At the end of this unit, the students will be able to:
1. Verbally differentiate between congruent and similar fingures
2. Formally prove the similarity of figures through the use of similarity postulates and theorems
3. Compute angle measures and segment lengths using similarity ratios
4. Create a scaled blueprint of their own bedroom
This unit will begin with a brief review of ratios. The students will then view videos that introduce similar figures through shape & size, similar triangles, polygons, and solids. They will visit perimeter, area, and volume of similar figures as well as applications of similarity.
Students will answer questions on a worksheet to show their understanding of the video. They will work with an online math website for skill building. They will have a formal written exam and the unit will culminate with a project in which the students will create a scaled drawing (blueprint) of their individual bedrooms. This can be taken one step further by adding technology and having them create their "floor plan" using design software.
This Discovery Education video begins with a quick review of ratios. It then introduces the concept of similarity in shape and size, using triangles, polygons, and solids. It visits the topics of perimeter, area, and volume. It also addresses some applications for similarity.
This video uses similarity to give a more in depth look at architecture and creating blueprints.
For this project, each student will work on their own, no partners or groups. This project is worth 50 points. A grading rubric is attached to this paper.
You are going to make a scale drawing of your bedroom. You will measure the dimensions of your bedroom in your house, including doors, closets, and windows. Also measure major items, such as furniture, in the room. Using a scale factor of your choice, you will draw an aerial view sketch of your room (like blueprints). These pictures are going up in the classroom, so you may want to color them or make them look nice.
Graph paper can be helpful in the making of the drawings, but your final picture may not be on graph paper. If you do your picture on graph paper, you must trace it on to plain white paper. Your picture must include a title, your drawing, and the scale factor you used.
On a separate sheet of paper, you must include all of the work you did to make your drawing. This paper must show the real dimensions of everything you have drawn, the scale factor you chose, and an explanation of how you found the scaled dimensions for each object.
This project will be started in class and completed at home. It will be due on Monday May 16th. This means that it should be complete and ready to hand in before you enter the classroom! 5 points will be taken off for each day it is late so please be on time.
Points Possible Points Earned
Scale Drawing Picture:
Bedroom only - in proportion 10/30
Bedroom with door, closet, windows, in proportion 15/30
Bedroom as above with 1 object, few errors, neat 20/30
Bedroom as above with 2 objects, no errors, very neat 25/30
Bedroom as above with 3 objects, no errors, extremely neat 28/30
Bedroom as above with 4 or more object, no errors, very neat, and colored 30/30
The separate paper:
All work shown 10/20
All work is correct 15/20
All work is explained 20/20
Example of a rough draft of a blue print using graph paper
Example of a final blueprint in color
Example of a final blueprint using construction paper for the elements in the room
Example of a blue print using www.floorplanner.com
Example of calculations page