Lifting a Lion: Using Proportions

Transcription

1 Overview Students will wrk in cperative grups t slve a real-wrd prblem by using the bk Hw D yu Lift a Lin? Using a ty lin and a lever, students will discver hw much wrk is needed t raise the ty lin. They will use prprtins t determine the frce needed t lift a real lin. Grade Levels: 4 6 Cncepts Multiplicatin Measurement Prblem slving Frce Simple machines Divisin Rati Wrk Energy Materials TI-15 Explrer calculatrs Hw D yu Lift a Lin? Wells, Rbert E. (Park Ridge, IL: Albert Whitman and Cmpany, 1996) Paper, pencils Ruler Pster paper Meter stick r thin, but nt pliable, bard with meter stick 3 pencils taped tgether in a triangular prism shape r ther bject fulcrum Small ty lin (r ther small bean-bag type animal) Stacking gram masses, r balls f clay r washers weighing abut 1 5 grams each Student activity sheet Assessment Thrughut the activities, questins are included fr frmative assessment. Student wrk samples shuld be used as a check fr understanding. Have the students use the TI-15 t shw their calculatins Texas Instruments Incrprated 1 educatin.ti.cm

2 Intrductin Read the first sectin f the bk Hw D Yu Lift a Lin? by Rbert E. Wells t the students. Discuss with the students the parts f a lever shwn in the bk. Demnstrate making a lever by using a 12-inch ruler with a pencil as a fulcrum. (Nte: D nt use the meter stick fr the demnstratin since ding s will reveal part f the slutin.) Place a 5-gram mass (lad) at ne end f the ruler. Place the pencil (fulcrum) at the 6-inch mark. Have students guess hw much weight it will take t lift the 5 grams. Place masses n the ther end f the ruler until the 5-gram mass is lifted. Mve the pencil t anther lcatin clser t the 5-gram mass. Have students predict hw much weight it will take t lift the 5-gram mass. Place masses n the ther end f the ruler until the 5-gram mass is lifted. Repeat the prcess with the fulcrum in tw ther lcatins. Write the infrmatin in a chart and have students lk fr patterns. Presenting the Prblem 1. Review the fur steps f prblem slving with the students: understanding the prblem making a plan carrying ut the plan evaluating the slutin 2. Have the students read the Prblem page and paraphrase the prblem. Make sure the students are clear n what the prblem asks. 3. Discuss with students infrmatin n the Prblem page. Make sure they understand hw t create a lever with the meter stick r bard and pencils. Remind them f the prcedures used in the Intrductin t lift the 5-gram mass. 4. If grups have difficulty with the prblem, use the Things t Cnsider page. This page prvides guiding questins t help the students cmplete the prblem-slving steps. 5. The presentatin shuld include the mathematics used t predict hw much weight it wuld take t lift the real lin Texas Instruments Incrprated 2 educatin.ti.cm

3 Evaluating the Results 1. After the presentatins are made, have students examine the varius slutins presented. Questins fr Students: v Hw are the presentatins similar? v Hw are the presentatins different? 2. Ask them t cmpare the numbers used. Questins fr Students: v Did all grups use the same numbers? v Why d yu think this is s? 3. Ask them t determine the reasnableness f the results. Questins fr Students: v Did each grup answer the questin? v D the numbers used make sense? v Did all f the grups cnsider all f the variables? 4. Ask them t evaluate hw each grup used the calculatr t slve the prblem. 5. Ask them t extend their thinking. Questin fr Students: v Hw des the weight f the lad impact the amunt f frce needed t lift it with a lever? 2016 Texas Instruments Incrprated 3 educatin.ti.cm

4 SOLUTIONS Lifting a Lin The Prblem: Hw much effrt will it take t lift a lin with a lever? In the first part f the activity, team members will make a chart shwing the amunt f wrk it takes t lift a ty lin with the fulcrum at varius distances frm the lin. Then they will predict the amunt f wrk it will take t lift a real lin with the fulcrum at different distances. Students will write an explanatin abut their slutin prcess. Answers will vary based n the explanatins. Using the Calculatr Using Prprtins Use the TI-15 calculatr t slve this prblem: Ms. Kleid is helping plan the refreshments fr Field Day. She wanted t knw everyne s favrite ice cream flavr s she culd rder enugh ice cream. She surveyed her class. Out f her class f 22 students, 10 students preferred chclate ice cream, 8 preferred vanilla, and 4 preferred strawberry. Ms. Kleid knws there are 531 students at schl. Hw can she predict hw many ice cream cups in each flavr she needs? Ms. Kleid decided she needs t knw the fractinal part f her class that likes each flavr. Since there are 22 students in her class, like chclate, like vanilla, and like strawberry. She decides t simplify the fractins. Hw des the result help Ms. Kleid? The display shws: 5 11 Pssible answer: The fractin is easier t calculate with, but it des nt help her Texas Instruments Incrprated 4 educatin.ti.cm

5 Ms. Kleid decided that simplifying the fractins desn t help at all. She needs t knw what 10 f 531 students is. Next she tries this: 22 The display shws: Des this answer make sense fr the number f peple in the schl wh like chclate ice cream? Hw d yu knw? What shuld Ms. Klein d abut the fractin part? What wuld happen if she simplified the mixed number? The display shws: Pssible answer: Yes the answer makes sense because a little less than half f the students in Ms. Kleid s class preferred chclate ice cream and 241 is a little less than half f 531. Ms. Kleid shuld rund the fractin part up t the nearest ne. Des the simplified fractin help? Pssible answer: n Try the ther tw fractins and multiply by 531 t predict the number f students wh will prefer vanilla r strawberry ice cream. D yu have fractinal parts? What shuld Ms. Kleid d with the fractinal parts t make sure there is enugh ice cream fr everyne? students in the schl prefer vanilla ice cream and students prefer strawberry ice cream. Yes there are fractinal parts. Mrs. Kleid shuld rund the fractinal parts up t the nearest whle number Texas Instruments Incrprated 5 educatin.ti.cm