 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 1, Part B:
Which Rock Is the Largest? (65 minutes)

In This Part: Measuring Surface Area | Measuring Volume | Measuring Weight

 You can measure a number of attributes of rocks -- for example, surface area, volume, and weight. Which of these attributes should you use to determine the largest rock? Let's collect measurements of each type, looking at surface area first. Note 3 The area enclosing a three-dimensional or solid object is referred to as the surface area. Imagine that a thin skin covers all the surfaces of your rock. How would you determine the size of this skin? For this activity, you'll need your rock, a sheet of tinfoil large enough to wrap around the rock, and pieces of grid paper with units of 1 cm2, 0.5 cm2, and 0.25 cm2. You can print this grid paper (PDF - be sure to print this document full scale) if you wish. Before you begin measuring, estimate the surface area of your rock. (Later, you can compare your estimate with the approximate surface area you've measured.)  Problem B1 How could you use the tinfoil to find the surface area of the rock? Why would you use this technique? Problem B2 What unit will you use? Is there more than one choice? Explain. By first estimating the number of units in a measure, we are forced to consider the size of the object in relation to a standard unit of measurement. If our estimates and approximations are far apart, then we have to reevaluate the size of the unit we chose. When we repeatedly estimate and measure, we improve our ability to measure accurately. It's this "measurement sense" that allows us to establish benchmarks for particular measures (e.g., "I know that 2 L is about the size of a common soda bottle, so I'd say that this container holds around 3 L"). Now take the tinfoil and wrap it around your rock, covering the surface area as best you can. Then superimpose the tinfoil that represents the surface area of your rock on the 1 cm2 grid paper and trace around it. Count the number of squares that are completely covered by the tinfoil. This is your inner measure. Then count the number of squares that are both completely and partially covered by the tinfoil. This is your outer measure. Find the average of the inner and outer measures. You can use that average as the approximate surface area of your rock.  Problem B3 How exact is your measurement? How might using a different unit give you a closer approximation? What else might you do to get a closer approximation? Measure your rock again, this time using sheets of grid paper with units of 0.5 cm2 and 0.25 cm2. Again, superimpose the tinfoil representing the surface area of your rock on each of the grids, trace around it on each sheet of grid paper, and calculate the surface area. Now compare your three approximations. In order to do this, you'll need to use the same units, so convert the first two approximations to units of 0.25 cm2. (Be careful here -- look at the grid papers and notice how many small squares equal a larger square.) Note 4 Problem B4 What do you notice about the approximate surface areas using different grids? What conclusions can you draw?   Video Segment In this video segment, Laura and David measure the surface area of a rock. They wrap tinfoil around it and then approximate its area using grid paper. Watch this segment after you've completed Problems B1-B4. What are some of the difficulties they came across? Did you experience similar or different problems? If you are using a VCR, you can find this segment on the session video approximately 8 minutes and 12 seconds after the Annenberg Media logo.      Session 1: Index | Notes | Solutions | Video