Counting in groups
Count in twos, fives, tens or twenties and write less.
Counting in twos
The Gumulgal people of Australia counted in twos. Their words: 1 = urapon, 2 = ukasar, 3 = ukasar-urapon (2 + 1), 4 = ukasar-ukasar (2 + 2).
How would the Gumulgal say 6?
What this lesson covers
The idea
Counting in groups of a certain size, and using the word or symbol for that group size to represent bigger numbers, is more efficient than tallying; common group sizes have been 2, 5, 10 and 20.
Counting in twos
The Gumulgal people of Australia counted in twos. Their words: 1 = urapon, 2 = ukasar, 3 = ukasar-urapon (2 + 1), 4 = ukasar-ukasar (2 + 2).
How would the Gumulgal say 6?
- ukasar-ukasar-ukasar
- ukasar-urapon
- urapon-urapon-urapon
Group the pebbles
There are 23 pebbles. Choose a group size. Count the marks you need: one for each full group and one for each pebble left over.
One symbol for a whole group
Counting in groups of a certain size, and using the word or symbol for that group size to represent bigger numbers, is more efficient than tallying; common group sizes have been 2, 5, 10 and 20.
Gumulgal: 3 = 2 + 1, 4 = 2 + 2, 5 = 2 + 2 + 1, 6 = 2 + 2 + 2.
Most people cannot tell at a glance how many objects there are in a group of 5 or more. That may be why the Roman system counts in 5s.
Notes
Counting in groups of a certain size, and using the word or symbol for that group size to represent bigger numbers, is more efficient than tallying; common group sizes have been 2, 5, 10 and 20.
Check yourself
5 = 2 + 2 + 1 is ukasar-ukasar-urapon. How many times does ukasar (two) appear in the Gumulgal name for 6?
Answer: 3
6 = 2 + 2 + 2, so the name is ukasar-ukasar-ukasar: 3 times.
Count 23 pebbles in groups of 5. How many pebbles are left over?
Answer: 3
23 = 5 + 5 + 5 + 5 + 3. There are 4 groups and 3 pebbles left over.
How many marks do you need to write 30 pebbles in groups of 10?
Answer: 3
30 = 10 + 10 + 10. Three marks instead of thirty.
Why is counting in groups better than a tally?
- A tally needs one mark for each object. One group symbol stands for many objects. — correct. Yes! Counting in groups needs far fewer marks.
- Groups make the number of objects smaller. The number of objects does not change. Only the way we write it does.
- A tally cannot be used at all. A tally works, but it needs as many marks as objects.