# See-Saw

### Task 58 ... Years 2 - 7

#### Summary

Students create a see-saw and explore balancing objects of different masses. The challenge is to make statements and draw diagrams that summarise the experience. For example:
Light things can balance heavy things if the heavy things move in and the light things move out.

#### Materials

• Your own ruler and a block to make a see-saw
• Objects to balance such as a washer, bolt, pencil, nut, stone, pop-stick, wooden cube

#### Content

• informal investigation of weight and mass
• concept of balance/equality
• basic arithmetic calculations
• reporting an investigation

#### Iceberg

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

The task is quite an open-ended exploration. Who knows what will be discovered?

There is a relationship behind what happens and it is expressed mathematically as M = Fd, where M = Moment (or Torque), F = Force at a distance d from the fulcrum (or balance point). The force in this case is downward and described as the weight of the object. Balancing happens when the Moment of one object is equal to the Moment of the other.

Example
If one object is exerting a force of 2 units at a distance of 6 units from the fulcrum, and the other object has a weight of 4 units, then it would have to be placed 3 units from the fulcrum (and on the other side) to effect a balance.
No one is expecting Year 2 students to express their understanding in this way, but an explanation such as:
Light things can balance heavy things if the heavy things move in and the light things move out.
or
If two things are the same you have to balance them the same distance out.
displays understanding of the essence of the system. It is also the principle behind the Number Equaliser in many classrooms - a balance on which students hang masses to explore equations.

The objective of the task is to encourage students to explain - orally, then in written word and picture - what they have discovered. Questions which might encourage this are:

• Tell me what you have found out so far?
• How did you discover that?
• If you had a real see-saw and a big fat kid and a little skinny kid, where would you place them to get a balance?
• Suppose I gave you two wooden cubes that where exactly the same, where would you place them to get a balance.
• Suppose I gave you three wooden cubes that were exactly the same, where would you place them to get a balance?
• The wooden cubes are over there. Experiment with them to see what you can find out.
• Do the measurement on the ruler help?
• What could you do to make your experiment more accurate?

#### 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.

It only takes each pair of students to have a ruler and the teacher to have a variety of objects for this activity to be a whole class investigation. But it need not be that all students work on it at the same time. It works well in an activity corner too.

You might be surprised at the outcome. A teacher at one remote Aboriginal school was.The playground had a real see-saw. After this task was used in class she found students of all ages gathered around it balancing younger students against older ones.

At this stage, See-Saw 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 See-Saw task is an integral part of:

• MWA Chance & Measurement Years 3 & 4