COUNTING SYSTEMS IN THREE PROVINCES

Joyce Amo, Thomas Podarua, Angela Polikran

Introduction

This is a grade 7 topic based on the Languages of the Sandaun, East New Britain and Madang Provinces. The specific Languages used in this lesson are:

a. Wamoduse – Sandaun Province
b. Kuanua – East New Britain Province
c. Manam – Madang Province

In the Wamoduse language, a base 4 counting system is used, while the Kuanua language uses base 10 and the Manam counting system uses base 5.

During the lesson the students are expected to:

a. Understand the number usage of the Wamoduse, Kuanua and the Manam counting systems.
b. Add and give answers in the Wamoduse, Kuanua and the Manam counting systems.
c. Compare the Bases in the Wamoduse, Kuanua and the Manam Counting Systems.

DESCRIPTION OF THE MATHEMATICS:

The table on the facing page shows the three counting systems of the Wamoduse, Kuanua and the Manam languages in comparison with the English system:

COUNTING IN WAMODUSE (Base 4), KUANUA (Base 10), and MANAM (Base 5)

NUMBER WAMODUSE KUANUA MANAM
1 Opa Tikai Teke
2 Umon-Nu Aurua Rua
3 Ehnu Autul Toli
4 No-oh Aivat Wati
5 No-oh mleng opa Ailima Lima
6 No-oh mleng umon-nu Laptikai Lima be teke
7 No-oh mleng ehnu Lavurua Lima be rua
8 Nu-Ju Lavutul Lima be toil
9 Nu-Ju Mleng Opa Lavuvat Lima be wati
10 Muti Opa Avinun Kulemoa
11 Muti Opa Mleng Opa Avinum ma tikai Kulemoa be teke
12 Muti Opa Mleng Umon-Nu Avinum ma aurua Kulemoa be rua
13 Muti Opa Mleng Ehnu Avinum ma autul Kulemoa be toil
14 Muti Opa Mleng No-oh Avinun ma aivat Kulemoa be wati
15 Muti Opa Mleng No-oh Opa Avinun ma ailima Kulemoa be lima
16 Muti Opa Mleng No-oh Mleng Opa Avinun ma laptikai Kulemoalima be teke
20 Muti Umon-Nu Aura vinum Tamoata di teke
24 Wali Yam Muti Tamoata di teke be wati

In the Wamoduse language which uses a base 4 counting system, notice that the base acquires a base word which is No-oh or 4, but at certain numbers the word base changes. That is at 8, 9, 10 and 24. The word Mleng (connective word) means a left over from 4 which is the base.

Example: 5 is No-oh Mleng Opa which is 4 and one left over from 4.

In the Kuanua Counting System notice that the numbers from 6 to 9 have common words as in 1 to 4.

Example: 1 is Tikai and 6 is Laptikai. So the word Tikai is common in 1 and 6. This doesn’t mean that it is a base 5 Counting System. It is a base 10 Counting System. Notice that the counting system acquires the base word which is Avinun at 10. At every multiple of 10, the base word changes.

Example: 10 is Avinun, 20 is Auravinun, 30 is Autulavinun and so on.

The word “ma” is the same as “and” or “plus” in English or Mathematics languages respectively.

Example: Avinun ma Tikai which is 10 and or plus 1.

In the Manam language, the Counting system is a base 5. The Counting System acquires its base word at 5, which is Lima. To continue counting from 6 to 9, the base is retained and the connective word “be” meaning “and” or adding the numbers 1 to 4 to the base which is five.

Example: 6 is Lima be Teke which is 5 and or plus 1.

You will realize that the base word changes at 10, 15, 20, 30, 40 etc… For example 10 is Kulemoa, 15 is Kulemoa Lima, 20 is Tamoata di Teke, 30 is Tamoata di Teke be Kulemoa and 40 is Tamoata di Rua. At 20 the connective word “di” means multiplication. It multiples 20 by the number from 1 to 5. Example: 20 is Tamoata di Teke which is 20 x 1, 40 is Tamoata di Rua which is 20 x 2 etc……

CONCLUSION:

The lesson is based on the counting system of the three languages. It can be taught at any grade level. Thus the counting system is not the only concept in the Papua New Guinea traditional mathematics. There are other mathematical concepts in traditional Papua New Guinea. For example: The Kuanua Money Value System from the Sandaun Province and so on. The three counting systems in the Wamoduse, Kuanua and the Manam languages are used especially in counting. While other mathematical concepts use different bases and words to describe their values. For example; measurements have their own words and base to describe a certain length.

LESSON PLAN

TOPIC: LANGUAGE OF MATHEMATICS: COUNTING SYSTEM (GR. 7)

OBJECTIVES:

The students will be able to:

a) convert the Metric system to bases four, five, and ten in the Wamoduse, Kuanua and Manam counting systems respectively.
b) Do addition in the three counting systems
c) distinguish the three different bases in the three languages
d) change the Wamoduse counting system into kina and toea

INTRODUCTION:

Teacher’s Activities
- Ask students to count in their own languages from 1 to 10
- Identify the base of the students’ counting systems
- Introduce Topic:
Language of Mathematics – Counting System
- Base 4 is in the Wamoduse Language
- Base 5 is in the Manam Language
- Base 10 is in the Kuanua Language.

Student’s Activities
- students count
- listen to the teacher

BODY:

Teacher’s Activities

Angela

- Explains the Wamoduse base 4 counting system.
Gives example 1) Convert 6 to Wamoduse Language
- Add 3 and 4 to give 7 using the Wamoduse language
eg. 6 = NO-OH MLENG UMONU
3 + 4 = 7 EHNU MLENG NO-OH WHICH IS NO-OH MLENG EHNU
(The base comes first)

Thomas

- Explains Manam base 5 counting system
Gives examples:
1) Convert 6 to Manam language.
6 is Lima be teke
2) Add 6 and 5 to give 11
Lima be teke be lima will give “Kulemoa be teke”
Joyce:

- Explains Kuanua base 10 Counting System.
Gives examples:
1) Convert 11 to Kuanua language
11 is Avinun ma Tikai
2) Add 10 and 3 to give 13
Avinun ma Autul = Avinun ma Autul

Break students into three groups.

Group 1 – Wamoduse language
Group 2 – Manam language
Group 3 – Kuanua language

Explain what each group is to do. (refer to demonstration by Angela, Thomas and Joyce)

Each of the 3 teachers supervises one group.
- Pin the problem on the board
- Ask students to come forward and ask them to present their answers.

Student’s Activities
- Listen to the teacher
- Look at the chart
- Listen to the teacher
- Look at the chart
- Listen to the teacher
- Get into three groups
- Work on the problem
- Representative from each group come and present answers
- Compare answers
- Listen to the teacher

CONCLUSION:

Teacher’s Activity:
- give an example:
Convert 12 to the Wamoduse, Kuanua and the Manam languages.

Student’s Activity:
- Wamoduse – Muti opa Mleng Umon-Hu
- Kuanua – Avinun ma Aurua
- Manam – Kulemoa be Rua

MATERIALS:
- Charts
- Cards

Angela and Joyce: Present Money System (Wamoduse & Kuanua)
This is done for interest!