Task A: First generate all proper fractions whose denominator is 100.

When given the box

the Next Numerator robot should give the bird 99 boxes:

…

The robot can be trained to give the bird one box and will stop when the scale stops tilting towards the number 100.

If you need help training Next Numerator ask for pictorial instructions.

Task B: Use the Next Numerator robot to make other sequences of fractions.

Predict. What sequence does Next Numerator produce when given

Write your answer here before running it.

Test. Was the result what you expected?

What sequence is produced when you change the number in the Denominator box to some other number, say 89?

Generalise. Explain in general what Next Numerator does.

Task C: Generate all denominators

Train a robot named Next Denominator that will change the box so that Next Numerator will work on the next denominator when finished. If you get stuck ask for the pictorial instructions.

Put Next Denominator and Next Numerator together to form a team. Package up your team in a box like this

and save your work.

If the All Fractions team of robots ran forever would the bird ever be given two identical boxes (the same numbers as the other one)?

Explain.

Do you think all the proper fractions will be generated if the robots ran forever?

If so, how would you convince a friend?

If not, can you give a proper fraction that will not be generated?

Are there boxes that will be generated that are equivalent to this box?

If so, give a few examples.

Task D: No repeated fractions

Load the No Copies team into ToonTalk. (It can be found in the Infinity section of the Tools section of the WebLabs web site.) Connect it to All Fractions with a bird and nest.