#### Table of Contents

## Teaching Statistics: Learning Objectives

- Interpret and present data using bar charts, pictograms and tables
- To know how to draw pictograms, including those where symbols mean 2, 5 and 10
- To draw block graphs

## National Curriculum

Teaching statistics is part of the UK national curriculum.

Statistics is the collection, organisation and understanding of different types of data. There are many ways we can show data, however in year two and three students are expected to learn the basics of statistics though pictograms, tally charts and block graphs and how to interpret them. For this, they must know how to count to at least 10.

## Why do we use statistics?

Teaching statistics is an important part of a student’s education; it gives them the knowledge to collect data and illustrate it efficiently and understandably. Teachers must teach students that representing/displaying data can be very helpful in problem-solving and maths investigation questions.

We use statistics to understand large amounts of information like for example: “How many cars drove past one street in a month?”, and “How many people took the train to work instead of using a bike this week?”. Teaching statistics can help us process large amounts of information by making it more manageable such as by determining averages or illustrating it in graphs or charts. Using charts and graphs also gives us an insight into how well something is working: “How many people used the school’s car park now it has been re-built?” and “Is there a difference?”.

There are so many things we can do with statistics but for young students, it is essential for them to know the basics of data handling and collecting. Teachers have found that teaching statistics can start with tally charts, pictograms, and block diagrams – you can learn through fun activities in groups or individually.

Here are some ideas of topics that students can collect data from:

- Coloured pencils in the class
- How other students get to school
- Students favourite ice cream
- How many siblings do each student have
- Stationary in the classroom: glue, books, toys…

## Tally Charts

When teaching statistics, teachers usually turn to tally charts first. Tally charts are a good way to collect data quickly and efficiently. It is faster than writing words, and you can place data in sub-groups to be able to analyse data more quickly and easily. What defines a **tally chart **is that it uses **marks** to represent numbers.

When collecting data, students must simply put a tally into the correct box. When the student gets a total of five tallies, the fifth line must be crossed through all four tallies.

This ultimately makes counting the total easier, it also encourages students to calculate figures in their head instead of using their fingers. If we know that there are at least three lots of five, and we also know that 3 x 5 is 15, we know the total of the tallies is 15.

Students can use tally charts to construct bar charts or pictograms.

**How to interpret tally charts: **

By teaching statistics students can interpret tally charts by looking at the column with the tallies. In this case, we have a tally chart with what types of ice cream people like.

We can interpret the chart as follows:

- How many people were asked about their favourite ice cream?
- What is the most liked ice cream? How many did they get?
- What is the difference between the most liked ice cream compared to the least liked?
- How many people liked Ice cream.

*You can explore further by asking students to construct their own chart we have set up an example:*

A classroom of 20 students was asked if they liked the afternoon or mornings better.

15 students said they preferred the afternoon.

5 students said they preferred the morning.

Show this information on a tally chart. The chart should look like this:

## Pictograms

Another way teachers approach teaching statistics is by using pictograms. A **pictograph** is a graph that uses pictures to represent quantity. Pictograms are set out and illustrated the same way as a bar chart, however, a pictogram uses columns instead of bars.

Pictograms are a simple and engaging part of statistics, not just this, some teacher will also use pictograms to introduce other types of graphs to collect data.

To draw a pictogram, teachers should encourage their students to collect data from other students in the classroom. Teachers can then represent the findings in a tally chart which then students can illustrate by creating a pictogram.

**How to interpret pictographs**

Interpreting pictograms can be fairly easy as long as students have read the question correctly.

Pictograms have no visual of numbers therefore some students might be confused about how to calculate a total. Pictograms should always include a key or a formula that will give them the key once they have completed this (However, this approach is not looked at in detail until higher education).

If we consider the key, we can easily work out what each symbol means. There are often symbols with different values, therefore students must pay extra attention to the key provided.

If you are thinking of teaching statistics teachers can explore pictograms further by asking students questions about the graph itself, for example:

- How many more does X have than Z?
- What is the value of symbol X?

## Block Diagram

Students will use **block graphs** – or block diagrams where items are shown on an X-axis – to present data. The number/value of the item is shown on the y axis whereas the item itself is shown on the x axis.

To read a block graph or any graph that has a Y and X axis, we must read the information correctly. To do that, we start reading the data from the X axis before moving on to the Y axis. So, for example:

To read how many hours Jackson has gamed this week, we look at the X axis – where his name should be – and then go up the Y axis to find out how many hours he has been playing for. In this case, Jackson has played a total of fifteen hours.

Drawing block diagrams is another easy process – students simply need to be careful where they put the information and how they illustrate data. Students can then explore their chart further by discussing differences with other classmates and their teacher.

The block graph is made up of separate blocks and students can count the clocks to find out the total of items. *“along the corridor, and up the stairs” *is a great saying for students to remember how to interpret information on block graphs.

## Worksheets:

**We have carefully created two different types of worksheets for your class to follow.**

**Worksheet One** contains basic activities which will allow students to explore statistics with tally charts, pictograms and block charts.

**Worksheet Two** gives students the opportunity to complete their own study by using their data handling skills through tally charts to block graphs.