*Explain how to teach fourth-grade students the concept of equivalence when working with fractions with unlike denominators (finding equivalent fractions).*

*1. List at least three prerequisite skills to working with fractions with unlike denominators.*

*2. Explain how the concept of finding equivalent fractions could be introduced using manipulatives.*

*3. Describe the steps for finding equivalent fractions.*

*4. Describe how you would help students transition from concrete manipulatives to more representative paper-and-pencil problems.*

*5. Provide at least six equivalent fraction problems you would use to test whether students have transitioned from concrete manipulatives to representative paper-and-pencil problems.*

When learning about equivalent fractions, it is important that a student understands the definition of the denominator and the numerator in order to understand which comes first. This allows the students to know what number precedes the other. They should also understand addition and division of whole sets to fractions and how this forms equivalent fractions from the whole set. Students should also understand the local common denominator and how it can be used in calculating the whole set into equivalent fractions.

Manipulatives are fundamental in when it comes to understanding fractions because students are able to have a clear mental picture of how fractions work. They include paper folding activities, circles, counters as well as Cuisenaire rods Teachers can use manipulatives at all levels of learning to enhance the understanding of fractions. Instructors can use manipulatives to introduce concepts generating equivalent fractions to promote understanding (Spitzer & Roddick, 2008).

Equivalent fractions are those that have similar values. The first step is involves multiplication of both the numerator and denominator by a whole nonzero number. The numerator and denominator must be multiplied by the same number to come up with equivalent fractions. For example:

1/3*4/4=4/12

1/3*5/5=5/15

Therefore, 1/3, 4/12 and 5/15 are equivalent fractions.

The concrete level is the basic level of knowledge. Manipulatives are important in this level because they help students investigate various concepts and consequently expand their knowledge and understanding. Pictures can be used to represent fractions because they are easily understood by the students. With the new understanding students can move on to more abstract concepts. For example, students start learning first by counting physical objects like balls. they are then able to work with pictorial representations of fractions before they can grasp complex ideas. These equations will help students solve for equivalent fractions.

When it comes to division, one gets the alternates the denominator dividing and multiplying by the other number. Students can be taught about fractions by being encouraged to initiate their own manipulatives by drawing a circle and dividing the whole according to the number of fractions and shading if they are adding or subtracting (Spitzer & Roddick, 2008).Continuous practice will help them calculate equivalent fractions with pen paper without manipulatives. If the figure has a whole number and a fraction, it is converted by multiplying the whole number by the denominator then added to the numerator. When multiplying mixed numbers you convert the whole into fraction and multiply the numerator by the numerator and vice versa. Then reduce the numbers by dividing by the GCD.

**Reference**

Spitzer, J. S., & Roddick, C. D. (2008). *Succeeding at teaching mathematics, K-6.* Thousand Oaks: Corwin Press.

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