TES Top 10 Resources: Averages and Spread

The following collection of resources have been assembled by the TES Maths Panel. They can be downloaded for free by registering on the TES website.

Everybody has their favourite example of how averages don’t really tell you what you want to know or how they are inappropriate for some situations. A deep understanding of averages and spread is important and becomes more important given the ever increasing amount of data. Our challenge is to make statistics and, in particular, averages and spread exciting and applicable to young people!

This top 10 list helps you to find exciting resources to inspire future statisticians.

GCSE maths: Frequency table match-up

Age Range: 11-16 Format: doc

This is a brilliant resource to match frequency tables with their mode, mean and range. I like the suggestion to write statements comparing the three data sets using averages/spread. This could easily be extended by looking into median, IQR, drawing charts from the data, coming up with different sets of data with a e.g. lower mean but higher spread, etc…

GSCE maths: mean, median, mode and range lesson

Age Range: 11-16 Format: PDF

One of my favourite Standard Unit Box activities! Students can work in teams to map cards with bar charts to their respective table with averages/spread. I like the fact that some information is missing and students need to fill the gaps. A great way to finish this activity is to discuss their bar chart(s) to table G – there are different correct answers. This provides a great opportunity to get the students to reason and mathematically justify their answer.

This activity is also a great way to start discussions to link the shape of a distribution with averages and spread.

Revision of average from frequency tables

Age Range: 11-16 Format: doc

This is a great thinking skills ‘sort it out’ activity ideal for revision. It contains exam questions with answers all jumbled up – pupils need to put processes in the correct order and complete the questions. Pupils can recall the method by organising the steps first – a great way to  avoid mainly teacher led activities and instead encourages team discussions.

Comparing data distributions

Age Range: 11-16 Format: web/ppt/xls

This is a great activity to show statistics used in context. Students could in a first step use the data (also provided as spreadsheet) to work out averages – they could even use ICT for this bit and then concentrate on the comparing of the data sets. This activity includes further great suggestions/potential creating box plots and histograms and analysing them.

Averages: haunted house-adventure game

Age Range: 11-16 Format: ppt (to be used on individual computers)

An animated adventure game in which students answer averages questions in order to progress through a haunted house. The author provides great suggestions how to use the game – e.g. students should show full workings of each question in their book. The game ends when they get two wrong – at this stage you could work through the questions with the students individually or even swap books and get students to spot mistakes of their peers.

Averages puzzle game

Age Range: 11-16 Format: ppt

A short activity where students need to interpret information (in form of clues) and use their knowledge of averages to solve the puzzle. This could make a fun starter/plenary activity … or even inspire students to create their own puzzle.

Averages card game

Age Range: 11-16

A touch of competitiveness is sometimes a great way to get students going. This card game (to be played in pairs) is a great way to get the students practising averages/spread. As suggested, it could be extended to an all-class activity at the end to find the averages from a frequency table.

Mean from a frequency table

Age Range: 11-16 Format: doc

I like this worksheet because it’s short and sharp and uses a known concept (the 5 star review system) which will be applicable to many students. This could be in particular useful when discussing misconceptions (e.g. ‘…in this 5 star system, anyone ended up with an average of 7 stars?’). This worksheet could easily be extended to find the other averages, spread, draw charts from the data etc.

Mean challenge

Age Range: 11-16 Format: xls

Great spreadsheet requiring students to enter numbers to give a given mean, mode, median and range. It creates a great opportunity to discuss problem solving skills and opens the doors to lots of rich questions. Could be used as starter to set them up for a similar task or as mini-plenary in-between to check pupils understanding.

Tarsia averages

Age Range: 11-16 Format: fjsw

A Tarsia Jigsaw activity on finding averages and the range is a great resource to ensure lots of practise and foster positive group work and co-operative learning. This tarsia (as every other tarsia) could easily be amended by making adjustments such as removing answers or  making deliberate mistakes. I also always have a stack of ‘empty’ triangles to extend the activity – e.g. this tarsia goes up to averages of 30 – ask students to come up with data sets to find an  average of 31, 32…

Anja Lehmann, Maths Secondary Panel

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