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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:
| 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:
| 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:
| 50 | 60 | 90 | 100 | 500 | 1 000 |
| L | LX | XC | C | D | M |
4.3 What number did the Roman “ C ” represent?
| (Note: In measurement 100 cm = 1metre) |
4.4 What number did the Roman “ M ” represent?
| (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:
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?
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:
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?
| 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:
| 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: =; ;<
| 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
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 …………….
3. Write down the missing numbers:
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?……………………..
| 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; |
ACTIVITY – WAYS OF COUNTING
1. NUMBER NAMES
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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