'Understanding averages' tutor notes

The aim of the Understanding averages topic area is to introduce learners to averages, calculating the mean and finding the range.

There are also some factsheets on the median and mode which are at Level 2 of the curriculum in England, Wales and Northern Ireland. These have been added to complete the subject but can be ignored if learners are interested in working Level 1 only.

Students may find it useful to look at the Written addition and subtraction and Written division sections before starting this module.

We'd love to hear your comments on the module; do you like the activity, what do you think of the worksheets? Send in your and your students' feedback.

How does this tie in with the curriculums?

• England
  HD1/L1.3 - Find the arithmetical average (mean) for a set of data.
  
• Wales
  As England.
• Northern Ireland
  As England.
• Scotland
  See www.aloscotland.com for details of the Scottish curriculum.

In the Skillswise module you'll find:

Understanding averages activity
This is an activity to help learners understand the mean value. The activity is in the form of a bar chart. The bar chart shows weekly shopping expenditure over 5 weeks where you input your own values for the bar chart. When data is in the chart you can calculate the mean. There is also the function to show an animation of the mean. Before showing this activity to your students have a look at the 'How to play' demonstration.

TOP TIP! To see the game completely full screen, press the F11 key on the keyboard. This takes away the distraction of the top browser bar. To bring the browser bar back, just press F11 again!

Understanding averages quiz
The learner can choose their level. Level A is the easiest, level C the hardest.
Students can print out a certificate if they score 50% or more in the quiz. This will appear as a link on the results page - click on the link and the certificate will appear in a new window. Students can write their name on the certificate once it's printed.

Understanding averages factsheets
You'll find curriculum references in the bottom left hand corner of the factsheets.
There are six factsheets for this module at Level 1. Factsheets 7, 8 and 9 are at Level 2.

• Factsheet 1 - What is an average?
• Factsheet 2 - How do you calculate the mean?
• Factsheet 3 - Decimal answers (impossible answers)
• Factsheet 4 - Distorted averages
• Factsheet 5 - Range
• Factsheet 6 - Averages glossary
• Factsheet 7 - Other averages: the median
• Factsheet 8 - Other averages: the mode
• Factsheet 9 - Mean, median and mode together

Understanding averages worksheets
There are six worksheets in total. You'll find curriculum references in the top right hand corner of the worksheets. They are printable resources to carry on the work learners have done online.

• Worksheet 1 - Calculating averages 1. Calculating averages with sets of whole numbers.
• Worksheet 2 - Calculating averages 2. Calculating averages with sets of whole numbers and decimals.
• Worksheet 3 - Calculating averages - problems 1. Problem solving.
• Worksheet 4 - Calculating averages - problems 2. Problem solving.
• Worksheet 5 - Shopping problems 1. A worksheet that can be used with the bar chart activity. Encourage learners to calculate the answers to the sums and then check them using the activity.
• Worksheet 6 - Shopping problems 2. Harder problems for learners to solve.

Technical help:

To get the most out of this topic area you need the following 'plug-ins':

• Flash
  The game in this topic section uses Flash. This is free to download and should only take a few minutes. You can follow the BBC WebWise instructions to download it to your machine.
  Find out more.

If you don't have Flash the same learning points are covered in the quiz and in the worksheets and factsheets.
If you are new to the web, why not try the BBC WebWise online course, Becoming WebWise? It's free, you can do it in your own time from any computer and it will take you through everything you need to know to use the web successfully in your teaching.
Get WebWise.

You can find out more about the technical requirements for Skillswise in our Help - Technical Information section.

Taking it further:

With Skillswise:
Visit the Skillswise Lesson plans section on Handling data (in the Tutor centre). Don't forget to visit Teaching inspirations for more ideas for teaching averages.

On the web:
Here's a suggestion of other places on the web where you might find useful resources for teaching averages.

• "Plop it!"
  Small arrows under this bar chart show the position of the mean, median and mode. You can change the height of the bars and watch the mean, median and mode arrows move accordingly. A good way to see how the three averages differ. This activity can be used to find graphs where one of the averages can be said to be more representative than the others.
• KS2 Bitesize
  Bitesize is a site linked to the Key Stage 2 National Tests. In the Data Handling section there is an activity, printable factsheet, worksheet and a test on the mode, median and mean.
• Smarties investigation
  Scroll down this page on the Adult Basic Skills Resource Centre at Abingdon and Witney College website until you see the Smarties investigation pdf link. Suitable for use with entry level and level one students, this is a fun activity for handling data developed by Di Mellor from Darlington College. And yes, it does involve eating Smarties!

Please note that the BBC is not responsible for the content of other websites.

Do you know of any great online resources for practising averages? Tell us about them!