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Ways of counting in local languages and different cultures

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 4

WHOLE NUMBERS AND THEIR RELATIONSHIPS

Module 5

WAYS OF COUNTING IN LOCAL LANGUAGES AND DIFFERENT CULTURES

Activity:

To describe and illustrate various ways of counting in local languages and different cultures throughout history [LO 1.2]

Now you are going to explore the world of number names and symbols to see how our number system developed.

1. NUMBER NAMES

1.1 You have been using numbers and counting on and counting backwards. See if you can remember the names for the numbers in some of our South African languages. In the table below write the name of a local language most commonly used in your area. Now write in the words in that language for numbers 1 to 10.

Table 1
Numbers English ………………………. Afrikaans
1 One   Een
2 Two   Twee
3 Three   Drie
4 Four   Vier
5 Five   Vyf
6 Six   Ses
7 Seven   Sewe
8 Eight   Ag
9 Nine   Nege
10 Ten   Tien

1.2 GROUP WORK

When children learn to count, they chant the numbers and move rhythmically to the music. Get together with some friends and make up a rap song to count from 11 to 20 in any South African language. Present this song to the rest of the learners.

1.3 Now write number names of another local language most used in your area. Also write the name of the language in the space provided in the second column.

Table 2
Numbers Other local language Numbers Other local language
11   16  
12   17  
13   18  
14   19  
15   20  

1.4 Try to find out the names for the following numbers and write them in the correct columns:

Table 3
Numbers Other local language English Afrikaans
100      
1 000      
10 000      

CHECKLIST: Number names

Table 4
  Yes No
1.1 I have written in number names for 1 to 10 in a local language that is used most in my area.    
1.2 I have made up a rap song to count from 11 to 20 with my friends. We performed it for the rest of the learners.    
1.3 I have written in number names for 11 to 20 in a local language that is used most in my area.    
1.4 I have found out and written in the names for 100; 1 000 and 10 000.    

ASSIGNMENT

You may do this in your own time, at school and/or at home, as your educator decides.

NUMBER SYMBOLS: READING and RESEARCH

(Research is when you need to look up information and use it to answer questions. Ask your educator to take you to the library to do the research in this section or use the computer to look up information on the Internet.)

READ: The following information tells you about counting systems. Now test your skills by answering the questions that follow.

2. Pre-history: People in ancient times

Thousands of years ago, before people could write, they had no knowledge of numbers and figures and they had to find ways of indicating how many animals or possessions they had. They put a small pebble in a bag for every animal they possessed, or carved notches on a stick.

  • Why did people start to need numbers?
  • Draw a stick with notches carved on it to show that the owner possessed 5 sheep.

2.3 Besides carving notches on a stick, what else did they use to show how many animals they possessed?

Ancient civilizations

3. The Babylonians

Many years later, people used signs or symbols to represent numbers. The Babylonians who lived in Mesopotamia made wedge-shaped notches in wood or pressed such marks into damp clay tablets.

RESEARCH: Ask your librarian to help you to find books with pictures and information about the Babylonians and their wedge-shaped writing.

3.1 Now see if you can draw a clay tablet with the following numbers in wedged-shaped writing: 1; 5; 10; 100; 1 000. Beneath each Babylonian number, write our number. (Use your researched information to do this.)

3.2 What was this wedge-shaped writing of the Babylonians called? Ask the librarian to help you to find the name in one of the books in the library.

4. The Romans

The Romans used a system that reminds one of the habit of counting on one’s fingers. One finger, for instance, represented number one. The V formed between the thumb and fingers of an open hand represented 5. To write their numbers, they used letters.

4.1 See if you can fill in the missing explanations of some Roman numbers:

Table 5
Roman numbers Explanation Our numbers
I   1
II   2
III   3
IV One less than five 4
V Shape made between thumb and fingers of open hand 5
VI One more than five 6
VII Two more than five 7
VIII Three more than five 8
IX One less than ten 9
X Crossed hands or arms 10

The Romans made great use of “more than” and “less than”.

4.2 See if you can complete the following by using the previous table:

Table 6
Roman numbers Explanation Our numbers
  One more than ten 11
  Two more than ten 12
  Three more than ten 13
  One less than fifteen 14
  Ten and five 15
  One more than fifteen 16
  Two more than fifteen 17
  Ten and eight 18
  One less than twenty 19
  Double ten 20

Certain letters represented larger numbers:

Table 7
50 60 90 100 500 1 000
L LX XC C D M

4.3 What number did the Roman “C” represent?

Table 8
(Note: In measurement 100 cm = 1metre)    

4.4 What number did the Roman “M” represent?

Table 9
(Note: In measurement 1 000 mm = 1 metre)    

5. The Ancient Egyptians

The Egyptians used a system of picture writing or pictography. The Egyptians’ picture numbers looked like this:

Figure 1
Figure 1 (Picture 3.png)

5.1 Study it carefully. The Romans used V and X a great deal. What number did the Egyptians use to write many of their numbers?

  • How did the Egyptians write 88? (Use the pictures above.)
  • Now try to write 10 257 as the Egyptians would write it. (Maybe our number system is not so bad after all!)

Our numbers do not look at all like those of the Babylonians or the Romans or the Ancient Egyptians, so from whom did we get our numbers?

6. The Hindu-Arabic symbols

At one stage they looked like this:

Figure 2
Figure 2 (Picture 4.png)

We obtained our 1; 2; 3; 4; 5; 6; 7; 8; 9 from the Arabs. Our “0” came from the Hindu people in India, via the Arabs, who adopted it. How would we cope without the “0”! Imagine trying to write two thousand and ten in numbers without any “0s”.

MENTAL CALCULATIONS TEST 1

Do you know these number combinations smaller than 20?

Table 10
1 9  3 =………………………………. 11 7 － 4 =………………………………..
2 7  5 = 12 8 － 3 =
3 8  7 = 13 11 － 5 =
4 0  5 = 14 17 － 8 =
5 7  9 = 15 1 － 0 =
6 6  8 = 16 13 － 8 =
7 4  8 = 17 14 － 9 =
8 6  5 = 18 17 － 9 =
9 6  7 = 19 13 － 4 =
10 4  7 = 20 16 － 7 =

MENTAL CALCULATIONS TEST 2

Revise combinations with larger numbers:

Table 11
1 48+ 9 =…………………………… 11 37 － 4 =…………………………….
2 68 + 7 = 12 1 001－ 3 =
3 87 + 9 = 13 43 － 5 =
4 55 + 9 = 14 66 － 8 =
5 90 + 90 = 15 1 － 0 =
6 50 + 60 = 16 83 － 8 =
7 80 + 50 = 17 35 － 9 =
8 17 + 8 + 6 = 18 170 － 90 =
9 54 + 8 + 7 = 19 130 － 40 =
10 94 + 4 + 7 = 20 160 － 70 =

MENTAL CALCULATIONS TEST 3

Replace * with the correct relationship sign: =; ; <

Table 12
1 9 + 6 * 7+ 8………………………. 11 9 – 5 * 4 + 0…………………………
2 2 + 9 * 6 + 6 12 6 + 7 * 9 + 4
3 13 – 9 * 11 – 8 13 11 – 7 * 14 – 8
4 15 – 7 * 13 – 5 14 12 – 8 * 4 + 2
5 5 + 8 * 6 + 7 15 9 + 5 * 6 + 8
6 13 – 6 * 11 – 4 16 6 + 9 * 7 + 7
7 2 – 0 * 2 + 3 17 15 – 6 * 17 – 9
8 9 + 7 * 8 + 7 18 7 + 8 * 8 + 6
9 17 – 8 * 15 – 7 19 6 + 14 * 36 – 16
10 1 – 0 * 1 + 0 20 15 – 6 * 34 – 25

MENTAL CALCULATIONS TEST 4.

1. Write down the missing numbers:

1.1 468 = …….. hundreds + …… tens + ……. units

1.2 2 350 = ….. thousands + …… hundreds +……… tens + 0 ………

1.3 8 642 = …… thousands + …….hundreds + …….tens + …..units

  • 7 thousands + 9 hundreds + 6 tens + 1 unit = ……………………….
  • 1 ten thousand = ………………………………

2. Write down the number that is:

2.1 one more than 999 ………………

2.2 five less than 101 ……………..

2.3. between 48 and 50 …………….

  • greater than one thousand and less than one thousand and two
  • ten fewer than 9 000

3. Write down the missing numbers:

  • If 7 + 8 = 15, then 17 + 8 = ……… and 70 + 80 = …………….
  • If 6 + 7 = 13, then 16 + 7 = ……… and 16 + 13 = ………..
  • If 14 – 6 = 8, then 140 – 60 = ………. and 16 + 8 = ……….

4. Encircle the largest number: 1 010; 1 001; 1 100

5. What number is 99 more than 9 901? ………………

6. What is the value of the 3 in the number 3 456?…………….

7. What number is 2 less than 1 001?……………………..

Assessment

Table 13
Learning outcomes(LOs)
 
LO 1
Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.
Assessment standards(ASs)
 
We know this when the learner:
1.1 count forwards and backwards in a variety of intervals (including 2s; 3s; 5s; 10s; 25s; 50s and 100s) between 0 and 10 000;
1.2 describes and illustrates various ways of counting in different cultures (including local) throughout history;

Memorandum

ACTIVITY – WAYS OF COUNTING

1. NUMBER NAMES

  • ICS to supply numbers 1 to 10 inclusive in eleven official languages.
  • Oral group work
  • ICS to provide numbers 11 to 20 inclusive in eleven official languages.
  • ICS to provide numbers: 100; 1 000 and 10 000 in eleven official languages.

ASSIGNMENT

2.1 They had to count their animals and possessions.

2.2 Drawing

2.3 They put a stone in a bag for each animal or possession.

3. Babylonians

3.1 Drawing

3.2 cuneiform writing

4.1 one; double one; three

4.2 XI; XII; XIII; XIV; XV; XVI; XVII; XVIII; XIX; XX

4.3 100

4.4 1 000

5. The Ancient Egyptians

5.1 I

5.2 see diagram

5.3 see diagram

6 The Hindu-Arabic symbols

Discussion

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