Can Pythagoras Swim?

Transcription

1 Overview Ativity ID: 8939 Mth Conepts Mterils Students will investigte reltionships etween sides of right tringles to understnd the Pythgoren theorem nd then use it to solve prolems. Students will simplify expressions multiple representtions of numers TI-34 MultiView penil using rdils nd exponents in this tivity. eqution solving pper Ativity exponents geometri representtions of two-dimensionl ojets Pythgoren theorem sissors Introdue the Pythgoren theorem first y tril nd error; then shre the formul with students. By experimenting, we re going to disover one of the most fmous theorems in ll of mth, nd proly the most fmous in geometry: the Pythgoren theorem. Consider the right tringle elow. Form squre long eh side of the right tringle. At this point in the tivity, give eh student (or group of students) the enlrged photoopy of the digrm ove (tthed). Now, ut eh of the smller squres long the outside edge nd long the dotted lines. Cn you use those eight piees to ompletely over the lrgest squre? Ask the students to summrize this tivity mthemtilly. Their voulry does not hve to e urte, ut they need to reognize tht if we squre the two smller sides of the tringle nd dd 008 Texs Instruments Inorported TI-34 MultiView Ativity p. 1 of

2 them together, the sum equls the squre of the lrger side. You ve just seen the Pythgoren theorem. In words, it sys tht the sum of the squres of the legs of right tringle equls the squre of the hypotenuse. Mthemtilly, the formul is: + =. Let s prtie. 6 The legs mesure 6 nd 8 units, so = 6 units nd = = = 100 = 100 = Therefore, = 10. Give the students more exmples of right tringles, using numers tht do not result in perfet squres. The TI-34 MultiView lultor is n pproprite tool. Let s use the TI-34 MultiView lultor for the following: () Find the pproximte length of the hypotenuse if the legs re 5 nd 10 units long. () Find the pproximte length of the missing leg if one leg is 6 in. nd the hypotenuse is 8 in. () Find the pproximte length of the hypotenuse if the legs mesure ½ nd ¾ m. Note: Be reful with frtion entry. The TI-34 MultiView will not give nswers in rdil form. Prior to ssigning the following worksheet, review simplifying squre roots y hnd with your students. In prt () ove, the lultor gve us n nswer of pproximtely When we simplify 15 y hnd, we get 5 5. Are these the sme? Explin. Follow these steps: 1. Press Then press. 3. Press to opy the previous nswer. 4. Press for the nswer: 5. Press Press to see wht equls. 7. Press for the pproximte nswer. 8. The sreen should show this: Clulte the ext nswer y hnd nd hek tht they re equivlent. 008 Texs Instruments Inorported TI-34 MultiView Ativity p. of

3 Cn Pythgors Swim? Nme Dte Diretions: Find the length of the hypotenuse. Do not round your nswers Mr. P. is putting pool in his yrd. He hs smll kyrd, nd therefore he must put in n oddshped pool rther thn retngulr one. He is not sure how muh the pool instlltion will ost, ut he knows the ompny will determine the ost using re nd perimeter of the pool. () Compute the perimeter of the pool. Divide the pool into regions; then find the missing lengths. (Hint: Use 1 &.) Your nswer should e rounded to the nerest unit. SHOW THE REGIONS. () Compute the re of the pool, using the regions you drew ove. The nswer should e rounded to the nerest squre unit. Show your work. 4. If eh squre ove is 4 ft y 4 ft, () wht is the perimeter of the pool in feet? () wht is the re of the pool in squre feet? 008 Texs Instruments Inorported TI-34 MultiView Worksheet p. 1 of 1

4 Answer Key Diretions: Find the length of the hypotenuse. Do not round your nswer = 5. = Mr. P. is putting pool in his yrd. He hs smll kyrd, nd therefore he must put in n odd-shped pool rther thn retngulr one. He is not sure how muh the pool instlltion will ost, ut he knows the ompny will determine the ost using re nd perimeter of the pool. I II III () Compute the perimeter of the pool. Divide the pool into regions; then find the missing lengths. (Hint: Use 1 &.) Your nswer should e rounded to the nerest unit. SHOW THE REGIONS = 4 units IV V VI () Compute the re of the pool, using the regions you drew ove. The nswer should e rounded to the nerest squre unit. Show your work. I: 1 3 () 3, II: 3() = 6, III: 1 3 () 3, IV: (4) = 8, 1 V: (3)(4) = 6, VI: 1 (6)(4) = 1 Totl = 35 units 4. If eh squre ove is 4 ft y 4 ft, () wht is the perimeter of the pool in feet? 4(4) = 96 ft () wht is the re of the pool in squre feet? 35(16) = 560 ft 008 Texs Instruments Inorported TI-34 MultiView Worksheet Answer Key

5 Student Hndout 008 Texs Instruments Inorported TI-34 MultiView Worksheet In-Clss Explortion