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Meaningful Math Activities that Help

A Workshop in Fraction Concepts

(Recommended length: two, two and one half hour sessions)

Rationale:

The National Council of Teachers of Mathematics, in their publication Standards, states that an understanding of fractions broadens students' awareness of the usefulness and power of numbers and extends their knowledge of the number system. For adult students therefor, being able to memorize and apply the algorithms for adding, subtracting, multiplying, and dividing fractions is not enough. It is critical that they understand the concepts and relationships underlying fractions in order to build a foundation for more advanced concepts and skills in mathematics. To do this effectively many different approaches to instruction become necessary. It is crucial that teachers be able to use physical materials, diagrams, and real-world situations in conjunction with ongoing efforts to relate the learning experiences to oral language and symbols. Since fraction symbols should be introduced in the classroom only after students have developed the concepts and oral language necessary for the symbols to be meaningful, teachers need to be able to carefully foster the students ability to make the connections to the concepts among the models, the activities, oral language, and the symbols.  Participants are, therefor, encouraged to think about their thinking processes as they experiment with the instructional activities and models and be able to discuss these processes with their peers.

Workshop Goal:

This workshop is designed to provide adult educators with practical instructional activities which help adult literacy students make the connections between fraction concepts and fraction operations through the investigation of  the variety of meanings applied to fractions, of whole number operations as they relate to fractions, the discovery of patterns in fraction operations, and the value of estimation in solving problems involving fractions in school , as well as in daily life.  Activities encourage participants, through the use of manipulatives, calculators, whole body movements and personal experience, to review (and in some cases to become aware of, or to develop) the "number sense" as it applies to fractions, which is essential to successful learning in mathematics .

Workshop Objectives:

Agenda

A. Welcome, Introductions and Opening activity:

            Ice Breaker Activity: What difficulties do your students have with fractions?

B. Session Overview and Negotiation

C. Fractions in our daily lives: at work, at home, in school.  

Brainstorm activity in large group or in small groups with feedback to large group.  This exercise helps to illustrate the practical applications of fraction manipulation  in everyday living as different from the use of fractions in specific work situations , or in fractions examples in the classroom

D. Five different models of fractions and why students need to recognize each one.     Demonstraton by presenters.

D. The need to use a variety of instructional strategies, activities, and manipulatives to aid in understanding fraction concepts.   Large group discussion and review of the principles of adult learning and learning in general.

E. Activities. Using Cuisenaire Rods, pattern blocks, beans, egg cartons, construction paper circles and rectangles, paper folding, and the multiplication tables to illustrate selected fraction topics:

F. Review, Reflections, and "Next Step"

The number of activities practiced in each session is negotiable and dependent on the time constraints.

End of first session.

Agenda

Day Two

A. Welcome and Review of First Session

B. Feedback from "Next Step" Assignment

C. Activities

D. Closure: Discovering Personal Algorithms

E. Workshop Evaluation

Meaningful Activities That Help

Number Sense

Workshop Evaluation

Workshop Goal:

This workshop is designed to provide adult educators with practical instructional activities which help adult literacy students make the connections between fraction concepts and fraction operations through the investigation of  the variety of meanings applied to fractions, of whole number operations as they relate to fractions, the discovery of patterns in fraction operations, and the value of estimation in solving problems involving fractions in school , as well as in daily life.  Activities encourage participants, through the use of manipulatives, calculators, whole body movements and personal experience, to review (and in some cases to become aware of, or to develop) the "number sense" as it applies to fractions, which is essential to successful learning in mathematics .