Panitia Matematik

METRIC SYSTEM

2010-06-25T18:34:00.000-07:00

Measuring Metrically with Maggie

Wow, I just flew in from planet Micron. It was a long flight, but well worth it to get to spend time with you!

My name is Maggie in your language (but you couldn't pronounce my real name!)

When I first arrived I couldn't understand how you measure things, but my friend Tom taught me all about measurement, and I am going to share with you everything he taught me.

The first thing Tom told me was that you can measure things using two different systems: Metric and US Standard.

Today is my day to learn Metric !

Tom says that if I understand 10, 100, and 1000 then I will have a very easy time learning the metric system. I wish I had ten fingers!

Liquids

Since it was such a long flight, the first thing I could use is something cold to drink.

But I want to know how much to ask for! So I can get a drink that is not too big or too small.

Tom says I only need to know about:

Milliliters
Liters

A milliliter (that is "milli" and "liter" put together) is a very small amount of liquid.

Here is a milliliter of milk in a teaspoon.

It doesn't even fill the teaspoon!

Tom says if you collect about 20 drops of water, you will have 1 milliliter:

20 drops of water makes about 1 milliliter

And that a teaspoon can hold about five milliliters:

1 full teaspoon of liquid is about 5 milliliters

Milliliters are often written as ml (for short), so "100 ml" means "100 milliliters".

But a milliliter is definitely not enough for someone who is thirsty! So Tom told me about liters.

A liter is just a bunch of milliliters put all together. In fact, 1000 milliliters makes up 1 liter.

1 liter = 1,000 milliliters

This jug has exactly 1 liter of water in it.

Liters are often written as L (for short), so "3 L" means "3 Liters".

Milk, soda and other drinks are often sold in liters.

Tom says to look on the labels, so the next time you are at the store take a minute and check out how many liters (or milliliters) are in each container!

Now I know that a milliliter is very small, and a liter is like a jug in size, I think I will ask for half a liter of juice!

So this is all you need to know:

1 Liter = 1,000 Milliliters

Mass (Weight)

Next I wanted to eat some chocolate ... so I should learn about mass. You often call it "weight", but it is only because of the gravity on your planet that items have weight!

Tom tells me that to understand mass, I should know these three terms:

Grams
Kilograms
Tonnes

Grams are the smallest, Tonnes are the biggest.

Let’s take a few minutes and explore how heavy each of these are.

Grams

A paperclip weighs about 1 gram.

Hold one small paperclip in your hand. Does that weigh a lot? No! A gram is very light. That is why you often see things measured in hundreds of grams.

Grams are often written as g (for short), so "300 g" means "300 grams".

Tom tells me a loaf of bread weighs about 700 g

Kilograms

Once you have 1,000 grams, you have 1 kilogram.

1 kilogram = 1,000 grams

A dictionary has a mass of about one kilogram.

Kilograms are great for measuring things that can be lifted by people (sometimes very strong people are needed of course!).

Kilograms are often written as kg (that is a "k" for "kilo" and a "g" for "gram), so "10 kg" means "10 kilograms".

When you weigh yourself on a scale, you would use kilograms. Tom weighs about 40 kg. How much do you weigh?

But when it comes to things that are very heavy, we need to use the tonne.

Tonne

Once you have 1000 kilograms, you will have 1 tonne.

1 tonne = 1,000 kilograms

Tonnes (also called Metric Tons) are used to measure things that are very heavy.

Things like cars, trucks and large cargo boxes are weighed using the tonne.

This car has a mass of about 2 tonnes.

Tonnes are often written as t (for short), so "5 t" means "5 tonnes".

Final thoughts about masst:

1 kilogram = 1,000 grams

1 tonne = 1,000 kilograms

Length

Measuring how long things are, how tall they are, or how far apart they might be are all examples of length measurements.

Tom says I should know about:

Millimeters
Centimeters
Meters
Kilometers

The smallest units of length are called millimeters.

A millimeter is about the thickness of a plastic id card (or credit card).

Or about the thickness of 10 sheets of paper on top of each other.

This is a very small measurement!

Centimeters

When you have something that is 10 millimeters, it can be said that it is 1 centimeter.

1 centimeter = 10 millimeters

A fingernail is about one centimeter wide.

You might use centimeters to measure how tall you are, or how wide a table is, but you would not use it to measure the length of football field. In order to do that, you would switch to meters.

Meters

A meter is equal to 100 centimeters.

1 meter = 100 centimeters

The length of this guitar is about 1 meter

Meters might be used to measure the length of a house, or the size of a playground.

Kilometers

When you need to get from one place to another, you will need to measure that distance using kilometers. A kilometer is equal to 1,000 meters.

The distance from one city to another or how far a plane travels would be measured using kilometers.

Final thoughts about measuring length:

1 centimeter = 10 millimeters

1 meter = 100 centimeters

1 kilometer = 1000 meters

Temperature

I was feeling a bit hot, so I asked Tom how to measure temperature.

So he showed me a thermometer. But I saw 2 sets of numbers!

Tom explained that a thermometer measures in degrees (°) of either Celsius or Fahrenheit.

"Why two scales?", I asked.

Tom said that some people like one scale and some like the other, and that I should learn both!

He then gave me an example: when water freezes the thermometer shows:

0 degrees Celsius on the left side,
but on the right side it shows 32 degrees Fahrenheit.

So there can be two numbers for the same thing!

He gave me more examples.

A hot sunny day might have a temperature of 30 degrees Celsius but would be 86 degrees in Fahrenheit.
Water boils at 100 degrees Celsius or 212 degrees Fahrenheit.
And you can bake cookies in your oven at a temperature of 180 degrees Celsius, but that would be 356 degrees Fahrenheit.

I decided to get my own thermometer, so I would learn about all this.

I hope you enjoyed learning all about metric measurement.

Now I must return home. Keep measuring until I see you again!!!!!!!!!

DECIMALS

2010-06-25T18:05:00.001-07:00

Decimals

A Decimal Number (based on the number 10) contains a Decimal Point.

Place Value

To understand decimal numbers you must first know about Place Value.

When we write numbers, the position (or "place") of each number is important.

In the number 327:

the "7" is in the Units position, meaning just 7 (or 7 "1"s),
the "2" is in the Tens position meaning 2 tens (or twenty),
and the "3" is in the Hundreds position, meaning 3 hundreds.

"Three Hundred Twenty Seven"

	As we move left, each position is 10 times bigger!
	From Units, to Tens, to Hundreds

... and ...

As we move right, each position is 10 times smaller.
From Hundreds, to Tens, to Units

But what if we continue past Units?

What is 10 times smaller than Units?

¹/₁₀ ths (Tenths) are!

But we must first write a decimal point, so we know exactly where the Units position is:
"three hundred twenty seven and four tenths"

And that is a Decimal Number!

Decimal Point

The decimal point is the most important part of a Decimal Number. It is exactly to the right of the Units position. Without it, we would be lost ... and not know what each position meant.

Now we can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this example:

Large and Small

So, our Decimal System lets us write numbers as large or as small as we want, using the decimal point. Numbers can be placed to the left or right of a decimal point, to indicate values greater than one or less than one.

17.591
	The number to the left of the decimal point is a whole number (17 for example)

As we move further left, every number place gets 10 times bigger.

	The first digit on the right means tenths (1/10).

	As we move further right, every number place gets 10 times smaller (one tenth as big).

Definition of Decimal

The word "Decimal" really means "based on 10" (From Latin decima: a tenth part).

We sometimes say "decimal" when we mean anything to do with our numbering system, but a "Decimal Number" usually means there is a Decimal Point.

Ways to think about Decimal Numbers ...

... as a Whole Number Plus Tenths, Hundredths, etc

You could think of a decimal number as a whole number plus tenths, hundredths, etc:

Example 1: What is 2.3 ?

On the left side is "2", that is the whole number part.
The 3 is in the "tenths" position, meaning "3 tenths", or 3/10
So, 2.3 is "2 and 3 tenths"

Example 2: What is 13.76 ?

On the left side is "13", that is the whole number part.
There are two digits on the right side, the 7 is in the "tenths" position, and the 6 is the "hundredths" position
So, 13.76 is "13 and 7 tenths and 6 hundredths"

... as a Decimal Fraction

Or, you could think of a decimal number as a Decimal Fraction.

A Decimal Fraction is a fraction where the denominator (the bottom number) is a number such as 10, 100, 1000, etc (in other words a power of ten)

So "2.3" would look like this:

And "13.76" would look like this:

1376

100

... as a Whole Number and Decimal Fraction

Or, you could think of a decimal number as a Whole Number plus a Decimal Fraction.

So "2.3" would look like this:

and

And "13.76" would look like this:

and

100

Those are all good ways to think of decimal numbers.

Let's learn

2010-06-25T18:01:00.000-07:00

Polyhedron

A polyhedron is a solid with flat faces (from Greek poly- meaning "many" and -edron meaning "face").

Each flat surface (or "face") is a polygon.

So, to be a polyhedron there should be no curved surfaces.

Examples of Polyhedra:

Triangular Prism	Cube	Dodecahedron

Common Polyhedra

	Platonic Solids
	Prisms
	Pyramids

Counting Faces, Vertices and Edges

If you count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron, you can discover an interesting thing:

The number of faces plus the number of vertices minus the number of edges equals 2

This can be written neatly as a little equation:

F + V - E = 2

It is known as the "Polyhedral Formula", and is very useful to make sure you have counted correctly!

Let's try some examples:

This cube has: 6 Faces 8 Vertices (corner points) 12 Edges
F + V - E = 6+8-12 = 2

This prism has:

5 Faces
6 Vertices (corner points)
9 Edges

Let's find the volume of cuboid

2010-06-25T17:55:00.000-07:00

Volume of a Cuboid

A cuboid is a 3 dimensional shape.
Therefore to work out the volume we need to know 3 measurements.

Look at this shape.

There are 3 different measurements:

Height, Width, Length

The volume is found using the formula:

Volume = Height × Width × Length

Which is usually shortened to:

V = h × w × l

Or more simply:

V = hwl

In Any Order

It doesn't really matter which one is length, width or height, so long as you multiply all three together.

Example: What is the volume:

The volume is:

4 × 5 × 10 = 200 units³

It also works out the same like this:

10 × 5 × 4 = 200 units³

Mathematics Link..

2010-02-20T20:19:00.000-08:00

http://www.mathsisfun.com/link-to-us.php

--> link di atas memang seronok. Dapat menambahkan pengetahuan dan pembelajaran yang baru.

Multiplication Table

2010-02-20T20:06:00.000-08:00

How to Learn
Your life will be a lot easier when you can simply remember the multiplication tables. So ... train your memory! First, use the table above to start putting the answers into your memory.Then use the Math Trainer - Multiplication to train your memory, it is
specially designed to help you memorize the tables.

Use it a few times a day for about 5 minutes each, and you will learn your tables.

Try it now, and then come back and read some more ...

So, the two main ways for you to learn the multiplication table are:
1.) Reading over the table
2.) Exercising using the Math Trainer

But here are some special "tips" to help you even more:

Tip 1: Order Does Not Matter

When you multiply two numbers, it does not matter which isfirst or second, the answer is always the same.
Example: 3×5=15, and 5×3=15
Another Example: 2×9=18, and 9×2=18
In fact, it is like half of the table is a mirror image of the other!
So, don't memorise both "3×5" and "5×3", just memorise that "a 3 and a 5 make 15" when multiplied.
This is very important! It nearly cuts the whole job in half.

In your mind you should think of 3 and 5 "together" making 15.
so you should be thinking something like this:

Tip 2: Learn the Tables in "Chunks"

It is too hard to put the whole table into your memory at once. So, learn it in "chunks" ...

A -->Start by learning the 5 times table.

B -->Then learn up to 9 times 5.

C -->Is the same as B, except the questions are the other way around. Learn it too.

D --> Lastly learn the "6×6 to 9×9" chunk

Then bring it all together by practicing the whole "10 Times Table"
And you have learnt your 10 Times Table!
(We look at the 12x table below)

Some Patterns
There are some patterns which can help you remember:
2× is just doubling the number. The same as adding the number to itself.
2×2=4, 2×3=6, 2×4=8, etc.

So the pattern is 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
(And once you remember those, you also know 3×2, 4×2, 5×2, etc., right?)
5× has a pattern: 5, 10, 15, 20, etc. It always end in either a 0 or a 5.
10× is maybe the easiest of them all ... just put a zero after it
10×2=20, 10×3=30, 10×4=40, etc.
9× has a pattern, too: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

Now, notice how the "units" place goes down: 9,8,7,6, ...? And at the same time, the "tens" place goes up: 1,2,3,...?

You can use this pattern to prompt your memory this way: the tens place will be 1 less than what you are multiplying by!

Example: 9×7 ... go 1 less than 7, so the tens place is 6, and then remember 63

PELIK TAPI BENAR

2009-08-10T22:03:00.000-07:00

Angka 8 yang luar biasa

Semua perkara dalam kehidupan manusia, sama ada baik atau buruk, adalah ditentukan oleh usaha sendiri. Angka atau nombor tidak ada kaitan untuk menentukan tuah, atau sebaliknya. Tetapi hal ini agak berlainan pula bagi seorang presiden Barrios dari Guatemala. Angka 8 menjadi suatu kebetulan yang tragis bagi dirinya. Beliau telah dibunuh pada pukul 8.00 malam, 8 Februari 1898, di alamat No.8, di Jalan 8. Suatu kebetulan yang cukup luar biasa!

TOKOH MATEMATIK - ARCHIMEDES - JURUTERA DAN TOKOH MATEMATIK TERKENAL

2009-08-10T21:44:00.000-07:00

Pernahkah adik-adik mendengar cerita tentang kisah seorang ahli matematik berlari tanpa memakai apa-apa pakaian? Hal ini sudah tentulah memang sangat melucukan! Peristiwa ini berlaku pada suatu zaman dahulu. Namun, oleh sebab peristiwa ini ganjil dan melucukan, tidak hairan jika peristiwa ini menjadi kisah yang popular sampai sekarang. Ahli matematik itu bernama Archimedes. Archimedes merupakan salah seorang tokoh yang terkemuka dalam sejarah perkembangan ilmu matematik dan kejuruteraan di dunia. Beliau berbangsa Greek. Dilahirkan pada tahun 287 Sebelum Masihi. Sepanjang hayatnya, beliau ialah seorang ahli matematik dan jurutera terkenal di tanah kelahirannya itu. Sejarah mencatatkan terdapat satu cerita yang menarik tentang diri beliau. Pada suatu ketika, Raja Syracuse telah memberikan emas kepada seorang tukang emas. Baginda menitahkan tukang emas itu menyiapkan sebuah mahkota. Apabila siap, berat mahkota itu memang sama berat dengan berat emas yang diberikan oleh baginda dulu. Namun, baginda mengesyaki tukang emas itu mungkin telah menipu baginda. Tukang emas itu mungkin mencampurkan perak dan merkuri (raksa) pada mahkota tersebut. Oleh yang demikian, baginda menitahkan Archimedes menyelesaikan masalah itu. Sudah tentulah Archimedes bersedih hati kerana tidak tahu bagaimana hendak menyelesaikan masalah itu. Setiap hari, Archimedes asyik memikirkan masalah itu. Suatu hari, semasa hendak mandi, beliau masuk ke dalam kolam mandi yang penuh dengan air. Apabila beliau masuk, sebahagian daripada air itu melimpah keluar. Kejadian itu memberikan akal kepada beliau untuk menyelesaikan jawapan tentang masalah berat mahkota tersebut. Oleh sebab terlalu gembira, Archimedes terus berlari ke istana sambil menjerit, "Eureka! Eureka!" (Saya sudah jumpa! Saya sudah jumpa!). Sedangkan pada ketika itu, beliau tidak berpakaian. Semasa hidupnya, Archimedes banyak mencipta mesin yang digunakan dalam peperangan. Banyak hasil fikiran beliau dalam bidang matematik dan sains masih digunakan sampai sekarang. Beliau meninggal dunia pada tahun 12 Sebelum Masihi.

Subtraction Without Regrouping - Borrowing

2009-06-18T19:29:00.000-07:00

As you know each digit of a number in our number system has a different place value (ones, tens, hundreds, thousands, etc)

Always subtract within the same place value column when subtracting numbers.
Subtraction is to find the difference.

Example:

85 - 54 = ?

Step 1

Show the kids that the problem has four columns: a ones column and a tens column.

Tens Ones

Step 2

Place the number to be subtracted below the first number, so that the tens and ones places are lined up as shown in step 3.

Draw a line under the bottom number.

Step 3

Write the problem in the columns

Tens Ones
8 5
- 5 4

Step 4

First, subtract the ones

Tens Ones
8 5

- 5 4

_____________

1

Next, subtract the tens

Tens Ones

8 5
- 5 4
_____________
3

Answer : 85 - 54 = 31

In this teaching, I am sure now you can get the answer to the problem of 85 – 54 with this two digit subtraction without borrowing which is 31 with absolutely no problem.

Subtraction Without Regrouping

2009-06-18T19:24:00.000-07:00

In subtracting one number from another, arrange the numbers according to the place values and carry out the operation column by column from right to left.

When two or more numbers are to be subtracted successively. It must be carried out in steps subtracting two numbers at a time.

There are few steps for teaching kids subtraction without regrouping within 1000.
1. First shows how to subtract using a place value chart. The following number sentence is given:
849 − 32 = ?

2. Rewrite the number sentence in a place value chart:

3. Complete the number sentence

849 - 32 = 817

What is subtraction?

2009-06-18T19:22:00.000-07:00

Subtraction is one of the four basic arithmetic operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with.

Subtraction is denoted by a minus sign in infix notation.

PPSMI: Penilaian masuki peringkat akhir

2009-06-18T19:15:00.000-07:00

Oleh ZULKIFLI JALIL dan SITI MAISARAH SHEIKH ABDUL RAHIM

Status quo dasar Pengajaran dan Pembelajaran Sains dan Matematik dalam Bahasa Inggeris (PPSMI) akan dimuktamadkan dalam beberapa minggu lagi.

Timbalan Perdana Menteri, Tan Sri Muhyiddin Yassin berkata, Kementerian Pelajaran yang diketuainya kini di peringkat akhir membuat penilaian terhadap kedudukan dasar itu sebelum taklimat mengenainya dibentangkan kepada Perdana Menteri, Datuk Seri Najib Tun Razak.

Tegas beliau, penilaian mengenai PPSMI akan mengambil kira pelan yang komprehensif, pandangan semua pihak serta sistem pendidikan negara.

Saintis Islam dalam bidang Matematik

2009-04-28T19:58:00.000-07:00

September
Matematik -- Sumbangan ilmuan Islam
MENURUT sejarah, zaman kegemilangan umat Islam dalam bidang ilmu ialah antara kurun ke-7 hingga 13. Salah satu bidang ilmu yang sangat tersohor ketika itu ialah matematik.
Tokoh-tokoh ilmuan Islam telah menyumbang dan mencipta pelbagai perkara baru dalam bidang Matematik seperti sistem perpuluhan dan operasi-operasi asas matematik yang mempunyai kaitan dengan soal-soal tambah, pengurangan, darab, bahagi dan eksponen.
Tokoh-tokoh matematik Islam juga memperkenalkan konsep `kosong’ dalam dunia matematik. Selain itu, mereka juga telah membangunkan konsep-konsep dan fungsi trigonometri; sin, kos dan tangen pada kurun ke-10.
Di bawah adalah tokoh-tokoh matematik Islam yang tersohor.
Al-Khawarizmi (780 - 850)
AL-KHAWARIZMI
Nama penuhnya ialah Muhammad Ibn Musa Al-Khawarizmi dan dikenali sebagai bapa algebra.
Beliau pakar dalam bidang matematik dan astronomi.
Antara buku-buku terkenal hasil tulisan beliau ialah Hisab Al-Jabr wal Mugabalah (Buku Pengiraan, Perbaikan dan Pengurangan) dan Algebra.
Pada kurun ke-12, Gerard of Cremona dan Roberts of Chester telah menterjemahkan buku algebra Al-Khawarizmi ke dalam bahasa Latin.
Terjemahan ini digunakan di seluruh dunia sehinggalah kurun ke-16.
Al-Kharkhi
AL-KHINDI
Al-Kharkhi atau nama penuhnya, Abu Bakr ibn Hussein dilahirkan di Kharkh, sebuah kawasan di Baghdad, Iraq.
Kepakaran dan sumbangan beliau meliputi aritmetik, algebra dan geometri.
Hasil tulisannya, Al-Kafi fi Al-Hisab (Kepentingan Aritmetik) adalah mengenai peraturan-peraturan pengiraan.
Al-Khindi (801-873)
Nama penuhnya ialah Abu Yusuf Yaqub Ibn Ishaq Al-Khindi. Antara sumbangan besar Al-Khindi ialah mengenai 11 teks yang menerangkan mengenai nombor dan analisis nombor.
Al-Battani (850-929)
AL-BATTANI
Al-Battani atau Muhammad Ibn Jabir Ibn Sinan Abu Abdullah adalah bapa trigonometri dan dilahirkan di Battan, Damsyik. Beliau putera Arab dan juga pemerintah Syria.
Al-Battani diiktiraf sebagai ahli astronomi dan matematik Islam yang tersohor.
Beliau berjaya meletakkan trigonometri pada tahap yang tinggi dan merupakan orang pertama yang menghasilkan jadual cotangents.
Al-Biruni (973-1050)
Beliau adalah antara orang yang pertama meletakkan asas kepada trigonometri moden.
Al-Biruni merupakan ahli falsafah, ahli geografi, astronomi, fizik dan ahli matematik.
AL-BIRUNI
Selama 600 tahun sebelum Galgeo, Al-Biruni telah membincangkan teori putaran bumi tanpa paksinya yang sendiri.
Al-Biruni juga telah menggunakan kaedah Matematik untuk membolehkan arah kiblat ditentukan dari mana-mana tempa

INTRODUCTION OF TWO DIMENSIONAL SHAPES

2009-04-27T18:27:00.000-07:00

PPSMI

2009-03-31T23:59:00.000-07:00

Wajarkah PPSMI diteruskan untuk tahap 1 di sekolah rendah?