Time Swing

Task 85 ... Years 4 - 8

Summary

The story context on the card catches attention, then, rather than explain how to set up an experiment, the card sets challenges. Students have to decide what the experiment is, how it might be set up, how to measure and the meaning of what is measured. Yes, it's an open-ended approach but students are likely to learn more and teachers are likely to learn more about students.

Materials

• Length of string and 3 steel nuts
• Watch, stop watch or other timing device supplied by the school

Content

• defining terms and agreeing on meaning
• measurement of length and time
• dependent and independent variables
• experimental design
• collecting, recording and interpreting data
• generalisation

Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

In Question 1 the students are going to first have to agree on what swing means - over and back? - around in a circle? - or over and back in the same plane? They will also have to find their working area, improvise a pivot point for the pendulum and agree on how they will measure. Making these decisions, carrying out the experiment and dealing with any difficulties that develop, sets up the background for the other challenges on the card.

In essence the task is built around the mathematician's question What happens if...? In this case:

• What happens if we change the length of the pendulum?
• What happens if we change the mass on the end?
• What happens if we change the angle through which the pendulum is first raised?
and how to control changing the variables to find out.

It involves a considerable amount of time measurement in seconds, measurement of the length of the pendulum and the application of average. It can develop into an extensive investigation and is easily adapted to a whole class situation. Some students will make their pendulums by slipping the nut onto the string and doubling the string to capture it at the centre. Others will want to tie their string from the highest point in the classroom.

What should be discovered is that only the length of the string affects the period of the pendulum (period meaning a swing over and back). Changing the mass doesn't change the period, nor does changing the angle of release (provided that small angles up to say 30 degrees are used). Students are also likely to meet this experiment in science or physics at some stage and learn that the mathematical result describing simple pendulum motion is:

where T = period, L = length of pendulum, g and are constants. The details of this formula don't particularly matter in the context of this task, but it does confirm that the period is directly related to the length, ie: length and period are the only variables involved.

Beyond the experiments on the card, students could research pendulums in popular science books and gather examples (if only in photo form) of pendulums in clocks, metronomes and other practical situations. If an interest in 'science-like' investigations has developed another one could be to experiment with distance travelled when a toy car is released from the top of a ramp. What happens if we change...?

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

This task is easy to set up as a whole class situation since lengths of string and various size nuts are easily obtainable. Most children will have suitable watches. Working in groups of three is about right and it is valuable to facilitate class discussion as data unfolds. It will be important to ask How have we worked like a mathematician? and there is also an opportunity to model how to write a report to others of what was investigated and what was discovered.

At this stage, Time Swing does not have a matching lesson on Maths300.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Time Swing task is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Chance & Measurement Years 9 & 10