Next, have students fold the same piece of paper in half horizontally to create six squares. Now ask the students what fraction this represents - four sixths. Because the shaded portion has remained equal, the fractions two thirds and four sixths are equivalent fractions. (Syracuse University, 2002).

Another useful manipulative would be to give students a sheet of paper with several circles on it. Each of the circles will be the same size, but divided into a different number of equal sections (2, 4, 6 and 8 sections). For the circle divided into two sections, ask students to shade in one half. For the circle divided into four sections, ask students to shade in two fourths. For the circle divided into six sections, ask students to shade in three sixths. For the circle divided into eight sections, ask students to shade in four eighths. Students will be able to see that the same amount of each circle is shaded in - explain that this is because all of those fractions are equivalent.

Students will be able to easily move from the concrete manipulative examples to the actual procedure of finding equivalent fractions. ...

(TeacherVision, 2008). Already understanding the relationship between multiplication and division, students should also be able to identify that you can divide both the numerator and denominator by the same number to produce an equivalent fraction in smaller numbers, or simpler terms.

That being said, the process of finding equivalent fractions involves the multiplication or division of the numerator and denominator of a fraction by the same number. This process allows for the addition and subtraction of fractions with uncommon denominators. Because we know that multiplying the numerator and denominator of a fraction by the same number will produce an equivalent fraction, we can do this to make an equivalent fraction with the same denominator as the fraction it needs to be added to, or subtracted from. Sometimes the numbers in both fractions will need to be multiplied to produce the least common denominator. To know which number to multiply the numerator and denominator by to produce the least common denominator, students must understand the concept of factors. For example, in the mathematical problem 2/3 + 1/2, the least common denominator is 6, because it is the lowest possible number that both 3 and 2 are factors of. To produce a denominator of 6 in both fractions, 2/3 must be multiplied by 2/2, and 1/2 must be multiplied by 3/3. The result is the addition of two fractions that are equivalent to the first fractions and share a common denominator: 4/6 + 3/6 = 7/6.

Students will be provided with the following set of problems to determine whether they have moved from the concrete to the representational:

1. List four fractions that are equivalent to 1/2.

2. Which of the following fractions is NOT equivalent to 3/4

a.
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