2. Heavy for Size:  Investigation 2.3

What can a good weight line show us about our earth materials?

2. Build weight lines

Individual 20 Mins

Distribute a tray of materials to each group and remind students of the contents of the containers: equal volumes of water, mineral oil, sand, and organic soil. Ask them to open their notebooks and locate their weight data and their rules for good weight lines.

The hardest part of building the weight line will be determining the interval to use between weight marks, and then to ensure that the intervals are evenly spaced on the line. The interval must be large enough to accommodate the necessary range on the strip of paper, and it must also be easy to work with. Some students may arrive at a good interval through trial and error. Others may use a folding technique, or arithmetic, or some combination of these (see box). As you circulate among the groups, listen to their strategies and head off any serious errors.

When students are satisfied with their weight lines, have them place the containers of materials in the appropriate places.

Geometry, arithmetic, trial and error: three good strategies.  A simple way to ensure that the intervals are reasonable and evenly spaced is to use geometry. Fold the paper strip in half to find the middle, fold again to find the quarter points, and continue halving by folding until there are intervals of reasonable size. With fourth graders, it's important to have a range that can be halved several times before getting fractions. If the range is 0 to 70 grams, the first fold will mark 35g, but the second fold will create intervals of 17.5g — not very helpful! If you use a range of 0 to 80 grams instead, successive folds will create intervals of 40g, 20g, 10g, and 5 g before running into fractions.

Another approach involves more planning, some arithmetic, and a measuring tape or ruler. If the paper strip is 40cm long, and the range is 0 to 70 grams, and the goal is to have a mark every 5g, you will need 14 intervals (70/5=14) of 2.85cm each (40/14=2.85). Round down to 2.5cm to simplify the measuring, then space the 5g intervals 2.5cm apart. The resulting weight line will use less than the full length of paper, but it will be manageable.

Students may arrive at some combination of these approaches, e.g., they could start by folding once or twice and then measure or make estimates to create smaller intervals. They could also use a ruler and a trial-and-error approach to creating the equal intervals.