Make sense of graphs
A) I have seen a distancetime graph created simply with a data logger. The device in question is a motion sensor which shows if an object is moved.
The sensor sends out pulses of high frequency noise and calculates the distance from the time it takes the echo to return.It is similar to the rangefinder of a Polaroid camera. It can give readings in metres or feet, can calculate the distance of an object to within 3mm and can measure distances up to 10m.
It can be bought from Data Harvest (tel: 01525 373666 www.data-harvest.co.uk) and the model you want is called Easy Sense Advanced. You also want a piece of software, Sensing Science Laboratory, which translates the data from the logger into a graphical representation.
The software is eligible for e-learning credits and many schools will have bought a site licence.
Start by drawing a distancetime graph similar to ones you see in textbooks on an interactive white board, such as the example at the top of the next column.
Have this on the board as pupils come in. Invite a volunteer to come to the front and ask them to move forward, backwards or stop as indicated by the graph (harder than it sounds but great fun).
Ask the class to describe the motion for each section, for example: lWhen you move faster, how does the distance-time graph change?
lIf you stand still, what will the distance-time graph of your movement look like?
lIf the distance-time graph is a straight line sloping upwards, how is the velocity changing?
lWhy has the original graph been drawn in straight lines?
lIs this is a true representation of travel?
Ask pupils to sketch the distance-time graph for the following movement.
Starting at 0.5m from the sensor, walk away from it at a constant velocity for 4m, stop for 3 seconds, then run back to the starting position at a constant velocity.
Show them another graph you have prepared earlier. Highlight different sections of it and ask pupils to describe the movement of the person creating the graph. Next, invite another pupil to try to replicate the movements.
Discuss with them how they might work out the average speed from the graph at different times.
Below is a screen shot of a graph created by the motion sensor. The distance (vertical) axis is shown up to 2m from the sensor marked in subdivisions of 0.5metres and the time (horizontal) axis is shown up to 20 seconds marked in subdivisions of 10 seconds, although this is not clear from this much reduced diagram. The user can change the options very simply.
Pupils could create their own versions with the equipment for their friends to copy. A great activity for a maths club too.
Other sensors that might fit into maths are a pendulum and timing gates for accelerations and rotary motion. Data loggers are used extensively in science classrooms - perhaps it is time we used them to collect real data for analysis in the maths classroom.
Can you suggest a starter or lesson ender for a lesson on percentages? My pupils know how to find percentages, but I would like a more unusual introduction or ending to the lesson.
How about multilink cubes or similar? Make some incomplete cubes, tell your pupils you are showing them, say, 20 per cent of the shape, and ask how many cubes for the complete shape (you should rotate the shape so that they can see if there are any hidden cubes).
Next extend this to a shape which is, say 120 per cent. Finally, ask pupils to devise their own problems for the class. If you have a digital camera then you could take photographs of the shapes and let other classes use the questions created by your group.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) www.nesta.org.uk to spread maths to the masses. Email your questions to Mathagony Aunt at email@example.com Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX