I was working with a teacher today preparing a sequence of work on data handling. We were keen to develop a sequence which got the pupils (who are working between 3A and 5C) talking about and interpreting the data. We were not looking to avoid data collection and graph drawing entirely but the emphasis is on stretching this group of mathematicians.
Our key focus was on identifying opportunities to present and interpret data to answer related questions. This will then lead to the pupils developing and posing further questions.
The stimulus we chose¬†for this work was the Olympics and as¬†I wanted to personalise the work I suggested we went for the Javelin competition. This video will open the work with a discussion of how the javelin final worked.
It will be keen for the children to understand that there were 12 competitors in the final, 4 of whom went out after 3 throws and 8 of whom went through to throw a total of six throws.
When looking at using data from international competitions it is always worth looking to Wikipedia as it is an amazing source of Olympic data.
Using the data from the final I copied the table below which to suit our needs has each throw rounded to the nearest whole metre rather than being to two decimal places.
¬†¬†¬†¬†¬†¬†¬†I am sure that looking at this you will be able to think of many different approaches to take but¬† this is what we went for. For ease and speed I am going to bullet point them.
- ¬†The pupils will find the mean of each athlete’s throws (no throws are marked as X and will not be counted)
- Next the children will construct simple line graphs showing the mean throws. The X axis will be the competitors by name or number of their final position and the Y axis will be the distance thrown. (Pupils will need to make sensible choices about where to start the Y axis and the increments of numbers)
However thanks to Susie Arnott I have realised that this is mathematically incorrect as it shows links between each throw which are actually discrete data. It would be more create to show the data on a scattergraph or some form of bar chart.
- The children will then answer questions about the data. We anticipate that they will find it mystifiying that Kovals (who came 2nd) only ranks 5th with his mean throws.
- Pupils will be asked to rank the athletes by mean throws
- Other tasks will also be finding the range, ranking by their first, last or shortest throws.
- Finally we also looked at really pushing the most able pupils and will ask them to make or write a commentary of the final. I try to ask children to tell the story of data and so this presented a perfect opportunity to do this. In the activity the children will be given opportunities to risk take and show their knowledge. They will use the data from the top eight athletes and represent them in the way that they think is the most effective. The teacher will question, prompt and probe without leading the children in their decision making.
- We anticipated that some children will create a line graph with eight different line graphs to represent each throw by¬† each athlete whilst other might record the positions after each round.
- This will then lead to further questions and explanations.
The next step would be to take the children out onto the field to recreate the final with foam javelins. We decided that the children might need to start on an imaginary 60 metre line to compete with the Olympians.
I hope that this is useful!