Context

Mixed numbers are those that have both a whole and a fractional part, such as 1 1/2 or 2 3/4. A clear and intuitive understanding of mixed numbers and operations with them is absolutely essential for the study of mathematics.

In practice, we deal with mixed numbers all the time. If you have ever cooked following a recipe, you have probably encountered ingredients measured in mixed numbers - for example, 1 1/2 cups of flour. Or, if you have traveled, you may have traveled 2 3/4 hours to reach your destination. Mixed numbers are a more natural and easier way to express values that are better represented by a combination of whole numbers and fractions.

Introduction

Normally, we learn to add, subtract, multiply, and divide whole numbers before we learn to perform these operations with fractions. Mixed numbers may seem complicated at first, as we need to perform these operations with both the whole and fractional parts of the numbers. However, with practice and understanding, you will see that it is just an extension of what you already know.

To perform operations with mixed numbers, it is often useful to convert the mixed number into an improper fraction, perform the operation, and convert the answer back to a mixed number. This will be one of the key concepts of this project.

Multiplication and division of mixed numbers may seem particularly challenging. However, these operations can also be simplified by converting the mixed numbers into improper fractions. And remember, practice is key. The more you practice, the easier it becomes.

Practical Activity

Activity Title: "MasterChefs with Mixed Numbers"

Project Objective

To understand operations with mixed numbers to become master chefs in the world of mathematics. Students will be encouraged to get their hands dirty to improve time management, communication, problem-solving, creative thinking, and proactivity skills.

Detailed Project Description

Groups of 3 to 5 students will create a "Mathematical Cooking Show." In this show, the "chefs" will prepare a fictional recipe where all the ingredients are quantities expressed in mixed numbers and all the actions are operations with these numbers.

Each group will have to choose a "Head Chef" who will be responsible for leading the show, an "Assistant Cook" who will measure and map out the operations with mixed numbers, and a "Cameraman" who will ensure that all actions and operations are clearly visible.

Required Materials

• Camera or smartphone for filming.
• Whiteboard or large sheets of paper to record the operations.
• Colorful pens.

Step-by-Step Guide for the Activity

1. Program Planning (1-2 hours): Students should first plan their cooking show. They should create a "recipe" in which the ingredients are mixed numbers and the culinary actions (whisking, chopping, mixing, etc.) correspond to mathematical operations (adding, subtracting, multiplying, dividing).
2. Filming the Show (1-2 hours): Next, students should film their cooking show, highlighting the operations with mixed numbers. It is important that all mathematical operations are explained step by step during filming.
3. Editing and Review (1 hour): After filming, students should review and edit the video, correcting any mathematical errors.
4. Project Report (2 hours): Finally, students should write a detailed report on the project. In it, they should explain the theory of mixed numbers, discuss the operations performed, the results obtained, the difficulties encountered, and the conclusions drawn. They should also include all research sources used.

Project Deliverables:

1. Mathematical Cooking Show Video: The filming of the show should be clear, fun, and didactic, effectively demonstrating the use of mixed numbers and their operations.
2. Project Report: The report should be clear and well-structured, with an introduction, development, conclusions, and bibliography. It should explain the theory of mixed numbers, the operations performed, the results obtained, the difficulties encountered, and the conclusions drawn. And finally, the bibliography used for the project.

The relationship between the deliverables and the activity is that the video will demonstrate the practice and application of operations with mixed numbers while the written report will allow students to reflect on what they did, consolidate their theoretical and practical learning, and communicate coherently and structured what they did, how they did it, the problems they encountered, how they solved them, and what they learned.