Learn Fractions With Cuisenaire RodRod Cuisenaire adalah sekumpulan rod/batang yang mempunyai bentuk segi empat tepat/rectangular, dengan setiap rod/batang mempunyai warna dan panjang yang berbeza. Rod yang terkecil adalah 1 cm panjang dan rod yang terpanjang adalah 10 cm.Cuisenaire rod juga tidak semestinya diperbuat daripada batang kayu atau plastik, tetapi guru juga boleh membuat improvisasi dengan kertas warna dengan panjang yang berbeza. Berikut adalah contoh rod dan warna mereka.

white = 1 cm.red = 2 cm.light green = 3 cm.purple = 4 cm.yellow = 5 cm.dark green = 6 cm.black = 7 cm.brown = 8 cm.blue =9 cm.orange = 10 cm.

Learn Fractions with Cuisenaire RodsUsing Cuisenaire Rods to name a FractionCara standard untuk menunjukkan pecahan dengan Rod cuisenaire adalah dengan meletakkan sebatang rod ke atas/disebelah rod yang lain untuk membandingkan saiz mereka. Rod boleh ditunjukkan secara menegak atau melintang seperti yang akan ditunjukkan dibawah.Misalnya;Arrange your rods to represent1/2and3/4using the purple rod as the denominator. In order to represent1/2using the purple rod as the denominator we must first express the fraction in equivalent terms. Since 2 red rods in a train equals 4 cm. we must multiply the numerator and denominator by 2 red rods.Take the numerator 1 * 2 red rods = 2Take the denominator 2 * 2 red rods = 4So representing1/2using the purple rod as the denominator equals2/4as shown below.2/4=Now, in order to represent3/4using the purple rod as the denominator. Since 1 purple rod equals 4 cm. we must multiply the numerator and denominator times 1 purple rod.Take the numerator 3 * 1 purple rod = 3Take the denominator 4 * 1 purple rod = 4So representing3/4using the purple rod as the denominator equals3/4as shown below.3/4 =

Learn Fractions with Cuisenaire RodsIdentify the Numerator and DenominatorCara standard untuk menunjukkan pecahan dengan Rod cuisenaire adalah dengan meletakkan sebatang rod ke atas/disebelah rod yang lain untuk membandingkan saiz mereka. Rod boleh diletakan secara melintang atau menegak. Rod pertama daripada pasangan rod pecahan adalah pengangka manakala rod yang kedua ialah penyebut.Misalnya, = 1/2 = 2/3 = 4/3 = 3/2Contoh Lembaran KerjaTuliskan pecahan yang diwakili rod.

1. = 2. =

Learn Fractions with Cuisenaire RodsLeast Common Denominator Cari LCD bagi pecahan dan 1/3. Pilih rod yang mewakili kedua-dua penyebut iaitu 2 diwakili oleh rod merah dan 3 diwakili rod hijau. Bina sambungan(rod yang dicantumkan) rod merah dan sambungan bagi rod hijau sehinggalah panjang mereka adalah setara. Setelah itu, kira panjang bagi setiap sambungan tersebut. 3 rod merah adalah bersamaan dengan 6 cm, dan 2 rod hijau adalah bersamaan dgn 6 cm. Oleh itu, LCD adalah 6. .

Let's try another example:Find the least common denominator for the fractions1/4and2/3. The denominator4will be represented by the purple rod and the3will be represented by the light green rod. Now we make our trains.

As shown above3purple rods = 12 cm. and4light green rods = 12 cm.

Learn Fractions with Cuisenaire RodsEquivalent FractionsWhen two fractions are equal in overall quantity or value they are called equivalent fractions. We can say that two fractions are considered equivalent when it can bedemonstratedthat each fraction can be used to represent the same amount of a given object.To Demonstrate an Equivalent Fraction: Equivalent fractions can best be shown bytrains(rods lined up end-to-end) of the same length. In comparing any set of trains showing equivalent fractions, the train with the smallest number of rodsrepresentsthe fraction in itslowest terms. There may be severalgroupsof equivalent fractions for each unit.For Example:Let's say the brown rod which represents 8 cm. is theunit(meaning it is equal to 1). We can show the following 3 equivalent fraction groups.

EQUIVALENT GROUP 1:

In the above example, the two fractions shown are equivalent to each other. This is evidenced by their equal length. In the equivalent fraction group 1, we used the white and red rods because both can be evenly divided into 8. We know there are no other fractions that belong in this equivalent group because there are no other rods equal in length to 1 red rod and 2 white rods.The numerator of each fraction is the number of rods used in the fraction. The denominator of each fraction is the number of rods that would be used if the train was equal in length to the unit. For example, in the first fraction of the equivalent fraction group 1, the numerator of2/8is the number of white rods used in the fraction (2) and the denominator of2/8is the number of white rods that would be needed to equal the unit in length (8). In the second equivalent fraction, the numerator of1/4is the number of red rods used in the fraction (1) and the denominator is the number of red rods (4) that would be required to equal the unit length.The following is another equivalent fraction group representing the unit 8.EQUIVALENT GROUP 2:

In equivalent group 2 we use the purple rods in addition to the white and red rods because the purple rods can also be divided into 8 evenly. As you can see the numerators of all 3 fractions are equal in length and the denominators are also equal in length.As stated above, the train with the smallest number of rods represents the fraction in its lowest terms. The fraction1/2is the fraction in its lowest terms.EQUIVALENT GROUP 1:In review we will use rods that are equal in length and that divide evenly into 10.

The fraction1/5is the fraction in its lowest terms.

Learn Fractions with Cuisenaire RodsAdding and Subtracting Fractions Before we add and subtract fractions we must find theLeastCommonDenominator (LCD). If theLeastCommonDenominator(also sometimes calledLeastCommonMultiple) is not obvious, we can always find the unit by finding the shortest rod that is a multiple of each denominator. Once we find theLeastCommonDenominator each fraction in the problem must be converted to an equivalent fraction expressed in terms of the common denominator (common terms) in order to be added together..

For Example:To add the fractions1/2 + 1/3we must first choose rods which represent both of the denominators. Just as in our example on finding the LCD, the denominator2would be represented by the red rod and the denominator3would be represented by the light green rod. Now create atrain(rods lined up end-to-end) of red rods and a train of light green rods until they are equal in length. (These trains are also known as multiples).Once you have created trains equal in length total the number of centimeters in each train. As shown below 3 red rods = 6 cm. and 2 light green rods = 6 cm. Therefore, the common denominator is6.

Now we must change each fraction into the terms of the common denominator. To do this, the numerator of each fraction must be mulitplied by the number of rods it takes to find theLeastCommonDenominator.1/2= Take the numerator 1 * 3 red rods =3/61/3= Take the numerator 1 * 2 light green rods =2/6Once you have the common terms just add your numerators.3/6+ 2/6=5/6is your answer.Now let's try a subtraction problem:1/2- 1/8= First we must find acommon denominator.We'll look at the unit or denominator to decide which rods to use. In this case red for2and brown for8will be used. Next we will make a train until we have rods of equal length.

We find that the common denominator is8in this case. We could keep stacking the red and browns together and find other common denominators, but remember we're looking for theLeastCommon Denominator.1/2=Take the numerator 1 * 4 red rods=4/81/8=Take the numerator 1 * 1 brown rod=1/8Once you have the common terms just subtract your numerators.4/8- 1/8=3/8is your answer.