Wondrous Tales of MeasurementAuthor(s): Marci A. Malinsky and Mark McJunkinSource: Teaching Children Mathematics, Vol. 14, No. 7 (MARCH 2008), pp. 410-413Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41199178 .

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you ever considered teaching mathemati- cal concepts through the use of children's lit- erature? One way to begin is to re-create how

children learned long ago - elders spinning yarns as twilight deepened, young people caught up in wondrous tales that taught them about their world. To help students make a tactile connection to the experience from long ago, all you need are a skein of yarn and eager students seated in a circle.

Integration of children's literature is a fun- . damental part of instruction in my mathematics classes. Emphasizing children's literature is crucial because it draws students into a story, makes them feel at home, and teaches mathematical concepts in a nonthreatening way. I begin my mathematics les- sons by reading stories to introduce mathematical concepts. Before long, my students are entranced, delighted, and surprised to realize that they are enjoying learning about mathematical ideas.

Begin by having the children sit in a circle. Holding the skein of yarn, explain that you will

read them a story and then they will retell the tale: After reading the story, you will hand the yarn to one of the students, who will begin to retell the story. When that student gets stuck, he or she will throw the skein of yarn to another student, who will take up the tale. Through repetition - spinning a yarn - the children will learn the story, just as chil- dren long ago learned stories.

The following is an example of a mini-unit on measurement that I teach to third graders using children's literature. The unit consists of three lessons, which address the concepts of measure- ment, angles, and circumference. The unit begins with nonstandard measurement and continues with exploration of the metric and English systems. Practical applications of measurement follow in the lessons on angles and circumference. The unit will take approximately five days to teach.

I begin the unit by sharing one of my favorite selec- tions from Alice in Wonderland, by Lewis Carroll:

"And how many hours a day did you do les- sons?" said Alice....

"Ten hours the first day," said the Mock Turtle: "nine the next, and so on."

"What a curious plan!" exclaimed Alice. "That's the reason they're called lessons,"

the Gryphon remarked: "because they lessen from day to day." (The Complete Works of Lewis Carroll p. 104)

41 0 Teaching Children Mathematics / March 2008

By Marci A. Malínský and Mark McJunkin

Marci A. Malínský, mmalinsky@astate.edu, teaches mathematics and science methods to early childhood education majors at Arkansas State University, Jonesboro, AR 72467. She is interested in writing articles and giving workshops on the integration of children's literature and mathematics. Mark McJunkin, mmcjunkin@astate.edu, teaches mathematics and science methods for midlevel teacher education majors at Arkansas State University, Jonesboro, AR 72467. He is interested in working on professional development of teachers and grants for schools in the surrounding area.

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Lesson One: Measurement To begin the lesson, toss out to the students ques- tions such as these: Before the invention of standard measuring tools such as rulers and yardsticks, how did people measure objects? How did our measure- ment system come about? After some discussion, give the students the following classroom items to use as nonstandard measuring tools - pencils, erasers, chalk, straws, and crayons - and have them measure the top of their desk (see fig. 1).

As the students are finishing up this activity, read aloud Twelve Snails to One Lizard: A Tale of Mischief and Measurement (Hightower 1997). Milo Beaver has a dilemma: He needs to patch a hole in his dam before the rainy season ends and the pond becomes dry. But what can he use to shore up his dam? If he uses a log, how will he know exactly how long it needs to be? Bubba Bullfrog tells Milo that "an inch is about as long as a snail, and a foot is about as long as a lizard." But are Milo and Bubba up to the task? As Evans, Leija, and Falkner (2001) note, "This is a humorous story of Milo and Bubba trying to measure a log, and using one animal after another as a (nonstandard) measuring tool" (p. 112). Now have the students, gathered in a circle and sitting on the floor, retell the tale. Toss the skein of yarn to a student and have him or her begin the retelling.

Another activity to help students understand the concept of nonstandard linear measurement is "Per- fect People" (Family Math 1992, p. 85). Give pairs of students lengths of string to measure one another and determine whether they are tall rectangles, short rectangles, or perfect squares. The guidelines are simple: Using a piece of string, exactly measure

your partner's height. Using the string, measure your partner's reach - that is, the length from the fingertips of your partner's outstretched arm to the fingertips of the other outstretched arm. If the string is longer than your partner's reach, he or she is a tall rectangle. If the string is shorter than his or her reach, your partner is a short rectangle. If the string is about the same length as your partner's reach, he or she is a "perfect square" (see fig. 2).

At this point, the class is ready to once again contemplate one of the initial questions: How did our measurement system come about? Ask the stu- dents how people were able to measure the length of an object, for example, and then communicate that length to someone else before a standard mea- surement system was created and adopted. Follow- ing this discussion, read aloud How Big Is a Foot? (My Her 1990). In this tale, a king tries to give his queen a very special present for her birthday. This is difficult, because she has everything. He decides to give her a bed, the one thing she does not have; in fact, no one in the kingdom has a bed because it has not yet been invented! The king has the queen lie on the floor and uses his foot to measure her length. He then gives the job of making a bed to his prime minister, who gives the task to the chief carpenter, who in turn gives the job to the lowly apprentice. In comparison with the king, the apprentice is a small man, and the bed turns out too short for the queen. Furious, the king throws the apprentice in jail. The apprentice thinks and thinks about the problem until finally he realizes he must know the size of the king's foot. The king has a sculptor make a marble replica of his foot. To this day, the size of the king's foot is our standard unit of measure. Of course,

Teaching Children Mathematics / March 2008 41 1

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IdMIIMl Measurement using nonstandard tools

Measure your desk- its length or width - with each of the following classroom items: a pencil, an eraser, chalk, a straw, and a crayon

Nonstandard measurement tool Number of nonstandard units

1. 1. _

2. 2.

3. 3.

4. ' 4.

5. : 5._

"everyone has a different-sized foot, so if we want to use, say, the king's foot as a standard, we will have to mark it permanently; we cannot very well lug the king around!" (SEDL 2004, p, 1.4).

Have the students retell this story, which sheds some light on the development of the English sys- tem of measurement and the derivation of the term ruler.

Principles and Standards for School Mathemat- ics states, "Students should understand measurable attributes of objects and the units, systems, and processes of measurement" (NCTM 2000). Discuss the importance of standard measurements and help students make the transition from nonstandard units to standard units of measure.

Continue the class discussion by asking stu- dents about the metric system's origin. How did it develop? The students will be interested to learn that "the French scientific community at the time of the French Revolution (c. 1790) chose as the stan- dard unit of length a distance they called a meter. It was chosen so that 10 million metersticks laid end to end would just fit between the North Pole and the equator" (SEDL 2004, p. 1.5). According to this system, "the Earth's circumference would measure 40 million meters - not far from today's value" (mathforum.org).

Lesson Two: Angles Read to the class The Greedy Triangle (Burns 1994). In this delightful tale, the triangle is never quite satisfied with itself, thinking it will be happy if it "has just one more side and one more angle." The triangle goes to the Shapeshifter and becomes a quadrilateral, a pentagon, and a hexagon until finally the shape has so many sides and so many

angles it does not know which end is up. One day the shape, now practically a circle, cannot keep from rolling down hill; it ends up tired, lonely, and sad. The shape returns to the Shapeshifter to become a triangle again. From then on, it stays busy "holding up roofs, supporting bridges, and becom- ing slices of pie and halves of sandwiches."

My students love turning this story into a Read- ers Theater production. The entire class becomes involved. Some students rewrite the story into parts for different actors, others read the parts, and others make lifesize illustrations of the triangle becoming a quadrilateral, a pentagon, a hexagon, and so on. At the end of the production, the students show the shape as relieved and happy to be a triangle again, able to enjoy "slipping into the place where people put their hands on their hips" so it can hear and share the latest news (Burns 1994).

Discuss the importance of angles and of different shapes in the world. Explain that the differences in shapes are due to the different angles within those shapes. Have the students point out as many shapes as they can observe within their classroom. Give them geoboards and rubber bands and have them work together to make a triangle, a quadrilateral, a pentagon, a hexagon, and so on. The students can present their designs, tell the names of their shapes, and point out the number of sides and angles for each figure.

Lesson Three: Circumference Read aloud the story Sir Cumference and the First Round Table (Neuschwander 1997). King Arthur has a problem: The table at which all his knights sit is so long that they all "have to shout to be heard." Sir Cumference and Lady Di of Ameter try various solutions to build a better table. Finally their son, Radius, proposes using a cross-section of a fallen tree for a table. Geo Metry has his men cut through the tree, Lady Di uses her height to measure, and the cross-section is just the right size.

Have the students retell this story as well. Discuss the ideas of circumference, diameter, and radius as presented by the characters in the story. Remind students that the radius is exactly half the diameter and that the circumference is the distance around the edge of the circle. Have the students cre- ate their own visual representation of the characters in the story by using a compass to make circles of various sizes. Then have the students draw a circle with a radius of one inch. Show them that the diam- eter will be exactly twice the measure of the radius.

41 2 Teaching Children Mathematics / March 2008

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Have the students complete the table in figure 3; this process will help them understand the relation- ship between the diameter and the circumference of circles of various sizes.

Check to see if the students notice a pattern in the relationship of the diameter to the circumfer- ence. With guided discussion, the students should be able to see that the circumference is always approximately three times the diameter. Explain that this relationship was first discovered by the Greek mathematician Archimedes. We now use the Greek symbol /r (pi) to represent the ratio of a circle's circumference to its diameter. This ratio is an approximate number; the most common decimal used for n (pi) is 3.14. The circumference can be computed by using the formula C = nd.

Conclusion By the end of this unit on measurement, the stu- dents have learned about nonstandard and standard measurement, angles, and circumference through the use of children's literature. They have had a chance to become involved in the stories, retell the tales to one another, and practice the skills referred to in the stories. They have experienced for them- selves how mathematical concepts are an integral part of their world. Perhaps you, too, will want to use children's literature to help your students expe- rience mathematics in an enjoyable, nonthreatening way. Take a skein of yarn and begin spinning yarns and wondrous tales!

References Evans, Caroline W., Anne J. Leija, and Trina R. Falkner.

Math Links. Englewood, CO: Teacher Ideas Press, 2001.

Family Math. Portland, OR: Northwest Equals of Port- land State University, 1992.

mathforum.orgAibrary/drmath/view/STSóó.html. National Council of Teachers of Mathematics (NCTM).

Principles and Standards for School Mathematics. Reston, VA: NCTM, 2000.

Southwest Educational Development Laboratory (SEDL) . Measurement and Science: Third and Fourth Grade Instructional Activities. Austin, TX: SEDL, 2004.

Children's Literature Burns, Marilyn. The Greedy Triangle. New York, NY:

Scholastic, 1994. The Complete Works of Lewis Carroll. Introduction by

Alexander Woollcott. Illustrated by John Tenniel. First Modern Library Edition. New York: Random House, 1979.

Hightower, Susan. Twelve Snails to One Lizard: A Tale of Mischief and Measurement. New York, NY: Simon and Schuster, 1997.

Myller, Rolf. How Big Is a Foot? 1962. New York, NY: Random House, 1990.

Neuschwander, Cindy. Sir Cumference and the First Round Table. Watertown, MA: Charlesbridge, 1997. A

Relationship of diameter to circumference

Radius Diameter Circumference 1 inch

2 inches 3 inches 4 inches 5 inches 6 inches

Looking across the rows of your table, think about your answers for the diameter and circumference of each radius. What do you notice about each diameter in relationship to the corresponding circumference? Can you deter- mine a pattern for the relationship between the diameter and the circumfer- ence of each circle? Think of some additional radius lengths and follow the same procedure.

The "Perfect People" activity

Have a partner measure you with a length of string. If your height is longer than your reach, you are a tall rectangle. If your height is shorter than your reach, you are a short rectangle. If your height is about the same as your reach, you are "perfect" - a perfect square.

Name:

I am a

Tall Rectangle

Perfect Square

Short Rectangle

Teaching Children Mathematics / March 2008 41 3

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