## Lesson: Adding and Subtracting Fractions and Mixed Numbers

Developing the Concept

Students have been introduced to adding and subtracting fractions and mixed numbers. They also have a visual image of what is happening in those operations. This lesson will develop those concepts and relate them to adding and subtracting whole numbers.

**Materials:** paper and pencil

**Preparation:** none

**Prerequisite Skills and Background:** Students should be able to find equivalent fractions by finding the least common denominator and simplify fractions by using the greatest common factor.

**Wrap-Up and Assessment Hints**

Having students estimate the sum or difference of two fractions before adding or subtracting will help them recognize unreasonable answers. For example, if they add and , they should recognize that both fractions are less than , so the sum should be less than one. Also, since both fractions are just a little less than , the sum should be close to 1. Students should recognize that is not a reasonable answer. Ask students questions such as, “Why do we have to have common denominators before we add or subtract two fractions?” and “Why do we only add the numerators and not the denominators when adding two fractions with like denominators?” By answering questions like these, students will improve their understanding of the concepts.

To challenge some of your best students, ask them open-ended questions such as, “If the sum of two fractions is , what could those two fractions be?” ( and , and , and so on) or “If the difference of two fractions is , what could those two fractions be?” ( and , and , and so on)