Two students were discussing unit fractions, that is, fractions like 1/2, 1/3, 1/4, 1/5, etc., with 1 in the numerator.
One student thought the fractions become larger as the denominators increase and the other thought the fractions become smaller. Explain what you would do to help them with this disagreement.
To help the students understand the relationship between the unit fractions and their denominators, you can use visual aids and examples.
1. Visual aids: Draw a number line and label it with the unit fractions, starting from 1/2, then 1/3, 1/4, 1/5, etc. Leave enough space between each fraction for comparison purposes. This will allow the students to see the fractions in order and intuitively understand their placement on the number line.
2. Examples: Use concrete examples to show that as the denominators increase, the unit fractions actually become smaller. Take specific fractions, such as 1/2, 1/3, and 1/4, and ask the students to divide a whole object (e.g., a pizza, a chocolate bar) into those equal parts. They will quickly see that the more parts the whole is divided into, the smaller each part becomes.
3. Common denominator: You can also introduce the concept of a common denominator to reinforce the idea that as the denominators get larger, the fractions become smaller. Take two fractions like 1/2 and 1/3, and explain that if we wanted to compare them visually, we can convert them to a common denominator like 6. Explain that when both fractions have the same denominator, it becomes clear that 1/3 is smaller than 1/2.
4. Mathematical reasoning: Encourage the students to think about the mathematical reasoning behind fractions. Remind them that the denominator represents the number of equal parts the whole is divided into. As the number of equal parts increases (bigger denominator), each individual part becomes smaller. Therefore, the fraction with a larger denominator represents a smaller part of the whole.
By using these strategies, the students should be able to gain a better understanding of the relationship between unit fractions and their denominators, and resolve their disagreement.