Cuisenaire rods are rectangular rods of different lengths and colors used to teach basic mathematical concepts. For example, a white rod is 1 cm long while a red rod is 2 cm long. They can be used to illustrate that 3/4 + 1/2 is equivalent to 5/4 or 1 1/4. To represent 3/4, the student would place a 3-cm light green rod over a 4-cm lavender rod. To represent 1/2, he would place a 1-cm white rod over a 2-cm red rod. He would find the common denominator by adding red rods together and lavender rods together until both rods were the same length. Because it would take 2 red rods to equal 1 lavender rod, he will understand that he must multiply the numerator and denominator of 1/2 by 2 to get 2/4. He will then add 3/4 + 2/4 to obtain an answer of 5/4. By comparing lengths, he should be able to see that 5/4 is equivalent to 1 1/4.
Many children develop their first intuitions about fractions while cooking with their parents. Children can see from looking at a measuring cup that 1/4 is less than 1/3 and that 3/4 is less than 2/3. Have the student measure 2/3 cup of flour. Place the flour in a mixing bowl and let him measure 2/3 cup of flour again. Let him refill the cup with the flour he has measured. He will see that 4/3 cup of flour will fill the measuring cup 1 1/3 times. After he develops a visual, hands-on appreciation of this fact, it is comparatively easy to teach him the method of converting an improper fraction to a mixed number by taking the quotient of the improper fraction and placing it next to the fraction made from the remainder and the denominator.
Comparing areas of sectors is another way of helping students develop a concrete understanding of fractions. Cut several circles of the same size out of construction paper. Cut one circle into halves, another into thirds and yet another into fourths. If a student wants to understand how to convert 3/2 into a mixed number, he can take 3 halves of a circle and understand that they will form 1 whole circle and that half of a circle will be left over. This can be represented as 1 1/2.
Young students have grown up with television and video games. Consequently, they are often frustrated by reading, which is slow and requires sustained attention. Students who enjoy working on the computer can take advantage of an abundance of interactive games designed to teach children how to convert between improper fractions and mixed numbers. This format is often visually appealing and less anxiety-provoking to children because mistakes are corrected by a message on a computer screen and not by a frustrated adult.