### MA 105: Measuring a Room

Name:

Names of those you worked with:

This is a graded activity. Work with a group of 2 or 3 other students. Each student in the group should hand in her or his own work.
1. Use the metric scale on a tape measure or ruler to measure the width of this piece of paper as accurately as possible. Write your measurement below.

2. The measurement you just wrote down is approximate -- the exact width of the paper cannot be measured. However, measurements may be more or less precise. To determine the precision of your ruler or tape measure, look at the smallest markings on it. The distance between these markings is the precision of the measuring device. What is the precision of your ruler or tape measure?

3. If your measuring device has a precision of 1cm your measurements will generally be correct to the nearest centimeter. In other words, they could be incorrect by up to 0.5 cm. (This is why we say that all measurements are approximate.) We indicate the accuracy of a measurement like this by writing the measurement, then a ± symbol followed by half the precision of the measurement tool; for example the length of this piece of paper is 28 cm ± 0.5 cm.

Did you measure the width of the paper using the full precision of your measuring tool? If not, do so now. In the space below, record the width of the paper with an appropriate indication of accuracy.

4. Estimate the width of your classroom in meters, from left to right. Write your estimate below.

5. Use your tape measure to measure the width of your classroom. Write your result along with an estimate of the maximum likely error.

6. Do you think this measurement is more or less accurate than your estimate? Why?

7. Measure the width of the classroom again three times. Change roles with your group members for each measurement so that each person in the group gets to try each part of the measuring process. Write your three new measurements below.

8. Are all of your group's measurements the same? Why or why not?

9. Your four measurements form a sample data set. Calculate the sample mean or average by adding your measurements and dividing by four (the number of measurements in the sample). Write your sample mean below.

10. Do you think the sample mean is a more accurate estimate of the width of the room than your first measurement? Why or why not?

11. Make four measurements of the distance from the front to the back of the classroom and find the sample mean for this distance. Record your calculations below.

12. Craftsmen use blueprints or patterns when planning and executing a project. Draw a simple pattern or model of the classroom below, labeling the left-to-right and front-to-back distances with the sample means you found.

13. Use your model of the room to determine how much molding you would need to cover all of the edges where the walls meet the ceiling of the room.

14. The distance around the outside of a geometric figure (like the ceiling of the room) is called its perimeter. Since perimeter is a distance it is measured in units of length like feet, yards, meters or centimeters.

In your own words, write a rule or instructions for finding the perimeter of any two-dimensional figure.

15. In your own words, write a rule or instructions for finding the perimeter of a rectangle. Can you use special properties of rectangles to make a simpler rule than the one you made up for any figure?

Extra Credit Do as much as you can of problem 17 on page 6 of your textbook. (If you like, you may turn in your answer on a separate sheet of paper.)