Statistics (Data) and Probability (Chance) 8
Collect data, record in picture graphs, column graphs, without and with technology
Resources: pencil, ruler, 1 centimetre grid paper, computer with a spreadsheet program (for example, Microsoft Excel)
EXPLICIT LEARNING
What could we do?
What language could we use to explain and ask questions?
Focuses
children’s
thoughts on
the concept,
exposing
current
understanding
and any
misconceptions
Reviews
chance and
data
Record, for example, chance is how likely something will happen
Record, data is information
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
Today brings an investigation about chance and data.

What do you know about chance and data?

Talk about chance and data with a friend.

Is anyone ready to share what they are thinking about
chance and data?

We’ve investigated chance and data.

And we found that chance meant how likely it was that
something would happen.

We described chance using words like likely, most likely,
least likely, maybe, definite, impossible and possible.

We found that data just means information. We found
that we needed data to be able to work out chance!

Imagine you have just woken up and haven’t looked
outside yet.
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Display some tally marks, a list, a table and a picture graph, for
example,
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
Now imagine someone asks you if you think there is a
chance that it might rain today.

Where would you look to gather some data?
Would you look outside?

Do you know what the chance of rain is without looking
outside?

So when we have some data, we can work out the
chance of something happening.

In maths, we love to measure things.

And we just love to measure chance! Let’s investigate!

We’ve investigated ways that we can gather data.

We asked questions and used tally marks to record the
data.

We found that tally marks are grouped in5s because 5 is
easy to subitise and easy to count by.

We recorded data in a list and in a table.

And we made picture graphs of the data.

We’ve investigated how we could then use the data to
work out the chance of something happening.
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
Today we’re going to collect some data to make another
kind of graph.

We’re going to make a column graph!

Let's start with a simple yes / no question: Did you walk
to school today?

Let’s record our data using tally marks.

Will we need labels for our tally marks?

What labels could we use?

Could we use the labels 'walk to school' and 'did not walk
to school'?

Raise your hand if you walked to school today

Could we record use a tally mark for each child?
Children record a tally mark for every hand raised for example,

Raise your hand if you did not walk to school today
Walk to school llll llll llll

Could we record use a tally mark for each child?

Could we record this data in a table?

What could be our title for our table?

Could we call our table 'Walk to school'?
Introduces
collecting data
and
representing it
in a column
graph top
Record the labels, for example,
Reviews
collecting data
in lists using
tally marks
Walk to school
Did not walk to school
Children who did walk to school today raise their hand.
Children record a tally mark for every hand raised for example,
Walk to school llll llll ll
Children who did not walk to school today raise their hand
Record the table title, for example,
Walk to School
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Reviews
recording data
in a table
Reviews row
headings
Reviews
entering data
Children record a table (or may have a table distributed to them), for
example,

How many rows and columns would we have?

Would we have 2 rows, one row to record the number of
children who walk to school and one row for the number
of children who did not walk to school?

Would we have 2 columns, one for the headings and one
for the numbers?

Might our column for the row headings be a little wider
so we can fit the writing in it?

What could be our row headings?

Could our rows headings be 'walk to school' and 'did not
walk to school'?

How many children walked to school?

Let’s count our tally marks, 5, 10, 12.

Where will we record that number?

How many children did not walk to school?

Let’s count our tally marks, 5, 10, 14.

How could we record that number?
Walk to School
Record the row headings, for example,
Walk to School
Record the numbers of children, for example,
Walk to School
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Introduces
recording data
in a column
graph
Distribute 1 centimetre grid paper to children.

Instead of drawing pictures in our graph, today we’re
going to draw columns using this grid paper.
Record the column graph title, for example,

Our column graph will need a title.

What could be our title for our column graph?

Could we call our column graph 'Walk to school'?

Every column graph has a straight vertical line, and a
straight horizontal line that meet at a vertex.

The horizontal line is called a horizontal axis.

And the vertical line is called a vertical axis.

Axis just means a line.

When we have 1 line we call it an axis. When we have
more than 1 we call them axes.

We’ve investigated other words that change when they
become plural.

Words like vertex and child.

When we have 1 child we say child. But when we have
more than one we change it to children!

When we have 1 vertex, we say vertex. But when we
have more than one we change it to vertices.

Axis is just like vertex. 1 axis, 1 vertex. 2 axes, 2 vertices!

Let’s record our vertical and horizontal axes.
Walk to School
Introduces
drawing a
vertical and
horizontal axis
Record the column graph axes, for example,
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Introduces
labelling the
horizontal axis
with column
headings
Introduces
labelling the
vertical axis
with numbers
Point to the columns we will be
using and label the horizontal axis,
for example,
Record numbers through each line
on the vertical axis, for example,
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
Each of our axes will need a label so that everyone will
know what data our graph is showing.

We’re going to draw 2 columns, one for the children who
walked to school, and one for the children who did not
walk to school.

Could we label the horizontal axis 'Walk to school' and
'Did not walk to school'?

We’re going to leave a space between the first column
and the vertical axis.

And we’re going to leave a space between the 2 columns.

So one of our columns will go here.

Let's label this column 'Walk to school'

And our other column will go here.

Let's label this column 'Did not walk to school'

Now our vertical axis needs labels to show how many
children walked to school and how many children didn’t.

If we’re recording how many, could we label the vertical
axis with numbers?

We’re going to record a number through every line so
that if a column reaches the line, we know that’s the
number of children.

When we label the vertical axis, it looks like a number
line!
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Introduces
recording
columns up to
the numbers
on the vertical
axis
Record the column for the 12 children who walked to school, for
example,
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
How many children walked to school?

Could we record a column that goes up 12 squares?

Will the column go up to where the number 12 is on the
vertical axis?

Let’s draw a column up to the number 12 on the vertical
axis!
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Record the column for the 14 children who did not walk to school, for
example,
Introduces
giving the axes
titles
Record the label for the vertical axis, for example,
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
How many children did not walk to school?

Could we record our column for the 14 children who did
not walk to school?

Will the column go up to the number 14 on the vertical
axis?

What do the numbers on the vertical axis tell us?

Do the numbers tell us the number of children?

Could we label the vertical axis 'Number of children'?
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Record the label for the horizontal axis, for example,
Reviews
differentiating
the
investigation
for children as
they
demonstrate
understanding

What does the horizontal axis tell us?

Does the horizontal axis tell us about the children coming
to school?

Could we label the vertical axis 'Children coming to
school'?
Allow children time now to engage in guided and independent
investigation (at the end of this teaching plan) of collecting data and
representing data in a column graph.
A child could be sitting next to a child who is investigating at a
different level. They will explain their current levels of understanding
to one another as they investigate. This is a research-based way to
accelerate learning for children at all levels.
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Introduces
constructing
column graphs
using
technology top
Introduces
using a
spreadsheet
Children sit in pairs at a computer with a spreadsheet program on it,
for example, Microsoft Excel

Do you think that everyone draws their own column
graphs or do you think there might be computer
programs that could do it? Let's investigate!

Have you ever used a spreadsheet program on a
computer?

Can a spreadsheet program make a graph for us? Let's
investigate!

First, let's identify what we can see on a spreadsheet

What column is this? Where is column A? Does column A
keep going forever?

What row is this? Where is row 1? Does row 1 keep going
forever?

What are the coordinates of this cell? Is this cell A1?
Children open the program to get a new sheet, for example,
Introduces
columns, rows
and cells
Children identify columns and rows, using the arrow keys to see that
they go on forever.
Children select a cell and take note of its name in the top left
window, for example,
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Introduces
moving
between cells
Children investigate moving between cells in various ways.
Introduces
selecting
‘enter’ to leave
a cell when
data has been
‘entered’
Display the table the children constructed previously, for example,
Introduces
entering data
into cells
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
How could we move between cells?

If we select the enter key, which cell do we move to?

Do we move to the cell below?

If we select the tab key, which cell do we move to?

Do we move to the cell to the right?

If we select the right / left / up / down arrow keys, which
cell to we move to?

Do we move to a cell right / left / up / down?

Can we use the mouse to select a cell?

So we have a few ways that we can move between cells.

There is one way that we need to do this after we have
entered data into a cell.

When we have entered data into a cell, we need to select
'enter' to leave the cell, to make sure the data has been
'entered'.

Does this spreadsheet look a little like a table?

Could we enter data into this table? Let's investigate!

Let's get started entering our data from our table onto
the spreadsheet
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Enter 'Walk to school' in cell A1 and 'Did not walk to school' in cell
A2, for example,
Introduces
enlarging
columns

Could we enter 'Walk to school' in cell A1?

Could we enter 'Did not walk to school' in cell A2?

Did the words spill out of the cells?

To resize the cells to fit the words, we can click and drag
at the end of column A.

Or we can double-click at the end of column A.

Could we enter the number of children who walked to
school in cell B1?

Could we enter the number of children who did not walk
to school in cell B2?

So have we made a table?
Resize column A by clicking and dragging at the end of column A, for
example,
Enter 12' in cell B1 and 14' in cell B2, for example,
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Introduces
inserting a
column graph
Select the insert toolbar, for example,
Select the 'column graph' icon,
for example,
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Do you think the computer could now construct a graph
using this data? Let's investigate!

Let's select the insert toolbar

Can you see some diagrams of graphs in this toolbar?

Because we're going to make a column graph, let's select
this icon
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Select the first icon, for example,
Select the plus sign near the top right of the graph to get a dropdown
menu. Then select the different elements to add, for example, axes
titles, for example,
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
Let's use the first diagram of a column graph

Please select the first icon and watch what the computer
does

Did the computer construct a column graph?

So we made the computer construct a column graph.

Let's make the column graph look like the column graph
that we constructed

So we'll need a Graph Title, and axes labels

Let’s select the plus sign near the top right of the graph
to get a dropdown menu.

Then let’s select the different elements to add, for
example, axes titles.

We can also tell the computer to change the numbers on
the vertical axis.

Has the computer program constructed a graph using our
data?
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Double click on a column and select the paint pot icon from the side
menu, for example,
Select the required colour from the icon at the bottom of the side
menu, for example,

If we wanted to we could change the colour of the
columns.

If we want to change just one column, we will double
click on a column and select the paint pot icon from the
side menu.

Select the colour you like from the icon at the bottom of
the side menu.

Did the column change colour?
Allow children time now to engage in guided and independent
investigation (at the end of this teaching plan) of collecting data and
representing data in a column graph using technology.
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Open the internet to Google Images

Search for 'child walking', for
example,
So we have constructed a column graph both with and
without technology.

If we wanted to we could change the column graph that
we made using technology, into a picture graph!

First we need to get the pictures that we want to use.

Let's use Google Images.

What picture could we use for a children walking?

Could we use a picture of a child walking?

Let's search for 'child walking'.

Let's choose one of the images by double clicking on it.

Now to save the image, we can right click and select 'save
image as' from the drop down menu.

Save the image as a jpeg (jpg) as 'child walking' into a
folder on your computer that you will be able to find
again easily.

Now that we have an image, we can use it to change our
column on our column graph into a picture graph!
Double click on the selected
image, for example,
Right click and select 'save
image as' from the drop down
menu, for example,
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Double click the
column to select
just that column,
then select ‘picture
of texture fill’ from
the side menu, for
example,

If we want to change just one column, we will double
click the column to select just that column, then select
‘picture of texture fill’ from the side menu.

Then we’ll select insert picture from ‘file’ at the bottom
of the side menu.

Navigate to the folder where you saved your picture and
select insert.

The picture has been inserted, stretched to fill the
column.

We can tell the computer to insert it as a whole lot of
smaller pictures if we want to.

Select 'Stack and scale with 1 unit per picture' from the
bottom of the side menu.

One picture now represents 1 child.
Select insert picture from ‘file’ at the bottom of the
side menu, for example,
Select 'Stack and scale with 1 unit per picture'
Allow children time now to engage in guided and independent
investigation (at the end of this teaching plan) of constructing
picture graphs using technology.
Children move to Guided and Independent Investigation now to investigate the concept at increasing levels of understanding over many learning sessions
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GUIDED INVESTIGATION
INDEPENDENT INVESTIGATION
REFLECTION
Resources: pencil, ruler, 1 centimetre grid paper, computer with a spreadsheet program (for example, Microsoft Excel)
What could we do?
Children:
1. sit in pairs
2. collect data as guided
by the teacher
3. construct a table
4. construct a graph
5. ask their friend
questions
6. answer their friend's
questions
7. repeat
What language could
we use to ask
questions and
explain?
 What data are we
using?
 How could you
construct a table of
the data?
 How could you
construct a graph of
the data?
What could we do?
Children:
1. sit in pairs
2. collect data that is neither too
easy nor to challenging
3. construct a table
4. construct a graph
5. repeat
What language could we use
to explain?
 The data I am using is ...
 I constructed a list using
tally marks by …
 I constructed a list using
numbers by …
 I constructed a table by ...
 I constructed a graph
by ...
What questions could
children discuss and record a
response to?
What is a table?
What is a graph?
How could we construct a
table?
How could we construct a
column graph?
How could we construct a
picture graph?
Children may be investigating concepts at a level that varies from other children. In one class, there may be children investigating the concept at Level 1 while another
child is investigating the concept at Level 4, Level 12 or even higher.
Regardless of the child's current grade, children need to investigate concepts at the level of their current understanding. This means that a child in a given
grade, who has current understanding at Level 5, will investigate at Level 6, then Level 7 etc.
If this makes you worried that they are investigating at a level much lower than their grade level, consider this: If the child is made to try to investigate at a
higher level than their current level of understanding, they will be building on an unstable knowledge base with gaps, and will continue to use inefficient strategies
often based on misconceptions, guaranteeing that their level of understanding will be the same at the end of the year as it was at the beginning of the year. If the
child is allowed to investigate the concept at their current level of understanding, they will correct misconceptions, fill gaps in their understanding and build a firm
knowledge base, as they move through the levels, investigating at a higher level by the end of the year.
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CONGRUENT
LEARNING
STATISTICS (DATA) AND PROBABILITY (CHANCE) 8 COLLECT DATA, RECORD IN PICTURE GRAPHS, COLUMN GRAPHS, WITHOUT AND
WITH TECHNOLOGY
These learning activities allow children to investigate and explain the concept in new and varied situations. ‘Doing’ mathematics is
simply not enough and is not a good indicator of understanding. As Einstein said, ‘If you can’t explain it simply, you don’t
understand it’! Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
at their current level of understanding. Differentiate learning for children working at all levels of the concept, including those
requiring extension, and allow children to differentiate their own learning, by varying the range and size of numbers investigated.

In small groups, children make simple two-column graphs about children in their group, for example, children who like cats or
dogs best, children who can swim and who cannot.

In small groups, children make simple three-column graphs about children in their group, for example, children who like cats,
dogs or guinea pigs best, children who can walk, come by car or come by bus to school.

Children use their data representations for Statistics (Data) and Probability (Chance) 9
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PROBLEM
SOLVING
STATISTICS (DATA) AND PROBABILITY (CHANCE) 8 COLLECT DATA, RECORD IN PICTURE GRAPHS, COLUMN GRAPHS, WITHOUT AND
WITH TECHNOLOGY
Problems allow children to investigate concepts in new and varied situations. Any problem worth solving takes time and effort –
that’s why they’re called problems! Problems are designed to develop and use higher order thinking. Allowing children to grapple
with problems, providing minimal support by asking strategic questions, is key. Differentiating problems allows children to solve
simpler problems, before solving more complex problems on a concept. Problems may not always be solved the first time they are
presented. Returning to a problem after further learning, develops both resilience and increased confidence as children take the
necessary time and input the necessary effort. As Einstein said, ‘It’s not that I’m so smart – I just stay with problems longer’. The
problem solving steps may be followed to solve problems.

On a graph about the pets owned by children in a class, there are 2 more dogs than cats. What might the graph have looked
like?

A table showed that there are more children with brown hair than blonde hair or black hair. What might the table look like?

A graph showed that 12 children came to school by car, 8 walked and 4 came by bus. What might the graph have looked like?
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Different representations of the same data
back
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Problem Solving Steps (back to Problems)
1. Read
2. Understand
3. Choose a strategy
Read the part that is
asking you to find out.
Read the information you
need to find it out.
Think about what you
could do to work it out.
4. Work it out
5. Check
6. Share
Use your strategy to work
it out.
Read the part that asked
you to find out.
Share and compare your
strategy and answer with a
friend’s strategy and
answer.
Did you find it out?
Need a 10 frame
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