See PDF version: Measuring Experiences for Young Children» [PDF, 345KB] 

Problem introduction
As part of a thematic unit on moving objects, children experimented to find out which toy car would travel the farthest distance after traveling down a ramp. By design, only one car could be on the ramp at a time, so children somehow needed to remember how far their favorite cars went.

Observed investigations
Children used counters to mark the ending points that showed how far the cars went. They also remembered the distances by stating the relative positions of the cars: “My car went all the way to the block center” or “The blue car was best. It almost went out the door!” Children quite naturally used comparison terms such as “longer,” “more farther,” and “went bigger” as they talked about the distances that the best cars traveled.

Problem conversations
The conversations about this problem centered on a car-race contest between the teacher’s best car and the class’s best selection. After a vote, the children released their favorite car on the ramp. To help them remember how far the car went, the teacher suggested measuring with a licorice stick, a nonstandard device this class often used. The number of sticks was counted and recorded so everyone could see the result. Then the teacher introduced her car, a rather puny vehicle. In fact, the teacher had selected her car because her tests had shown that the vehicle would not travel a great distance. After excessive bragging by the teacher (“My car is going farther than your car!”), she released the car. As expected, the car traveled a short distance. As children cheered, the teacher reminded them that they must measure the distance traveled for her car as well. This time, however, the teacher had eaten the licorice stick so that the remaining section was about one-fourth of the original piece. As a result, the recorded number created the appearance that the teacher’s car traveled farthest. Immediately, a lively conversation erupted. Shouts of “That’s not fair!” and “That’s not right!” progressed to more general reasoning: “You didn’t do it right” and “Do it again.” The conversation further progressed to more specific justifications: “Use the same licorice sticks to count” and “The stick’s gotta be the same size!”

Follow-up activities
The teacher introduced many similar situations throughout the year. Children measured distances that balloon rockets traveled with differing lengths of Unifix-cube trains. They weighed objects with small and large teddy-bear counters. They poured glasses of orange drink using different cup measures. By the end of the year, children were frequently reminding the teacher to “do it fair!”

Connections to the Standards
The expectations of “use repetition of a single unit to measure something larger than the unit” and “measure with multiple copies of units of the same size” (NCTM 2000, p. 102) are both essential to understanding the car-race problem. The teacher’s introduction of the element of competition in an appropriate way for young children initiated the idea of fair measurement. Although most children did not understand why the measurements were incorrect, they did understand that something about the process was unfair.