Solutions for Session 1, Part A

See solutions for Problems: A1 | A2 | A3 | A4

 Problem A1 Answers will vary. Some answers might be the rock's length, surface area, volume, weight, color, and texture.

 Problem A2 A measurable property is a property that can be quantified using some kind of unit as a basis. For example, length is measurable, since there is a unit of length (an inch, a centimeter, etc.) and we are counting or measuring the number of units in our object. A non-measurable property is one without a standard unit. When we combine objects with a measurable property, the property must increase. If we wanted to measure some of the properties not commonly measured, we would have to invent a method to do it. For example, to measure texture, we could look at the curvature over the small areas of the object; if the curvature doesn't change much, we could say that the texture of the object was smooth. Some interesting modern research in mathematics focuses on such "nonstandard" measurements.

 Problem A3 Answers will vary. For those listed in our solution to Problem A1, we can measure length in centimeters, surface area in square centimeters, volume in cubic centimeters, and weight in grams.

 Problem A4 Answers will vary. We could measure the length of the rock using a ruler or tape measure. We could measure the weight using a scale, the volume using a beaker of water (for displacement), and the surface area using tinfoil.