Students Can Write Their Own ProblemsAuthor(s): Patricia C. HosmerSource: The Arithmetic Teacher, Vol. 34, No. 4 (December 1986), pp. 10-11Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41193030 .

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Students Can Write Their Own Problems By Patricia C. Hosmer

For years, my class of third grad- ers has written their own holiday problems, which I have typed and copied so all classmates could enjoy their friends' work. We had had the standard problems about Santa and Christmas trees, menorahs and dreidls, so this past year I decided to vary the format. I asked the children to do a little research on holiday cus- toms in one of the countries of their ancestors and then to develop a math- ematically related question about the custom. For many students the as- signment involved a trip to the library. After it was completed, several par- ents commented, "I didn't know any- thing about holiday customs in Italy, Russia, . . . ." Then the problems came in; some were quite long and involved, but in almost all the child's own words were clear and needed little or no revising. Some children asked one question; several asked three!

Most children wrote a paragraph explaining the custom before they presented the problem. My class was a microcosm of America, so I learned about Diwali, the Indian festival of lights; Christmas customs in China, Ethiopia, central Africa, Italy, Ire- land, Germany, and the Ukraine; and Hanukkah customs in Poland and Russia.

Some problems were complicated, and not all children were able to solve the most difficult ones. The problems were written so that their solution

Patricia Hosmer teaches at the Hawken School, Lyndhurst, OH 44124. She is interested in people around the world. In 1985 she traveled to Kenya.

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required all the mathematical opera- tions we had studied, through simple division. The most difficult problems demanded careful reading and re- quired a solution of several steps.

Some planning is needed if this ac- tivity is to succeed. During the fall the third-grade students had been writing 4 'thought problems" for each other. I had written some paragraphs to go with our history lessons, and I asked children to write four problems using data in the paragraphs. These prob- lems also showed a wide range of mathematical understanding. This ex- perience encouraged me to go further and ask children to write a mathemat- ical problem based on a book that we were reading in class or one they were reading for pleasure at home or based

on some numbers pertinent to their family life. Children used their ad- dresses, phone numbers, and ages; one used his dog's license number in a problem.

Almost daily, mathematics instruc- tion in my class involves problems that I dictate to the students. We discuss the solutions, noting the vari- ous methods of solving them. This discussion gives me insight into how children work problems, and I often learn why they have certain diffi- culties by watching them work in small groups and by listening to them explain their results.

Young children must have a wide variety of experiences in writing be- fore they can develop the skills needed for clear, concise explana- tions. The teachers at our school put great stress on problems, first present- ing them orally and then in writing, finally having children construct their own problems to share with others. The results are being seen in other disciplines, and we expect some trans- fer to instruction in computer lan- guages.

Now for a few selected problems by some of my third graders:

1. In Germany, Advent lasts for twenty-four days. In the von Trapp family each sister has the same num- ber of sisters as brothers and each brother has twice as many sisters as brothers. Each child gets one present each day of Advent. How many presents do all the children get? (Carwil James)

2. Hanukkah lasts for eight days and nights. On the first night you use two candles. (Hanukkah candles burn

Arithmetic Teacher

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so fast you have to use new candles every night.) On the second night you add a candle. Each night you add one more candle. The custom is to light two menorahs every night if you have two children. Hanukkah candles come fifty in a pack. If you have two children, how many more candles will you need than are in one package of candles? (Becky Davis)

3. If two pounds of potatoes make ten latkes (potato pancakes), how many pounds will we need to make thirty latkes? (Erica Lieberman)

4. In China the Christmas festival is known as Sheng Dan Jieh, the Holy Birth Festival. Many kinds of paper decorations and evergreens fill the churches and homes. The Chinese call the Christmas tree the tree of light. They don't use candles, but the tree is

decorated with three dozen paper flowers, five dozen colored paper chains, and two dozen cotton snow- flakes. How many ornaments are placed on the tree all together? (Chris Davis)

5. During the Christmas season in Italy, families that have mangers set them up. Musicians sing before the manger, and guests kneel before it. In one town, there were thirty-seven houses and twenty-one had mangers. In each house that had a manger, two musicians sang to it. Five guests also knelt in front of it. (a) How many guests and musicians are in this town? (b) How many more houses still need mangers? (c) How many guests and musicians would be visiting this town if every family had a manger? (Patrick Quigley)

6. For Diwali (an Indian festival of lights) I bought forty fireworks. Each was supposed to give five sparks and then explode once. Unfortunately, three did not work at all, five only sparked, and four only exploded, (a) How many sparks appeared? (b) How many explosions occurred? (Arun Shivashankaran)

7. The Irish celebrate St. Stephen's Day on 26 December. A group of boys sang eight Christmas carols at each house. Each carol had five verses. The boys sang at ten houses. How many verses did they sing? (Colleen Shanahan)

8. Ukrainians celebrate Christmas on 6 January. For thirty-nine days before the holiday, people observe a partial fast. On what day do they start their fast? (Sarah Janicki) m

from the File

Estimation Ì

MUNCHIE MEASUREMENTS , , *L :_ Î^tl IIP^

Snacks (e.g., chocolate bars, pack- ^£**=ш*'-м*ь1' ' ' aged cheese crackers, granóla bars, ^^^^^ЖшЛ ' 1 bananas, pretzel sticks) x^'^X*^'^-P'wftrTlm^fel^ V 1 Centimeter rulers ^^J^^ŽT^^"^ ПТТТТГТТПТП lii^^^^^^^^^^^ ^¿^*

Procedure: Mark out or remove the weight information from each package or

wrapper. Put one snack into each bag and fold over the top. Divide the class into

groups of two to four students each and give each group a paper bag. Have students remove the snack from the bag and examine it. Then have them estimate its length and weight and record their estimates. Next, have them measure and

record the snack's actual length and weight. Find error points (the difference between the estimates and the actual measurements) with a calculator. Compare the heaviest, lightest, longest, and shortest measurements. Finally, let students eat what they have measured!

From the file oř Barbara Disharoon, Western Maryland College, Westminster, MD

21157

I -Readers are encouraged to send in two copies of their classroom-tested ideas for "From the File" to the managing editor for review.-

December 1986 И

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