A small shepherd boy was responsible for taking 23 sheep to pasture each day. These sheep would graze freely all day, and in the evening the boy was to round them all up and drive them home. Unfortunately, the boy could not count, so each day he had difficulty deciding whether he had found all of the sheep before returning home.
(a)
Devise a method (other than teaching the boy to count) that would make it possible for him to be sure he had all of the sheep.

MOVE ON ONLY WHEN INSTRUCTED!

(b)
The sheep’s owner came up with a simple scheme. It involved making, for each sheep, a string necklace that would fit around the sheep’s neck. In the morning, the boy would take the necklaces and place them all around his own neck. What should he do with them in the evening?
(c)
The “necklace idea” spread throughout the region and soon all the young people tending sheep went to the meadows with string necklaces around their necks. One day, an argument arose between a shepherd and a shepherdess as to which was tending the largest number of sheep. Resolving the argument was made difficult since neither could count. Can you describe a method by which they could resolve their argument while leaving their sheep grazing undisturbed?
(d)
What is possible to determine about two sets if one does not know how to count?

You give Malika some blocks. You tell her,“I’ve given you some blocks. Can you give me the same number of pencils?” How can Malika know she has given you the same number of pencils, without knowing how to count? How would she know if she gave you too many? Too few? Use the definition of one-to-one correspondence to explain your reasoning.

The Japanese counting words are (in order): ichi, ni, san, shi, go, roku, sichi, hachi, kyu. What is the Japanese word for 6? How do you know?
2025-09-03 01:08:36