Linear functions: Experimental approach

by Irini Perissinaki

Here we are, at the basketball court yard,
students from Spain, Finland and Greece

...together with our teachers.

Worksheets are handed to us

A fellow student is reading the fable
"The crow and the pitcher"

and another one translates it in Greek

We are asked to form small groups
of 4-5 students.

and perform an experiment with a tube

filled half way with water.

We drop marbles inside it
and measure the water's level.

We write down our observations.

Each time the waterlevel raises
by the same amount.

This is really interesting.

We shortly discuss it.

We all do so well!

So close to the end!

Now the water level is at 120 mm,
the target level!

After dropping 12 marbles inside.

We are ready for the graph.

We plot the points carefully.

Wow! Its a line!

We got a line too!

A few more questions to fill.

Short discussion and we get
one more worksheet.

Three students to fill three pots
a ball, a cone and a pyramid

Same amount of water
but different water level

We carefully examine
all three water levels.

So low at the ball!

We are now ready to pick
the correct graphs.

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Monday 11^th to Friday 15^th of April was certainly a week of great action. 10 students from Finland and 9 from Spain had come to visit us, as participants to the Erasmus+ program “EL ESPAÑOL, PASAPORTE ENTRE CULTURAS”. We, being the hosts, had arranged quite a lot of events to welcome them.

On this frame, an experimental approach to linear functions was planned for Wednesday 13^th of April 2016. Right after the morning assembly, all students of A3 Class, together with our visitors, arranged themselves to the basketball court to get action.

The crow and the pitcher activity

The crow and the pitcher

pen In a spell of dry weather, when the Birds could find very little to drink, a thirsty Crow found a pitcher with a little water in it. But the pitcher was high and had a narrow neck, and no matter how he tried, the Crow could not reach the water. The poor thing felt as if he must die of thirst.

Then an idea came to him. Picking up some small pebbles, he dropped them into the pitcher one by one. With each pebble the water rose a little higher until at last it was near enough so he could drink.

Moral: Necessity is the mother of invention.

The lesson was based on the fable “The crow and the pitcher” in which a crow raised the water level in a pitcher by throwing inside small pebbles. Students were instructed to repeat the task by throwing marbles inside a pluviometer. They should raise the water level from 100 mm to 120 mm. As they added the marbles one by one, they kept notes for the water level and then plotted it as a function of the number of the marbles. This function was linear and its explicit formula was to be found. They all did so well in this task!

The three curves activity

In the second part, the pluviometer was replaced by other pots: a sphere, a square pyramid and a cone (stand on their peaks) and the marbles by small amounts of water (same for all three solids), injected to them. Again, students would focus on the water levels, which were not linear functions of the water amount injected, as indicated from the three graphs plotted on their worksheet. But which graph corresponds to which solid? Students managed to unravel this riddle. Can you?

Teaching matterial and team work

The crow and the pitcher fable
Activities ("The crow and the pitcher" and "The three curves")
Team work: completed worksheets

GeoGebra files (cone-pyramid-ball.ggb and demonstration.ggb)