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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?

  • 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:

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

  • 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

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

Questions & Answers

What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Berger describes sociologists as concerned with
Mueller Reply
Read about ancient clocks like_ hour glass, water clock and sun dial for a quiz and hand on Activity in the class
Neha Reply

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Source:  OpenStax, Mathematics grade 4. OpenStax CNX. Sep 18, 2009 Download for free at http://cnx.org/content/col11101/1.1
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