Grade 7 Mathematics Unit 6 Measuring Perimeter and Area Designing a Landscaped Patio Created by Mr. Papple

Introduction: You are the owner of a large company that specializes in landscaping. Your company has been getting lots of calls from new customers because of the beautiful work that you do. One of the largest companies in Canada has just opened a superstore in your home town and has contacted you to design the main entrance to the store. The owner of the superstore believes that if there is a unique and welcoming entrance to the store, more customers will shop there. If you and your employees can design an entrance way that the owner of the superstore is pleased with, he will offer you a lucrative contract to design and build all of the entrance ways for each superstore across Canada. This is the opportunity you have been waiting for. It is now time for you to actually use the skills you learned in Math class and apply them to a real world situation. Think back to when you were sitting in Math class and asked yourself “when am I ever going to do this in real life?” NOW.

Task: The owners of a large superstore shopping centre want to build a patio in front of the main entrance to attract more customers. Your task is to design the tiled surface of the patio. The owner of the superstore is a Math genius and wants you and your team to fill the entire space of the patio using different geometric shapes, but not just any geometric shapes. The owner only wants you to fill the entire space with Triangles, Parallelograms, Rectangles and Trapezoids. There is one hitch. You must include at least three of the shapes in your design (Triangles, Parallelograms, Rectangles and Trapezoids). Because the owner of the superstore is really into Geometry, his one specification is that no shape can have the same area. Your Mathematical skills and understanding of Perimeter and Area of different geometric shapes will be on display, literally. You need to ensure you find the proper formulas for finding the Area and Perimeter of the shapes requested by the owner. You may need to make multiple attempts at designing your patio until you get it right. You need to prove that each shape has a different area.

Task Continued: Before you begin construction of the patio, the owner has requested that you show ALL blueprints to him. He is looking for the Perimeter and Area formulas for each shape with an example. You must have keep in mind the scale listed on the attached diagram of the patio. You must include the proper units of measurement. None of the geometric figures you have on your design can have the same Area. The shape of the patio has the shape shown below. Each square on this plan has a side length of 10cm. Here is a blueprint of the patio. YOU WILL BE PROVIDED WITH COPIES OF THE ENTRANCE WAY TO HELP YOU PLAN YOUR PATIO.

Process: You will have your choice of how you want to tackle this job. You can either work with a partner, or you can work on your own. You will need to look online to find a website that will show the proper formulas for finding the Perimeter and Area of Triangles, Parallelograms, Rectangles and Trapezoids. Record each website on your “Reflection Sheet” Create a “Formula Book” to show how to find Perimeter and Area (be sure to copy the websites you used to find the formulas) For each shape, you must accurately draw and label the shape and find the Perimeter and Area using the formulas Draw the blueprints of the patio for the superstore (you will probably have to make multiple attempts) KEEP ALL OF YOUR BLUEPRINTS TO SHOW THE OWNER THE PLANNING PROCESS Calculate the Perimeter and Area for each geometric figure shown on the blueprint ensure that none of the shapes have the same Area

Process Continued: When you have finished, you must complete a Reflection Sheet, explaining where your formulas came from, the process that you took to design the patio and why you designed it the way you did. Remember to include specific Mathematical terms to impress the owner of the superstore with your in depth knowledge

Helpful Websites: Triangle: Basic-mathematics.com Math Goodies http://www.basic-mathematics.com/perimeter-of-a-triangle.html (Perimeter) Math Goodies http://www.mathgoodies.com/lessons/vol1/area_triangle.html (Area) Parallelogram: Math Open Reference http://www.mathopenref.com/parallelogramperimeter.html (Perimeter) AAA Math http://www.aaamath.com/geo78_x2.htm (Area)

More Helpful Websites: Rectangles: Maths Teacher.au http://www.mathsteacher.com.au/year7/ch12_length/06_rect/rect.htm (Perimeter) Math is fun.com http://www.mathsisfun.com/area.html (Area) Trapezoids: E Funda.com http://www.efunda.com/math/areas/TrapezoidGen.cfm (Perimeter) Wikipedia http://en.wikipedia.org/wiki/Trapezoid (Area)

Evaluation: After you have completed each of the five steps listed in the “Process” you will need to submit your plans and blueprints to the owner of the superstore for his approval. You will need to submit: Your formula book with examples for each figure All of the blueprints you have created along the way to design this patio All of your calculations for every figure used in the patio Reflection Sheet You will be formally assessed by Mr. Papple from the assignment rubric found in the Essential Materials section.

Conclusion: After completing this WebQuest, you will have applied the use of design, area and perimeter to a real life situation. You will also have demonstrated your ability to research specific formulas and use them to complete your blueprints. Your reflections will demonstrate your understanding of this task because of the subject specific terminology that you used to impress the superstore owner.

Essential Materials: Head to Mr. Papple’s website to print out a copy of the patio entrance template. http://mrpapple.pbworks.com/w/file/51331515/Designing%20a%20Patio%20Template%281%29.docx Mr. Papple will have copies of the patio available in class. For a copy of the rubric for this activity, you can access it from Mr. Papple’s website. http://mrpapple.pbworks.com/w/file/61845982/Designing%20A%20Patio%20Rubric.docx

Reflection Sheet: Written Component: Website used for Perimeter of a Rectangle: Website used for Area of a Rectangle: Website used for Perimeter of a Triangle: Website used for Area of a Triangle: Website used for Perimeter of a Parallelogram: Website used for Area of a Parallelogram: Website used for Perimeter of a Trapezoid: Website used for Area of a Trapezoid: Written Component: Now that you are almost done, please answer the following questions in your own words to explain in detail how you problem solved throughout this assignment. Explain the process that you took to plan and design your patio Explain how many times it took you to perfectly fill the patio space with shapes that had different areas Choose two of the formulas that you used to find the Area of the different shapes, and explain in words how you found the Area.