Contextualization

In mathematics, one of the foundational concepts we work with is proportions. Proportional relationships are all around us, from the ingredients in the food we eat, to the money we save and spend, and even the speed at which we travel. They involve two quantities that change together in a consistent way.

Exploring Proportions is an important part of math education because it helps us understand and compare quantities that decrease or increase together. This understanding extends beyond the mathematics class and plays a significant role in other subjects, such as physics, chemistry, economics, and even in daily life activities such as shopping and cooking.

In this project, we will probe deeper into the proportions and their various aspects. We will relate it with some real-world problems and scenarios and learn various concepts and methods to solve problems involving rates, ratios, and proportions.

Introduction

Proportional relationships describe the relationship between two or more quantities that change together in a certain way. For instance, if you're baking cookies, the recipe might call for 2 cups of sugar and 3 cups of flour. This is a proportional relationship because the amount of sugar and flour increase at the same rate. If you double the sugar, you also double the flour.

In mathematics, the concept of proportions also extends to geometry, where similar shapes are an example of proportional relationships. Similar shapes have the same shape but different sizes, and the sizes are in proportion to one another.

Understanding and calculating proportions is a math skill that is not only crucial for solving advanced math problems but also for making many real-life decisions. For example, it can help you decide whether a 500g product selling for $5 is a better deal than a 750g product selling for $8.

Resources

Here are some resources to help you understand the concept in a more comprehensive manner:

1. Math is Fun - Proportions. This webpage includes clear definitions and examples of proportions, making it an excellent starting point for learning about the topic.

2. Khan Academy - Ratios, rates, and proportions. Video lessons with practice problems that cover ratios, rates, and proportions in depth.

3. Illustrative Mathematics – Grade 7. The unit involves proportional relationships.

4. LearnZillion - Understand proportional relationships. Here you can find a video explanation and interactive practice problems.

5. Math Antics - Ratios And Rates - This YouTube video explains ratios and rates in a fun and engaging way.

Practical Activity

Activity Title: "Exploring the world of Proportions through baking and scaling"

Objective of the project:

To understand the concept of proportional relationships in a fun and engaging way, let's turn our math knowledge into an edible reality. The aim is to explore and grasp the concept of proportions through the relatable task of baking. Students will apply the knowledge to scale up or down a given recipe and ascertain its impact on the overall ingredients' quantity. Along with math, students will also learn the basics of baking - a skill that extends beyond the classroom.

Detailed description of the project:

Students will work in groups of 3-5 members. Each group will be given a simple baking recipe that serves a specific number of people. The recipe includes a list of ingredients along with their quantities. The challenge is to scale the recipe up or down to serve a different number of people. The students will need to calculate the new quantities of ingredients while maintaining the proportional relationship.

For instance, if the original recipe serves 4 people and the students need to modify it for 2 or 8 people, they will have to correctly work out the new proportions for every ingredient in the recipe. They will then bake the adjusted recipe to verify if the proportions were maintained correctly.

In addition, each group will also compare the cost-effectiveness of two product options in a grocery store, using proportional reasoning to determine the best buy.

By the end of this activity, students will have a practical understanding of proportional relationships and how they can help solve real-life problems.

Necessary materials:

• Recipe with ingredients and quantities.
• Baking utensils and equipment.
• Access to a grocery store (for cost comparison activity).
• Sufficient time to bake and enjoy their creations.

Detailed step-by-step for carrying out the activity:

1. Each group will receive a different baking recipe, including the ingredients and their quantities, which serves a specific number of people.

2. The recipes should be scaled up or down to cater to a different number of people. Here, students can use their understanding of proportions to adjust the quantities of ingredients accordingly.

3. Once all the ingredients are revised, the group will shop for their ingredients based on this adjusted recipe.

4. While shopping, students will also do a cost comparison activity. For instance, if a 500g product sells for $5 and a 750g equivalent sells for $8, they need to decide which is a more cost-effective buy.

5. After buying the needed ingredients, students will bake following the adjusted recipe.

6. Enjoy the delicious creation!

Project Deliverables:

In addition to the practical part of the project, students will also deliver a written document detailing their journey through the project. This document should contain four main sections:

1. Introduction: The students will provide context to the report, explain why understanding proportions is important, and detail the objectives of the project.

2. Development: This section should cover the theory behind proportions, detail the activity, and the methodology used. It should also present and discuss the results obtained, including the adjusted recipes, the cost comparison activity, and any other findings.

3. Conclusion: Here, students will provide a summary of their learnings and insights gathered through the project. They need to emphasize their understanding of proportional relationships and their real-world applications.

4. Bibliography: Students must list down all the sources they consulted during the project. They can refer to books, web pages, videos, or any other resources they used.

The deliverable grants students a pathway to show their understanding of the concept, their ability to apply it in practical scenarios, and their collaborative teamwork skills. The written document should contain all the details about the work done, including the thought process behind all decisions, details of the calculations, and results. This will help in understanding each group's approach towards the project, their level of understanding, and how well they applied their theoretical knowledge into practice.