Introduction and Context of the Project

Context

The set of rational numbers is a vast and well-known set constituted by all those numbers that can be expressed as a fraction in which the numerator and the denominator are integers. This means that all fractions are rational numbers. We use rational numbers in countless situations every day. For example, whenever we divide a pizza into equal slices we are dealing with fractions (i.e., rational numbers). In other words, rational numbers are intrinsically connected to our daily life.

Moreover, the ordering of rational numbers (or comparing fractions) is an extremely useful skill. Imagine you and your friends are sharing a chocolate bar. The fairest way to do that is by making sure everybody gets the same amount of chocolate. But, without comparing the rational numbers, how can you tell who got the bigger piece of chocolate?

Introduction

In this project, we are going to explore the concept of rational numbers and specifically how to order them. Ordering two or more rational numbers means figuring out which one is greater, smaller or if they are the same. For example, how can we tell which is greater, 1/2 or 1/3? Or, which is smaller 1/4 or 2/5? To answer those questions, we will need to understand how to order rational numbers.

There are multiple strategies for comparing fractions, including: comparing to a benchmark fraction, such as one whole; comparing to a fraction with a denominator of 1; drawing a picture; using equivalent fractions; etc. We will be exploring many of these different strategies throughout the project.

Hands-On Activity: "Ordering Rational Numbers"

Activity Title

"Ordering Rational Numbers"

Learning Objectives

This project is designed to help students understand the concept of ordering rational numbers, as well as to apply this concept in a fun and interactive way.

Project Description

Students will work in groups of 3-5 to create a board game where player movement is determined by correctly answering questions on comparing rational numbers.

Project Timeline: This project will span the course of one month, from game creation to classroom presentations.

Materials

1. Poster board or cardboard for the game board.
2. Construction paper, crayons, colored pencils, markers for decorating the game.
3. Game pieces (such as game tokens or small objects) to represent players on the game board.
4. Die.
5. Small envelopes.
6. Notecards (small enough to fit into envelopes).
7. Computer and/or encyclopedia for research.

Step-by-Step Instructions

1. Creating the Game Board: Have teams create a game board in any format they would like. There should be enough squares on the board for at least 10 turns of the game.

2. Creating the Questions: Have students create a set of questions involving comparing and ordering rational numbers. Example: "Which is greater, 2/3 or 3/4?"

3. Setting up the Questions: The questions should be written on notecards, which will be placed in envelopes and hidden around the game board.

4. Game Play: The rules of the game should clearly state how players will move around the board based on the outcome of the fraction comparisons.

   • For example, a player may move ahead two spaces if they correctly answer a question or move back one space if they answer incorrectly. Or, different questions could be worth different numbers of spaces.

5. Test Run: Once their game is complete, the group should play through the game to make sure the rules work and to make any necessary adjustments.

6. Final Presentations: Each group will present their game to the class, explaining the rules.

Project Deliverables and Connection to Suggested Activities

In addition to creating a board game, students will create a written report that includes the following components:

1. Introduction: Describe the real-world applications of ordering rational numbers and provide a statement of the purpose of their project.

2. Development: Describe the activities that were implemented and explain the theory and methodology behind the creation and implementation of the game. Discuss any challenges encountered and how they were solved. Provide step-by-step instructions and clear descriptions of the game and its rules.

3. Conclusions: Explain what students learned and any conclusions they drew from the project and their experiences comparing and ordering rational numbers in a game format.

4. Bibliography: List all sources consulted for the development of the game and the creation of the report.

This written report should be comprehensive, providing organized and thorough documentation of the entire project process, from the research that went into developing the questions to the implementation of the game itself. It should showcase the group's collaboration and individual contributions to the project's success.