**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: **

- Identify the ways that adults actually use fractions in their daily lives.
- Identify the common problems adults have when dealing with fractions
- Demonstrate the five ways of "seeing" fractions using concrete models.
- Recognize the underlying fraction concepts illustrated through a variety of concrete models.
- Address the importance of "fair share", "counting", and "relative size" when teaching about fractions.
- Explain the disadvantages of introducing symbols prematurely in instruction, i.e., before fraction concepts and vocabulary are familiar to the student
- Explore strategies and activities for teaching the various "fraction topics.
- Investigate the use of metacognition in developing personal algorithms for working with fractions.

**Agenda**

A. Welcome, Introductions and Opening activity:

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

B. Session Overview and Negotiation

- Review Workshop Rationale and Objectives (Brief information lecture by presenter/s)
- Feedback from "Ice Breaker" activity. In small groups, using one or two words on individual "Post its" participants list adult student's major problem areas when dealing with fractions. -Results are posted and group prioritizes by categorizing and ordering. This may be done by selected member/s of the several groups or by group consensus.
- What research tells us about students and fractions. (Brief information lecture by presenter/s)
- Negotiation by consensus of the activities presented in the workshop. These will reflect the priority needs of students as perceived by participants and the information related to research about students and fractions.

**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.

- part of a whole
- part of a set
- ratio/probability
- division
- spot on a number line

**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:

- part of a whole -
*geometry*of regions - part of a set
- ratio/probability
- as division
- spot on a number line
- Circles vs rectangles as models
- Equality or "fairness" as it relates to fractions.
- Equality of parts when parts are moved in space
- Value of fractions as numerator or denominator changes
- Counting in fractions to improve understanding
- Improper fractions
- Equivalent fractions

**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**

- Relative size of fractions
- Finding the part when the whole is known
- Finding the whole when one part is known
- Finding the whole when more than one part is known
- Vocabulary of fractions, "Fraction Words"
- Addition
- Subtraction (using the missing addend)
- Multiplication
- Division

**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 .