Prerequisite skills to working with fractions with unlike denominators.
- Cross-multiplication of the two fractions and addition of the two results to get the numerator of the answer
- Multiplication of the two denominators together to get the denominator of the answer
- Writing up the answer as a fraction
- Finding the LCM of the two denominators
- Increasing the terms of each fraction so that the denominator of each equals the LCM
- Substituting these two new fractions for the original ones and add
How the concept of finding equivalent fractions could be introduced using manipulative
Manipulative are physical objects that are designed to make explicit and concrete representation of mathematical ideas that are abstract. They are both tactile and visual appeal and can be manipulated by learners through hands-on experiences (Hougas, 2003). A number of time students need in a bid to progress from concrete to abstract comprehension is subject to the variation in the concept as well as the student factor. Equivalent fraction concept may be initiated and practiced at the concrete as well as pictorial levels in one grade, and then reviewed at these levels and practiced at the abstract level in the next grade. When students can use different manipulative to represent the same concept, their ability to understand subsequent math concepts is enhanced. When a new manipulative is going to be used in an equivalent fractions lesson, one should allow students time to examine it and explore its use before giving them concrete directions.
Describe the steps for finding equivalent fractions.
In mathematics, two fractions may be said to be equivalent if they both have the same value. It is a pertinent math skill to know how to convert a fraction into an equivalent. One of the methods of forming equivalent fraction is by multiplying the numerator and the denominator by the same number. When the numerator and denominator are multiplied by the same number we obtain an equivalent fraction and even though the numbers in the new fraction will be different, the fractions will have the same value. Additionally, an equivalent fraction can be achieved by dividing the numerator and the denominator by the same number.
Aiding students transition from concrete manipulative to more representative paper-and-pencil problems.
Having initially taught equivalent fraction concept a description and modeling is used with concrete objects the students are then provided with many practice opportunities using concrete objects. When students demonstrate mastery of skill by using concrete objects, description and modeling is utilized in performing the skill. All that they need to do is to draw pictures that give the correct presentation of the concrete objects. This accentuates the representational level of understanding. Consequently, many practice opportunities are provided where students draw their solutions or use pictures to problem-solve. When students demonstrate mastery drawing solutions, a description is made on how to perform the skill using only numbers and math symbols a stage referred to an abstract level of understanding. After students master performing the skill at the abstract level of understanding, it should be ensured that the students maintain their skill level by providing periodic practice opportunities for the math skills.
- Examples of fraction problems
- If Mark is in procession of ten crayons that he is supposed to divide amongst his two friends, how many will each friend get?
- If mark has ten crayons that he is supposed to divide amongst his friends so that each of them gets two. How many of those friends should he have?
- A fourth grade class has a total of 120 students. Suppose that the students are divided into three groups during a football match, what is the number of students that will be in each group? To get the answer, simply divide 120 by 3 and u get 40 (students).
- The selling price for four cardigans is $6.00. What would be the cost for one cardigan? To get the answer, simply divide 6.00 by 4 to get $1.50.
- Give examples of three fractions that are equivalent to 1. Equivalent fractions: 3/3, 5/5, 8/8
Hougas, L. (2003) Using Manipulatives to Teach Fractions, Viterbo University, retrieved from < http://learningandteaching.org/Research/Papers/Hougas.pdf>