Sally s Sally s family is planning to build a new house. Today they are looking at possible designs for Sally s bedroom. So far, they are thinking about the six rooms below. 9 16 12 A 6 B 10. 11 11 9 C D 15 11 8 E 11 F 1. If you were choosing, which room would you choose? Why? 2. Which bedroom looks like it gives Sally the most space to play? Sally s Student Materials Page 1 of 7
3. Which bedroom looks like it gives Sally the most space for hanging pictures or posters? Draw the bedrooms on grid paper. 4. Find the perimeter and area for each room, and record your answers on the table page. Leave the trim pieces and floor tiles columns blank for now. Use your table to answer the following questions. 5.) Which room has the most play space? 6.) Which room has the most wall space? 7.) Are your answers to questions 5 and 6 the same as your answers to questions 2 and 3? Why or why not? Sally s parents have agreed that she can have pink tile on her floor and yellow trim around the sides of her bedroom. The pink tiles are each 1 foot by 1 foot. The yellow trim pieces are each 1 foot long and are very narrow. They fit right next to the wall at the edge of the floor. 8.) How are perimeter, area, trim pieces, and floor tiles related? 9.) How many tiles and how many trim pieces does each room need? Fill in the answers on your table. Sally s Student Materials Page 2 of 7
Sally s grandmother comes over and looks at their plans. She says that Sally s bedroom could be much more interesting if they considered triangles! Sally doesn t think a triangular room would be best, but she decides to listen to her grandmother anyway. She does ask about fitting square tiles into a triangle, and her grandmother tells her that they can be cut in pieces to fit. She shows Sally these two right triangles. 8 ft 10 ft 12 ft 13 ft 6 ft Triangle G 5 ft Triangle H 10.) Draw these triangles on your grid paper and complete your table for each of them. Hint: You could draw two triangles together to make a rectangle. Will that help to find the area? Although Sally doesn t want a triangle-shaped bedroom, she starts to think about other possibilities. Her bedroom doesn t have to be one rectangle or one triangle! She could use more than one shape. Sally s Student Materials Page 3 of 7
Sally makes these two rooms by putting shapes together. 10 ft 10 ft 8 ft 9 ft 6 ft 6 ft 5 ft 6 ft J 11 ft 6 ft K 11.) Draw these rooms on grid paper and complete your table for them. 12.) Now, fill in the table below for bedroom J. J Table left triangle center rectangle right triangle total (add the three values for each row) perimeter area Compare the totals from this table to the perimeter and area of bedroom J on your Room Table. 13.) Is the total of the perimeters of the three shapes the same as the perimeter of bedroom J? Is putting trim pieces around the edges of each shape the same as putting trim pieces around the edges of the room? 14.) Is the total of the areas of the three shapes the same as the area of bedroom J? Is putting floor tiles in each shape the same as putting floor tiles in the room? Sally s Student Materials Page 4 of 7
Now think about bedroom K. 15.) If you add the perimeters of the two rectangles, will you have the perimeter of the room? Why or why not? 16.) Will the areas of the two shapes equal the areas of the room? Why or why not? Sally s parents are beginning to wonder how complicated her room will be, and they are getting worried. They tell her that her room must meet three conditions: She must use 150 or fewer floor tiles. She must use 50 or fewer trim pieces Her room must be made of rectangles and/or triangles. On grid paper, design a possible bedroom for Sally. Be sure it meets her parents conditions! 17.) Draw your room on grid paper. Now think about what Sally s parents have said. Do you think their conditions are reasonable? Could Sally design something that is difficult to build? How much freedom should Sally have? 18) List at least three conditions that you feel Sally s parents should give her. At least one should be different from the ones above. 19.) Design a room to meet those conditions and draw it on grid paper. 20.) Make a sketch of Sally s family s house that includes the bedroom you designed in number 19. Sally s Student Materials Page 5 of 7
Room Table Room Perimeter Number of Trim Pieces Area Number of Floor Tiles A B C D E F Triangle G Triangle H J K Sally s Student Materials Page 6 of 7
Rooms 9 16 12 A 6 B 10 11 11 D 9 C 11 15 11 8 E F Sally s Student Materials Page 7 of 7