The Mah Projecs Journal Page 1 LESSON PLAN TUBICOPTERS & MORE OBJECTIVE The goal of his lesson is wo-fol:1) Suens raw conclusions from graphs wihin conexs an 2) Suens use hese conexs o iscern he meaning of slope an inerceps. To mee hese objecives i is very imporan ha he eacher use he opporuniy inheren in he lesson o have suens wrie an iscuss heir houghs. This lesson is heavy on oral & wrien responses raher han numerical. HELICOPTER (ay 1) This firs segmen of he lesson is base on he "Ploing a Disance- Time Graph" app from AbsorbLearning.com (hp://bi.ly/10yyito). In general, he app has a helicoper moving lef o righ while graphing he relaionship of is horizonal isance (0-16 m) o ime (0-10 sec). Since he graph is no ploing aliue, he suens are challenge o reconcile he shape of he graph o he fligh pah of he helicoper. I is exacly ha cogniive conflic ha makes his aciviy so valuable. 1) Click he helicoper o sar he ime, bu on move i. Since here is no change in horizonal isance as ime expires, he graph is a horizonal line a = 0. 2) Click he helicoper an lif i sraigh up. As ime expires, he horizonal isance sill oes no change, herefore he graph is ienical o ha of #1. 3) Click he helicoper an move i a a moerae pace o he righ. The line now plos iagonally because isance increases as ime increases. 4) This ime, ask he suens BEFORE you sar he app, Wha will he graph look like if he helicoper goes backwars? The helicoper will have o go forwar firs, bu he graph oes no go backwars. The graph has a ownwar (negaive) slope when he helicoper goes backwars, because he isance from he saring poin ecreases as ime increases. The app plos poins up an own, bu never plos backwars (o he lef), because ha woul imply ha he helicoper was moving back in ime. 5) Again, promp he suens before you sar he app, Wha is i abou he fligh of he helicoper ha affecs he seepness of he graph? Show flighs of various raes, even changing he rae wihin he same fligh, o show how faser raes prouce seeper lines. 6) Now ha suens unersan ha he faser he helicoper goes, he seeper he line is graphe, ask he class, How o I ge i o graph a verical line? Move he helicoper as fas as possible in an aemp o ge a verical line. The iea is ha a verical line implies being in all places a he same ime, which of course is impossible. This gives us anoher reason for an unefine slope, besies he inabiliy o ivie by zero in he raiional slope formula. 7) Have suens commi o heir own skech before he reveal on his one. Poin ou ha he halfway poin is foun on he isance axis, no he ime axis. Conceps Inerpreing graphs, paricularly in regars o he meaning of slopes an inerceps. Time: 2 hours. Maerials Suen Hanous Compuer wih Inerne Preparaion Free online app from AbsorbLearning.com hp://bi.ly/10yyito www.mahprojecs.com
The Mah Projecs Journal Page 2 LESSON PLAN TUBICOPTERS (coninue) BATH TUB (ay 2) For his secon segmen of he lesson, i is suggese o have suens wrie all heir responses o he bah ub quesions before having hem iscuss heir answers wih each oher. This will help rive home he overall concep of slope emphasize by he bah ub conex. 8) DEPTH fill B wai si C D bah E ou F ry G rain A TIME 9) AB represens when he eph of he waer is increasing (posiive) while GH represens when he eph of he waer is ecreasing (negaive). 10) When you sep ino a ub, he waer rises faser han when he waer is flowing form he fauce. 11) I rains faser han i fills. You can ell because he slope is greaer (absolue value of, echnically), han AB. 12) Because he waer eph is greaer when a person is siing in he ub han when hey are no. H FLAGPOLE (Conribue by Larry McGehe, Consulan, Dayona Beach, FL) This hir segmen of he lesson asks he suens o rea values on he axes an o prouce heir own skech, forcing he suens o compare-n-conras he wo graphs in conex. 13) The flag is repeaely being yanke up he pole, wih a pause as he person pulling on he rope exchanges hans. The final long horizonal line is he flag reaching is final heigh. 14) The suens shoul be encourage o rea he y-axis for his value, an shown how he heigh of 5 meers is mainaine for several secons. 15) Suen versions shoul look somehing like he iagram on he righ. LEMONADE STAND This fourh segmen of he lesson focuses on he meaning of boh x- an y- inerceps. I woul be helpful o emphasize ha each one has a leas one coorinae value of zero. 16) There are negaive values because of he iniial cos o open he san. A ime zero, you sar in he re. 17) I represens he number of sales require o break even. A his poin, your profi is zero, you have neiher mae nor los money on he lemonae san. PRACTICE/ASSESSMENT The answers o his secion are: 18) B 19) D 20) C 21) A h www.mahprojecs.com
The Mah Projecs Journal Page 3 TUBICOPTERS & MORE HELICOPTER 1) Why oes he graph plo horizonally when he helicoper says saionary? 2) Why oes he graph plo horizonally when he helicoper goes up? 3) Why oes he graph plo oblique lines (iagonally) when he helicoper goes forwar? 4) Why oes he graph plo ownwar when he helicoper goes backwars? Is here a way o ge he graph o plo backwars? 5) Wha eermines he seepness of he graph? 6) If a horizonal line implies being in he same place a all imes, wha woul a verical line imply? 7) Skech a graph of he ime an isance for a helicoper ha goes fas o he halfway poin, hovers for awhile, hen goes backwars fas unil i is jus shy of he saring poin, hen goes forwar again slowly. www.mahprojecs.com
The Mah Projecs Journal Page 4 TUBICOPTERS (coninue) BATH TUB The graph below represens he waer level of a bah ub over ime. I shows he ub filling, he waer urne off, someone siing in he ub, bahing, hen geing ou, rying off an finally he ub raining. D E DEPTH B C F G A TIME H 8) Mark he graph for each of hese: fill, wai, si, bah, ou, ry, rain. 9) Why is he slope of AB posiive while he slope of GH is negaive? 10) Why is he slope of CD greaer han ha of AB? 11) Does he ub rain slower or faser han i fills? How can you ell? 12) Why is DE higher han BC? Why is DE longer han FG? www.mahprojecs.com
The Mah Projecs Journal Page 5 TUBICOPTERS (coninue) FLAG 13) Wha was happening o he flag in he iagram on he righ? heigh (m) 5 1 14) If he flag was raise o he op of he pole, wha is he approximae heigh of he flagpole? 1 5 10 ime (sec) heigh (m) 15) I is sai ha he American Flag is excie o go up, bu sa o come own. Therefore, he Miliary raises he flag quickly wih no pauses, bu brings i own slowly, wih small pauses uring han exchanges. Skech a graph ha reflecs his meho. 5 1 1 5 10 15 ime (sec) LEMONADE STAND 16) Why oes he graph show profi values below zero? Profi 17) Wha is he meaning of he poin where he graph crosses he horizonal axis? 0 Amoun Sol www.mahprojecs.com
The Mah Projecs Journal Page 6 TUBICOPTERS (coninue) PRACTICE Mach each of he following scenarios wih one of he graphs below. a) b) c) ) 18) Johnny runs up he sree, bu quickly urns an runs home a he same spee. 19) Jennifer is riing her bike home. She ges a fla ire. She can fix i, so she walks he bike he res of he way home. 20) Jamie is several blocks from home. She is walking o her frien s house which is even furher from home. Halfway here, her frien picks her up in a car an she ries he res of he way. 21) Jackson runs o his frien s house, hangs for a shor while, an hen walks home. www.mahprojecs.com