What is a Maths Representation?

Pictograms are used in KS1 as an introduction to bar charts and tables.

They use pictures to represents quantities or data in simple ways.

Children are first introduced to pictograms where one picture represents ones of the object for example:

OOOO = 4 balls

However this could be inefficient when counting larger quantities.  In this case each image could represent more than 1.  For example, on the left each football is worth 2.

At first it appears that Alex scored two goals but in fact he scored four.  

Jack did not score half a goal, however as each football is worth two, half of two is one so Jack scored one goal.

Tables are used in maths to arrange information or data usually in columns and rows.  

The purpose of this is to make it easier to read large amount of information in a more organised and structured way.

The data from these can then be taken to be represented in charts and graphs.

These are the next step from pictograms as the data is given a value rather than a picture.

Tally charts are quick and simple ways of recording and counting frequencies.  For example the table on the left has a vertical line representing each time an animal was seen.  Rather that writing 1 then crossing it out and then writing 2 and so on, another line can simply be added until the counting has finished making it quicker and easier to record.

1 = |

2 = ||

3 = |||

4 = ||||

However when tallies get to five they are grouped which is more efficient to count.

5 = ||||

6 = ||||  | 

7 = ||||  || 

8 = ||||  |||
9 = ||||  ||||
10 =  |||| ||||

25 = |||| |||| |||| |||| ||||

A bar chart is a chart of graph that displays information using rectangular bars of different heights or lengths that are proportionate to the value it represents (these have usually been collected from tables)

They are helpful to show relative sizes and to summarise data in a visual way.  For example on this bar chart, the taller bar for the cheese shows that this is the most popular pizza topping, whereas tuna is the least.

The vertical axis (y-axis) usually is the number and the horizonal axis (x-axis) usually shows the different options or categories.

Bar charts are use to represents categorical or discrete data.

A pie chart is an excellent way of representing data in a circular graphs/chart when comparing parts of a whole.

The sections of the pie chart are proportional to the size of the data it represents.  

In the case of the pie chart to the right, this could represent the following:

5 children in total (5 sections) were asked if they preferred drawing or painting.

3 out of the 5 children preferred drawing (represented by the 3 white sections)

2 children out of the 5 preferred painting (represented by the 2 blue sections).

Pie charts are also an excellent way to introduce children to fractions by representing the same data like this:

3/5 or three-fifths preferred drawing

2/5  or two-fifths preferred painting

This can also be extended in to percentages:

1/5 = 20%

3/5 = 3 x 20% = 60%

2/5 = 2 x 20% = 40%

60% of children preferred drawing

40% of children preferred painting.

Pie charts can also become more challenging as each section is worth more than one.

When children are older, they learn how to draw pie charts of their own.

A bar model is a visual way of helping to represent numbers in order to help children to solve problems.  The 'bars' are rectangles that are proportional to the size of the number they represent.  

It has become a popular method in primary schools since adopting the mastery approach to learning

Cuisenaire rods can be used as concrete resources for this.  However bar models are used to help children to move from the concrete to abstract using pictorial representations.

In the case of the example to the left this demonstrates the total is 10.  7 + 3 = 10.

Also that 10 - 3 = 7

10 - 7 = 3

3 + 7 = 10

Line graphs are also used to plot information from charts and tables in order to see patterns that change over time.

At first children will be taught how to get information from line graphs but as they get older they will learn how to draw their own line graphs. These types of graphs provide extra cross-curricular links with science.

They are useful as children can quickly spot trends in results.  For example, the line graph on the right shows that the temperature outside is getting hotter as the day progresses.