Area and Perimeter
Introduction: Hook question: How can you use geometry to improve your school structure?
2 Direct Instruction
Students have been hired as the architects in charge of the design of the new school that is going to be constructed outside of the city. They need to evaluate the problems of the actual school facilities so that the design of the new school includes all the proposed solutions and modifications to the problems we are currently facing. To do this:
Students will participate in an outdoor activity, in which they are going to walk around the school facilities and identify existing problems or design opportunities that can be solved by using Math. They may take pictures along the way or notes of different problems or design opportunities that arises their interest.
Students will walk around the classroom to share and discuss the different problems or design opportunities they found. The teacher will play some music to indicate they have to walk and each time the music stops they must share their ideas with a friend.
After listening to different ideas, students will get in group of 3 and will choose one problem to focus on.
They will prepare adesign brief to focus their understanding about that problem, which includes the context for the problem, the proposed solution, and the justification of how it will help improve their school structure and benefit the school community.
They must draw an initial sketch of the proposed design in milimetric paper, including the following specifications as part of their designs:
- A circle
- A rectangle
- A parallelogram
- A trapezoid
- 2 different types of triangles
3 Guided practice
As architects, students need to delimit the land they are going to build on. Students will choose the area and perimeter of the piece of land their structures will occupy by following these steps:
Given a set area to build on, record the different possible values for the perimeter of the structure in a worksheet that contains 3 different tables. Each group member will be responsible of completing one table by giving different specific dimensions that will fit in the land they have to build on. They will be working with 3 different fixed areas. They must record their values for perimeter in each table, and identify patterns they can observe in all of these cases.
Students will receive a constant perimeter for their structures and they need to find the different possible areas to be recorded in a worksheet that contains 3 tables. Each group member will be responsible of completing one table by giving different specific dimensions. They will be working with 3 different fixed perimeters. They must record their values for areas in each table, and identify patterns they can observe in all of these cases.
Each group must observe their initial sketch and choose the dimensions they consider more appropriate for their structures.
Based on the dimensions you chose for the piece of land you are going to build on, each group must create a blueprint of the proposed design (visual learners) or a model (kinesthetic learners), by following the steps described below:
1. Observe your initial sketch and label the dimensions of the piece of land where your structure is going to be built.
2. Measure and label all the dimensions of the different figures included in your design: circle, rectangle, parallelogram, trapezoid, and triangles to fit perfectly in the piece of land you are working on.
3. Calculate the area, perimeter, and circumference of all the figures of the proposed structure.
4. Build your model or blueprint following the chosen measures.
To construct their blueprints or models they may consult the following link: www.HowStuffWorks.com
4 Independant Practice
Students will work independently IXL skills related to are, perimeter and circunference
5 Wrap up
As a wrap up of the unit of area and perimeter, students will present their blueprints or models to the class. This day the class will start with meditation followed by the presentations. They will be divided in 2 groups:
Group 1: BUILDING AREA. This group includes all the students whose blueprints or models are proposals to solve problems related to the physical structure of classrooms, stores, library, cafeteria or any other building structure.
Group 2: RECREATION AND SPORTS AREA: This group includes all the students whose blueprints or models are proposals to solve problems related to sports fields, swimming pool, playground, gardens, etc.
Group 1 will present during the first period and group 2 during the second period.