The Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center


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1 Resource Overview Quntile Mesure: Skill or Concept: 1010Q Determine perimeter using concrete models, nonstndrd units, nd stndrd units. (QT M 146) Use models to develop formuls for finding res of tringles, prllelogrms, trpezoids, nd circles. (QT M 256) Excerpted from: The Mth Lerning Center PO Box 12929, Slem, Oregon Mth Lerning Center This resource my e ville in other Quntile utilities. For full ccess to these free utilities, visit The Quntile Frmework for Mthemtics, developed y eductionl mesurement nd reserch orgniztion MetMetrics, comprises more thn 500 skills nd concepts (clled QTxons) tught from kindergrten through high school. The Quntile Frmework depicts the developmentl nture of mthemtics nd the connections etween mthemtics content cross the strnds. By mtching student s Quntile mesure with the Quntile mesure of mthemticl skill or concept, you cn determine if the student is redy to lern tht skill, needs to lern supporting concepts first, or hs lredy lerned it. For more informtion nd to use free Quntile utilities, visit Prk Forty Plz Drive, Suite 120, Durhm, North Crolin METAMETRICS, the METAMETRICS logo nd tgline, QUANTILE, QUANTILE FRAMEWORK nd the QUANTILE logo re trdemrks of MetMetrics, Inc., nd re registered in the United Sttes nd rod. The nmes of other compnies nd products mentioned herein my e the trdemrks of their respective owners.
2 Set C1 Geometry: Tringles & Qudrilterls Set C1 H Activity 3 ctivity Finding the Perimeter & Are of Prllelogrm Overview Students find the perimeter nd re of n index crd, then cut the crd nd tpe the two resulting pieces together to form prllelogrm tht is not rectngle. Then they find the perimeter nd re of the prllelogrm. As they do so, they discover tht multiplying the length of one side y the other does not yield the re of nonrectngulr prllelogrm. After students investigte further y creting two more prllelogrms, the techer shres the formul for finding the re of prllelogrm, nd sks the clss to explin nd pply it. Skills & Concepts H clssify qudrilterls H determine the formul for the re of prllelogrm y relting it to the re of rectngle H use formuls to determine the perimeters nd res of rectngles nd prllelogrms You ll need H Strt with Rectngle (pge C1.30, run copy on trnsprency) H Squre Inch Grid Pper (pge C1.31, run severl clss sets nd one copy on trnsprency) H Finding the Are of Prllelogrms (pges C1.32 nd C1.33, run clss set) H pper to msk prts of the overhed H overhed pens H 3" x 5" index crds or pieces of construction pper, 3 per student H clss set of rulers H scissors H severl rolls of scotch tpe H use pproprite tools nd units to mesure ojects to the precision of oneeighth inch Instructions for Finding the Perimeter & Are of Prllelogrm 1. Write the words perimeter nd re on the ord. Hve students pirshre the definition of ech term, nd then sk volunteers to shre their definitions with the clss. Briefly review the formuls for finding the perimeter (2l + 2w) nd re (l w) of rectngle, nd give students ech n index crd. Ask students to mesure the length nd the width of the index crd in inches, nd use the informtion to find its perimeter nd the re. Hve them use piece of scrtch pper or the crd itself if they need to do ny writing s they determine these mesurements. 2. When most students hve finished, disply just the first instruction on the Strt with Rectngle overhed, nd work with input from the clss to record the perimeter nd re of the index crd. Then revel the second tsk on the overhed. Write 3" in the lnk s you red the instruction with the clss, nd give students time to mesure nd mrk their crds s specified. Ask them to e s precise s possile in their mesurements. Show the rest of the tsks on the overhed one y one. Red ech tsk with the clss nd give students time to complete it efore moving on to the next. Tke time to discuss ech question, nd record the nswers on the overhed. Ask students to e certin they hve formed prllelogrm tht is not rectngle efore they use ny scotch tpe. Bridges in Mthemtics Grde 5 Supplement C1.25
3 Set C1 Geometry: Tringles & Qudrilterls Activity 3 Finding the Perimeter & Are of Prllelogrm (cont.) Set C1 Geometry: Tringles & Qudrilterls Blckline Run one copy on trnsprency. Strt with Rectngle 1 Find the perimeter of your rectngle in inches. Find the re of your rectngle in squre inches. 16" 3" 15 sq in 2 Mesure over long the top of your rectngle nd mke smll mrk. 3 Drw digonl line from the lower lefthnd corner to the mrk. 4 Cut long the line. Wht 2 shpes do you hve now? How do you know? right isosceles tringle, trpezoid 5 Comine the 2 shpes to mke prllelogrm tht is not rectngle. Tpe the edges together. 6 Find the perimeter of your prllelogrm to the nerest eighth of n inch. Find the re of your prllelogrm in squre inches. 7 Here is the formul for finding the re of prlellogrm tht is not rectngle. Explin how nd why it works. 3. The lst question on the overhed Are of prlellogrm sks students = se height or to h find the perimeter nd re of the prllelogrm they formed when they cut nd tped the index crd. When you rech this point, mke squreinch grid height (h) h pper ville, nd give students some time to investigte t their tles. Some my elieve tht the re is still 15 squre inches ecuse they didn t dd nything se () or tke nything wy when they formed their prllelogrm. Press them to find wy to prove this, using the grid pper or some other method. Other students my need to trce the prllelogrm onto the grid pper nd count the squres nd tringles to discover tht the re hs remined the sme, even though the perimeter hs chnged. 4. When most students hve found the perimeter nd re of the prllelogrm, reconvene the clss. Ask volunteers to shre their results nd strtegies. Most will likely report tht the perimeter is 18 1 /2 inches, nd the re is 15 squre inches. Here re some questions to pose during the discussion: Is the perimeter of the prllelogrm the sme s the perimeter of the originl rectngle? Why or why not? Is the re the sme? Why or why not? Does the formul for finding the perimeter of rectngle still work with this prllelogrm? Does the formul for finding the re of rectngle help you find the re of the prllelogrm? If so, how? If not, why? Students The perimeter chnged when we mde the crd into prllelogrm. It ws 3 y 5, so the perimeter ws 16 inches. Now it s out 4 1 /4 inches long the digonl side nd still 5 inches long the top. Two times 5 is 10, nd two times 4 1 /4 is 8 1 /2, so tht s 18 1 / 2 inches now insted of 16. When you cut it on the digonl like tht, it definitely mkes the sides longer. Students It s still 15 squre inches for the re, though. We trced it on the grid pper nd counted the squres nd tringles. It cme out to e exctly 15 squre inches. C1.26 Bridges in Mthemtics Grde 5 Supplement
4 Set C1 Geometry: Tringles & Qudrilterls Activity 3 Finding the Perimeter & Are of Prllelogrm (cont.) You cn t use the regulr formul to find the re of the prllelogrm. If you multiply 4 1 /4 times 5, it s more thn 20 squre inches. But you cn see tht the re is relly 15 squre inches, not 20 squre inches. I know onefourth is.25, so I put in on my clcultor. It cme out to e Tht s 21 1 /4 squre inches, ut the prllelogrm is relly only 15 squre inches. 5. Work with students input to summrize their findings y sketching the rectngle nd the prllelogrm on the whiteord nd recording the perimeter nd re of ech. P = 16 in P = 18 1 /2 in 6. Erse the overhed. Give students ech nother index crd. Repet the process second time, ut hve them mesure nd mrk over 2 inches insted of 3 inches this time. When they cut long the line, they will discover tht they hve formed right sclene tringle nd trpezoid. Hve them comine these two shpes to mke second prllelogrm, nd find the perimeter nd re of this figure. Invite couple of volunteers to trce their new prllelogrms on the Squre Inch Grid overhed nd shre their strtegies for determining the re = 15 sq. in. Toy s Strtegy Eric s Strtegy Toy I just imgined cutting off the tringle t this end nd sliding it over to the other side. You cn see it will still e 15 squre inches. Eric I surrounded the tringle t this end with rectngle. Tht rectngle is 6, so the tringle is 3 squre inches. If you do tht with the tringles t oth ends, nd then dd their res to the squre in the middle, it comes out to e , nd tht s 15 squre inches. Bridges in Mthemtics Grde 5 Supplement C1.27
5 Set C1 Geometry: Tringles & Qudrilterls Activity 3 Finding the Perimeter & Are of Prllelogrm (cont.) 7. Summrize students findings on the whiteord. Then give them nother index crd, erse the overhed, nd repet the process once more. This time, hve students mesure nd mrk one inch over long the top of the crd, drw the digonl, mke the cut, identify the two shpes tht result ( right sclene tringle nd trpezoid), comine the two shpes to mke prllelogrm, nd find the perimeter nd re. Invite couple of volunteers to trce their prllelogrms nd shre their strtegies for finding the re. 8. Summrize the third set of findings on the whiteord, nd sk students to shre ny oservtions they cn mke. How nd why did the perimeter chnge from one prllelogrm to the next? Why did the re remin the sme ech time? P = 16 in Set C1 Geometry: Tringles & Qudrilterls Blckline Run one copy on trnsprency. Strt with Rectngle P = 18 1 /2 in 1 Find the perimeter of your rectngle in inches. Find the re of your rectngle in squre inches. P = 16 in 16" 3" P = 17 in 15 sq in 2 Mesure over long the top of your rectngle nd mke smll mrk. 3 Drw digonl line from the lower lefthnd corner to the mrk. P = 16 in P = 16 1 /2 in 4 Cut long the line. Wht 2 shpes do you hve now? How do you know? right isosceles tringle, trpezoid 9. Disply the informtion t the 5 Comine ottom the 2 shpes of the to mke overhed, prllelogrm tht which is not rectngle. gives Tpe the formul for finding the re the edges together. of prllelogrm tht is not rectngle. Ask students to discuss nd explin how the formul works, 6 Find the perimeter of your prllelogrm to the nerest eighth of n inch. Find the re of your prllelogrm in squre inches. sed on their experiences during this ctivity. 7 Here is the formul for finding the re of prlellogrm tht is not rectngle. Explin how nd why it works. Are of prlellogrm = se height or h height (h) h se () 10. Give students ech copy of Finding the Are of Prllelogrms. Review the instructions on oth sheets with the clss. When students understnd wht to do, let them get strted. Pln to ssign unfinished work s homework or setwork the following dy. C1.28 Bridges in Mthemtics Grde 5 Supplement
6 Set C1 Geometry: Tringles & Qudrilterls Activity 3 Finding the Perimeter & Are of Prllelogrm (cont.) Set C1 Geometry: Tringles & Qudrilterls Blckline Run clss set Set C1 Geometry: Tringles & Qudrilterls Blckline Run clss set NAME DATE NAME DATE Finding the Are of Prllelogrms pge 1 of 2 Finding the Are of Prllelogrms pge 2 of 2 The height (h) of prllelogrm tells how fr one side is from its opposite side. The height of prllelogrm must e perpendiculr to the se () of the prllelogrm. h Here re the formuls for the re of rectngle nd the re of prllelogrm. The re of rectngle = length width or l w or lw. The re of prllelogrm = se height or h or h. 3 Find the re of ech figure elow. Use the formuls. Show your work. 6 cm 1 Use the letter h to lel the height of ech prllelogrm elow. Use the letter to lel the se. If the height is not shown, use your ruler to drw it in, nd then lel it. 4 cm 4 cm 6 cm c d 4 For ech of the prllelogrms elow: drw in the height. mesure nd lel the height nd the se to the nerest centimeter. find nd record the re nd show your work.. 2 To find the re of prllelogrm, multiply se times height. Try it for yourself. Mesure the se nd the height of the prllelogrm elow in centimeters. Multiply the two mesurements. Is the nswer correct? Use leled sketch, numers, nd words to explin. Bridges in Mthemtics Grde 5 Supplement C1.29
7 Set C1 Geometry: Tringles & Qudrilterls Blckline Run one copy on trnsprency. Strt with Rectngle 1 Find the perimeter of your rectngle in inches. Find the re of your rectngle in squre inches. 2 Mesure over long the top of your rectngle nd mke smll mrk. 3 Drw digonl line from the lower lefthnd corner to the mrk. 4 Cut long the line. Wht 2 shpes do you hve now? How do you know? 5 Comine the 2 shpes to mke prllelogrm tht is not rectngle. Tpe the edges together. 6 Find the perimeter of your prllelogrm to the nerest eighth of n inch. Find the re of your prllelogrm in squre inches. 7 Here is the formul for finding the re of prlellogrm tht is not rectngle. Explin how nd why it works. Are of prlellogrm = se height or h height (h) h se () C1.30 Bridges in Mthemtics Grde 5 Supplement
8 Set C1 Geometry: Tringles & Qudrilterls Blckline Run severl clss sets nd one copy on trnsprency. Squre Inch Grid Pper Bridges in Mthemtics Grde 5 Supplement C1.31
9 Set C1 Geometry: Tringles & Qudrilterls Blckline Run clss set nme dte Finding the Are of Prllelogrms pge 1 of 2 The height (h) of prllelogrm tells how fr one side is from its opposite side. The height of prllelogrm must e perpendiculr to the se () of the prllelogrm. h 1 Use the letter h to lel the height of ech prllelogrm elow. Use the letter to lel the se. If the height is not shown, use your ruler to drw it in, nd then lel it. c d 2 To find the re of prllelogrm, multiply se times height. Try it for yourself. Mesure the se nd the height of the prllelogrm elow in centimeters. Multiply the two mesurements. Is the nswer correct? Use leled sketch, numers, nd words to explin. C1.32 Bridges in Mthemtics Grde 5 Supplement
10 Set C1 Geometry: Tringles & Qudrilterls Blckline Run clss set nme dte Finding the Are of Prllelogrms pge 2 of 2 Here is the formul for finding the re of prllelogrm. The re of prllelogrm = se height or h or h. (Since rectngle is specil kind of prllelogrm, this is lso the formul for the re of rectngle.) 3 Find the re of ech figure elow. Use the formuls. Show your work. 6 cm 4 cm 4 cm 6 cm 4 For ech of the prllelogrms elow: drw in the height. mesure nd lel the height nd the se to the nerest centimeter. find nd record the re nd show your work.. Bridges in Mthemtics Grde 5 Supplement C1.33
11 C1.34 Bridges in Mthemtics Grde 5 Supplement
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