Year 5 Teaching Sequence 2 – Ordering numbers (three days)
Prerequisites:
 Locate four-digit numbers on a 0-10000 line (1000s labelled) (see Year 4 Spring teaching sequence 2 and oral and
mental starter bank 2)
 Round four-digit numbers to the nearest 100 (see Year 4 Summer teaching sequence 1)
 Compare four-digit numbers and find a number in-between (see Year 4 Summer teaching sequence 1 and oral and
mental starter bank 2)
Overview of progression:
Children round four-digit numbers to the nearest multiples of 10, 100 and 1000. They use this approximation to find a total.
They learn how to read five- and six-digit numbers, including how commas or thin spaces are used to separate groups of
three digits, e.g. the number of thousands from the hundreds, tens and ones. They compare and order six-digit numbers
using the < and > signs, and find a number in-between.
Note that children need to be aware of how both commas and thin spaces are used to separate groups of three digits as
different countries use these differently. The comma means a decimal point in many countries and so the International
System (SI) suggests that large numbers be represented as groups of three digits separated by narrow spaces, not by
commas. Chn are more likely to see narrow spaces being used in printed text, and commas in English handwritten texts
where it is more difficult to show narrow spaces. Note that spaces and commas are not always used for four-digit numbers.
Watch out for children who are not using their knowledge of rounding three-digit numbers to the nearest ten to help them
to round four-digit numbers to the nearest 10.
Watch out for children who insert commas after the first three digits, rather than before the last three digits, working
back through the number to do this, as this will not help them to be able to read the number.
Watch out for children who cannot read a number in which zero is a place-holder (e.g. 342,056) or who cannot ‘cross the
thousands’ when adding one, ten or one hundred, e.g. 478,000 + 10 = 488,000 or 479,000)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS2 – Aut – 3days
Objectives:
 Order a set of numbers up to 1 million
 Compare numbers up to 1 million, find a number in-between, use < and > signs
 Round four-digit numbers to the nearest 10, 100 or 1000
Whole class
Group activities
Paired/indiv practice
Resources
Sketch a line from 5570 and 5580 and ask
children to copy it onto their whiteboards. Think
of a number that is between 5570 and 5580 and
mark it on your line. Which number is it closer to?
Which is the nearest multiple of ten? Ask a few
children to show their boards and to say which
multiple of ten their number rounds to.
Now think of a different number that will round to
5580 when you round it to the nearest ten. Write
it on your board, show me. Now write a number
that will rounds to 5570 when you round it to the
nearest multiple of ten.
Call out four-digit numbers and ask children which
multiple of 10 they are closer to. They write the
correct multiple of 10 on their whiteboards.
Now sketch a line from 5500 to 5600. Work with
a partner to think of a number between 5500 and
5600 which will round to 5500 when rounded to
the nearest 100. Mark it on your line. Share
children’s whiteboards. What would we round 5550
to? Explain that we would round 5550 up to 5600.
Now show me a number closer to 5600 than 5500.
Call out four-digit numbers and ask children which
multiple of 100 they are closer to. They write the
correct multiple of 100 on their whiteboards.
Group of 4-5 children
Sketch a line on the flipchart from 4600 to
4700. Ask a child to think of a number
between the two and to mark it on the line
but not to write the number. Ask children to
discuss in pairs what the mystery number
might be and to write an estimate on their
whiteboards. Tell children that they can
choose two multiples of ten for you to put on
the line. When they have reached an
agreement (e.g. 4650 and 4660) ask the child
at the flipchart to mark on where these two
numbers might be. Do you want to change
your estimate? Ask the child to reveal the
mystery number and say how s/he decided
where to mark the number. Repeat with
another child.
Repeat, but this time with 5000 at one end of
the line and 6000 at the other, asking a child
to mark a number in between. After a while
say that they can choose two multiples of 100
to place on the line (e.g. 5500 and 5600). Ask
children to write their estimates on their
boards. Could the number be 5525? Why not?
Draw out that the number is closer to 5600
Children work in pairs to shuffle a
pack of 0-9 digit cards, and take
four to make a four-digit number.
They discuss which two multiples
of ten it lies between, sketch a line
between the two multiples of 10
and mark on the number they made.
They ring the nearest multiple of
10.
They discuss which two multiples
of hundred the number lies
between, sketch a line between the
two multiples of 100 and mark on
the number they made. They ring
the nearest multiple of 100.
They discuss which two multiples
of hundred it lies between, sketch
a line between the two multiples of
1000 and mark on the number they
made. They ring the nearest
multiple of 1000.
Repeat with other four-digit
numbers.
Easier: Children have a 3000-4000
landmarked line (100s labelled).
 0-9 digit cards
 3000-4000
landmarked
line, 100s
labelled (see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS2 – Aut – 3days
Draw a line from 5000 to 6000 and mark on a
number in between. Which multiple of one
thousand is it closer to? Share children’s’ boards.
Now think of a new number which will round to
5000 when rounded to the nearest thousand. Now
think of a number that will round to 6000.
Display a table of distances between places around
the world (see resources). Show how to use this
table to find the distance from London to Delhi.
What multiples of ten lie either side of 5907?
Sketch a line on your whiteboards to show 5907
between 5900 and 5910. So what is 5907 to the
nearest 10 miles? To the nearest 100 miles?
Sketch a number line on your whiteboards to show
this. And to the nearest 1000 miles? Sketch a line
to show this.
Repeat with two four-digit distances.
What is the shortest distance between two cites
on the table? And the greatest? The closest city
to London? And the furthest away? You might
want to show some of these cities on a globe so
that chn appreciate where they are. Look where
Tokyo and Sydney are in relation to London.
Approximately how far do you think it is around
the widest part of the Earth? (Approximately
25,000 miles.)
than to 5500 for example. Ask the child to
reveal the answer. If you have a number
which rounds to 5600 not 5550, you made a
good estimate.
Easier: Think of, and mark the numbers on
the line yourself rather than asking a child,
and then progress to asking a pair to do this.
If necessary begin with three-digit numbers
between 600 and 700 before moving onto
four-digit numbers between 4600 and 4700.
Group of 4-5 children
Display the table of distances. If someone
lived in Tokyo and travelled to every city on
the table and back in between each trip,
roughly how far would that person travel?
What could we do to help us answers this?
Round each to the nearest 1000 and add up
the number of 1000s. What do we need to do
now? Agree that you need to double the total
as the person came home in-between. So
rounding is helpful when we want an
approximate answer.
Harder: Plan a world trip. Estimate the
distance travelled from Tokyo to Delhi, onto
Frankfurt and so on, finding each distance on
the table and rounding to the nearest 1000.
They make at least four numbers
between 3000 and 4000 and mark
them on the line.
They write the four numbers
underneath, and write the nearest
multiple of 10, 100 and 1000 at the
side of each.
Ask chn to choose at least 6 fourdigit distances from the table (see
resources) and to round them to
the nearest 10, 100 and 1000 miles,
sketching number lines to show
where the distances lie between
neighbouring multiples of 10, 100
and 1000.
Easier: Chn choose 3 three-digit
numbers to round to the nearest 10
and 100, and then choose 3 fourdigit numbers to round to the
nearest 10, 100 and 1000.
Harder: Chn also include a few
five-digit distances. Challenge chn
to think of a four-digit number
that would be rounded up when
rounding to the nearest 10, down
when rounding to the nearest 100
and up when rounding to the
nearest 1000 (e.g. 6926).
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
 Table of
distance
between cities
from around
the world (see
resources)
 Globe
Y5 Maths TS2 – Aut – 3days
Write 1,351,468 and 1 351 468 on the board. Ask
chn to discuss with their maths partners how to
read these two numbers. Take feedback and agree
what the number is and how it is said. Discuss how
in the first way of recording the number, commas
are used to group digits in groups of three when
we write big numbers, and often thin spaces are
used when numbers are printed as in the second
way of writing the same number. Explain how the
grouping helps us to read the numbers. Cover the
first three digits, and read the number as one
thousand, four-hundred and sixty-eight. Now
reveal the digit 5. What is the number now? Fiftyone thousand, and four-hundred and sixty-eight,
the 5 and 1 before the last three digits tells us
how many thousands there are. Reveal the 3, and
now three-hundred and fifty-one thousand, and
four-hundred and sixty-eight. The digits 351 tell
us how many thousands there are. Finally reveal
the digit 1, and now one million, three-hundred and
fifty-one thousand, and four-hundred and sixtyeight. Write the number which comes before this
number on your whiteboards, and the next three
numbers.
Write four other seven-digit numbers on the
board and ask chn to work out how to read them.
Group of 4-5 children
Display the following table:
Planet
Diameter in
miles
Distance to the
Sun
in miles
Earth
7,926
92,957,100
Jupiter
88,846
483,632,000
Mars
4,222
141,635,300
Mercury
3,032
35,983,610
Neptune
30,778
2,798,842,000
Saturn
74,898
888,188,000
Uranus
31,763
1,783,950,000
Venus
7,521
67,232,360
Chn work in pairs to each roll a 0-9
dice six times to generate two sixdigit numbers. They decide which is
larger and write the corresponding
equalities. They record a number
in-between.
After they have played the game
at least five times, they write all
the numbers in a list from the
smallest to the largest.
Harder: Chn record the number in
between using < or > signs, e.g.
234,739 < 240,000 < 241,827.
 Table as
opposite
 0-9 dice
Which is the smallest planet? And the
biggest? Write a list of planets in order of
size. What is the diameter of Mercury to the
nearest 10 miles? 100 miles? 1000 miles?
Repeat rounding the diameters of other
planets.
Which planet is closest to the Sun? And
furthest away? Write a list of planets in
order of their distance away from the Sun.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y5 Maths TS2 – Aut – 3days