Project-Based Instruction

Transcription

1 -Benchmark Lesson Perimeter Authors: Title of Lesson: Perimeter Date of Lesson: Length of Lesson: 2 days Description of the Class: Name of Class: Geometry Grade Level: 10 th Honors or Regular: Regular Source of the Lesson: Google. (n.d.). Retrieved May 04, 2011, from Google Earth: &topic=23730&answer= Concepts: Perimeter of regular shapes is a useful tool for the real world in many places, especially in the construction department. Also, symmetry can be used to reduce the number of calculations needed in a problem. Objectives: SWBAT: - Calculate the perimeter of different shapes and figures using their properties. - Relate perimeter to the content of the final product. - Use computer software as an aid to calculate the perimeter of a real life building with real measurements. State Standards: Texas Essential Knowledge Standards: Geometry b) Knowledge and skills. (4) Geometric structure. The student uses a variety of representations to describe geometric relationships and solve problems. The student is expected to select an 2007 The University of Texas at Austin

2 appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) in order to solve problems. (8) Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to: (F) Use conversions between measurement systems to solve problems in real-world situations. (11) Similarity and the geometry of shape. The student applies the concepts of similarity to justify properties of figures and solve problems. The student is expected to: (D) Describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems. College and Career Readiness Standards: III. Geometric Reasoning A. Figures and their properties 1. Identify and represent the features of plane and space figures. 2. Make, test, and use conjectures about one-, two-, and three-dimensional figures and their properties. C. Connections between geometry and other mathematical content strands 3. Make connections between geometry and measurement. IV. Measurement Reasoning A. Measurement involving physical and natural attributes 1. Select or use the appropriate type of unit for the attribute being measured. C. Measurement involving geometry and algebra 1. Find the perimeter and area of two-dimensional figures. VIII. Problem Solving and Reasoning A. Mathematical problem solving 1. Analyze given information. 2. Formulate a plan or strategy. 3. Determine a solution. 4. Justify the solution. 5. Evaluate the problem-solving process. Page 2 of 8

3 I. Key Cognitive Skills C. Problem solving 1. Analyze a situation to identify a problem to be solved. 2. Develop and apply multiple strategies to solve a problem. 3. Collect evidence and data systematically and directly relate to solving a problem. Safety: No safety precaution in needed for this lesson. Materials List and Advanced Preparations: At least one laptop per groups of 2 students with access to Google Earth software, worksheet, connection to a printer, markers. Page 3 of 8

4 ENGAGEMENT Show students this video: =KwXBMGdSWmI Today we are going to find out the perimeter of your own house or apartment complex. You are working in groups of 4, but for this activity, you will pair up with a member of your group. Then, let s take a look at how the Google Earth software works and how you can find your home there. Also, you will learn how to use the software tools to calculate the perimeter of your home. Instructions are also listed on the worksheet. What is perimeter? How can you find it? Does anybody know how the Google Earth software works? Time: 10 Minutes [is the sum of all of the sides of a figure? To find it you have to find out the measurement of the sides of the figure you are given and then add them up] [No] [Yes, you type in the name of the place you are looking for and the software will show it to you] Page 4 of 8

5 EXPLORATION With your partner, decide whose home you will use to do the activity. Teacher goes over the software instruction with students. Your goal is to find the perimeter of your chosen home as if you were hired to calculate the budget needed to fence your house or apartment complex. For those who live in complex apartments, calculate the entire complex s perimeter. What it the shape of your lot? Is it regular or irregular? How would you calculate the perimeter if you did not have access to Google Earth? Time: 25 Minutes [Answers vary] [Regular] [Irregular] [Go around the block with a GPS] [Use a tracking app on my iphone] [Using a long measuring tape] Page 5 of 8

6 EXPLANATION Now, we will discuss about how the properties of geometric shapes can aid you on calculating the perimeter. Draw the picture of the equilateral triangle. When we think about the square, how many pieces of information do you need to calculate its perimeter? Why? So what would be a formula for calculating the perimeter of a square? What about the rectangle? What about the formula? There are many types of triangles. How can you use triangle properties to help you calculate its perimeter? For example, let s study one specific case: you are given an equilateral triangle and only the length of its height. Can you figure out the perimeter of the triangle? Formula? What other properties of triangles can you use for your advantage? Time: 25 Minutes [One. Since a square is a polygon with equal sides, once you know the length of one side, you multiply it by 4 to get the perimeter] [4s, where s is the side of the square] [Two. We need the lengths of the longer and the shorter sides]. [2b+2h, where b is the base and h is the height os the rectangle] [Given only the height of an equilateral triangle, we can use trigonometry to find its side and then multiply it by 3 to get the perimeter. The fact the all angles are the same and that the height bisects both the angle and the base will aid the calculations]. [3s, s=side of triangle] [For a right triangle, we could use the Pythagorean theorem to figure out the length of the remaining side, given 2 sides] [For isosceles triangles, we could use the fact that 2 sides are equal and then implement the Pythagorean Page 6 of 8

7 theorem again to figure out the length of the base, if we are given an extra information, such as the length of the height of that triangle, and the measurement of one angle] Formula? What is the specific name of the perimeter of a circle? How many pieces of information do you need for this one? What it the formula of the circumference of a circle? What if we had a semicircle? What about the other shapes we talked about in the area lesson? [2s+b. where s=length of one of the equal sides and b=base] [Circumference] [One. Either the radius or the diameter] [C=2r =d ] [C=r =, that is, divide the circumference in half] [We also saw a trapezoid and a parallelogram] [For the trapezoid, we need to know the length of the two bases and the height in order to figure out the perimeter] [For the parallelogram, we need the length of the two different sides, since a parallelogram has the two parallel sides equal to each other] Page 7 of 8

8 ELABORATION Now, we will look at the blueprint we used on the area lesson. After changing my carpet, I decided that I also needed to change my base boards as well. So, now you will need to help me find the perimeter of my living room and how many base board bars I need to buy. Use what we ve learned so far as an aid for your calculations. If the cost of a 16 long base board is $2.16, how much will it cost to put these around my living room? How is perimeter relevant to your kite construction? Time: 20 Minutes [Answer depends on the number of bars obtained] [By knowing the perimeter of the shape we decide the kite will be, we can figure out how much wood sticks we will need to build it. Then, we can also minimize the costs of our final product] EVALUATION Students will turn in their worksheets with all calculations and work and total cost of the repair. Time:10 Minutes Page 8 of 8