The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Age 11 to 14 Challenge Level:
Look carefully at this video of a tangled light blue ribbon. The
tangle was originally made by the
Twisting and Turning method, but in the video it is manipulated
in a number of ways. Can you explain what is happening? Can you see
some properties of this tangle that the video is trying to
demonstrate? Do you think these properties hold for any tangle?
Can you work out the fraction associated with the tangle in the
video? You'll need to decide on an initial configuration and
orientation, so let's say that:
the zero tangle would have the two ropes parallel to the green
twisting always occurs on the green axis in the direction of
the green arrow;
turns are a quarter turn about the blue axis in the direction
of its arrow.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.