How much do the cubes weigh in grams?
4. Make meaning
Purpose of the discussion
The purpose of this discussion is to bring forward the idea that weight is a property that can be increased in small or large increments.
Students can see just “how much heavier” some cubes are than others; they can even express the weight differences with some precision.
Engage students in the focus question
How much weight do I have to add to cube A to make it the same weight as cube B?
Draw students’ attention to the weight difference between pairs of cubes by asking a series of questions cast in this form:
- How much weight do I need to add to cube A to make it the same weight as cube B?
This is a different way of asking the question, “How much heavier … ?” It avoids focusing attention on the individual weights of the cubes and instead highlights the size of the difference between them. It also emphasizes the additive nature of weight. Start by asking students about cubes that are fairly close together:
- How much would I have to add to the acrylic cube to make it weigh the same as the PVC cube?
[about 3 grams] - How much would I have to add to the pine cube to make it weigh the same as the oak cube?
[about 6 grams]
Detours: Seeing the cubes arrayed on the weight line, students may again wonder how it is possible that objects of the same size can have such different weights. Some students may again think that the cubes are hollow or filled with some unseen material. Assure them that every cube is solid and made of the same material all the way through. Back up the claim by showing them the cubes that have been cut in half.
Continue asking about pairs of cubes until the students seem to grasp that weight is a property that can be increased in small and large increments.
A Thought Experiment:
To foster understanding of the continuous nature of the weight line, ask students to imagine cubes made of other materials, and to say where those cubes might fit on the weight line. Consider all suggestions, both serious (e.g., a cube made of glass or brick) and more frivolous (e.g., a cube of banana, or ice cream, or cotton candy). Ask students to defend their suggested locations and to “guesstimate” the weights of their imaginary cubes in grams. By the end of the exercise, students should be clearer that every point on the weight line represents a different weight; that there are no gaps; and that a new object can be added between any two points on the line.
As you end the session, tell students that they can continue to think about and write down even more ideas for cubes that they could add to the line. Students may also reflect on the following question:
- Why use grams?
