find the area in square centimetres.
Draw a ‘T’-shape on squared paper (preferably
as an IWB background).
Agree its area with your maths partner. Take
feedback and discuss how children found the
area. Draw out that they could count the
number of squares, or they could divide the
shape up into rectangles and find the area of
each. For example they could divide the shape
into two rectangles one measure 5 by 2, and
the other 3 by 2, or into two 2 by 2 squares
and a 5 by 2 rectangle.
What is its perimeter?
Draw the following shape:
Group of 4-5 children
Give children cm2 paper and ask them to
draw at least two non-rectilinear
shapes with an area of 18 cm2 each on a
separate piece of cm2 paper. Try and
make your shape look different from
your neighbour’s. Measure the
perimeter of each to the nearest
millimetre. Put the shapes in order of
perimeter.
Challenge children to draw a shape with
the same area but with a perimeter
greater than that with the greatest
perimeter, and also a shape with
perimeter less the smallest perimeter.
Easier: Children use whole squares.
Harder: Say that the sides of shapes
do not all measure a whole number of
centimetres.
Children find areas of letters
drawn on squared paper, and
measure their perimeters to the
nearest millimetre.
Easier: Children use a calculator
to help to find the total
perimeter.
Harder: The letters include more
diagonal lines and so the areas
and perimeters are more difficult
to work out.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 cm2 paper
 Activity sheets
of compound
shapes (see
resources)
NB: these sheets
and those for the
next two sessions
are drawn to scale
so that one
centimetre square
does in fact
measure one
centimetre.
However, printing
and photocopying
may alter this
slightly and you
may need to
enlarge/reduce a
little to
compensate.
Y5 Maths TS_M1 – Aut – 4days
Talk to your partner about how you could find
the area of this shape. Take feedback,
focusing on how children worked out the area
of the partially covered squares. Annotate the
letter to show how the pairs of incomplete
squares each form half of a rectangle
measuring 2 by 1, and so we can find their
area. Alternatively children may see the
smaller of the partial squares fitting with the
larger to make one whole.
How could we find its perimeter? Do you think
the answer will be a whole number of
centimetres? Draw out that children will need
to use a ruler to measure one of the diagonal
sides, but not both as they are the same.
Draw a hexagon on a plain background:
Label one of the sides 5cm and explain that
this is a regular hexagon. What do we mean by
Group of 4-5 children
Give children cm2 paper. Talk to your
partner about how you could draw a
triangle with an area of 4cm2. Take
feedback and draw out that they could
draw a 2 by 4 rectangle and cut it in
half diagonally to form a right-angled
Children find the perimeter of
regular polygons (see resources)
using a calculator to help, and the
perimeter and area of irregular
polygons.
Harder: Also challenge children to
draw an irregular but symmetrical
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Activity sheet
of polygons
(see resources)
 Rulers marked
in cm and mm
 Calculators
Y5 Maths TS_M1 – Aut – 4days
regular? Talk to your partner about how we
could find the perimeter of this shape.
Take feedback and draw out that although we
could measure each side, as it is a regular
hexagon we can just multiply 5cm by 6 to find
the perimeter. What if it was an irregular
hexagon?
Repeat, this time drawing a regular pentagon
with sides shown as 6cm 7mm. How could we
enter this measurement into the calculator?
Draw out that we could enter it as 6.7 or 67
depending on whether we want an answer in
centimetres or millimetres. Enter 6.7 × 5 = to
find the perimeter in centimetres.
Draw the following right-angled triangle on
squared paper:
Talk to your partner about what might be the
area of this triangle. Take feedback drawing
out how children found the answer. Children
may have seen two 2 by 1 rectangles sliced in
half, or see the whole triangle as half of a 4
by 2 rectangle.
Draw the following irregular hexagon on
squared paper.
triangle. (They could also draw an 8 by 1
rectangle.) Ask children to draw the
triangle.
hexagon with an area of 16cm2.
Talk to your partner about how you
could use this to help you to draw a
triangle with an area of 8cm2. Sketch
the following triangles:
Which of these two triangles do you
think will have the greatest perimeter?
Why?
Ask children to work in pairs to draw at
least three triangles with an area of
6cm2 and to find their perimeters.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS_M1 – Aut – 4days
How could we find the perimeter of this
shape? Discuss how two sides are two units
long, and four are the same number of units
long and would need to be measured.
How could we find the area? Talk to your
partner about what you think the area might
be. Take feedback asking children to explain
how they arrived at their answer. Draw out
that there are 12 whole squares, and three
squares are cut in half, four times, so four lots
of 1½ squares, making another 6 squares, so
the total area is 18 square units in total.
If our hall was having a new floor and the price
was worked out based on its area, how do you
think we could work out the area? Would we
measure it in square centimetres? Agree that
it would be more likely to measure the hall’s
length and width in metres, and so the area
would be measured in square metres. If the
hall is free, go and do this. If not, measure it
in advance and display the measurements,
explaining that you rounded up to the nearest
metre. So what is the area of the floor? How
Easier: Children may find it easier to
cut out several copies of the first
triangle and stick them together to
form new triangles.
Harder: Challenge children to draw at
least two other triangles with an area
of 8cm2 and six other triangles with an
area of 6cm2.
Group of 4-5 children
Draw round a leaf on cm2 paper.
Together estimate its surface area,
agree how to include partially covered
squares, for example pairing them up to
make a whole square, or rounding the
area of each partially covered square to
the nearest half square.
Use a piece of string to help find the
perimeter.
Show children a range of leaves. Which
Children estimate which shapes
have the greatest and least
perimeter and which have the
greatest and least area (see
resources). They record their
guesses and then measure to find
out.
They then estimate and measure
the area and perimeter of four
rectangles, using calculators
where necessary.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Five or six
leaves of
different
perimeters and
areas
 String
 cm2 paper
 Activity sheet
of shapes (see
resources)
 Calculators
Y5 Maths TS_M1 – Aut – 4days
do you think this would be written? Show
children how square metres are written. How
many square centimetres do you think might
be in a square metre? If we had a square, one
metre by one metre, what would be the length
of each side be in centimetres? And what is
100 multiplied by 100? Agree that one square
metre is 10,000cm2.
How do you think the area of our playground
might compare with the hall floor area? Twice
as much? Three times?
When might we use measure area using square
millimetres? Take a range of suggestions. How
many square millimetres do you think there are
in one square centimetre? Talk to you partner
about how you could work it out. Agree that
one square centimetre is 100mm2. What might
we measure in square kilometres? Take a range
of suggestions. Talk to your partner about how
many square metres there are in a square
kilometre. Agee that there are a million square
metres in a square kilometre.
Write the following areas on the board:
12m2, 120m2, 12cm2, 28cm2, 12mm2, 28mm2
Which of these do you think could be the area
of a bedroom floor? The surface area of a
little finger nail? One side of a credit card?
of these do you think have a greater
surface area than the first leaf? Ask
children to make an estimate of the
area for each leaf, based on their
experience of the first.
Repeat, this time find the perimeter of
the first leaf, and then predicting
which leaves will have a greater
perimeter.
Give a leaf to each child and ask them
to draw round it on squared paper to
find its approximate area, and to use a
piece of string to help find its
perimeter.
Compare the result with children's
estimates.
Easier:/Harder: Children’s
approximations will vary in accuracy
according to how they are able to take
partial squares into account.
Harder: Ask children to work in
pairs to agree an order of the
shapes first according to size of
area and then according to size of
perimeter, before measuring
them. Children's estimates of
perimeter are likely to be more
accurate.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Rulers marked
in cm and mm
Y5 Maths TS_M1 – Aut – 4days