Introduction
Have you ever wondered how mathematics can help us solve problems in everyday life?
Polynomials are not just expressions written in a mathematics textbook. They can be used to represent quantities, describe patterns, calculate areas, and solve real-world problems.
In this WebQuest, you will become a Mathematical Problem Solver. You and your team will explore polynomials, investigate how they work, and discover how they can be applied to a real-life situation.
Your challenge is to use what you learn about polynomials to solve a practical problem and explain your solution to others.
Task
Your group will investigate how polynomials can be used to solve a real-world problem involving area and dimensions.
Imagine that a community wants to create a rectangular garden. The length and width of the garden are represented by polynomial expressions.
Your task is to:
- Review the basic concepts of polynomials.
- Identify the parts of a polynomial expression.
- Perform operations involving polynomials.
- Use multiplication of polynomials to determine the area of a rectangular space.
- Create a visual representation of your garden.
- Present your solution and explain how you used polynomials to solve the problem.
Your final product will be a “Polynomial Garden Plan” containing your polynomial calculations, diagram, explanation, and final answer.
Process
Step 1: Review the Basics
Begin by researching the following:
- What is a polynomial?
- What are terms, coefficients, constants, and variables?
- What is the degree of a polynomial?
- What are like and unlike terms?
Create a short list of important concepts that your group discovers.
Step 2: Explore Polynomial Operations
Review how to:
- Add polynomials
- Subtract polynomials
- Multiply polynomials
Work through several examples with your group and check your answers using an online mathematics resource or calculator.
Step 3: Solve the Garden Problem
Your community wants to build a rectangular garden.
The length is:
(x + 5) meters
The width is:
(x + 3) meters
Determine the area of the garden using the formula:
Area = Length × Width
Therefore:
A = (x + 5)(x + 3)
Expand and simplify the expression.
Then choose a value for x and calculate the actual dimensions and area of the garden.
Step 4: Design Your Garden
Create a simple diagram of your garden.
Your diagram should show:
- Length
- Width
- Polynomial expression for the area
- Simplified polynomial
- Actual dimensions based on your chosen value of x
- Actual area
You may use Canva, Google Drawings, PowerPoint, or another digital drawing tool.
Step 5: Create Your Presentation
Prepare a short presentation explaining:
- What polynomials are
- How you multiplied the polynomial expressions
- How you obtained the area
- How your chosen value of x changed the dimensions
- Why polynomials are useful for solving real-world problems
Step 6: Present and Reflect
Present your Polynomial Garden Plan to the class.
After presenting, discuss:
“How can polynomials be useful outside the mathematics classroom?”
Write a short reflection about what you learned and which part of the activity you found most challenging.
Evaluation
| Criteria | Excellent (4) | Good (3) | Developing (2) | Beginning (1) |
|---|---|---|---|---|
| Understanding of Polynomials | Clearly explains polynomial concepts and uses them correctly. | Shows good understanding with minor errors. | Shows partial understanding. | Shows limited understanding. |
| Mathematical Accuracy | All calculations and answers are correct. | Most calculations are correct. | Several errors are present. | Many calculations are incorrect. |
| Application | Correctly applies polynomials to the garden problem and clearly explains the solution. | Applies polynomials appropriately with minor errors. | Application is incomplete or unclear. | Has difficulty applying the concept. |
| Visual Presentation | Diagram is clear, creative, complete, and well-organized. | Diagram is clear and complete. | Diagram contains some missing information. | Diagram is incomplete or difficult to understand. |
| Presentation & Teamwork | All members participate and explain the solution clearly. | Most members participate effectively. | Limited participation or explanation. | Little evidence of teamwork or preparation. |
Total: 20 points
Conclusion
Congratulations, Mathematical Problem Solvers!
Through this WebQuest, you explored the basic concepts and operations of polynomials and applied them to a real-world situation. You discovered that polynomial expressions can be used to represent quantities and solve practical problems such as determining the dimensions and area of a garden.
Take a moment to reflect on your learning:
- What did you learn about polynomials?
- Which step was the most challenging for you?
- How did technology help you complete the activity?
- Where else could polynomials be used in real life?
Remember, mathematics is not only about finding the correct answer. It is also about understanding problems, exploring solutions, and applying what you learn to the world around you.
Credits
Use the following resources to help you complete the WebQuest:
- Khan Academy – Algebra — Lessons and practice activities related to algebra and polynomials.
- CK-12 Foundation — Free mathematics lessons and resources.
- Desmos — Online graphing calculator that can be used to explore mathematical expressions.
- Math is Fun – Polynomials — Basic explanations and examples of polynomials.
Students should use the resources to investigate the concepts rather than simply copy answers.