Big Banana Peel - Center for Math and Science Education

Big Banana PeelTopicMathematical reasoningKey QuestionHow much of a banana is edible?FocusStudents will determine what percentage of a banana isedible.Guiding DocumentsProject 2061 Benchmark• Numbers can be written in different forms,depending on how they are being used. Howfractions or decimals based on measuredquantities should be written depends on howprecise the measurements are and how precisean answer is needed.NRC Standards• Use appropriate tools and techniques to gather,analyze, and interpret data.• Think critically and logically to make the relationshipsbetween evidence and explanations.• Use mathematics in all aspects of scientific inquiry.NCTM Standards• Collect, organize, and describe data• Use problem solving approaches to investigateand understand mathematical content• Develop and apply a variety of strategies to solveproblems, with emphasis on multi-step and nonroutineproblems• Verify and interpret results with respect to originalproblem• Acquire confidence in using mathematicsmeaningfullyMathMeasurementmassEstimationRatioAveragingWriting a formulaGraphingIntegrated ProcessesObservingCollecting and recording dataComparing and contrastingGeneralizingMaterialsA supply of bananasBalancesMetric massesBackground InformationThis may be the students’ first experience in writinga formula. If so, the development of a formula needsto be discussed. In this case, the edible portion of abanana (E in the formula) is to be expressed as apercentage (or fraction) of the total mass of the banana(T in the formula). Thus, if one-half of the banana isedible, the formula would be E=1/2T. Most bananas willcome very close to fitting the formula E=.65T or E=2/3T.Students may reason that the coefficient of T mustbe less than one since the edible portion has a massless than the total. The best information for determiningthe formula for this group of bananas is given by theaverage percentage. The function of an average is tohelp guard against significant error. In this case, theaverage will be in the neighborhood of 65%, dependingon the ripeness of the banana. Percentages are notnormally used in such formulas, so 65% is not anappropriate form. It should be converted to a decimalsuch as .65. The formula becomes E=.65T.This activity provides students with a realistic experiencewhich shows that measurement is always anapproximation. They are asked to find the total mass(edible part and peel) of the banana. They are thenasked to find the separate masses of the pulp and thepeel. The sum of these two may differ by just one gramfrom the total mass since students are measuring tothe nearest gram and therefore rounding.Fact pages are included that provide informationabout the science of the banana plant, the nature ofbanana as a food product, the origin of bananas, andsources of bananas as an agricultural commodity.Management1. Before students begin, have them predict andrecord the edible percentage of the banana. Theedible portion must be defined. Here, it is the pulp,not the peel.2. Students may work in groups of four or five, eachgroup sharing a banana and pooling the results withother groups to find the average percentage.Procedure1. Begin by administering the four point true-false quizto heighten interest and peak curiosity. Students mayindicate their responses by showing thumbs up for“I think this is a true statement” and thumbs downfor “I think this is a false statement.” (No sidewaysthumbs!) The four statements are these:MATH + SCIENCE: A SOLUTION 105 © 1987 AIMS Education Foundation

TheTruth About BananasScientific NameFamily: MusaceaeGenus: MusaSpecies: Musa acuminata (common banana)Musa paradisica (plantain banana)Food ValueWater: 75.7%Protein: 1.1 gFat: 0.2 gCarbohydrates: 22.2 gWhich of these statements are true?a. The banana is a berry.b. Bananas grow on trees.Food Energy:Approximately 1 calorie per gramVitamin A: 190 IUThiamine (B 1): 0.05 mgRiboflavin (B 2): 0.06 mgPhosphorous: 26 mgPotassium: 370 mgVitamin C: 10 mgNiacin: .7 mgCalcium: 8 mgIron: .7 mgSodium: 1 mgc. Pound for pound, bananas are the most widely sold fruit in the United States.d. Bananas are highly nutritious and easily digestible.There are over100 varieties ofbananas!The Banana PlantYou may be surprised to learn that bananas are berries! Aberry is a simple fruit having a skin surrounding one ormore seeds in a fleshy pulp. Botanists classifygrapes, tomatoes, currants, and bananas as berries.Bananas grow on a tropical plant that is not atree—it has no trunk. Bananas are gigantic herbsthat spring from underground stems. What appears to be the trunk is a false stem formedby tightly wrapped leaf sheaths that grows to a height of three or more meters. From thetop, 10-20 large oblong to elliptical-shaped leaves fan out. It takes 5-18 months to growthe one stalk of bananas it bears. Bananas on the stalk point upward. After harvesting,the plant is cut down and the underground rootstock produces new shoots for the next plant.MATH + SCIENCE: A SOLUTION 107 © 1987 AIMS Education Foundation

Theof BananasIt is generally agreed that the banana originated in Malaysiaand the East Indies. It is frequently referred to in ancient Hindu,Chinese, Greek, and Roman literatureand in sacred texts of Orientalcultures. It is said that the armiesof Alexander the Great fighting in Indiawere the first Europeans to learn about bananas.Theophratus, in a book written in the 4th century B.C. andconsidered to be the first scientific botanical work known,described the banana. The Arabs introduced bananas to theNear East and Mediterranean. They came to the CaribbeanIslands and Mexico shortly after Columbus’ voyages. It isinteresting to note that the Polynesiansintroduced bananas throughout the Pacificregion during their migration.The name of one species, Musasapientum, means “fruit of the wise men.”This name derives from the legend thatsages in India sat under banana plantsduring times of meditation. Today wise men, women,boys and girls eat bananas because they are such anexcellent and nutritious food.Sources of SupplyIn the Western Hemisphere:Ecuador (largest exporter) MexicoHonduras (chief export) Dominican RepublicPanama (chief export) BrazilCosta RicaColumbiaGuatemalaIn Asia:TaiwanIn Africa:Canary IslandsEthiopiaCameroonGuineaNigeriaNext time you are in a store, carefully examine the label on a bunch of bananas.Generally, the source country is named on it in small type. See how many differentsource countries you can find on banana labels!!MATH + SCIENCE: A SOLUTION 108 © 1987 AIMS Education Foundation

The Banana as FoodPound for pound, bananas are the most widely soldfruit in the United States. They are the most importantof all commercial fruits, close to the combined productionof all citrus fruits.Bananas are an excellent food source of potassium, vitamins A & C, and quickenergy. They are low in protein and fat. They are an excellent between-meal snackand one of the most easily digested and nutritious natural foods. A medium-sizebanana has about 125-130 calories, or about one calorie per gram. Bananas arerecommended for low-fat, low-sodium diets.Bananas come with their own wrapping, ready to go into lunch boxes. They aretasty sliced on breakfast cereals, in fruit salads, and gelatin desserts. Bananas areused in the preparation of flavoring. Vacuum dehydration yields banana crystals, alight-brown powder used in ice cream, bakery products and milk-based beverages.“Tree-ripened” would not make good advertising for bananas. If allowed to ripen onthe plant they are starchy, mealy, or rotten and therefore inedible. They are sent tomarket green and are ripened in air-tight rooms with controlled humidity andtemperature. These conditions permit nearly all of the starch to be converted intosugar for good taste. The banana is at its best eating condition when the brightyellow peeling is flecked with brown specks, known as “sugar specks.” Look forplump, well-filled fruit.A plantain is a cooking variety of banana that islarger than our common banana. It is a staplefood in the tropics. Plantains are starchy whengreen and take the place of potatoes. Plantain chipsare the Latin-American equivalent of our potato chips!MATH + SCIENCE: A SOLUTION 109 © 1987 AIMS Education Foundation

MATH + SCIENCE: A SOLUTION 110 © 1987 AIMS Education FoundationBanana ABanana BBanana CBanana DBanana EBanana FBanana GBanana HSumAverageThe Big Banana Peel!Prediction: What part of a banana is edible?%Complete the table.Total Mass (g)Mass ofPeeling (g)Mass of EdiblePart (g)Ratio of Edible (g)Total Mass (g)Percent of Bananathat is EdibleFrom this data, write three things you now know about these bananas.

MATH + SCIENCE: A SOLUTION 111 © 1987 AIMS Education FoundationLet E stand for Edible and T for the total. E= ___ TWrite a formula to show the amount of the edible portion.AverageHGFBananaEDCBA0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%Construct a bar graph showing the percent of each banana that is edible.The Big Banana Peel!