Year 6 Teaching Sequence Autumn D1 – Handling data: frequency tables, bar charts, pie charts and
line graphs (four days)
Prerequisites:
 Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate;
draw conclusions and identify further questions to ask (see Year 5 teaching sequence D5)
 Construct line graphs and understand where intermediate points have and do not have meaning (see Year 5 teaching
sequence M2/D2)
 Know multiplication and division facts for the 2 - 10 times tables (see oral and mental starter bank D1)
Overview of progression:
Grouped data is used in frequency tables and bar charts. Children draw line graphs and read intermediate points. They
match stories to line graphs and write their own stories to accompany line graphs. Children learn how to construct, interpret
and compare simple pie charts.
Note that for discrete data, the actual bars, not the left and right edges of bars, are labelled with the range they
represent.
Watch out for children who try to write numbers in the boxes (as if for a block graph) rather than across the lines on the
vertical axis and so have difficulties when drawing bars with the axis labelled in twos, fives, tens or twenties.
Watch out for children who don’t take numbers into account when comparing segments between different pie charts.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_D1 – Aut – 4days
Objectives:
 Solve problems by collecting, selecting, processing, presenting and interpreting data, using ICT where appropriate; draw
conclusions and identify further questions to ask
 Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs
 Interpret pie charts
Whole class
Group activities
Paired/indiv practice
Resources
Display the charts of age profile in a village
and in a new modern housing estate (see
resources).
Discuss the grouping on the horizontal axis.
Why didn’t they draw a bar for every age?
With a wide range like this it’s helpful to
group data. Where would you put someone who
is 10½? Agree that they would be included in
the bar for 10 and each age would need to be
collected as a whole number.
What’s different about the two charts? Why
do you think they are different? What do you
think a chart like this would look like for our
village/town/city/estate?
Roughly how many people live in Little
Steignton? How can you tell? Approximately
how many more people are in the 61-70 age
bracket than over 80?
Approximately how many people are there
aged 40 or less in each place? And over?
Agree answers with a partner.
Group of 4-5 children
Launch the ITP Data handling, choose your own
data, enter age ranges as opposite and enter
numbers for people watching a children’s film.
Click on the vertical bar chart icon, enter a
title, and also click on the far right bar to
display percentages.
Children work in pairs to
shuffle two packs of 1-10
cards (in two different piles).
They take one off each pile
and find the product. They
record the results in a
grouped frequency table, first
predicting which range will
have the highest frequency:
Product Tally Frequency
1-20
21-40
41-60
61-80
81-100
They stop when one group has
reached 20. They draw a bar
chart to show their results.
Easier: Children use a
multiplication table if they
struggle with finding some
products (see resources).
They stop when one range has
reached 10.
Harder: Children construct
 Bar charts of
age profiles
(see
resources)
 ITP Data
handling
 Packs of 1-10
cards
 Multiplication
table (see
resources)
What sort of film do you think these people
might be watching? Why do you think that?
Make a list of films currently showing. What do
you think the age profile might be for each of
these? Modify the numbers on the graph to
show this.
How might the age profile be different at
different times of day? Would this be the same
every day? Why not? Discuss the differences
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_D1 – Aut – 4days
Draw a vertical axis from 0 to 50 labelled
‘product’ in steps of 2 and horizontal axis
from 0 to 15 labelled ‘multiplier’. Write the
title ‘A line graph to show multiples of 3’.
Explain that you are going to draw a graph to
show the three times table. What is 0 times
3? Draw a point at 0, 0. What is 1 times 3?
Draw a point at 1, 3, explaining that you go
along 1, and up 3. Ask children to help you to
plot points up to 10 lots of 3 and then join
them with a straight line. How much does the
line go up each time? Why? Write the
following multiplications on the board:
3 × 6.5, 3 × 13, 4 1/3 × 3
How could we use our graph to solve these
multiplications? Draw out extending the line,
and reading intermediate points.
If we were to sketch a graph for the 6 times
table how might it look different? Take
children’s suggestions, but do not comment on
them as they will find out for themselves
during the individual practice activity.
between weekends, working days, school
holidays, any cheap deal evenings/matinees etc.
Harder: Ask children to sketch a bar chart for
different scenarios.
Group of 4-5 children
Give children sets of temperature data (see
resources). Both these tables show data about
temperatures. What sort of graphs could we
use to show this data?
Sketch a line graph to show the change in
temperature over a day. Why do you think the
temperature changes over the day? Why might
it not be at it’s hottest during the afternoon?
Discuss how the heating may be on at certain
times, but not during the day as the owners
might be at at school and work. What might the
temperature have been at 19:00? How do you
know? So we can read off intermediate points
on this graph. Could we do this with
temperatures around the UK? Discuss how it
would make no sense to draw line to join the
points as the intermediate points would not
have any meaning. A bar chart may be a better
graph to show this information.
What do you think a room temperature line
graph might look like for our classroom? Ask
children to work in pairs to sketch a line graph
and compare them, asking children to explain
their graphs.
Harder: Ask children to think what a line graph
might look like which shows both the
temperature inside the classroom and the
temperature outside during a 24-hour period.
their own frequency table,
choosing their own ranges.
Children draw a line graph to
show both the 6 and 9 times
tables. They choose a scale
for the vertical axis according
to what paper they have.
In pairs they write a
multiplication question that
they can answer using the
graphs, e.g. 6 × 4.5. They use
calculators to check.
Easier: Children draw graphs
to show both the 2 and 4
times tables on cm2 paper,
with the vertical axis draw in
steps of 2. They use their
graph to find the answers to
questions such as 4.5 × 2 and
3 × 7.5 and use a calculator to
check.
Harder: Children also draw a
line for square numbers on the
same graph and write about
what they notice.
 Temperature
data (see
resources)
 Graph paper
 Calculators
 cm2 paper
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_D1 – Aut – 4days
Draw a vertical axis and a horizontal axis
meeting at the origin. Label the horizontal
axis Time, the vertical axis Noise level and
write zero at the origin. Imagine the noise
levels in school throughout the day. When
might it be at the quietest? Will there be no
noise then? Discuss the events that might
affect the noise level, for example the
caretaker and teachers arriving in the
morning, the arrival of children into the
playground, children entering the school and
settling down for lessons/assembly, children
going out at break time etc. Ask children to
help you to sketch the graph of the noise
levels against time during the morning.
Discuss the resulting graph. When was the
noise level at its highest? Why? When was
the noise level constant?
Ask children to work in pairs to draw a similar
graph to show the noise level during the
afternoon. They share their graph with
another pair explaining the changes in
direction/steepness of the line on the graph.
Group of 4-5 children
Display the following story:
Sam and his family are walking up a mountain.
They start off at a brisk pace, but slow down as
they get tired and the mountain gets steeper.
They stop at the stop for lunch, and then start
walking down, slowly at first as it’s so steep.
Towards the bottom they start to speed up as
the terrain becomes easier and they can see a
tea shop!
Ask children to work in pairs to sketch a line
graph with speed on the vertical axis and time
on the horizontal axis. Compare the shapes of
their graphs. Some children may be tempted to
make their graphs look mountain-shaped, but
their graphs will look pretty much the opposite!
Sketch the following graph:
Children match stories to line
graphs and then work in pairs
to write a story to go with
each line graph (see
resources).
Easier: Children draw a line
graph to go with a story.
 Activity
sheets of line
graphs and
stories (see
resources)
Time
This graph is connected with the same story.
What label might be on the vertical axis? Why
do you think that?
Ask children to think about how the family’s
heart rates may have varied. Will a graph of
heart rate against time look more like the first
graphs or the second? How will it be different
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_D1 – Aut – 4days
Sketch the following two pie charts on the
board:
School A: Sports outside school
cycling
swmming
dancing
football
School B: Sports outside school
cycling
swmming
dancing
football
These are called pie charts, the segments do
look a little like pieces of pie! Children voted
for their favourite sport outside of school.
Talk to your partner about what you think the
pie charts show.
Which is the most popular sport outside of
school for children from school A? School B?
Children voted for their favourite sport
to the first graph?
Easier: Sketch graphs to show speed, height
and heart rate all without labels on the vertical
axes, display the story and ask children to
discuss what the missing labels might be.
Group of 4-5 children
Show children a collection of cereal packets.
Which of these cereals do you think is the
healthiest? What makes one cereal healthier
than another? Give one to each child. Point out
the nutritional information panel and ask each
child to write down the percentage protein,
carbohydrates (divided into sugar and nonsugar), fibre and other elements (salt, added
vitamins and minerals for example). This may be
displayed as grams per 100g rather than a
percentage.
How many degrees would 1% present on a pie
chart? Draw out that this would be 3.6 degrees
as there are 360° around a point. Ask children
to multiply each of their percentages by 3.6 to
find the numbers of degrees necessary to
represent each proportion on a pie chart. Ask
children to draw circle, and use a protractor to
draw each segment.
Compare the cereals. What can we say about
these cereals? Which is the healthiest? Which
has most sugar? And fibre? Do your lists of
percentages or pie chart make this information
clearer? Why?
Easier: Help children to round figures to the
nearest degree.
Ask children to write down
the number of hours (out of
24) that they spend sleeping,
at school, eating, watching TV,
hobbies, anything else. Ask
them to draw a pie chart to
show how they spend their
day. They will need to work
out how to divide the circle
into 24.
Ask them to compare their pie
charts with others.
Easier: Give children pie chart
outlines.
 Five cereal
packets
 Compasses,
protractor
 Calculators
 Activity
sheets of pie
chart outlines
(see
resources)
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_D1 – Aut – 4days
outside of school. The results are from 32
children in Year 6 in School A. Talk to your
partner about how you could work out how
many children voted for each sport. Take
feedback, agreeing that half the children
voted for cycling, and as half of 32 is 16, then
16 children must have voted for cycling.
The second chart shows the results from 64
Year 6 children. Did more children vote for
cycling in school A or B? Discuss how a higher
proportion of children in school A voted for
cycling but the actual numbers of children
were the same. Ask children to work out the
numbers of children who voted for each sport
in school B.
How do you think this pie chart would differ
for our class? Sketch what you think it might
look like.
Take feedback.
© Original teaching sequence copyright Hamilton Trust, who give permission for it to be adapted as wished by individual users.
Y6 Maths TS_D1 – Aut – 4days