Division of fractions – three tasks
This activity is intended for secondary students who have been taught how to use division with fractions in previous years but exhibit basic
related difficulties, for example:
• Students have difficulty to interpret a situation as involving division when the divisor is a fraction.
• Students have difficulties with using the invert-and-multiply method for bare division problems.
It is designed to adopt a bottom-up approach to help students connect informal strategies for three familiar division situations to pictorial representations and to formal solution methods. The activity is divided into two parts and is planned to spread over two separate lessons. In Part 1, students work at three tasks in pairs. The student work produced is gathered and assessed by the teacher in preparation for the follow-up discussion session to be held in the Part 2. Here the teacher strives to help students with connecting arising informal strategies to pictorial representations and to formal division methods.
Potential for PD
This activity targets an important aspect of the mathematics curriculum; understanding the algorithm for division with fractional divisors. It aims at concept development starting from students’ representations on three division situations. Developing an understanding of formal mathematical procedures is not an easy task and this activity demands a good dose of IBL related skills from the teacher. The activities are well suited for national contexts that afford only small and first steps to IBL. Currently, the tasks are close-ended and structured, but still what happens in class can have an IBL flavour. For learning to unstructure tasks teachers could use these activities in PD module “tackling unstructured tasks” (REF).
The lesson plans were first tried out as part of a study of a student teacher that was carried out as part of her dissertation for the B.Ed. degree. A full description of her lessons and her results are given in her dissertation.