A. Pretend you are working with a grade five child who has learned how to represent fraction situations with simple proper fractions such as

1

2

3

4

2

5

11

15

1

2

The student with whom you are working has some mild learning challenges. The teacher has asked you to work with this student on understanding the concepts of adding and subtracting fractions and on teaching the the processes involved in adding and subtracting fractions.

1. Describe the child with whom you are working. Tell about such things as age/grade, gender identity, learning style, suspected or diagnosed disabling condition, personal interests and a brief educational history.

2. Then present one addition and one subtraction story problem that would be appropriate for this particular child. Ensure that each problem involves only simple fractions with single-digit denominators.

a. Each of the story problems must be presented to the student in such a way that the student feels it is relevant to him or her.

b. Each of the story problems must be presented to the student in such a way that it acts as a lead-in to (that is, a reason for) teaching how to add/subtract fractions.

c. Make sure that each problem is significantly different from the others.

d. For each story problem, include a strategy for teaching the student how to add/subtract simple fractions. Your strategy must involve the appropriate use of concrete materials and/or pictures/drawings. Explain your strategy in detail, showing/telling how you would use the manipulatives/pictures to enhance student learning. The strategy must help the student understand why each step in the algorithm actually works mathematically. It is not enough to simply state the steps in the algorithm.

e. The instructional strategy you present for each story problem must address the learning challenges faced by the student you profiled.

B. Next pretend you are working with a grade seven student. This student understands the concept of equivalent fractions and knows how to generate equivalent fractions. He also knows how to add and subtract fractions. The teacher has asked you to work with the student on understanding the concepts of multiplying and dividing fractions and on learning the processes involved in multiplying and dividing fractions.

1. Describe the child with whom you are working. Tell about such things as age/grade, gender identity, learning style, suspected or diagnosed disabling condition, personal interests and a brief educational history.

2. Present one multiplication and one division fraction story problems that would be realistic and interesting to this student.

a. Each of the story problems must be presented to the student in such a way that the student feels it is relevant to him or her.

b. Each of the story problems must be presented to the student in such a way that it acts as a lead-in to (that is, a reason for) teaching how to multiply/divide fractions.

c. Make sure that each problem is significantly different from the others.

d. For each story problem, include a strategy for teaching the student how to multiply/divide simple fractions. Your strategy must involve the appropriate use of concrete materials and/or pictures/drawings. Explain your strategy in detail, showing/telling how you would use the manipulatives to enhance student learning. For the multiplication story problem ensure that the strategy helps the student understand why each step in the algorithm works mathematically. For the division story problem, it is not necessary for the strategy to explain why the steps in the division algorithm work the way they do mathematically. However, the strategy must include a concrete or pictorial representation that will help the student find the answer to the question posed in the story problem.

e. The instructional strategy you present for each story problem must address the learning challenges faced by the student you profiled.

f.. Assume that the student knows how to generate equivalent fractions.

g. Assume that the student is familiar with improper fractions and mixed numbers, and that he/she can convert one to the other.

Do not use mixed fractions use only a single proper fraction. Use only single digit numerators and denominators.

It is not necessary to reduce final answers to lowest terms.