Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

CONTENTS OF CURRICULUM UNIT 23.03.06

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Content Objectives
  4. Teaching Strategies
  5. Teaching Implementation
  6. Lessons
  7. Classroom Activities
  8. Resources
  9. Appendix
  10. Implementing District Standards
  11. Works Cited

Division of Fractions in Algebra, from real-life applications to abstract equations

J. Ulises Reveles

Published September 2023

Tools for this Unit:

Teaching Strategies

This unit will use three teaching strategies: visualization, real-life context, and practice.

The visualization Strategy

Visual representations help students understand the division of fractions. In particular, the unit uses the rectangular model and the number line to demonstrate the division process. Students can create and manipulate rectangles and number lines, as illustrated in the introduction, to see how one fraction is divided by another, thus making it easier to grasp the concept. Furthermore, most importantly, to visualize the general definition of division presented in the introduction, division of a/b asks how many copies of b are in a.

The Real-Life Context Strategy

The students connect the division of fractions to real-life contexts, making the concept more meaningful and relatable to them. This curriculum unit presents two sets of word problems with real-life scenarios where the division of fractions is applied. For example, students solve problems related to sharing food among friends, dividing ingredients for a recipe, buying fractions of pounds of fruits, and finding the cost of fractions of pounds of produce. Significantly, by contextualizing the division of fractions, students can understand its practical applications and see the concept's relevance in their everyday lives.

The Practice and Application Strategy

The lesson provides ample opportunities for practice and applications, a crucial element when teaching the division of fractions. The unit includes a set of exercises that gradually increase in complexity, starting with problems that only involve integers, in which the students can familiarize themselves with the procedures and then progress to more challenging problems that involve the division of fractions, which is the core of this unit. Students will develop fluency and confidence in dividing fractions utilizing ample practice. Additionally, by incorporating real-world problem-solving tasks, group work, and discussions, students can deepen their understanding which helps them apply their skills in different contexts.

Implementing a combination of these strategies in this unit can enhance students' comprehension and retention of the division of fractions. In summary, by engaging students through visualization strategies, real-life contexts, and practice and application, this unit creates an inclusive and effective learning environment that fosters a strong foundation in this important mathematical concept.

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