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Young children show an early interest in measuring. They want to know how tall they are and how much they weigh, and they want to measure the ingredients to make cookies. We wanted to tap this natural enthusiasm for measuring by involving students in activities that would encourage them to think mathematically about the need for creating measuring tools with numerical scales.
Many mathematical ideas must be addressed before students can understand measuring scales on rulers, measuring cups, and thermometers. These ideas include understanding the importance of repeating the same-sized unit to determine a measure; understanding that units of different sizes yield different numerical measures of the same object; and realizing the inefficiency of measuring with individual units, such as wooden rods that are each 1 centimeter long, as opposed to connected units, such as a centimeter ruler.
First-grade students in two schools, one in a large city and one in a rural and suburban area, participated in activities that addressed these ideas. The authors, one in each school, led the activities.
Developing a Numerical Scale for a Linear Ruler
Students should measure lengths using individual nonstandard units before they begin working with nonstandard rulers and numerical scales. The following beginning linear activities focus on measuring with individual nonstandard units.
Using individual nonstandard units
We used Rolf Myller's How Big Is a Foot? (1991) to kick off the measurement investigations. This delightful story tells about a king who asked an apprentice carpenter to build a bed that is six feet long and three feet wide. The carpenter measured with his own small feet rather than the king's large feet and, thus, made a bed that was too small. After hearing the story, the students worked in groups to explore what happens when different-sized units are used to measure the same object. Each group was given ten individual "king size" footprints and ten individual "carpenter size," shorter footprints to measure the lengths, widths, and heights of objects in the room. The students recorded the measures first using king-footprint units, then using carpenter-- footprint units. Their task was to answer the question "What happens when we measure something with long footprints, then with short footprints?"
Several problem-solving situations arose during this activity. One group was overheard...