Using a Lifeline to Give Rational Number a

More documents

Recommendations

Info

$MATH 622 Selected Topics in Modern Algebra I$

$MATH 621 Selected Topics in Advanced Calculus II$

Give RationalTouchences to time in the sample problem. They were encouragedto look for such phrases as “about thesame time”; “21 months older”; “last year”; “September20, 1986”; “3 months before”; “5 years, 3months”; and “at Christmas.” Hunt emphasized thatthe story of Lu Lynne is not a good example of afamily history because it lacks organization andsound grammatical structure. The purpose of thepractice problem was to help the students considerthe many ways in which one can refer to time andto notice that some times are exact, whereas othersare approximate.The students were then instructed to use 0 torepresent the month of Lu Lynne’s birth. They wereto find points on the number line that correspondedto the times that they had underlined in the sampleproblem. Before completing that activity, the studentsfirst needed to become accustomed to using aparticular month as the origin. Middle-grades studentstended to think of 1 January as 0, rather thanSeptember 1986. Another difficulty that studentsfaced was the tendency to label the number linewith just the years (1985, 1986, 1987, 1988, etc.)while neglecting to label the points with integers(–1, 0, 1, 2, etc.). One benefit of this project was thatstudents began to understand the importance of theorigin and the relationships of all other numbers tothe origin.The students quickly realized that not all thedates could be represented by integers. This discoveryprompted a discussion about the practicalityof different representations. For example, a decimalnumeral is not a particularly good choice for representingtwo months. The students also discoveredthat some common fractions are more useful thanothers for representing time. For example, theyfound that halves, thirds, fourths, sixths, andtwelfths are useful for representing numbers ofmonths as parts of the year.Instructions: Below is a sample of a biography that might havebeen submitted by a student as part of her Lifeline Project.Work with your group to underline all of the phrases that makereferences to time. Using 0 to represent Lu Lynne’s birth date,work with your group to find points on the number line thatrepresent the times of the events you have underlined.Lu Lynne’s BiographyLu Lynne’s birthday was Sept. 20, 1986. Her brother, Billy,was 21 months older than she. Lu Lynne began to walk whenshe was 9 months old. Her family moved to Kansas when shewas about 3 years old. Her dad had graduated from school therein January of 1981 so he was glad to move back. Six monthsafter his graduation, he and Lu Lynne’s mother were married inAustin, Texas. They bought their first home in March of the followingyear. They didn’t sell that house until December of 1990.Billy was hospitalized 3 months before the house sold. He wasvery sick and had surgery at that time. Lu Lynne was the starpoint guard for her basketball team when she was 10 1/2. Shehad only begun playing the year before. Before that she had hadno interest in sports. When she was younger all she wanted todo was read. She won an award for reading at the honors’ programin May, 1994. Reading a book about basketball is whatbegan to interest her in sports. Lu Lynne’s mother graduatedfrom nursing school in June of 1997. She had had to postponecompletion of her degree because Kiki, Lu Lynne’s little brother, is5 years 3 months younger than Lu Lynne. Once Kiki enteredschool, Lu Lynne’s mother was able to finish her training. Thefamily celebrated her graduation with a trip to Disney World inAugust of the year following her graduation. They had begunsaving for vacation at Christmas in 1995.Fig. 1 Lu Lynne’s storyVOL. 7, NO. 4 . DECEMBER 2001 211
Hunt then placed a large number line on theboard and asked students to label and positionsticky notes on the number line to represent eachof the times in Lu Lynne’s biography. The studentshad particular difficulty in representing negativenumbers that included fractions. For example, inthe story, Billy was 21 months older than Lu Lynne.The students had to determine that 21 monthsbefore Lu Lynne’s birth would be represented aseither –1 9/12 or –1 3/4. A common mistake thatstudents made was to place –1 3/4 between 0 and–1 rather than between –2 and –1.The Personal-Lifeline ProjectAFTER THE STUDENTS HAD SOME EXPERIENCEplacing rational numbers on a number line, Huntassigned the task in figure 2. She used the practiceproblem to illustrate that personal lifelines aremore interesting if they include events that happenat various times. In their projects, the studentswere required to include events that had happenedbefore and after they were born and at variousMake a personal lifeline (number line) using the month andyear of your birth as 0. Dates of events that occurred prior toyour birth will be represented with negative numbers, andthose afterward will be represented with positive numbers.You may include any events and as many as you like, althoughthe minimum number (including your birth) is ten. At leastthree of those events must have occurred 3 to 5 years beforeyour birth. For example, suppose that your parents were married5 years before you were born. That event would be placedon the number line at –5 (negative 5). Or suppose that youmoved to El Paso when you were 3 years old. That event wouldbe placed on the number line at +3 (positive 3).Events should be recorded showing your mathematical power.For example, if you began to crawl at 9 months old, you wouldplace that event on the number line at 3/4, since 9 months outof 12 months would be the fraction 9/12, which simplifies to3/4. Choosing such events as the births of siblings, when youbegan to walk, when you learned to ride a bike, when your parentsmet, when you cut your first tooth, and so on, should befun for your family. Please do not include obvious events, suchas your first birthday (at +1), your second birthday (at +2), andso on. You should label each point with words or pictures thatcommunicate the event.Finally, you should include a reflection concerning the mathematicsyou learned or strengthened by doing this task, as wellas your thoughts concerning the task.Fig. 2 Personal-lifeline promptName of Classmate: ___________________________ Measured accurately______ At least 3 to 5 years on negative sideof lifeline______ From 12 to 14 years on positive sideof lifeline______ Positive and negative sides of lifelinein correct places______ Illustrations and labels for eachgraphed event______ At least 3 events before your birth(negative events) and 7 events afteryour birth (positive events)______ Birth as 0______ Correct numerical representation foreach point______ Used mixed numbers and a varietyof common fractions (other than justhalves, fourths, and thirds)______ Dots in proper place for each pointgraphed______ Points graphed in appropriate placeconsidering the time stated______ Integer labels above yearly tickmarks______ Year intervals divided into useful,uniform partitions______ Other ________________________________ Other ________________________________ Other __________________________Fig. 3 Personal-lifeline student critiquetimes during the year. The students were encouragedto choose events other than those representedby whole numbers, such as first birthday, secondbirthday, and so on. The students brainstormedpossible events that they might include in their personallifelines. The students who objected to submittingpersonal information were allowed tochoose historical, rather than personal, events fortheir lifelines.Some events that interested students were theirparents’ first meeting or marriage, the births ofsiblings, cutting or losing a first tooth, saying firstwords, learning to ride a bike, moving to a newhome, and special vacations or celebrations, alongwith important historical events and births anddeaths of famous people. The students used thislist as a starting point but were encouraged to interviewfamily members and choose interestingevents in the histories of their families. The assignmentoffered opportunities for earnest communicationbetween adolescents and adult familymembers.212 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL
Page 1: Using a Lifeline toNumbers aPersona
Page 5 and 6: CRITERIONLEVEL 4LEVEL 3LEVEL 2LEVEL

Using a Lifeline to Give Rational Number a

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?