# Hole Math

By Hanson, Elizabeth | Teaching Children Mathematics, January 1996 | Go to article overview

# Hole Math

Hanson, Elizabeth, Teaching Children Mathematics

"'Holey' cow! A million is a lot."

"Today we are going to work on hole numbers."

"There are a hole lot of ways to use your math manipulatives."

Students need concrete materials to manipulate in their study of mathematics. Teachers, therefore, need classroom sets of manipulatives that require limited storage space; are interesting to the students; require little time or energy to ensure that pieces are not lost, broken, or used in hazardous ways; and are flexible enough to be used in teaching many different mathematical concepts. School boards need to show concern for public money as they provide funding for such instructional materials.

Filling such a big order could be difficult, but our school has found a manipulative to do all those things and more, such as inspiring creative-writing activities, supplying material for art projects, and improving the environment by decreasing the amount of material sent to the local landfill.

This mathematics manipulative of the nineties was in the school computer laboratory waiting to be discovered. Once recognized, it spread throughout the K-6 building, leaving few curricular areas untouched. The material, in case the reader has not yet guessed, is the strip of holes that moves computer paper through a printer.

Students routinely remove these strips from the sides of their printouts before turning in assignments. By the end of a typical day, the computer laboratory trash can overflows with these strips of holes. Cleaning up at the end of one day sparked an idea.

When a fifth-grade mathematics class visited the laboratory to work on a spreadsheet assignment, the teacher began to muse aloud. "I wonder how many holes are thrown out on an average day in the laboratory? How long do you think it would take to collect a million holes? How much room would we need to store a million holes? Would they fill a shoe box? The hall showcase? The whole computer laboratory?"

The challenge had been issued. Energy immediately began to surge through the room. Charts were quickly drawn up to record random guesses on the various topics. Random guessing was soon set aside as data were collected. Calculating and serious estimating began. Cooperative groups formed naturally as students with similar ideas for conducting tests or similar hypotheses on results began discussions and research. The numbers of holes per sheet, students per class, and sheets per box of paper were used in calculations. Strips of holes were counted, stacked, and measured, as were shoe boxes, the showcase, and the room. Mathematical discussions, sometimes bordering on arguments, were impossible to contain in one room or class.

The project had begun! Students rapidly began using "holes" in these discussions to refer to the strips with holes in them - we will use their terminology throughout, when appropriate. A special "in" basket on a counter in the computer laboratory replaced the trash can when students began saving the holes from their work. As the basket filled, it was emptied into a plastic grocery bag. The plastic bags filled quickly, and shopping bags were found to hold more efficiently the growing collection of holes. While regular computer lessons went on in the laboratory, groups of students came to conduct further research, measuring or weighing the collection.

The computer-laboratory teacher met with teachers at different grade levels, and a plan was developed for counting the holes. The entire school was now involved - or was soon to be. Learning place-value concepts was the mathematical objective of the activities.

Counting Begins

Counting began in earnest in March. First graders were the first to get involved. They practiced their counting skills by cutting the long strips of holes, many several pages long, into strips of ten. The ten-strips and any leftover holes were stored in separate containers labeled "tens" and "units," which were placed in each classroom. …

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