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Using a Lifeline to Give Rational Number a

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Hunt then placed a large number line on theboard and asked students <strong>to</strong> label and positionsticky notes on the number line <strong>to</strong> represent eachof the times in Lu Lynne’s biography. The studentshad particular difficulty in representing negativenumbers that included fractions. For example, inthe s<strong>to</strong>ry, Billy was 21 months older than Lu Lynne.The students had <strong>to</strong> 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 <strong>to</strong> place –1 3/4 between 0 and–1 rather than between –2 and –1.The Personal-<strong>Lifeline</strong> ProjectAFTER THE STUDENTS HAD SOME EXPERIENCEplacing rational numbers on a number line, Huntassigned the task in figure 2. She used the practiceproblem <strong>to</strong> illustrate that personal lifelines aremore interesting if they include events that happenat various times. In their projects, the studentswere required <strong>to</strong> 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 <strong>to</strong>your 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 <strong>to</strong> 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 <strong>to</strong> 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 <strong>to</strong> crawl at 9 months old, you wouldplace that event on the number line at 3/4, since 9 months ou<strong>to</strong>f 12 months would be the fraction 9/12, which simplifies <strong>to</strong>3/4. Choosing such events as the births of siblings, when youbegan <strong>to</strong> walk, when you learned <strong>to</strong> ride a bike, when your parentsmet, when you cut your first <strong>to</strong>oth, 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 <strong>to</strong> 5 years on negative sideof lifeline______ From 12 <strong>to</strong> 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 in<strong>to</strong> useful,uniform partitions______ Other ________________________________ Other ________________________________ Other __________________________Fig. 3 Personal-lifeline student critiquetimes during the year. The students were encouraged<strong>to</strong> choose events other than those representedby whole numbers, such as first birthday, secondbirthday, and so on. The students brains<strong>to</strong>rmedpossible events that they might include in their personallifelines. The students who objected <strong>to</strong> submittingpersonal information were allowed <strong>to</strong>choose his<strong>to</strong>rical, 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 <strong>to</strong>oth, saying firstwords, learning <strong>to</strong> ride a bike, moving <strong>to</strong> a newhome, and special vacations or celebrations, alongwith important his<strong>to</strong>rical events and births anddeaths of famous people. The students used thislist as a starting point but were encouraged <strong>to</strong> interviewfamily members and choose interestingevents in the his<strong>to</strong>ries of their families. The assignmen<strong>to</strong>ffered opportunities for earnest communicationbetween adolescents and adult familymembers.212 MATHEMATICS TEACHING IN THE MIDDLE SCHOOL

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