Designing a Parking Lot

 

Name: Lisa Fefferman

 

Title of Lesson: Designing a Parking Lot

 

Date of Lesson: 5th 6 Weeks, Thursday of Week 3

 

Length of Lesson: 50 min

 

Description of Class: Geometry

 

Source of Lesson:

 

TEKS addressed:

a) Basic understandings.

(1) Foundation concepts for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students continue to build on this foundation as they expand their understanding through other mathematical experiences.

(2) Geometric thinking and spatial reasoning. Spatial reasoning plays a critical role in geometry; shapes and figures provide powerful ways to represent mathematical situations and to express generalizations about space and spatial relationships. Students use geometric thinking to understand mathematical concepts and the relationships among them.

(4) The relationship between geometry, other mathematics, and other disciplines. Geometry can be used to model and represent many mathematical and real-world situations. Students perceive the connection between geometry and the real and mathematical worlds and use geometric ideas, relationships, and properties to solve problems.

 

 

The Lesson:

I.         Overview

            The students will design a parking lot with a given area. They must use their knowledge      of area in different shapes to come up with the most effective parking lot. They will then      compare area and perimeter length. A figure out how to make the perimeter the smallest           using the same area.

 

II.            Performance or learner outcomes

            The students will be able to:

¤       Connect algebra to geometry by solving for unknown values

¤       Find which shape (or combination of shapes) result in the largest parking lot and why

¤       Determine which shape has the smallest perimeter and why

 

III.         Resources, materials and supplies needed

¤       Graph Paper

¤       Calculators

 

IV.          Supplementary materials, handouts

¤       Parking Lot Worksheet

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Five-E Organization

 

Teacher Does

Student Does

Engage: (5 mins)

The teacher will ask the following questions to the class.

 

The students will be working on answering the questions on their own.

 

Questions:  

1. A rectangle and a circle have the same area of 8. Is the perimeter and circumference the same length?

2. Find the radius of the circle, and use that to find the circumference.

3. Find the all the possible perimeters of the rectangle. Why are there multiple perimeters?

 

Expected Student Response:

 1. No

 

2. r = 1.6, C= 10.048

 

 

3. 1x8, P= 18

     2x4, P= 12

The perimeter depends on the length and the width. Since those are unknown, the perimeter will change as a result.

 

 

                                                                

Evaluate

Decision Point Assessment (DPA) – The teacher will makes sure all the students understand that different shapes can have the same area, but the perimeter of each will be different.

 

Explore: (25 mins)

The students will be given a worksheet to work in groups where they will design a parking lot with a given area. They must find a shape that will fit the most cars possible using the given area.  Each spot must be _____ x _____. Be sure to make room for an aisle. It must be at least one or two car lengths (See parking spot dimensions). The aisle width will be dependent on how you plan to construct the lot.  You must also be an exit and an entrance path.

 

Student will complete the worksheet. They will use graph paper to help them with the design.

 

 

Questions:  

1. How many cars did you fit in your lot?

2. What is the area the parking spots.

3. What is the area of the aisles?

Expected Student Response:

Answers will vary depending on studentŐs parking lot design.

 

 

 

 

 

Evaluate

DPA:  The teacher will walk around the classroom to make sure that they stay on task and to guide them when necessary.

 

 

Explain: (10 mins)

The teacher will lead a group discussion.

 

Questions:

1. Which design fit the most cars?

2. Why was that design the best?

 

Students will discuss their results with the other groups to find the best model.

 

Expected Student Response:

Answers will depend on students design?

 

 

 

    

Evaluate

DPA – The teacher will make sure that each person is participating in the class discussion.

 

 

Extend / Elaborate: (10 mins)

Build a fence to go around your parking lot.

 

 

Questions:

1. What is the length of your fence?

2. Using the same area, build a new parking lot with a different perimeter.

3. What shape will your lot be if you wanted to use the lease amount of fencing?

4. The most?

 

 

 

 

 The students will get back in their groups and work on the next assignment.

 

 

Expected Student Response

Answers will vary depending on the students design. The perimeter is the smallest with a shape that is the most compact. In other words, a shape that has the lengths and widths which are almost the same, if not the same. See engagement.

   

Evaluate

DPA –  When the area is the same why is the perimeter the smaller in a circle than in a square?