Tme Frame: 3-4 Da Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Teacher Reource for Unt Leon : Lnear Model Refreher Math Content Standard: S-ID.6, 7, S-IC. S.ID.6 Repreent data on two quanttatve varable on a catter plot, and decrbe how the varable are related. a) Ft a functon to the data; ue functon ftted to data to olve problem n the contet of the data. Ue gven functon or chooe a functon uggeted b the contet. Emphaze lnear, quadratc, and eponental model. b) Informall ae the ft of a functon b plottng and analzng redual. c) Ft a lnear functon for a catter plot that ugget a lnear aocaton. S.ID.7 Interpret the lope (rate of change) and the ntercept (contant term) of a lnear model n the contet of the data. S.IC. Undertand tattc a a proce for makng nference about populaton parameter baed on a random ample from that populaton. Math Practce: 2, 4, 5 2. Reaon abtractl and quanttatvel. Th oberved when tudent label ndependent and dependent varable on the catter plot and when the graph the lne of bet ft. 4. Model wth mathematc. Th oberved when tudent complete the table of data, make the catter plot, and determne the lne of bet ft. 5. Ue approprate tool trategcall. Th oberved when tudent make meaurement of dtance dropped and determne the lne of bet ft. Pror Knowledge - Determne lne of bet ft - Make a catter plot - Interpret meanng of lope - Interpret meanng of (r) - Able to ue LINREG on graphng calculator Student Frendl Target - I can create a catter plot. - I can determne a lne of bet ft ung technolog and graph t. - I can nterpret lope and ntercept n a contet. - I can make predcton ung a lne of bet ft. - I can nterpret an (r) value. - I can determne redual and ue them to ae ft. Eental Queton: From a catter plot, how are two quanttatve varable related? Academc Language: Redual, lope, model, nference, lne of bet ft, catter plot. Dfferentaton: Poble method would be to let tudent chooe ther own et of data to eplore.
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Procedure: Sample Actvt: (Poble pre-aement ak tudent to complete -4 n group of 2-4 before debrefng a a whole cla) The table below repreent data collected from puttng together a hoppng cart tran. Shoppng Cart Tran Number of Cart Length (cm) 2 38 3 69 4 202 5 234 7 295 0 390 4 57 20 709 Data from www.npraton.com/freetral/npredata ) Create a catter plot; then determne a lne of bet ft wth our calculator. Graph the lne on the catter plot. Record the equaton for the lne. 2) Interpret the -ntercept and lope of our lne of bet ft wthn the contet. 3) Interpret the meanng of (r) (the correlaton coeffcent) and ue t to eplan the valdt of our lne. 4) Your brave frend decde to make a hoppng cart tran of 2 cart. How long do ou predct the tran to be? Another data et for tudent to analze and dcu: Cand Bar Servng Calore Sze (g) Almond Jo 45 220 Bab Ruth 60 275 Butterfnger 60 270 Caramello 45 208 Heath 39 20 Herhe 43 20 Kt Kat 42 28 Krackel 4 20 Mlk Wa 58 262 Mound 53 258 Nutrageou 5 260 Pada 52 240 Data from www.npraton.com/freetral/npredata 5) Create a catter plot; then determne a lne of bet ft wth our calculator. Graph the lne on the catter plot. Record the equaton for the lne. 6) Interpret the -ntercept and lope of our lne of bet ft wthn the contet. 7) Interpret the meanng of (r) (the correlaton coeffcent) and ue t to eplan the valdt of our lne. 8) A Sncker bar contan 57 gram per ervng. How doe our predcton for calore compare to the 27 actuall n the bar? Through whole-group, drect ntructon, dcu redual value wth the cla wth the followng nformaton. Ung the catter plot and lne of bet ft, we can fnd the redual value. The redual for a pont the dfference between the oberved value of the dependent varable and the value predcted b the lne of bet ft. Redual oberved predcted 2
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Redual can be ued to determne whether a lnear model a good model for decrbng the data. The um of redual for a et of data 0 for the deal mathematcal model. Ung the cand bar data, group of tudent wll fnd the followng: Cand Bar Servng Calore Oberved Predcted Redual Sze (g) Almond Jo 45 220 220 223.4-3.4 Bab Ruth 60 275 275 273.5.85 Butterfnger 60 270 270 273.5-3.5 Caramello 45 208 208 223.4-5.4 Heath 39 20 20 203.3 6.87 Herhe 43 20 20 26.47-6.47 Kt Kat 42 28 28 23.3 4.87 Krackel 4 20 20 209.8.2 Mlk Wa 58 262 262 266.48-4.48 Mound 53 258 258 249.8 8.9 Nutrageou 5 260 260 243.4 6.86 Pada 52 240 240 246.47-6.47 The dcuon queton wll ak group of tudent to eplan what a redual value mean (for ntance, -3.4 how that the oberved value/pont appromatel 3 below the predcted value/lne of bet ft). Whle tll n group, tudent wll need to conclude that the um of redual for a lne of bet ft 0. Ak tudent to work n group of 2-4 on the correlaton coeffcent handout. Each group wll receve one et of data, and each tudent receve the tak eplanaton handout; the group wll then hare ther fndng wth the cla and dcu the general outcome. Allow each group to jutf whether the thnk ther data mot lnear. Ak the cla to organze the group correlaton coeffcent n order of ncreangl bet ft. Emphaze that the correlaton coeffcent ndcate whether or not a lnear model the bet ft for et of data. Be ure to addre the followng queton durng the dcuon. - Whch correlaton coeffcent value ndcate a good ft? The value that are cloet to or - are better than one that are not. - What doe a negatve correlaton coeffcent ndcate? A negatve lope for the regreon lne. A potve correlaton coeffcent? A potve lope for the regreon lne. A correlaton coeffcent that zero? A lnear model would not be approprate for the data. - What contence do ou oberve about the redual plot? The hould dpla a random catter. Cloe the dcuon b akng group to complete the error anal n whch tudent ued onl the redual or the correlaton coeffcent to foter a dcuon on the necet of ung the value together to determne whether a data et hould be modeled wth a lnear equaton. After tudent are comfortable wth the above procedure, the cla move on to the Barbe Bungee Jump Actvt that follow. Student handout for the pre-actvte a well a for the Barbe Bungee Jump follow. A vdeo for ntroducng Barbe Bungee Jump can be found at http://www.outube.com/watch?vcws3mvje7l4&nr&featureendcreen 3
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Bungee Jump Barbe Leon Scorng Gude Standard Completel meet tandard Partall meet tandard MP5 Correctl meaure dtance dropped and Meet 6-8 of record n table the completel S-ID.6/MP2 Scatter plot created wth ae labeled meet crtera. S-ID.6a/MP4/MP5 Lne of bet ft determned and recorded S-ID.7 Slope nterpreted correctl S-ID.7 Y-ntercept nterpreted correctl S-ID.6 Lne of bet ft graphed on the catter plot S-ID.6b Redual calculated and recorded correctl S-ID.6b Redual eplaned correctl S-ID.8 Meanng of r eplaned correctl S-ID.6a Correct predcton made Fnal Bungee Jump predcton ucceful Rarel meet tandard Meet fewer than 6 of the completel meet crtera. Student Handout for the mult-da leon follow. 4
Student Self-Aement for Leon Ratng: : I ve never een th topc and wouldn t even know how to begn. 2: I ve heard or een th before, but don t know how to tart or complete the problem. 3: I know the topc and can work through the problem but am unure whether I am correct. 4: I feel confdent that I could preent m work and oluton to the cla. 5: I feel that I could correctl teach th topc to another tudent f aked. Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Target I can create a catter plot. I can determne a lne of bet ft ung technolog and graph t. I can nterpret lope and ntercept n a contet. I can determne redual and ue them to ae ft. I can nterpret an (r) value. I can make predcton ung a lne of bet ft. Self-Ae on Shoppng Cart Tran Self-Ae on Cand Bar Self-Ae on Barbe Bungee Jump Drecton: Repond to the followng n complete entence wth correct academc vocabular.. Eplan the contetual meanng of the -ntercept of a model ft to data. 2. Eplan the contetual meanng of the lope of a model ft to data. 3. Eplan how the anal of redual and the correlaton coeffcent ued to verf the valdt of a lne of bet ft. 5
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Student Reource Learnng Target: - I can create a catter plot. - I can determne a lne of bet ft ung technolog and graph t. - I can nterpret lope and ntercept n a contet. - I can make predcton ung a lne of bet ft. The table below repreent data collected from puttng together a hoppng cart tran. Shoppng Cart Tran Number of Cart Length (cm) 2 38 3 69 4 202 5 234 7 295 0 390 4 57 20 709 Data from www.npraton.com/freetral/npredata ) Create a catter plot; then determne a lne of bet ft wth our calculator. Graph the lne on the catter plot. Record the equaton for the lne. 2) Interpret the -ntercept and lope of our lne of bet ft wthn the contet. 3) Interpret the meanng of (r) (the correlaton coeffcent) and ue t to eplan the valdt of our lne. 4) Your brave frend decde to make a hoppng cart tran of 2 cart. How long do ou predct the tran to be? 6
Cand Bar Servng Calore Sze (g) Almond Jo 45 220 Bab Ruth 60 275 Butterfnger 60 270 Caramello 45 208 Heath 39 20 Herhe 43 20 Kt Kat 42 28 Krackel 4 20 Mlk Wa 58 262 Mound 53 258 Nutrageou 5 260 Pada 52 240 Data from www.npraton.com/freetral/npredata Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 5) Create a catter plot; then determne a lne of bet ft wth our calculator. Graph the lne on the catter plot. Record the equaton for the lne. 6) Interpret the -ntercept and lope of our lne of bet ft wthn the contet. 7) Interpret the meanng of (r) (the correlaton coeffcent) and ue t to eplan the valdt of our lne. 8) A Sncker bar contan 57 gram per ervng. How doe our predcton for calore compare to the 27 actuall n the bar? 7
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Learnng Target: - I can determne redual and ue them to ae ft. - I can calculate correlaton coeffcent and ue them to ae ft. Ung the catter plot and lne of bet ft, we can fnd the redual value. The redual for a pont the dfference between the oberved value of the dependent varable and the value predcted b the lne of bet ft. Redual Oberved Predcted Cand Bar Servng Calore Oberved Predcted Redual Sze (g) Almond Jo 45 220 Bab Ruth 60 275 Butterfnger 60 270 Caramello 45 208 Heath 39 20 Herhe 43 20 Kt Kat 42 28 Krackel 4 20 Mlk Wa 58 262 Mound 53 258 Nutrageou 5 260 Pada 52 240 Dcu the followng wth our partner. Record our anwer below. How are redual related to the data and the lne of bet ft? Eplan what redual value of -3, 0, and 5 mean. Predct what the redual of an deal model would be. What the um of the redual? Wh do ou thnk th occur? Gve a ummar of what a redual value how. 8
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 The followng are the data et to be ued n the eerce. Heght and weght of tudent: Heght (n) Weght (lb) 76 200 70 85 68 70 69 75 70 200 65 60 66 60 67 75 7 205 74 25 Number of people n a part and total bll for dnner: People Bll ($) 8.50 3 29.30 5 63.75 0 92.55 6 60.35 4 48.75 2 42.35 2 32.55 3 50.65 5 85.25 Hour of leep the nght before the ACT and core on the ACT: Sleep Score (hour) 8 25 9 28 7 2 0 26 8.5 8 6.5 6 5.5 25 28 9 29 7 9 6 26 7.5 23 8.5 24 6.5 27 8.5 2 0 9 9 20 Year nce 995 and tudent enrollment: Year Student 537 2 577 3 625 4 665 5 720 6 770 7 832 8 895 9 960 0 030 9
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Elevaton of Arzona cte and average dal temperature. Elevaton (feet) Temperature ( ) Phoen: 06 84.5 Page: 4288 69 Flagtaff: 6923 59.9 Wnlow: 4856 70.4 Tucon: 2402 83.6 Caa Grande: 404 86.5 Grand Canon: 6923 62.8 Yucca: 83 82.7 Age of an ndvdual and number of contact contaned n ther cell phone. Age # of phone contact 5 20 230 32 26 66 02 2 503 6 465 8 856 23 25 46 288 44 465 33 05 0 86 55 42 50 560 25 432 Horepower of an automoble and ga mleage. Horepower Ga Mleage (mpg) 45 8.2 50 7.2 445.6 320 2.7 286 8.8 0
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Tak: You wll receve a et of data where ou are to:. Ue the table and formula gven to calculate the correlaton. 2. Decrbe the relatonhp ung th numercal value. 3. Prepare to dcu a a group wh (or wh not) our et of data more lnear than the other group. 4. Ung technolog, calculate the lne of bet ft. 5. Compute the redual for our data. 6. Create a redual graph that plot the ndependent value veru the redual calculated for that partcular data pont. 7. Be prepared to how our redual graph to the dcu the choce made n tak #3. Would ou tck wth the cla frt choce? Wh? Decrbng relatonhp numercall. When decrbng relatonhp between two varable, ou hould addre each of the followng: Drecton (potve or negatve) Strength of the relatonhp Devaton from the overall pattern Correlaton meaure the drecton and the trength of a lnear relatonhp. Suppoe we have data on varable and for n ndvdual (, ),(, 2 2),,( n, n) and we have the mean, and tandard devaton, for each varable. The correlaton defned a: Wrappng It Up: r n Student were gven data for the average alar of major league baeball plaer from 970 to 200. Jmm group calculated the correlaton coeffcent to be 0.94 and concluded that a trong potve lnear relatonhp wa preent. John group made a redual graph of the ame data whch hown below. John group clamed that the data wa not lnear. Whch group do ou agree wth and wh? Data Source: http://www.baeball-almanac.com/chart/alar/major_league_alare.html
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 2 Ue the formula to calculate the correlaton between heght and weght of tudent. Heght (n) Weght (lb) 76 200 70 85 68 70 69 75 70 200 65 60 66 60 67 75 7 205 74 25 n r
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Ue the formula to calculate the correlaton between hour of leep and the core on the ACT. Sleep (hr) Score 8 25 9 28 7 2 0 26 8.5 8 6.5 6 5.5 25 28 9 29 7 9 6 26 7.5 23 8.5 24 6.5 27 8.5 2 0 9 9 20 r n 3
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 4 Ue the formula to calculate the correlaton between number of people n a part and total bll for dnner. People Bll ($) 8.50 3 29.30 5 63.75 0 92.55 6 60.35 4 48.75 2 42.35 2 32.55 3 50.65 5 85.25 n r
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 5 Ue the formula to calculate the correlaton between ear nce 995 and tudent enrollment. Year Student 537 2 577 3 625 4 665 5 720 6 770 7 832 8 895 9 960 0 030 n r
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 6 Ue the formula to calculate the correlaton between elevaton of Arzona cte and average dal temperature.. Elevaton (feet) Temperature ( ) Phoen: 06 84.5 Page: 4288 69 Flagtaff: 6923 59.9 Wnlow: 4856 70.4 Tucon: 2402 83.6 Caa Grande: 404 86.5 Grand Canon: 6923 62.8 Yucca: 83 82.7 n r
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Ue the formula to calculate the correlaton between age of an ndvdual and number of contact contaned n ther cell phone. Age # of phone contact 5 20 230 32 26 66 02 2 503 6 465 8 856 23 25 46 288 44 465 33 05 0 86 55 42 50 560 25 432 r n 7
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 8 Ue the formula to calculate the correlaton between horepower of an automoble and ga mleage. Horepower Ga Mleage (mpg) 45 8.2 50 7.2 445.6 320 2.7 286 8.8 n r
BARBIE BUNGEE JUMP - I can create a catter plot. - I can determne a lne of bet ft ung technolog and graph t. - I can nterpret lope and ntercept n a contet. - I can make predcton ung a lne of bet ft. - I can nterpret an (r) value. - I can determne redual and ue them to ae ft. Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 Overvew: You wll tart b attachng rubber band to a Barbe doll' ankle and then meaurng how far he wll fall before reboundng. Then add addtonal rubber band and meaure the drop. Contnue to add rubber band and meaure the drop then create a mathematcal model or equaton that can predct the dtance a Barbe doll wll fall for a gven number of rubber band. Lat of all, a fnal bungee jump pot wll be announced. Ung the predcton equaton, determne the number of rubber band to gve Barbe the greatet thrll. Let Barbe take the plunge, and ee how well our predcton model worked. (Dclamer: no Barbe were njured durng the creaton of th actvt. Other acton fgure uch a Storm Trooper, G.I. Joe ma be ubttuted.) # of rubber band Dtance Dropped (to the top of head) 2 3 4 5. Complete the table. 2. Plot the pont on the grd. Label and cale the graph. 3. Fnd the equaton of the lne of bet ft. Record t here. (dtance) a + b(rubber band) r 2 r 4. Gve an nterpretaton of the lope for the equaton. 9
Math 3 Unt Leon S-ID.6, 7, S-IC. Math Practce 2, 3, 4 5. Gve an nterpretaton of the -ntercept for the equaton. 6. Graph the lne of bet ft on the catter plot of our data. Calculate and record the redual for through 5 rubber band. Eplan how thee redual ae the ft of the functon. 7. Interpret r for our lne of bet ft. 8. Ue the lne of bet ft to predct how far he would fall wth 0 rubber band. 9. Your ntructor wll pecf a locaton for the fnal bungee jump. Ue our equaton to determne the number of rubber band to gve Barbe the greatet thrll n th bungee jump. Th mean he hould come a cloe a poble to the ground wthout httng her head. When ou have determned the number of rubber band, make th bungee cord and let Barbe jump. Wrte a report that reflect our undertandng of the Barbe Bungee Jump outcome. Anwer the followng queton wthn our paragraph. Drecton: Repond to the followng n complete entence wth correct academc vocabular.. Eplan the contetual meanng of the -ntercept of a model ft to data. 2. Eplan the contetual meanng of the lope of a model ft to data. 3. Eplan how the anal of redual and the correlaton coeffcent ued to verf the valdt of a lne of bet ft. 20