Ext 6-8 Sampler

41 RatiosofRationalNumbers Lesson23, 7ETeacherGuide 66 Objectives26, 46: To find the ratios of rational numbers. Materials: Fractionbars Ratios of Fractions In this lesson, studentswill learn to findunit rates whengiven a ratioof two fractions, insteadof twowhole numbers as onpage36.Distribute a set of fractionbars to each student. Writeon theboard: Tomake greenpaint, an artist used gallonof blue paintwith gallonof yellowpaint. The artist nowhas tomixmore greenpaint. This time she isusing1gallon of yellowpaint.Howmuchbluepaint should sheuse? Ask students tohelpyouwrite aproportion. The first time theartistmixed thepaint, howmuchbluepaint did sheuse?Howmuchyellowpaint? Write the first ratio. ( 1 ⁄ 3 — 1 ⁄ 2 ) Canyouhelpwriteaproportion to solve this problem?What is the second ratio? (The second ratio is shownbelow.) Write theproportion: Use fractionbars tomodel thisproblem.Hold up the 1 ⁄ 2 fractionbar. Whatdoes this represent inour problem? (The amount of yellowpaint sheused first.) Now theartistwants touse1gallonof yellowpaint. Holdup the 2 ⁄ 2 fractionbar. Howdoes this compare to theamount of yellowpaint sheused the first time she mixed thegreenpaint? (It is twice asmuch.) Which fractionbar represents theamount of blue paint sheused the first time? ( 1 ⁄ 3 ) So,which fraction bar representshowmuchbluepaint she shoulduse this time? ( 2 ⁄ 3 ) Howdoyouknow this? (It is twice as much as sheusedbefore, 2 ⁄ 3 of agallon.) Writeon theboard: Nowwewill solve thisproblemby crossmutliplying. Writeon theboard: n = 2 • n =2 • n = Howdowedivide fractions? (Multiplyby the reciprocal of thedivisor.) What is the reciprocal of 1 ⁄ 2 ? ( 2 ⁄ 1 or 2) Encourage students todivide the fractions 1 ⁄ 3 and 1 ⁄ 2 . How muchbluepaint should sheuse? ( 2 ⁄ 3 gallon) Didyouget the sameanswerwhenyoudivide the fractions? (yes) ⅓gallonof bluepaint = n gallons of bluepaint ½gallonof yellowpaint 1gallonof yellowpaint ⅓gallonof bluepaint = n gallons of bluepaint ½gallonof yellowpaint 1gallonof yellowpaint Writeon theboard: Tomakepurplepaint, shemixes 3 ⁄ 4 gallonof redpaint for every 1 ⁄ 2 gallonof bluepaint. If sheuses 1gallonof bluepaint, howmuch redpaint should sheuse? Ask students towrite aproportion to represent this problemand solve. ¾gallonof redpaint = n of redpaint ½gallonof bluepaint 1gallonof bluepaint Have studentsdemonstratehow to solve thisproblem using fractionbars andby crossmultiplying also. n = n = =1 gallons of redpaint Read the information at the topof thepage together to summerize3ways to find ratios of rational numbers. Workproblems 1 and3 together as a class.Have students complete the rest of thepageon their own. Skill Builders 26-5 Conceptual Understanding 66 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Ratiosof Rational Numbers Solve. 1. ________ _____________ 2. ________ _____________ 3. If of an inch onamap corresponds to of amile, howmanymileswill 1 inch represent? _____________ 5. One-fourthof awading pool is filled ineach of anhour. What fractional part of the pool is filled in 1 hour? _____________ 4. It rained of an inch in of anhour inBaltimore.At this rate, howmuch rain fell in 1 hour? _____________ 6. Anahas painted of her bedroom.Sheused of a gallon of paint.Howmany total gallons of paint will she need? _____________ Luisamowed of the lawn in of an hour.What fractionof the lawn will Luisamow in1hour? Draw apicture: Use a fractionbar: Use aproportion: + + = Luisawill mow_____of the lawn in 1 hour. Maria’s grandmother walks of amile in of an hour.Howmanymiles per hour does shewalk?Draw a picture andwriteaproportion to solve theproblem. hr. hr. hr.=1 hour + + _____________ = _____________ = n __ = __ 1 n = 3 s n = s 3 n = Crossmultiply andsolve. Change to twelfths. Part B 3 4 3 4 1 inches mile gallon hour 2 4 1 2 1 2 3 5 3 4 x2 x2 Grade7 PartB