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Tatami mats are 6 feet long and 3 feet wide. People in Japan measure the size of a room by how many tatami mats it takes to cover the floor.
1) Make a floor plan below. Draw a room 12 feet long and 12 feet wide. Then draw in tatami mats on the floor of the room. Your drawing should show how many tatami mats will exactly cover the floor of the room.
Tatami mats can exactly cover a floor that's 12 feet long and 12 feet wide. "Exactly" means that there are no mats that overlap and no gaps where the floor shows through.
2) Draw a room smaller than 12 feet by 12 feet. Choose the length and width so that you can exactly cover the floor with tatami mats. In your drawing, show how the tatami mats cover the floor of the room.
3) Draw a room larger than 12 feet by 12 feet. Again, choose the length and width so that you can exactly cover the floor with tatami mats. In your drawing, show how the tatami mats cover the floor of the room.
4) For rooms Four, Five, and Six below, figure out whether the floor can be exactly covered with tatami mats (no overlapping mats and no gaps). This time, figure it out without drawing the whole floor plan on grid paper. It's OK to make a sketch, though. Explain or show how you figured out your answer for each room.
Room Four is 11 feet wide and 15 feet long.
Room Five is 15 feet wide and 18 feet long.
Room Six is 9 feet wide and 9 feet long.
5) How can you decide whether tatami mats can exactly cover a floor without drawing the floor plan? Write down a rule that works for any room, no matter what length and width.
Here is the full version of the task including an overview, sample solution, instructions for classroom use, characterizing performance (scoring), and samples of student work (about 108K).
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Page updated 18 June 2001 For further information please contact wilcoxs@pilot.msu.edu |
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