 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum          A B  Notes for Session 3, Part B Note 5 When measuring objects using the metric system, it is important to establish benchmarks for common lengths, such as meter, decimeter, and centimeter. In addition, you should actually make the measurements and compare your estimates to your measurement data. Reconciling the differences between your estimates and measures will help you improve your ability to make reasonable estimates using the metric system. Note 6 Be aware that errors in approximating 100 m are going to be compounded tenfold when using your 100 m distance to approximate 1 km (since 100 • 10 = 1,000 m). You may want to check the distance using a car or bicycle odometer. When you know the approximate time it takes you to walk 1 km on flat terrain, then you can use time to estimate distances (e.g., I walked for 20 minutes, so I know I have traveled about 2 km). Note 7 Whereas the base unit for volume is the cubic meter, most practical day-to-day situations find us determining the capacity of smaller containers, and thus cubic centimeters or cubic millimeters might also be used. The relationship between cubic centimeters and milliliters (1 cm3 = 1 mL) and between cubic decimeters and liters (1 dm3 = 1 L) is an important one to establish. Models can help people visualize these relationships. If you have metric base ten blocks, then the "small units cube" (1 cm3) is equivalent to 1 mL, and the "thousands cube" is equivalent to 1 dm3; this cube, if hollow, will hold 1 L. Compare a milliliter and a cubic centimeter as well as a liter and a cubic decimeter. If possible, pour 1 L of water into a hollow decimeter cube. Note 8 If you are working in a group, it is worth the time and effort to have groups of four people construct a cubic meter, using metersticks as the edges of the large cube. If supplies are limited, make 1 m3 as a model for the whole group to observe. Participants can hold the metersticks in place or tape them together. Some people may have difficulty listing the equivalent measures for 1 m3. A common error is to think that there are 1 cm3 in one cubic meter. Use the model to show that this amount is much too small. Try listing an equivalent measure for each dimension before finding the volume. For example, since 100 cm = 1 m, the length, width, and height of the cube are all 100 cm, and you can find the volume by multiplying length times width times height. Note 9 Since you will be pouring liquids in and out of bottles to find the capacity, this can get a bit messy. But to fully understand the size of metric units, it is important to actually do the measurements. If there is time, test more than one type and brand of liquid. Is there the same amount of liquid in a 1 L bottle of soda as in a 1 L bottle of water? Or test many 1 L bottles of the same brand. Is the capacity consistent from one bottle to the next? Be sure to discuss or reflect on your findings. Note 10 If you are working in a group and you did not discuss the difference between mass and weight during Session 1, do so now. Have everyone explain in their own words how mass and weight differ. Ideally you want to have available a variety of scales: pan balances, three-arm balances, spring scales, and a metric bathroom scale. Note 11 If you are working in a group, when finding materials that have masses of approximately 1 g, 100 g, 500 g, and 1 kg, work individually. You can use more than one object to reach the target mass: Place the objects in a plastic bag and then label the bag with the combined mass. As a group, discuss each quantity, answering questions like "What does a mass of 1 g feel like?" and "What common items have a mass of 1 g?" Each group member should examine the different samples and then weigh them again, using the different scales. Note 12 If you do not have a metric bathroom scale, you can use a conversion factor to change pounds to kilograms. Since 1 kg = 2.2 lb., you can find someone's weight in kilograms by dividing his or her weight in pounds by 2.2. Note 13 This activity focuses on reasoning deductively about mass, but it does not further one's knowledge of metric measures. The problems, however, do show that there are many ways to measure without using units. Note 14 You might be tempted to solve this problem in a similar way to part (c), by first placing four coins on each of the pans. This enables you to conclude that the heavy coin is one of the four (one pan will go down!). You can then make additional comparisons in order to identify the heavy coin. There is, however, another way to solve this problem that takes only two steps. Hint: The first weighing does not involve all eight coins. Can you figure out how to identify the heavy coin?   