Standard Measure Concept Cartoon

This cartoon was developed to assess students’ ability to:

• reason about the weight of different sized pieces of the same material
• represent the relative weights on a weight line
• understand the additive property — that weights of all the tiny pieces of an object are equal to the weight of the object

This cartoon is typically used after Investigating Standard Measures 3, Do very tiny things have weight?.

Things to look for in student responses

Student responses indicate how they use qualitative, non–numeric spatial information in the drawing of the broken potato chip (that shows pieces of different relative size) to make inferences about relative weights of each piece, represent those inferences on the weight line, and then reason about the weight of all the pieces added together.

Do children use size to infer relative order on the weight line (inferring the following weight order: e > b > d > c > or = to a)?

Do they go further and infer the absolute magnitude of the weights on the line? That is, do they realize that “e” should has a weight of about 2 grams (because it is half the size of the whole chip which weighs 4 grams), “b” has a weight of about 1 gram (because it is about half the size of “e”), and that “d” has a weight about midway between 0 and 1 because it is half the size of “b”?

Do students realize that although a and c are very tiny pieces they still have some weight, or do they place them at 0 or below zero? (Note children often think tiny things weigh nothing at all or even have negative weights.)

Finally, do students realize that weight of all the broken pieces together equals the weight of the unbroken chip (4 grams)? Encouraging students to consider the additive sum of the pieces helps them see the problems with assuming tiny pieces weigh nothing at all.