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

Transcription

1 Resource Overview Quntile Mesure: Skill or Concept: 80Q Multiply two frctions or frction nd whole numer. (QT N ) Excerpted from: The Mth Lerning Center PO Box 99, 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 00 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 0, Durhm, North Crolin 77 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 A9 Numer & Opertions: Multiplying Frctions Set A9 H Activity ctivity Generliztions Aout Multiplying Frctions Overview Students sketch nd solve vriety of frction multipliction comintions on grid pper. The techer then guides them to the generliztion tht the product of ny two frctions cn e found y multiplying their numertors nd then multiplying their denomintors. Skills & Concepts H find the product of two unit frctions with smll denomintors using n re model H multiply frctions using the stndrd lgorithm H plin the reltionship of the product reltive to the fctors when multiplying frctions You ll need H Frctions to Multiply (pge A9.0, run copy on trnsprency) H Multiplying Frctions (pges A9. & A9., run copy of ech sheet on trnsprency, nd clss set) H red, lue nd lck pens for the overhed H pper to msk portions of the trnsprency H Student Mth Journls H colored pencils Instructions for Generliztions out Multiplying Frctions. Hve students open their mth journls to the work they did during the previous session. Ask them to pir-shre ny oservtions they cn mke so fr out multiplying frctions. After minute or two, sk volunteers to shre their thinking with the clss. = 6 = 6 = = 8 Are = 6 Are = 6 Are = Are = 6 6 Students When you multiply frction y, it stys the sme, like times is just. It seems like when you multiply one frction y nother, the nswer is lwys smller thn wht you strted with. Yeh, like times is 6. It s kind of weird, ecuse usully when you multiply, you get igger nswer. It mkes sense if you rememer tht is relly one-fourth of fourth. I think you cn just get the nswers y multiplying cross. Bridges in Mthemtics Grde Supplement A9.

3 Set A9 Numer & Opertions: Multiplying Frctions Activity Generliztions Aout Multiplying Frctions (cont.) Techer Multiplying cross? How re you thinking out tht, Brinn? Brinn Cn I show t the ord? Look, we know tht fourth of fourth is sixteenth, right? So just multiply times, nd you get, nd times nd you get 6. Or times is 6. We showed tht on our ords yesterdy. But look wht hppens when I write the numers nd multiply cross. times is, nd times is 6! x = 6 x = 6 Techer So, you re sying tht if you multiply the numertors, nd then multiply the denomintors, you get the sme nswers we did when we uilt nd sketched the comintions? Tht s n interesting oservtion. Do you think it will work every time? Let s keep the ide in mind s we look t some more prolems tody.. Explin tht you hve some more frction multipliction prolems for the clss tody. Then show the first prolem on the Frctions to Multiply trnsprency. Red the first prolem with the students, nd work with their input to record the phrse tht will help them think sensily out the comintion. Hve students pir-shre estimtes, nd sk severl volunteers to shre their thinking with the clss. Set A9 Numer & Opertions: Multiplying Frctions Blckline Run one copy on trnsprency. Frctions to Multiply = one hlf of three-fifths Students We know it s going to e less thn We think mye the nswer is going to e 0 three fifths would e 0. If you use my ide out multiplying cross, you get 0. ecuse it s only hlf of tht. ecuse hlf of one fifth is one tenth, so mye hlf of. Work with input from the clss to frme rectngle on the grid tht is / y /. Then shde in the resulting region, nd sk students to identify the re of the rectngle reltive to the whole grid. Set A9 Numer & Opertions: Multiplying Frctions Blckline Run one copy on trnsprency. Frctions to Multiply = one hlf of three-fifths A9.6 Bridges in Mthemtics Grde Supplement

4 Set A9 Numer & Opertions: Multiplying Frctions Activity Generliztions Aout Multiplying Frctions (cont.) Students So, the nswer is, right? Tht doesn t mke sense! It should only e hlf of. But there re oxes colored in nd in the row, so it s. Wit minute! There re 0 oxes in the whole grid. We mrked hlf on one side nd top, nd the prt we colored in is 0. long the. When there is generl greement tht the nswer is 0, record it on the trnsprency. Then show the nt comintion. Red it with the clss nd write verl trnsltion elow the prolem. Hve students open their journls to the nt ville pge, record the comintion, nd outline rectngle. Give them minute or two to solve the prolem, shring nd compring their work with others nery s they work. Then invite volunteer to the overhed to shre his or her thinking with the clss. Set A9 Numer & Opertions: Multiplying Frctions Blckline Run one copy on trnsprency. Frctions to Multiply = 0 one hlf of three-fifths We shded in 0 of the rectngle. = 6 two-thirds of three-fourths Sergio First I mrked in the re it ws 6. Tht s relly 6 on one side of the grid. Then I mrked on the other side. When I colored ecuse there re oxes in the whole grid.. Repet step with the lst comintion on the trnsprency,. This time, however, students will hve to decide wht size rectngle to outline efore they model the comintion. = four-fifths of two-thirds Techer Cn someone come up nd mrk dimension of long the side of this grid? Mri? Mri Sure! Just mrk down the side, like this. Bridges in Mthemtics Grde Supplement A9.7

5 Set A9 Numer & Opertions: Multiplying Frctions Activity Generliztions Aout Multiplying Frctions (cont.) = four-fifths of two-thirds Techer Do you ll gree tht this shows of the side of the grid? Tlk with the person nt to you for minute, nd then let s her wht you think. Students Yep, we gree. It s down the side. We don t gree. There re 7 squres down the side. If you mrk of them, it s like 7, not. I think you cn t use tht whole grid. You hve to mke one where you cn show fifths on one side nd thirds on the other. 6. After some discussion, work with input from students to outline rectngle tht will work for this comintion. Then mrk the dimensions, shde in the region tht results, nd record the nswer t the overhed, s students do so in their journls. = 8 four-fifths of two-thirds 7. Give students ech copy of the Multiplying Frctions sheets nd disply the corresponding trnsprencies t the overhed. Review nd discuss the tsks with the clss. Give students the option of working on these sheets independently, in pirs, or with you. A9.8 Bridges in Mthemtics Grde Supplement

6 Set A9 Numer & Opertions: Multiplying Frctions Activity Generliztions Aout Multiplying Frctions (cont.) Set A9 Numer & Opertions: Multiplying Frctions Blckline Run clss set nd copy on trnsprency. NAME DATE Multiplying Frctions pge of Set A9 Numer & Opertions: Multiplying Frctions Blckline Run clss set nd copy on trnsprency. NAME DATE Multiplying Frctions pge of Ech of the pictures elow shows the results of multiplying one frction y nother. Lel ech of the shded regions with its dimensions nd re. Then write multipliction eqution to mtch 6 7 x 6 7 = c Solve ech of the multipliction prolems elow. For ech: outline rectngle on the grid tht will work for oth frctions. drw nd lel the dimensions nd re, nd write the nswer. write the prolem nd nswer in words. 8 = 8 = 8 8 Tw o-thirds of four-eighths is eight twenty-fourths. 7 8 = Fill in the chrt to solve ech of the prolems elow. Multipliction Expression two-thirds of = two-thirds = 6 = Word to Mtch Leled Sketch Answer 9 9 c 8 0 = Sr sys tht to multiply two frctions, ll you hve to do is multiply one numertor y the other, nd multiply one denomintor y the other. Do you gree? Why or why not? 8. After students hve completed the worksheets, discuss the fourth prolem with the group, nd guide them to the generliztion tht the product of two frctions is found y multiplying the numertors nd then multiplying the denomintors. Also, sk students to plin why the product of two frctions is smller thn either of the fctors. Students Multiplying two frctions is like finding frction of frction. Hlf of hlf hs to e smller thn hlf. Or, like if you find fourth of hlf, it s only n eighth. It goes the other wy, too. A hlf of fourth is n eighth. Independent Worksheets See Set A9 Independent Worksheets for more prctice with multiplying frctions. Bridges in Mthemtics Grde Supplement A9.9

7 Set A9 Numer & Opertions: Multiplying Frctions Blckline Run one copy on trnsprency. Frctions to Multiply = = = A9.0 Bridges in Mthemtics Grde Supplement

8 Set A9 Numer & Opertions: Multiplying Frctions Blckline Run clss set nd copy on trnsprency. nme dte Multiplying Frctions pge of Ech of the pictures elow shows the results of multiplying one frction y nother. Lel ech of the shded regions with its dimensions nd re. Then write multipliction eqution to mtch 6 7 x 6 7 = c Fill in the chrt to solve ech of the prolems elow. Multipliction Expression = two-thirds of two-thirds = 6 = Word to Mtch Leled Sketch Answer 9 9 Bridges in Mthemtics Grde Supplement A9.

9 Set A9 Numer & Opertions: Multiplying Frctions Blckline Run clss set nd copy on trnsprency. nme dte Multiplying Frctions pge of Solve ech of the multipliction prolems elow. For ech: outline rectngle on the grid tht will work for oth frctions. drw nd lel the dimensions nd re, nd write the nswer. write the prolem nd nswer in words. 8 = Two-thirds of four-eighths is eight twenty-fourths. = 7 8 = c 8 0 = Sr sys tht to multiply two frctions, ll you hve to do is multiply one numertor y the other, nd multiply one denomintor y the other. Do you gree? Why or why not? A9. Bridges in Mthemtics Grde Supplement