MULTIPLICATION BY 10 AND 100 IN THE TARI REGION

Michael Warako, Winis Yupi, Joan Fiyava.

INTRODUCTION

In every society in Papua New Guinea, people in one way or the other used some form of Mathematics in their daily life. In fact, this was done without realizing that some mathematics was involved in anything they did. They were not conscious of what they did as it was in their daily activities. Consider, for instance, the Moka system in the highlands. During this particular ceremony, pigs, kina shells, traditional salt and many others, were lined up and counted in their own dialect before presenting them to whomever they intended to give them to. In the same manner, in the following pages, we will talk about some of the traditional mathematics used by the Tari people of the Southern Highlands Province in their counting systems in terms of concrete objects. The entire province has more than 7 languages and as a result, traditional mathematics varies from language to language. In the Tari language there are four operations involved in the traditional mathematics of performing their daily activities. However, addition and multiplication are used more often than division and subtraction.

DESCRIPTION OF MATHEMATICS

There are many aspects of modern mathematics involved in any event that people are engaged in; even though they may not understand what they do, the mathematical concepts are used but not realized. The four operations mentioned earlier are involved but unnoticed. The table below explains the link between the traditional mathematics in the counting system. Some selected counting numbers from both of these areas are compiled in the following, tabulated below to show the relationship.

NORMAL TRAD. TARI NORMAL MODERN

Mbira ……………………………………………………………… 1
Kira……………………………………………………………….… 2
Teperia………………………………………………………….… 3
Maria………………………………………………………………. 4
Turia…………………………………………………………….... 5
Warakaria……………………………………………………….… 6
Karia………………………………………………………………… 7
Halira……………………………………………………………..… 8
Tiria………………………………………………………………..… 9
Pira……………………………………………………………….… 10
Pira Ni Mbira……………………………………………………. 10+1=11
Pira Ni Kira…………………………………………………….... 10+2=12
Pira turia Ni Mbira…………………………………………….. 10*5+1=51
Pira Turia Ni Kira…………………………………………….… 10*5+2=52
………… . etc…………
Pira Pira Mbira……………………………………………..…. 10*10*1=100
Pira Pira Mbira Ni Mbira…………………………………... 10*10*1+1=101
Pira Pira Kira…………………………………………………… 10*10*2=200
Pira Pira Tepira………………………………………………. 10*10*3=300

NOTE: ‘NI’ MEANS ADDITION (+)

Example. 1. Pira Ni Halira = 10 + 8 = 18
2. Pira Teperia Ni Warakaria = 10*3+6=36

NOTE ALSO THAT WHERE THERE IS NO ‘NI’ IT INVOLVES MULTIPLICATION (x)

Examples: 1. Pira karia = 10*7 = 70
2. Pira Pira Teperia = 10*10*3 = 300

BASE TEN TRAD. TARI BASE TEN MODERN

Pira Mbira…………………………………………………… 10*1=10
Pira kira ………………………………………………..….. 10*2=20
Pira Tepira……………………………………………….... 10*3 = 30
Pira Maria ……………………………………………..….. 10*4 = 40
Pira Turia ………………………………………………….. 10*5 = 50
Pira Warakaria………………………………………….... 10*6 = 60
Pira Kairia ……………………………………………..….. 10*7 = 70
Pira Halira ……………………………………………..….. 10*8 = 80
Pira Pira ………………………………………………….…. 10*10 = 100

Pira Pira Kira …………………………………………..…. 10*10*2 = 200
Pira Pira Tepira…………………………………………... 10*10*3 = 300
Pira Pira Maria ……………………………………….…… 10*10*4 = 400

NOTE: WHEN NUMBERS ARE NOT BEING SEPARATED BY THE WORD ‘NI’ THEN THERE IS MULTIPLICATION INVOLVED. (REFER TO ABOVE TABLE)

Activity

Find the products of the following.

1. (a). 10*2 =
(b). 10*10*2 =
(c). 10*5*10 =
(d). 7*10*10 =
(e). 10*10*10 =

2. Write the above expression in Tari language.

(a)………………………………………………………………………………..
(b)………………………………………………………………………………..
(c)………………………………………………………………………………..
(d)………………………………………………………………………………..
(e)………………………………………………………………………………..

EXPLANATION

when and where unnoticeable mathematics were used, there never existed any figures in the Tari traditional mathematics. In substitution of figures such as 1, 2, 3, 4…. etc, they just used words in their language when they counted certain material goods. There was no abstract counting. People counted with real and concrete materials, for example: one pandanus was counted as “Mbira” or two pigs were counted as “Kira” in the Tari language. See above table.

Mbira and Kira by themselves cannot act as a traditional counting system if there were not concrete objects/materials in general. The objects like pigs or pandanus are concrete that allow Mbira and Kira to be the traditional counting number. Comparing this with the modern counting system, the counting numbers, (1, 2, 3, 4,….. etc.) are abstract. Thus traditional people would not understand, although the modern mathematics learners would understand the abstract idea.

TEACHING PLAN

In teaching the topic: Multiplying by tens (10’s) and hundreds (100’s) from the 7A maths text book (page 49), we will relate it to the base ten (10) counting system of the traditional mathematics of the Tari language. However, to begin teaching the topic of multiplication by tens and hundreds we will first consider the normal (modern) decimal numbers and identify what they mean. This will be futher explained with the aid of the normal key notes.

After explaining the table of Tari numbers, we will proceed to fig. 2. This in fig. 2 will then be further explained with the assistance of the base ten key notes.

The Modern concept of multiplying tens (10’s) and hundreds (100’s) is as follows:

PRODUCT THINK WRITE

7*80 7*8*10 560
10*200 10*2*10*10 2000
10*50 10*10*5 500

The traditional Tari concept of multiplying tens (10’s) and hundreds (100’s) within the counting system are as follows. From the tables listed earlier we can form multiplicative combinations from:

TENS

Pira mbira = 10*1 = 10
Pira kira = 10*2 = 20
Pira Repira = 10*3 = 30
Pira Karia = 10*7 = 70

HUNDREDS

Pira Pira Mbira = 10*10*1 = 100
Pira Pira Tepira = 10*10*3 = 300
Pira Pira Turia = 10*10*5 = 500
Pira Pira Pira = 10*10*10 = 1000

NOTE: Pira Pira Pira = 1000

CONCLUSION

Traditional counting systems involved many modern mathematical ideas especially the four major mathematical operations as explained above. Each and every counting number in the traditional counting sequence is a result of forming numbers by means of addition, multiplication and division without realizing it. Therefore we would like to make a strong recommendation that different language groups in PNG for whom modern mathematics is not their language or culture, should learn their own traditional counting system in their own languages first in pre-schools or “Tok Ples Skuls” before they proceed to primary and secondary schools and to learn modern mathematics.

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