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Posted on April 16th, 2014, by


  1. On the board write the fraction problems: 1/5+3/5 (vertical), 3/4*1/5 (horizontal), 5/6-3/8 (vertical), and 5/9+7/15 (vertical). Also, write the numbers 7, 10 and 24.
  2. Review fractions: We know how to do the first two problems. When we add or subtract fractions with the bottoms the same, we do the top and keep the bottom. 1/5+3/5=4/5. When we multiply fractions we do the top AND the bottom. 3/4*1/5=3/20.
  3. Review Prime factors: Remember factors can be written in any order! 7 is a prime number. The only multiplication problem we can write is 1*7. 10 is not prime so we can write the problems 2*5 and 1*10. 24 is not prime but there are many problems we can write. 2*12, 3*8, 4*6, and 1*24. If we write 24 as the product of primes we get only one problem 2*2*2*3.
  4. Fraction pies: When we look at 5/6-3/8 we see a problem. The bottoms are not the same so we cannot keep the bottom. If we try to use some pie pieces to make a circle and use some pieces from the 6/6 pie and some pieces from the 8/8 pie, we can’t make a flat circle with the mixed pieces. We have to make the bottoms (pie pieces) the same size.
  5. Multiply by one: Any time you multiply by one the result is the same number.
  6. Choosing the fraction to multiply by: 5/6-3/8 have bottoms of 6 and 8. The prime factors of 6 are 2*3 and the prime factors of 8 are 2*2*2. Write these factors before the 6 and 8 in the problem. Mark out what is the same in both numbers (2) and mark them out. Then take the remaining numbers and multiply the other fraction by the fraction with that number on top and bottom.

5  *  4  =  20    2*3       6  *  4  =  24            – 3  *  3  =   9   2*2*2      8  *  3  =  24                          11                          24

  1. Repeat with 5/9+7/15. (3’s are marked out.)
  2. Assign the appropriate number of problems from their math book. Monitor their work carefully to ensure mastery.


Students will solve 9 out of 12 problems on the test for adding and subtracting fractions with unlike denominations.

This lesson plan is grounded on the cognitivism theory since students learn the way to solve the problem discussed in the class. The teacher provides students with the key with the help of which they can solve the problems they solved during the lesson and similar problems. Students can apply the learned model of solving problems involving adding fractions with different denominators. In such a way, students can apply the learned skills in similar situations successfully because they know the way how to solve the problem. The major strength of the cognitive approach is the consistency learners develop as they learn to do tasks in the same way over and over again. However, the cognitive approach has a considerable drawback since the learner learns the way to accomplish the task, but this way may not always be the best way or suited to the learner or the situation.

The use of the effective theory of design can enhance the effectiveness of the learning during the lesson. The theory of design, such as Gagne’s theory or Wiggin’s theory can help educators to plan the lesson carefully and to reach the lesson goals successfully. The design of the lesson helps the teacher to convey the knowledge and to develop target skills in students and facilitates the perception of the learning material by students. However, the design should match the goal of the lesson.

In this regard, it is possible to refer to Gagne’s theory and Wiggin’s theory. Wiggins’s theory of backwards design is effective, when it is applied to the learning material that students already know and this model is the best applied to revise the learned material. The drawback of this theory is the backward movement from the end goals, which students may not fully understand, if the learning material is new for them, to the learning material proper and development of the target skills. Instead, Gagne’s nine step theory includes nine key steps which teachers can use in the lesson to develop the target skills and knowledge students have to learn during the lesson. The lesson is effective when students need to develop new skills systematically. The major drawback of this theory is the complexity and steady movement of students from the old material to the new one.

Nevertheless, the Gagne’s nine step theory is the best to apply to the suggested lesson plan because this model allows the teacher to lead students steadily from setting goals and the revision of old material and skills, which students already have, to the development of new skills and elimination of difficulties, which they have in regard to adding fractions with different denominators. The goals of the lesson will be achieved only when the educator receives positive feedback from students.

Thus, the lesson plan discussed above can be developed in different perspectives. In this regard, the cognitive approach is effective but not the best one. Instead, the constructivist approach is worth trying because this approach will help students to try to solve the set problems on their own using their own skills and abilities. As they have certain experience of using fractions with different denominators they can apply their knowledge and skills to the new problems they face during the lesson. At any rate, they should try. As they start thinking, the educator should just help them and to give insights to possible solutions. As a result, students will learn how to solve the set problems and elaborate their own approaches which will be suitable for them. Finally, the Gagne’s nine step theory is the best design theory that can be applied to this lesson.

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